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A search for supernova neutrinos with the Sudbury Neutrino Observatory Heise, Jaret 2002

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A S E A R C H F O R S U P E R N O V A N E U T R I N O S W I T H T H E S U D B U R Y N E U T R I N O O B S E R V A T O R Y By Jaret Heise B.Sc.(Hon), University of Saskatchewan, 1993 M.Sc, University of British Columbia, 1996 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF T H E REQUIREMENTS FOR T H E D E G R E E OF D O C T O R OF PHILOSOPHY in T H E FACULTY OF GRADUATE STUDIES DEPARTMENT OF PHYSICS AND ASTRONOMY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December 2001 © Jaret Heise, 2001 In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Physics and Astronomy The University of British Columbia 6224 Agricultural Road Vancouver, B C , Canada V6T 1Z1 Date: C W ^ l o ^ ^4 , 2 C Q 1 Abstract The Sudbury Neutrino Observatory (SNO) is an underground Cerenkov detector designed to detect neutrinos from astrophysical sources. The fiducial mass of the detector consists of 1000 tonnes of D 2 0 , which provides sensitivity to all neutrino flavours. Since much of the energy released in the supernova burst is expected to be carried by the muon and tau neutrinos, the supernova signal recorded by the SNO detector is of particular importance. In addition, SNO is also sensitive to the prompt electron neutrino signal expected from capture processes during core collapse. Various supernova models are investigated and predictions of the SNO supernova signal are studied using simulated Monte Carlo data. A data analysis program to identify neutrinos from a galactic supernova burst has been installed in the online system at SNO. The program automatically analyzes burst data and it is anticipated that a manual alert to the Supernova Early Warning System could be issued within 20-30 minutes with negligible possibility of a false alarm. The burst identification algorithm currently in use both online and offline provides detection sensitivity beyond the far edge of our galaxy. A search for supernova neutrinos was performed using 241.0 days of data collected over the time period between November 2, 1999 and January 4, 2001. No candidate bursts were observed over this period, which places a 90% confidence level upper limit of < 3.5 galactic supernovae per year. i i Table of Contents Abstract ii List of Tables xiii List of Figures xviii Acknowledgments xxvi 1 Introduction 1 1.1 Neutrino Properties 1 1.2 Neutrino Sources 2 1.2.1 Big Bang 2 1.2.2 Gamma-Ray Bursts 3 1.2.3 Supernovae 4 1.2.3.1 Relic Supernovae 4 1.2.4 Solar Fusion Reactions 5 1.2.5 Cosmic Ray Interactions in the Atmosphere 6 1.2.6 Nuclear Reactors 6 1.2.7 Radioactivity in the Earth 6 1.3 Study of Supernova Neutrinos 7 1.4 Study of Supernova Neutrinos at SNO 7 2 Supernova Physics 9 2.1 Introduction 9 2.2 Supernova Classifications 9 2.2.1 Type I Supernovae 10 ii i 2.2.1.1 Type la 11 2.2.1.2 Type lb, Ic 12 2.2.2 Type II Supernovae 12 2.2.2.1 Type II-P, II-L 13 2.3 The Physics of Gravitational Collapse 13 2.3.1 Standard Stellar Evolution 14 2.3.2 The Pre-Supernova Star 15 2.3.3 Core Collapse 15 2.3.4 Neutrino Trapping 16 2.3.5 Core Bounce and Shock Breakout 17 2.3.6 Neutrino Breakout 17 2.3.7 Explosion 18 2.3.8 Cooling 20 2.3.9 Aftermath 20 2.4 Expected Frequency of Supernovae 21 2.4.1 Relative Frequency of Supernova Types 21 2.4.2 Galactic Supernovae 21 2.4.2.1 Historical Supernovae 22 2.4.2.2 Supernovae in Other Galaxies 23 2.4.2.3 Supernova Remnants 24 2.4.2.4 Iron Abundances 26 2.4.2.5 Stellar Evolution Rates 26 2.4.2.6 Neutrinos 26 2.4.2.7 Summary 26 2.4.3 Local Group Supernovae 27 iv 3 Supernova Neutrinos 30 3.1 Introduction 30 3.2 Supernova 1987A 30 3.2.1 Detected Supernova Neutrinos 31 3.2.1.1 KII Detector 31 3.2.1.2 1MB Detector 32 3.2.1.3 Baksan Detector 34 3.2.1.4 LSD Detector 34 3.2.1.5 Homestake Detector 36 3.2.1.6 Summary 36 3.3 Neutrino Signal 37 3.3.1 Core Infall and Neutrino Trapping 38 3.3.2 Core Bounce and Neutrino Breakout 38 3.3.3 Explosion 39 3.3.4 Cooling 39 3.3.5 Supernova Neutrino Summary 40 3.4 Potential Physics 40 3.4.1 Constraints on Supernova Models 40 3.4.2 Neutrino Physics 41 3.4.2.1 Neutrino Mass Measurement 42 3.4.2.2 Neutrino Lifetime 44 3.4.3 Early Alert 44 4 The SNO Detector 46 4.1 Introduction 46 4.2 Detection Mechanisms 46 4.2.1 Charged Particle Detection 47 v 4.2.2 Gamma Ray Detection 49 4.2.3 Neutron Detection 50 4.2.3.1 Pure D 2 0 Phase 51 4.2.3.2 Salt Phase 51 4.2.3.3 N C D Phase 52 4.2.3.4 Neutrons in the H 2 0 Region 53 4.3 Neutrino Interactions 53 4.3.1 Charged Current 53 4.3.1.1 Ve + p n + e+ Reaction 54 4.3.1.2 ue + d Reactions 55 4.3.1.3 ue + 0 Reactions 56 4.3.2 Neutral Current 57 4.3.2.1 vx + d Reactions 57 4.3.2.2 v^r + 1 6 0 Reactions 57 4.3.3 Elastic Scattering 59 4.3.3.1 v + e~ -» v + e~ Reactions . 59 4.3.3.2 Interaction Summary 59 4.4 Detector Backgrounds 60 4.5 Detector Components 63 4.5.1 Acrylic Vessel 63 4.5.2 Water Systems 64 4.5.2.1 Light Water System 64 4.5.2.2 Heavy Water System 65 4.5.2.3 Cover Gas System 66 4.5.3 Photomultiplier Tube Array 66 4.6 SNO Electronics 67 vi 4.7 SNO Trigger 69 4.8 SNO Data Acquisition 71 4.9 SNO Calibration 71 4.9.1 Low Level Calibrations 72 4.9.2 Optical and Energy Calibrations 72 4.9.3 Physics Calibrations 73 4.10 The SNO Monte Carlo Package 74 5 SNO Supernova Monte Carlo 76 5.1 Introduction 76 5.2 Supernova Signal Formalism 76 5.3 Supernova Models 80 5.3.1 Introduction 80 5.3.2 General Predictions 81 5.3.3 Beacom and Vogel Model 81 5.3.4 Burrows et al. Model 85 5.3.5 Bruenn Models 89 5.3.5.1 Bruenn 15 M© Model 90 5.3.5.2 Bruenn 25 M 0 Model 93 5.3.6 Liebendorfer Model 93 5.3.7 Supernova Model Summary 96 5.4 SNO Supernova Neutrino Kinematics and Cross Sections 100 5.4.1 Introduction 100 5.4.2 Charged Current 100 5.4.2.1 Ve + p n + e+ Reaction 100 5.4.2.2 ue + d Reactions 102 5.4.2.3 ve + O Reactions 104 vii 5.4.3 Neutral Current 105 5.4.3.1 vx + d Reactions 105 5.4.3.2 u^-r 1 6 0 Reactions 105 5.4.4 Elastic Scattering 106 5.4.5 Interaction Summary 109 5.5 SNO Targets 110 5.6 Event Sampling 113 5.7 SNO Monte Carlo Settings 113 6 S N O Supernova Neutrino Signal 115 6.1 Introduction 115 6.2 SNO Supernova Neutrino Interactions 115 6.2.1 Beacom and Vogel Model 116 6.2.2 Comparison to Beacom and Vogel Published Results 121 6.2.3 Burrows et al. Model 122 6.2.4 Comparison to Burrows et al. Published Results 127 6.2.5 Bruenn Models 129 6.2.5.1 Bruenn 15 M 0 Model 129 6.2.5.2 Bruenn 25 M 0 Model 132 6.2.6 Liebendorfer Model 132 6.2.7 Neutrino Interaction Summary 134 6.3 Supernova Neutrino Interaction Rate 137 6.3.1 Beacom and Vogel Model 138 6.3.2 Burrows et al. Model 138 6.3.3 SNO Supernova Neutrino Energy Distribution 143 6.3.3.1 Beacom and Vogel Model 143 6.3.3.2 Burrows et al. Model 144 viii 6.4 Modifications to the Neutrino Signal 144 6.4.1 Time Delay 144 6.4.2 Neutrino Oscillations 148 6.4.2.1 Vacuum Oscillations 148 6.4.2.2 M S W Oscillations 148 7 S N O Supernova Observed Event Signal 151 7.1 SNO Observed Supernova Counts 151 7.1.1 Beacom and Vogel Model 152 7.1.2 Burrows et al. Model 154 7.2 SNO Observed Supernova Counts at Various Distances 157 7.3 SNO Supernova Time Spectrum 161 7.3.1 Beacom and Vogel Model 161 7.3.2 Burrows et al. Model 161 7.3.3 Prompt Signal 167 7.4 SNO Supernova NHIT Spectrum 169 7.4.1 Beacom and Vogel Model 171 7.4.2 Burrows et al. Model 171 7.5 SNO Supernova Vertex Position Distribution 174 7.6 SNO Supernova Angular Distribution 174 8 S N O Supernova Analysis 183 8.1 Introduction 183 8.2 SNO Background Events 183 8.2.1 Instrumental Backgrounds 184 8.2.1.1 P M T Flasher Events 184 8.2.1.2 P M T Failure Events 185 8.2.1.3 High Voltage Breakdown 185 ix 8.2.1.4 Neck Events 186 8.2.1.5 Electronic Pickup 187 8.2.2 Physics Backgrounds 187 8.2.2.1 Muon Spallation 187 8.3 SNO Supernova Analysis Threshold 188 8.4 Supernova Signal Above Analysis Threshold 192 8.4.1 Beacom and Vogel Model 192 8.4.2 Burrows et al. Model 194 8.5 Signal Loss 195 8.5.1 Analysis Threshold 195 8.5.2 Data Reduction Cuts 197 8.6 Summary 199 9 S N O Supernova Monitoring Programme 204 9.1 Introduction 204 9.2 Online Supernova Monitor 204 9.2.1 Level 1 206 9.2.1.1 Burst Trigger 206 9.2.1.2 Run-Specific Thresholds 208 9.2.1.3 Offline Performance 209 9.2.2 Level 2 212 9.2.2.1 Burst Classification 213 9.2.2.2 Analysis Summaries 217 9.2.2.3 Communication 221 9.2.3 Level 3 224 9.2.3.1 Threshold 224 9.2.3.2 Event Reconstruction 225 x 9.2.3.3 Locating the Supernova 227 9.2.3.4 Analysis Summaries 232 9.2.3.5 Communication 234 9.2.3.6 Burst Causes 234 9.2.4 Level 4 238 9.2.4.1 SNEWS 239 9.2.4.2 Communication 240 9.2.5 SNO Supernova Response Time 240 10 SNO Supernova Sensitivity 242 10.1 Introduction 242 10.2 SNO Detector Livetime 242 10.3 SNO Distance Sensitivity 245 10.3.1 NHIT Trigger Parameter . . 246 10.3.2 N E V E N T Trigger Parameter 247 10.3.3 Detector Livetime 249 10.4 Burst Identification Efficiency 251 11 Analysis of 241 Days' Data 254 11.1 Introduction 254 11.2 Data Selection 254 11.3 Search Criteria 255 11.4 Search Background 257 11.5 Search Results 258 12 Conclusion 263 Bibliography 265 A The Sudbury Neutrino Observatory Collaboration 275 xi B Using the Supernova Signal Formalism 278 C Estimate of the Observed Signal Due to Oxygen Reactions 281 C l Hardware Threshold 282 C . l . l Beacom and Vogel Model 283 C.1.2 Burrows et al. Model 284 C.2 Analysis Threshold 284 C.2.1 Beacom and Vogel Model 286 C.2.2 Burrows et al. Model 287 C.3 Summary 287 C.3.1 Beacom and Vogel Model 287 C.3.2 Burrows et al. Model 288 D Online Analysis Using 100 Supernovae 290 E Milestones Relevant to S N O Supernova Monitoring 294 xii List of Tables 1.1 The three generations of leptons and their associated neutrinos in the Stan-dard Model of particle physics 2 2.1 Recent observed galactic supernovae 23 2.2 Estimates of the mean interval between supernovae in the Milky Way galaxy by various methods 27 2.3 Estimates of the mean interval between supernovae in nearby galaxies. . . 28 3.1 Time and energy information for the events recorded at LSD, possibly asso-ciated with SN1987A 35 3.2 Summary of detectors that recorded neutrino events from SN1987A 36 4.1 Cerenkov radiation energy threshold values in H 2 0 and D 2 0 for various charged particles 48 4.2 Summary of supernova neutrino interactions in the SNO detector, including the energy threshold, the final state detectable particles and whether or not there is any asymmetry in the charged lepton angular distribution 61 4.3 Radioactivity levels in various regions of the SNO detector 63 4.4 Summary of sources used to calibrate the SNO detector 75 5.1 Specifications relating to the degeneracy parameter, rj, for the Burrows et al. model 88 5.2 Summary statistics for various supernova models 98 xii i 5.3 Number of interaction targets in the SNO detector for the various supernova neutrino reactions 112 5.4 Detector characteristics specified in the supernova neutrino Monte Carlo simulations 114 6.1 Neutrino counts for a supernova at 10 kpc calculated for the Beacom and Vogel supernova model using the SNO supernova generator with no detector energy threshold 117 6.2 Average energy and angular distribution values for 50000 sampled neutrinos and their associated final state detectable particles in the Beacom and Vogel model with no detector energy threshold 119 6.3 Comparison of supernova source parameters determined using the SNO su-pernova generator and Beacom and Vogel published values 122 6.4 Comparison of neutrino counts for a supernova at 10 kpc calculated using the SNO supernova generator and values published by Beacom and Vogel. 123 6.5 Neutrino counts for a supernova at 10 kpc calculated for the Burrows et al. model using the SNO supernova generator with no detector energy threshold. 125 6.6 Average energy and angular distribution values for 50000 sampled neutrinos and their associated final state detectable particles in the Burrows et al. model with no energy threshold 126 6.7 Comparison of supernova source parameters determined using the SNO su-pernova generator and Burrows et al. published values 127 6.8 Comparison of neutrino counts for a supernova at 10 kpc calculated using the SNO supernova generator and values published by Burrows et al 128 6.9 Neutrino counts for a supernova at 10 kpc calculated for the Bruenn 15 M 0 model using the SNO supernova generator with no detector energy threshold. 130 xiv 6.10 Neutrino counts for a supernova at 10 kpc calculated for the Bruenn 25 M© model using the SNO supernova generator with no detector energy threshold. 131 6.11 Neutrino counts for a supernova at 10 kpc calculated for the Liebendorfer 13 M 0 model using the SNO supernova generator with no detector energy threshold 133 6.12 Comparison of the prompt signal between supernova models at 10 kpc for time t < 10 ms from core bounce 135 6.13 Comparison of the total signal between supernova models at 10 kpc for time t < 500 ms from core bounce. 136 6.14 Comparison of the signal due to reactions involving oxygen between super-nova models at 10 kpc for time t < 500 ms from core bounce 137 6.15 Comparison of the full duration signals for the two generic supernova models at 10 kpc 138 7.1 SNO supernova detected particle counts above NHIT = 16 P M T s using the Beacom and Vogel model for a supernova at 10 kpc 153 7.2 Average NHIT and angular distribution values for final state electrons/positrons simulated in the SNO detector above the detector hardware threshold of 16 PMTs according to the model of Beacom and Vogel 154 7.3 SNO supernova detected particle counts above NHIT = 16 P M T s using Burrows' model for a supernova at 10 kpc 156 7.4 Average NHIT and angular distribution values for final state electrons/positrons simulated in the SNO detector above the detector hardware threshold of NHIT = 16 P M T s according to the model of Burrows et al 157 7.5 Comparison of the signal for relative time t < 100 ms above the detector hardware threshold between two generic supernova models at 10 kpc. . . . 170 xv 8.1 SNO supernova detected particle counts above NHIT = 34 P M T s using the Beacom and Vogel model for a supernova at 10 kpc 193 8.2 Average NHIT and angular distribution values for final state electrons/positrons simulated in the SNO detector above the supernova analysis threshold of 34 PMTs according to the model of Beacom and Vogel 194 8.3 SNO supernova detected particle counts above NHIT = 34 P M T s using the Burrows model for a supernova at 10 kpc 196 8.4 Average NHIT and angular distribution values for final state electrons/positrons simulated in the SNO detector above the supernova analysis threshold of 34 PMTs according to the Burrows model 197 8.5 Data reduction cuts used for the supernova analysis 199 8.6 Comparison of the prompt signal above the detector hardware threshold between two generic supernova models at 10 kpc for relative time t < 100 ms.200 9.1 Level 1 burst monitor NHIT100 trigger thresholds during different detector activities 208 9.2 Total average Level 1 burst rate experienced during difference detector op-erating conditions 211 9.3 Burst rate due to various causes as identified by the Level 2 burst classifica-tion algorithm 215 9.4 Characteristics of bursts classified as spallation events when 50 events are required to form the burst trigger 216 9.5 Rate of bursts due to various causes in which 35% or more of the events remain after the Level 2 analysis stage 238 9.6 Expected time required to perform the SNO burst analysis and issue an alert to SNEWS 241 xvi 10.1 The 100 ns coincidence trigger thresholds during various detector running conditions and their associated NHIT100 livetime fractions for the period from November 2, 1999 to January 4, 2001 243 C l SNO particle detection efficiencies above the detector hardware threshold of 16 PMTs for various final state particles 283 C.2 SNO detection efficiencies above the supernova analysis threshold of 34 PMTs for various final state particles 286 C.3 Summary of estimated contributions above both the hardware and analysis thresholds from reactions involving oxygen to the supernova signal using the Beacom and Vogel model 288 C.4 Summary of estimated contributions above both the hardware and analysis thresholds from reactions involving oxygen to the supernova signal using the Burrows model 289 E . l Summary of milestones relevant to SNO supernova monitoring 295 xvii List of Figures 2.1 Supernova classification taxonomy, which is based on the observation of spectral lines and light curves 10 3.1 Electron/positron energies and relative times for the events identified by the Kamiokande II, 1MB and Baksan detectors during SN1987A 33 4.1 Cross section schematic of the SNO detector 47 4.2 Ring of Cerenkov light detected from a 10 MeV electron event simulated in the SNO detector 50 4.3 Feynman diagram for the Ve + p —> n + e+ charged current reaction 54 4.4 Feynman diagrams for the ve + d —>• p + p + e~ and Ve + d^>-n-rn + e+ charged current reactions 56 4.5 Feynman diagram for the ux + d-^ux+p + n neutral current reaction. . . 58 4.6 Feynman diagrams for the v + e~ -> v + e~ elastic scattering reaction. . . 60 5.1 Supernova neutrino luminosity as a function of time in the Beacom and Vogel model 83 5.2 Fermi-Dirac neutrino energy distribution in the Beacom and Vogel model. . 84 5.3 Supernova neutrino luminosity as a function of time in the Burrows et al. model 87 5.4 Supernova neutrino average energy as a function of time using the Burrows et al. model 88 5.5 Fermi-Dirac neutrino energy distribution in the Burrows et al. model. . . . 89 xvm 5.6 Supernova neutrino luminosity spectrum in the Bruenn 15 M 0 model. . . . 91 5.7 Supernova neutrino average energy spectrum using the Bruenn 15 M 0 model. 92 5.8 Supernova neutrino luminosity spectrum in the Bruenn 25 M 0 model. . . . 94 5.9 Supernova neutrino average energy spectrum using the Bruenn 25 M 0 model. 95 5.10 Supernova neutrino luminosity spectrum in the Liebendorfer 13 M 0 model. 96 5.11 Supernova neutrino average energy spectrum using the Liebendorfer 13 M 0 model 97 5.12 Elastic scattering recoil electron angular distribution for ve,ue, v^T and V^T supernova neutrinos using the energy spectrum of Beacom and Vogel. . . . 108 5.13 Cross sections for the main supernova neutrino interactions in the SNO detector 110 5.14 Cross sections for supernova neutrino interactions involving oxygen in the SNO detector I l l 6.1 Neutrino interaction rate for a supernova at 10 kpc according to neutrino type in the SNO detector as a function of time using the model of Beacom and Vogel 139 6.2 Neutrino interaction rate for a supernova at 10 kpc according to neutrino type in the SNO detector as a function of time using the model of Burrows et al 140 6.3 Neutrino interaction rate for a supernova at 10 kpc according to region type in the SNO detector as a function of time using the model of Burrows et al. 141 6.4 Neutrino interaction rate for a supernova at 10 kpc according to interaction type in the SNO detector as a function of time using the model of Burrows etal 142 6.5 Neutrino counts per unit energy as a function of time for a supernova at 10 kpc using the model of Beacom and Vogel. 145 xix 6.6 Neutrino counts per unit energy as a function of time for a supernova at 10 kpc using the model of Burrows 146 6.7 Energy-dependent time delay as a function of neutrino mass for a supernova at 10 kpc according to the Burrows et al. model 147 6.8 M S W matter neutrino oscillations in the high- and low-density resonance layers of a supernova 149 7.1 SNO supernova detected particle counts as a function of supernova distance from Earth 158 7.2 Fraction of Milky Way stars as a function of distance from the Sun according to the Bahcall and Soneira model of the galaxy 159 7.3 SNO supernova detected particle counts as a function of supernova distance from the Sun expressed as the fraction of Milky Way stars using the Bahcall and Soneira model of the galaxy and the Burrows supernova model 160 7.4 SNO supernova detected particle count rate above NHIT = 16 PMTs for the different neutrino types according to Burrows' model 162 7.5 SNO supernova detected particle count rate above NHIT = 16 P M T s ac-cording to Burrows' model for the different region types 163 7.6 SNO supernova detected particle count rate above NHIT = 16 P M T s ac-cording to Burrows' model for the different interaction types 164 7.7 SNO supernova detected particle count rate above NHIT = 16 PMTs ac-cording to Burrows' model at 10 kpc for the different particle types 165 7.8 Cumulative SNO supernova detected particle count rate above the detector hardware threshold of 16 PMTs according to Burrows' model at 10 kpc for the different particle types during the pure D 2 0 phase 166 xx 7.9 Cumulative SNO supernova detected particle count rate above the detector hardware threshold of 16 PMTs according to Burrows' model at 10 kpc for the different particle types during the salt phase 167 7.10 SNO supernova detected particle count rate above NHIT = 16 PMTs accord-ing to Burrows' model for the different particle types using only neutrinos from a single supernova at 10 kpc 168 7.11 SNO supernova detected particle NHIT distribution above NHIT = 16 PMTs for the pure D 2 0 phase according to the Beacom and Vogel model 172 7.12 SNO supernova detected particle NHIT distribution above NHIT = 16 PMTs for the salt phase according to the Beacom and Vogel model 173 7.13 SNO supernova detected particle NHIT distribution above NHIT = 16 PMTs for the pure D 2 0 phase according to Burrows' model 175 7.14 SNO supernova detected particle NHIT distribution above NHIT = 16 PMTs for the salt phase according to Burrows' model 176 7.15 SNO supernova detected particle vertex position distribution above NHIT = 16 PMTs for the pure D 2 0 phase according to the model of Burrows et al. 177 7.16 SNO supernova detected particle vertex position distribution above NHIT = 16 PMTs for the salt phase according to the model of Burrows et al. . . 178 7.17 SNO supernova detected particle COS9SN distribution above NHIT = 16 PMTs for the pure D 2 0 phase according to the model of Burrows et al. . . 181 7.18 SNO supernova detected particle COSOSN distribution above NHIT = 16 PMTs for the salt phase according to the model of Burrows et al 182 8.1 Average background event rate for various analysis NHIT threshold settings using data chosen for the solar neutrino analysis 190 xxi 8.2 Average background event rate above the NHIT=34 analysis threshold as a function of time during the period from November 2, 1999 to January 15, 2001 using data chosen for the solar neutrino analysis 191 8.3 Signal loss measured using 1 6 N data as a function of source position in the detector, resulting from the use of the data reduction cuts chosen for the supernova analysis 198 8.4 SNO supernova detected particle NHIT distribution where the shaded area indicates the supernova signal excluded by using an analysis threshold of NHIT = 34 PMTs 202 8.5 NHIT as a function of time showing the expected supernova signal, the detector background and the effect of the analysis NHIT threshold 203 9.1 Schematic overview of the SNO data flow system 205 9.2 Expected detector count rate in the presence of a supernova burst 207 9.3 Level 1 burst rate as a function of the N E V E N T burst trigger parameter studied offline during the period between November 2, 1999 and January 4, 2001 210 9.4 Level 1 burst rate as a function of the time between bursts, determined offline for the period between November 2, 1999 and January 4, 2001. . . . 212 9.5 Level 2 analysis summary text message 218 9.6 Level 2 analysis summary histograms showing the raw burst data before the data reduction cuts have been applied 219 9.7 Level 2 analysis summary histograms showing the burst data after the data reduction cuts have been applied 220 9.8 Level 2 popup window alerting the detector operator that a burst has been . identified as "Unknown" by the burst classification algorithm 222 xxii 9.9 Level 2 popup window alerting the detector operator that a burst in which 35% or more of the events have passed the data reduction cuts 223 9.10 The number of bursts removed using various Level 3 threshold values. . . . 225 9.11 Probability of locating a supernova at various distances as a function of the angular deviation from the true supernova location for both the pure D 2 0 and salt detector modes 229 9.12 The angular difference between the actual supernova position and the posi-tion specified by the Level 3 analysis during pure D 2 0 operation 230 9.13 Probability of locating a supernova within various angular areas as a function of supernova distance for both the pure D 2 0 and salt detector modes. . . . 231 9.14 Level 3 analysis summary text message 233 9.15 Level 3 analysis summary histograms showing various distributions for all burst events that are reconstructed within the detector volume 235 9.16 Level 3 analysis summary histograms showing various distributions for burst events that are reconstructed within the D 2 0 region 236 9.17 Level 3 analysis summary histograms showing various distributions for burst events that are reconstructed within the H 2 0 region 237 9.18 Level 3 burst rate as a function of the time between bursts, determined offline for the period between November 2, 1999 and January 4, 2001. . . . 239 10.1 SNO supernova livetime as a function of time for the period from November 2, 1999 to January 4, 2001 244 10.2 SNO supernova distance sensitivity as a function of the online burst trig-ger NHIT threshold determined using simulated data sets that employ the Burrows supernova model 247 10.3 SNO supernova distance sensitivity as a function of the number of events required to form the burst trigger 248 xxiii 10.4 SNO supernova distance sensitivity as a function of time using the default parameters for the period from November 2, 1999 to January 4, 2001. . . . 249 10.5 SNO supernova distance sensitivity as a function of time using the online burst monitor parameters for the period from February 23, 2000 to January 4, 2001 250 10.6 SNO burst identification efficiency as a function of supernova distance for both the pure D 2 0 and salt operating phases 252 11.1 Supernova burst search livetime as a function of time for the period from November 2, 1999 to January 4, 2001 256 11.2 The number of bursts identified by the burst search parameters as a function of the number of events required to form the trigger 258 11.3 The number of bursts for various burst trigger requirements as the different search criteria are applied 259 11.4 The upper limit of the supernova rate as a function of distance for various confidence levels 261 11.5 The upper limit of the supernova rate as a function of livetime for various confidence levels assuming no supernova observation 262 D . l Level 3 analysis summary histograms showing various distributions for all burst events that are reconstructed within the detector volume using events from 100 supernovae at 10 kpc simulated according to the Burrows supernova model 291 D.2 Level 3 analysis summary histograms showing various distributions for burst events that are reconstructed within the D 2 0 region using events from 100 supernovae at 10 kpc simulated according to the Burrows supernova model. 292 xxiv D.3 Level 3 analysis summary histograms showing various distributions for burst events that are reconstructed within the H 2 0 region using events from 100 supernovae at 10 kpc simulated according to the Burrows supernova model. xxv Acknowledgments From my first involvement with SNO in May 1996 to the final touches on my thesis in December 2001, a significant amount of time and effort has been invested both by myself and a host of others. As a result, I have many people to thank for their assistance, support and imparting of knowledge. I want to start first by extending my deepest thanks to my supervisor Dr. Chris Waltham for guiding me through the Ph.D. journey from start to finish. Now that all has been said and done, I am better able to appreciate the direction I was given as well as the flexibility I was afforded. And I know I will miss his wry sense of humour. The quality of this thesis has benefitted greatly from the contribution of the super-visory committee that has followed my progress throughout my term as a Ph.D. student. Members of this group include Dr. Douglas Beder, Dr. Douglas Scott and Dr. Chris Hearty. The university examiners Dr. Matthew Choptuik and Dr. Philip Loewen and the external examiner Dr. John Beacom also deserve my gratitude for their thorough reading of my thesis and for many useful comments. Furthermore, this thesis would not have been possible without the work performed in conjunction with members of the SNO Supernova Working Group. My association with Dr. Clarence Virtue, Dr. Reda Tafirout and Mike Schwendener has been extremely rewarding, and I want to thank them for putting up with me. I want thank Reda in particular for his tireless work on the supernova monitoring system in general and for his help with the burst analysis. I also want to express my appreciation for the privilege of being part of the SNO group at U B C , whose members include Dr. Rob Komar, Christian Nally, Dr. Thomas Kutter and xxvi Siong Ng (as a summer student). Rob in particular deserves heaps of praise for the insight he has provided over the years and for the key role he played in my Ph.D. education. For all the computer know-how they passed along, I want to thank Rob, Christian and Doug Maas. A large debt of gratitude must be paid to the members of the SNO collaboration, including not only the project scientists, but also members of the SNO site staff and the detector construction crew. I consider myself fortunate to have worked with the group of wonderful people who have been drawn to this project. In particular I wish to acknowledge the guidance of Dr. Richard van de Water, Dr. Hardy Seifert, Dr. Peter Doe, Dr. Davis Earle and Dr. Hugh Evans. I learned a great deal from each one of these people. Peter warrants special mention for the pain and suffering he endured while helping to edit my thesis. Eddie Gore of Eddie's Sports Bar in Sudbury and the members of his staff also deserve my heartfelt thanks for the friendship and hospitality (not to mention beer!) that they have provided over the years. While many names should be included, I want to be sure to recognize Kelly Morrison, Cyndi Dwyer, Vicky Brouillard, Joe (Guisseppe) Vocaturo and of course Randy Brunelle. They are some of the best ambassadors to Northern Ontario anyone could hope to know. As with my M.Sc. thesis, I once again wish to acknowledge the hospitality of my relatives Don, Carol, Jonathan and Matthew Wilkie and my land people Ingrid Pinel and Terry Pask, and thank them for making Vancouver feel like home for the last 8 years. I know that I won't eat so well once I leave. My parents have been supportive of all my endeavours, and for having that environment I consider myself very fortunate. It is my sincerest hope that this thesis will offer them comfort well into their old age. I also want to extend thanks to my two brothers: Brett, who never let me forget how little money I made as a graduate student; and Jordan, who xxvii will probably read more of this thesis than anyone else in my family. Thanks also go to Charles the Cat for illuminating discussions on neutrino physics. Last but not least, thanks go to my wife Kara for the support she was able to give and for the patience she was able to find. xxviii Come quickly, I am tasting stars! - Dom Perignon, upon discovering champagne. xxix Chapter 1 Introduction The neutrino was first proposed in 1930 by Pauli [1] to account for the apparent missing energy and momentum in nuclear beta decay reactions. A series of experiments performed between 1950 and 1956 by Reines and Cowan [2] confirmed the existence of the neutrino by recording evidence of the electron antineutrino. To make the discovery, Reines and Cowan identified signatures of neutrinos from fission reactors using the inverse beta decay reaction Ve +p ->• n + e+. (1.1) In 1995, Reines was awarded the Nobel Prize in physics for this important work in the detection of the neutrino. 1.1 Neutrino Properties Neutrinos are classified as leptons, which are fundamental particles in the Standard Model of particle physics. They come in 3 flavours, one associated with each of the three lepton families, as indicated in Table 1.1. As with the electron, muon and tau particles, neutrinos also have corresponding distinct antiparticles. Because they possess no electric charge, neutrinos only participate in weak and gravitational interactions, and have extremely low reaction cross sections as a result. This is the principal reason why neutrinos are so difficult to detect. As a neutral particle without a magnetic moment, neutrinos are not deflected in locally or globally distributed electric and magnetic fields. For a long time, the neutrino mass was assumed to be zero; however, recent evidence of neutrino oscillation indicates that 1 Chapter 1. Introduction 2 the neutrino mass is non-zero [3],[4]. The evidence for neutrino oscillation also constrains the sum of masses of neutrinos listed in Table 1.1 to be between 0.05 and 8.4 eV/c 2 [4]. Present upper limits for the masses of neutrinos as determined by direct measurement are found to be: mUe < 3 eV/c 2 , mUlt < 0.19 M e V / c 2 and mVr < 18.2 M e V / c 2 [5]. Generat ion Lep ton Neu t r ino First electron, e~ electron neutrino, ue positron, e + electron antineutrino, Ve Second muon, p~ muon neutrino, antimuon, p+ muon antineutrino, I7 M Third tau, T~ tau neutrino, vr antitau, r + tau antineutrino, VT Table 1.1: The three generations of leptons and their associated neutrinos in the Standard Model of particle physics. 1.2 Neutrino Sources Neutrinos are produced in a wide range of physical processes, and may constitute most of the normal matter that exists in the universe1. The recent neutrino oscillation evidence [4] indicates that the contribution to the critical density of the Universe is 0.001 < f2„ < 0.18. From some of the most violent processes imaginable to radioactive decays observed on the Earth, neutrinos play a vital role. Various neutrino sources are briefly mentioned below, ordered according to the magnitude of the event that produces them. 1.2.1 Big Bang When the temperature of the early universe was greater than 10 1 0 K and matter densities were still very high, neutrinos remained in equilibrium with matter through weak interac-tions. The universe cooled quickly and 1 second after the Big Bang neutrinos decoupled 1 Approximately 2/3 of the total matter in the universe is believed to be in the form of "dark energy" [6]. Chapter 1. Introduction 3 from the rest of the matter in the universe. As the universe expanded, the temperature of all the matter in it, including photons and neutrinos, decreased over time. The current temperature for the cosmic electromagnetic background radiation is measured to be T0y = 2.725 ± 0.001 K [5]. Neutrinos decouple from matter before photons, and cool strictly due to the expansion of the Universe. However, photons cool more slowly. When temper-atures in the early Universe fall below 6 x l O 9 K (T ~ rae), photons and electron/positron pairs that were once in equilibrium through the reaction e+e~ «-» 77 now only interact via the e+e~ —>• 77 reaction. This effectively heats photons compared to neutrinos, which means that the neutrino temperature for the current epoch, TQl/, is lower than the photon temperature and is given by [7]: Therefore, the present temperature of neutrinos from the Big Bang is expected to be 1.9 K , and the average neutrino energy2 is then (E„) = 3.15 kTv — 5 x 10~ 1 0 MeV. At these energies, the mean free path of neutrinos exceeds the size of the Universe. Therefore neutrinos remaining from the Big Bang cannot be detected with present technology. In the Universe today, the number density of neutrinos produced at the time of the Big Bang is approximately 100 c m - 3 per neutrino species [7]. 1.2.2 Gamma-Ray Bursts Gamma-ray bursts (GRBs) are among the least understood phenomena in the universe. G R B events are characterized by a burst of 0.1 to 1 MeV photons with a duration ranging from ~30 ms to ~100 seconds [8]. Observations of GRBs imply that the photon events are due to the energy dissipation of a relativistically expanding "fireball", whose primal cause is not yet known. Two possible progenitors for G R B events are the merger of compact objects, such as neutron stars and black holes, and explosions of supermassive stars. 2The expression for the average energy (E) = 3.15 kT is true for relativistic fermions that obey the Fermi-Dirac energy distribution. The corresponding expression for relativistic bosons is (E) = 2.7 kT. (1.2) Chapter 1. Introduction 4 The observed 7 rays are thought to be produced by synchrotron emission of electrons accelerated by internal shocks within the expanding fireball. It has also been suggested that high energy neutrinos might be produced as a result of the dynamics within the fireball. In one scenario, high energy neutrinos are expected to be produced by the decay of charged pions created in interactions between photons and high energy protons, which are also accelerated by the shock. These photo-meson interactions are expected to convert a significant fraction of the fireball energy to neutrinos of energy Eu > 10 1 4 eV [9]. Neutrinos with lower energies of approximately 2-25 GeV or higher may be produced by inelastic nuclear collisions [10]. 1.2.3 Supernovae Supernovae resulting from gravitational collapse are prodigious sources of neutrinos. When a massive star depletes its supply of nuclear fuel, it collapses and the gravitational poten-tial energy of the star is carried away by neutrinos of all flavours. Moreover, neutrino interactions with the infalling material are thought to help sustain the shock wave that ultimately ejects the outer layers of the star into space. The fundamental role that neu-trinos play in the collapse of a massive star was confirmed in 1987 when neutrino events were observed from SN1987A. The average energy for supernova neutrinos is in the range between 13-20 MeV. However, the tails of the energy distribution can extend as high as 100 MeV. 1.2.3.1 Relic Supernovae Throughout the evolution of the Universe, many supernova explosions have taken place. In fact, it is estimated that 1 supernova event occurs every second somewhere in the Universe3. Neutrinos from supernovae that occurred in other galaxies in the distant past are called 3There are on the order of 100 billion galaxies in the Universe. Assuming a conservative rate of 1 supernova every 500 years yields an overall rate of approximately 5 supernova per second occurring in the Universe. Chapter 1. Introduction 5 relic neutrinos. The flux of relic supernova neutrinos depends critically on the rate of supernovae as a function of time. Supernova rates that were either low in the past or high in the very distant past lead to a relic supernova signal that is difficult to measure today. For exam-ple, if the supernova rate should peak at redshifts4 of order 2-3, the energies of the relic neutrinos would be redshifted below typical detector thresholds. Some information about the supernova rate over time is provided in studies performed by Pei and Fall [11], which indicate that the star formation rate was much higher at redshifts z ~ 1 than at the present epoch. The average energy for relic supernova neutrinos is approximately 5 MeV, with the high energy region of the energy distribution extending beyond 50 MeV [12]. 1.2.4 Solar Fusion Reactions The energy that powers main sequence stars like our Sun comes from the nuclear fusion reaction Ap ->4He + 2e + + 2ve + 26.73 MeV. (1.3) Protons are converted to a particles, positrons, neutrinos and a surplus of energy. This re-action can proceed through different channels and as a result neutrinos of different energies are produced. The primary source of neutrinos in the Sun is via the p-p reaction: p + p-> d + e+ + ue. (1.4) However, these neutrinos are difficult to detect because they have relatively low energies (E < 0.42 MeV). The largest flux of high energy solar neutrinos comes from the 8 B reaction 8 B-> 2 4 He + e+ + ue. (1.5) 4The phenomena of redshift is analogous to the Doppler shift in sound waves. Energies observed on Earth are lower than those measured at the distant source by a factor (1 + z), where z is the redshift. Chapter 1. Introduction 6 These neutrinos have an energy spectrum that extends to approximately 15 MeV. Detectors such as the Sudbury Neutrino Observatory and Super-Kamiokande have been designed to observe these 8 B neutrinos. 1.2.5 Cosmic Ray Interactions in the Atmosphere Neutrinos are also produced in the Earth's upper atmosphere due to hadronic cascades originating from interactions with cosmic rays: Through the decay of pions and muons, high energy muon and electron neutrinos (and an-tineutrinos) are produced in the ratio of 2:1. In 1998, the Super-Kamiokande collaboration was able to demonstrate that atmospheric muon neutrinos oscillate into another flavour of neutrino [3]. The range of energies for atmospheric neutrinos is from approximately 100 MeV to 10 GeV [13]. 1.2.6 Nuclear Reactors Nuclear reactors generate power using the fission of radioactive elements such as 2 3 5 U , 2 3 8 U , 2 3 9 P u and 2 4 1 P u . Many of the fission products subsequently decay through beta emission, producing copious numbers of electron antineutrinos. The average energy of neutrinos produced in fission reactors is approximately 5 MeV, with the energy spectrum cutting off at roughly 8 MeV. 1.2.7 Radioactivity in the Earth Radioactive decay of natural elements (mainly 2 3 8 U and 2 3 2 T h ) in the interior of the Earth produces neutrinos as well as 40% of the observed outflow of heat from the Earth's sur-face [14]. The energy of these neutrinos falls in the range 1-2 MeV. p - > X + TT ->• X + p + V f i - ^ e +ue + u^. (1.6) P —r X + 7T —y X + p + —r e + f e + Up. (1.7) Chapter 1. Introduction 7 1.3 Study of Supernova Neutrinos Neutrinos from supernovae are interesting for many important reasons. Unlike photons, neutrinos carry information about the physics processes that occur in the core of the collaps-ing star. Therefore, the supernova neutrino signal offers the best means of understanding the mechanism that governs supernova dynamics. With this understanding also comes a more refined understanding of the nucleosynthesis processes that occur in supernovae. Primordial nucleosynthesis is responsible for producing stable light elements such as hy-drogen, helium and lithium, but the temperatures found in the cores of collapsing stars are required in order to overcome the Coulomb barrier associated with the higher mass elements. Therefore, the majority of the heavy elements in the Universe are the result of supernova explosions5. 1.4 Study of Supernova Neutrinos at SNO To study supernova neutrinos, it is necessary to construct a detector with a large volume of material in order to compensate for the low neutrino cross section. The Sudbury Neutrino Observatory (SNO) is such a detector, with 1700 tonnes of ultrapure light water (H 2 0) surrounding 1000 tonnes of ultrapure heavy water (D 2 0) . The use of heavy water provides SNO a unique perspective on neutrinos in general. A l l other neutrino detectors that are currently in operation are mainly sensitive to electron neutrinos and antineutrinos during a supernova burst. However, neutrinos of all flavours are able to participate in reactions which breakup the deuterium atom, providing SNO with a sensitivity to neutrinos of all types. This is particularly important in the case of supernova neutrinos, because most of the energy is expected to be carried away from the collapsing star by and uT neutrinos and antineutrinos. One other feature of the supernova signal about which SNO is expected 5 This includes us! The carbon and oxygen in our bodies was produced during the death of a massive star. Chapter 1. Introduction 8 to provide insight is the prompt burst of electron neutrinos resulting from electron capture reactions in the core. Other currently existing detectors are not able to separate the electron neutrino signal from the electron antineutrino signal as well as SNO can. In addition to information about the supernova mechanism, it is also possible to use supernova neutrinos to learn more about the properties of neutrinos. Analysis of the neu-trino signal from a supernova explosion may provide the best means of directly measuring the muon and tau neutrino mass. Since SNO has a unique sensitivity to these neutrino flavours, it is expected to provide one of the best measurements of the muon and tau neutrino mass. Estimates suggest that analysis of the supernova signal observed in SNO might be able to limit the muon or tau neutrino mass to 30 e V / c 2 [15]. No other type of terrestrial experiment has the possibility of placing such a stringent limit. In order to gain as much information as possible from the next galactic supernova, it is crucial to have a monitoring programme in place to detect the neutrino burst. The neutrino signal is expected to precede the visible signal by up to several hours, due to the time required for the shock wave to emerge from the envelope of the collapsed star. Therefore, the prompt detection of neutrinos from a supernova can be used to alert the astronomical community. Observations of the onset of the electromagnetic signal have never before been observed with modern instruments. Chapter 2 Supernova Physics 2.1 Introduction A supernova is defined as a highly energetic outburst resulting in the complete disruption of a star. Gravitational collapse refers to the inward collapse of the core of a massive star which has exhausted its nuclear fuel, and is expected to produce a very large number of neutrinos in the process. Only certain types of supernovae undergo gravitational collapse. However for most of this thesis, the term "supernova" is assumed to mean a supernova resulting from gravitational collapse that releases a large number of neutrinos. 2.2 Supernova Classifications Astronomers classify supernovae according to their optically observed properties. The two main types of supernovae, Type I and Type II, are distinguished on the basis of their electromagnetic spectra and their "light curves", which describe the time variation of the optical luminosity values. Typical light curves for both Type I and Type II start with a rise in luminosity that lasts for approximately 10 days, followed by a decline which lasts on the order of a year. But there are differences in the spectra that distinguish them from one another, which are discussed in the sections below. Type I supernovae are further subclassified as Types la, lb and Ic, while Type II su-pernovae can be labelled as either Type II-L or II-P as indicated in Figure 2.1. This 9 Chapter 2. Supernova Physics 10 classification scheme is purely phenomenological, so the classes do not necessarily corre-spond exactly to physical processes. The underlying processes that gives rise to Type I and Type II supernovae are quite different, however the explosion energies in both cases are remarkably similar. H/noH SNII ^ ^ ^ ^ ^ ^ ^ ^ H SNI light curve shape Si / no Si Figure 2.1: Supernova classification taxonomy, which is based on the observation of spectral lines and light curves. (After Cappellaro and Turatto [16]) 2.2.1 Type I Supernovae The primary feature used to classify a Type I supernova is the absence of hydrogen lines in its spectra at maximum light output. In general, the light curves of different Type I supernovae tend to be quite homogeneous, with similar luminosity and spectral evolution, and thus likely a consequence of uniform initial conditions. A Type I supernova begins in an evolved binary system where one of the stars is a Chapter 2. Supernova Physics 11 white dwarf consisting mainly of carbon and oxygen1. To trigger the explosion, the white dwarf begins accreting matter from the companion star, which is possibly a supergiant or a main-sequence star. The hydrogen accreted from the companion star is quickly con-verted into helium before the explosion takes place, which explains its later absence in the absorption spectra of all Type I supernovae. When a sufficient amount of accreted mass has accumulated, a thermonuclear explosion is ignited, which is observed as a supernova explosion. Negligible neutrino emission is expected for supernovae arising from this type of physical process. Unlike Type II supernovae, the temperatures reached during nuclear burning are too low to support reactions that produce neutrinos (see Section 2.3.6). In the model described above, the progenitor stars for Type I supernovae are not par-ticularly massive since they evolve into white dwarfs, and additional mass is required to produce the instability that leads to an explosion. This characteristic appears to agree with observations, since the majority of Type I supernovae are found in elliptical galaxies, which contain very old populations of low-mass stars. Star formation in elliptical galaxies ended long ago. One possible reason for this might be that all of the interstellar gas in elliptical galaxies condensed into stars at the time the galaxy formed leaving no material for future star formation. 2.2.1.1 Type l a Type I supernovae are further subdivided according the appearance of the early-time spec-trum. Type la supernovae are characterized by strong absorption near 6150 A attributed to the presence of silicon. About 80% of Type I supernovae fall into the Type la category. Due to their brightness and consistent light output, Type la supernovae are used in determining distance scales in the Universe2. xLow mass stars are unable to burn elements beyond carbon and oxygen. Our Sun, for instance, will end its life as a white dwarf. 2 Recent analysis using Type la supernovae has indicated that the expansion of the Universe is acceler-ating! [17] Chapter 2. Supernova Physics 12 2.2.1.2 T y p e lb , Ic Type lb supernovae lack the silicon spectral lines but instead show prominent helium lines in the spectrum, and Type Ic have neither the silicon or the helium lines. Supernovae exhibiting these features likely arise from gravitational collapse, but have previously lost their outer layers of hydrogen and possibly helium [18]. 2.2.2 Type II Supernovae Type II supernovae on the other hand are identified by the presence of hydrogen in their spectra at maximum light output. The luminosity peaks for Type II supernovae usually last for about 100 days, which is longer than for Type I. While the maxima tend to be less bright than Type I supernovae, the tails of the light curves for Type II supernovae often extend for longer periods of time. The standard model for a Type II supernova is a massive star ( M > 8 M©), which has reached the end of < 30 million years3 of evolution on the main sequence when the pressure from fusion reactions can no longer support the gravitational pressure of the outer layers of gas. The star collapses inward, and when the density of the core reaches nuclear density the collapse "bounces" and a shock wave propagates outward. The interaction of this shock wave with the outer material is thought to contribute significantly to the explosion. According to prevailing theories, neutrinos originating from nuclear reactions in the collapsing core deposit sufficient energy behind the shock wave, enabling it to then completely eject the outer material. After bounce, the core continues to collapse until a neutron star, or possibly a black hole, is formed. In this model, 99% of the total binding energy of the star is carried away by neutrinos, leaving only 1% of the energy to be released in the kinetic energy of the ejecta and in electromagnetic radiation. A n expanding shell of 3While our Sun is expected to live for a total of 10 billion years, massive stars have higher luminosities and burn their fuel faster. The stellar lifetime is roughly given by T oc 1/M25 [19]. For instance, a 20 M© star is expected to burn hydrogen for 10 million years [20]. Chapter 2. Supernova Physics 13 gas continues to radiate radio waves and X rays for another ten thousand years. What remains is an expanding nebula and a central neutron star which often appears in the form of a pulsar, a pulsating source of radiation in some or all electromagnetic wavelengths. The pulsed emission is due to the interplay between the fast rotation and strong magnetic fields (10 1 2 -10 1 3 G) in these objects. Unlike Type I supernovae, which can be found in all types of galaxies (but mainly elliptical), Type II supernovae occur almost exclusively in the arms of spiral galaxies that are created in the process of star formation4. As such, spiral arms contain young stars which are more likely to be massive and therefore candidates for Type II supernovae. 2.2.2.1 T y p e II-P, II-L Type II supernovae are subclassified according to their light curves. After the maximum peak, some Type II supernovae are observed to have almost constant luminosity values for periods up to 2-3 months. These are designated as Type II-P (plateau) supernovae, of which SN1987A is a prime example. Supernovae for which the light curve falls more rapidly are known as Type II-L (linear). The length of the plateau is thought to depend on the envelope mass of the progenitor star [16]. 2.3 The Physics of Gravitational Collapse This section describes a standard model for the gravitational collapse mechanism, which may result in a supernova of Type II or Ib/Ic. Various models exist to account for the processes involved in such a collapse, and they have many common features which are described below. References [21], [22], [23] and [24] provide an overview of this topic. A more detailed discussion of specific models can be found in Section 5.3. 4 Supernova explosions are also thought to compress the surrounding interstellar medium and promote further star birth. Chapter 2. Supernova Physics 14 2.3.1 Standard Stellar Evolution A star begins life when matter condenses from an interstellar cloud consisting of mainly hydrogen and helium with some small admixture of heavier elements. The protostar con-tracts under the influence of gravity and begins to heat up until the core temperature is high enough (107 K) to ignite hydrogen burning through nuclear fusion5. The thermal pressure from nuclear burning reactions provides a balancing force to counteract the inward gravitational attraction, resulting in a state of hydrostatic equilibrium. Eventually, the supply of hydrogen in a star is reduced to a point where the pressure generated by its burning is no longer sufficient to support the overlying mass of material. When this happens, the stellar core starts to collapse, causing the temperature to increase until it is high enough to burn the helium that was produced in the first stage of the star's life. The unburned hydrogen forms an outer layer that surrounds the burning helium core. The fusion of helium into carbon proceeds until the supply of helium is diminished and the star again contracts, heats up and a subsequent burning reaction involving the fusion of more massive atoms ignites. This process is repeated, producing progressively heavier elements in rapid succession. The products of successive nuclear burning stages are arranged in concentric shells, with the heaviest elements in the centre and hydrogen in the outer envelope. This is the well-known "onion skin" structure of a pre-supernova star. By its nature, the fusion process creates fewer combustion products at each step of the burning process, such as during the fusion of hydrogen into helium where four hydrogen atoms are required to create one helium atom. Therefore each burning stage takes less time than the one preceding it. Hydrogen burning lasts for several million years; however, the last few stages last only a few years or months. The final burning stage of a pre-supernova star lasts only about a day. 5 The minimum mass required to attain a core temperature of 107 K and begin hydrogen burning is about 0.08 M0. Chapter 2. Supernova Physics 15 2.3.2 The Pre-Supernova Star At the very end of their lives, massive stars are able to burn heavy elements such as oxygen and silicon to produce 5 6 Fe. This isotope of iron is the most strongly bound of all elements, which means that further fusion or fission reactions result in the absorption, rather than the production, of energy. Therefore, 5 6 Fe does not burn, but accumulates in the core of the star. The onion-skin structure of the star now has a relatively small iron core at the centre surrounded by shells of silicon, oxygen, neon, carbon, helium and an outer layer of hydrogen. For objects with masses greater than the Chandrasekhar mass limit Mch, the degeneracy pressure of the relativistic electron gas can no longer support the pressure being exerted due to gravity. The Chandrasekhar mass limit is given by [21]: Mch = 5 . 8 F e 2 M 0 , (2.1) where Ye is the fraction of electrons per nucleon (Ye = Z/A, where Z is the average charge and A is the average atomic number). For an iron-nickel core, the mass limit is Mch ~1.2 M©. Notice that this limit does not depend on the density of the star, but on the composition. When a mass of iron exceeds this limit, it will begin to compress under its own gravity. 2.3.3 Core Collapse The electron degeneracy is unable to prevent the star from collapsing further once the mass of iron in the central core of the star exceeds the Chandrasekhar mass limit. For massive stars, the mass of the core is typically in the range Mcore ~ 1.4 — 2.0 M 0 . Two additional instabilities also contribute to core collapse. The most important of the two processes is electron capture. As the temperature and density in core rises, the rate of electron capture reactions also increases: e~~ +p ->• n + ve. (2.2) Chapter 2. Supernova Physics 16 This stage of collapse is also referred to as neutronization because of the neutron produced in the final state. The electron neutrinos that result from this reaction are able to escape during this early stage of collapse because the neutrino, mean free path is much greater than the size of the star. As a consequence, electron capture serves to decrease the energy and the number of particles in the core and therefore the pressure, which increases the rate of collapse. A second process that contributes to core de-stabilization is called photodisintegration. Energetic photons are able to dissociate the stable iron nuclei through the reactions [24]: 7 + 5 6 Fe-> 13 4He + 4n (2.3) 7 + 4 He -> 2p + 2n. (2.4) Although these reactions increase the number of particles in the core, they are endothermic and therefore require energy in order to take place. The result is that the average kinetic energy of the particles decreases and so does the pressure. While photodisintegration also contributes to the de-stabilization of the core in lower mass stars, it is thought to be the dominant process in higher mass stars. 2.3.4 Neutrino Trapping Core collapse continues and electron neutrinos are still able to diffuse out of the core until densities approaching p « 10 1 2 g/cm 3 are reached. At these densities not even neutrinos can escape as the mean free path for neutral current ve scattering becomes less than the size of the core for time scales on the order of milliseconds. At this point, all energy becomes trapped within a radius of approximately 30 km inside the core. The spherical shell at this radius, separating the inner region which is opaque to neutrinos and the outer region which is transparent to neutrinos, is known as the neutrino sphere. Neutrinos at a radius less than the neutrinosphere are considered to be trapped, whereas those beyond the neutrinosphere radius are free to propagate outward. Chapter 2. Supernova Physics 17 After neutrino trapping occurs, collapse continues and the core density continues to increase. 2.3.5 Core Bounce and Shock Breakout Finally, the density in the core reaches the density of nuclear matter, p = 2.7 x 10 1 4 g/cm 3 . At this point matter cannot compress any further due to the nucleon degeneracy pressure. Unlike the electron degeneracy pressure which was overcome with sufficient mass ( M c o r e > Mch), there is no possibility of further substantial collapse once regions are compressed to nuclear densities. There is however, a small amount of compressibility in this state and the momentum of the infalling material carries the collapse beyond the point of equilibrium, compressing the core to a density even higher than nuclear densities. When this happens, a "bounce" occurs. A shock wave is created inside the core and begins propagating outward and interacting with the outer layers of matter, which are still falling inward toward the core. The shock wave is a discontinuity in pressure, density and temperature, and its effect is to compress and heat the matter it passes through. The shock starts deep inside the core at a radius of approximately 10 km, and moves outward with a velocity of about 70 km/ms 2.3.6 Neutrino Breakout At approximately 1 ms after bounce, the shock hits the neutrinosphere, and neutrinos created in the high-temperature wake are able to stream outward. This is called the "neutrino break-out" or "neutrino flash". The temperatures directly behind the shock wave are now sufficiently high to produce other flavours of neutrinos through a variety of Chapter 2. Supernova Physics 18 neutral current pair processes6 including [25]: • Pair annihilation: 7 + 7 # e + + e —> u + u (2.5) • Plasmon decay: plasma excitation —>e+ + e —> u + u (2.6) • Photoneutrino: 7 + e —> e + v + v (2.7) • Bremsstrahlung: e + (A, Z) ->• (A, Z) + e +u + u. (2.8) Photoneutrino processes dominate at lower temperatures (10 8-10 9 K ) , while the main con-tributions at higher temperatures (10 9-10 1 0 K) are due to pair annihilation. The plasma processes dominate at high densities over the full range of temperatures [26]. 2.3.7 Explosion The next necessary stage in this evolution is the "explosion", in which the outer material of the star is completely ejected. However, when the shock wave reaches a distance of a few hundred kilometers from the centre of the star both it and the explosion are stalled. Part of the reason that the supernova fails to explode promptly is due to the energy lost as the shock wave passes through regions of high temperature with high densities of heavy nuclei in the vicinity of the core. Photodisintegration reactions (Equation 2.3) can occur in these regions and require large amounts of energy (kT ~ 9 MeV per nucleon in heavy nuclei), which removes energy from behind the shock. The slow-down of the shock wave is further aggravated by the emission of neutrinos. Protons resulting from the photodisintegration reactions above readily capture electrons. Since these reactions take place above the neutrinosphere, the neutrino emitted in this process can escape, thereby removing energy from the star. Additional energy is carried away by neutrinos that are created in pair production reactions in the high temperature 6 The temperatures are not sufficiently high to create muon and tau particles via the charged-current process. Therefore, muon and tau neutrinos and antineutrino are created via neutral current processes. However, veVe pairs can be created through both neutral- and charged-current reactions. Chapter 2. Supernova Physics 19 environment. The net result is that both temperature and pressure are sharply reduced in the shock wave causing it to stall, while matter continues to fall through it. Failure or success of the prompt shock depends primarily on the amount of material the shock has to traverse before it emerges from the iron core. Relatively low mass stars have correspondingly small iron cores, and may explode via the prompt shock mechanism. Once the shock has emerged relatively easily from the small core, the lower core temperature of smaller stars will also favour the prompt explosion. At low temperatures, electron capture processes no longer decrease the pressure and reduce the energy in the core, therefore the mass of the inner core increases and expands to energize the outgoing shock wave. A different mechanism is necessary for more massive stars. While many of these neu-trinos were described in earlier sections as being "trapped", they do diffuse out of the core on longer time scales. Neutrons and protons behind the shock absorb a small fraction of this ~10 5 3 erg/s neutrino luminosity diffusing out from the newly forming neutron star. This addition of energy from neutrinos effectively revives the shock wave, which will then expel the outer material from the star [27]. Since only a small fraction of the neutrinos interact, the material in the vicinity of the shock wave does not suffer greatly from dimin-ishing energy reserves or pressure. Therefore, neutrino heating is most effective at a radius of about 150 km, where the probability of neutrino absorption is not too low and yet the temperature is not so high that the matter there emits a large number of neutrinos. As a result, the value of 150 km becomes the bifurcation radius: all the matter within this boundary ultimately falls into the core, while the matter outside is expelled. The neutrinos that re-heat the shock wave diffuse out of the core over several hundred milliseconds, therefore this mechanism is referred to as the "delayed" explosion. Chapter 2. Supernova Physics 20 2.3.8 Cooling The neutron star that remains behind after the explosion cools by emitting neutrinos over a timescale of tens of seconds. Neutrinos of all flavours are emitted as vV pairs through reactions such as those mentioned in Equations 2.5, 2.6, 2.7 and 2.8. In fact most of the neutrinos are emitted during this phase as the star sheds its binding energy almost completely in the form of neutrinos, each carrying approximately 15 MeV. However, if the progenitor star is particularly massive, the flux of neutrinos emitted during the cooling stage may be truncated due to the formation of a black hole. 2.3.9 Aftermath After the explosion, the shock wave continues to move outward through the outer envelope. Various kinds of electromagnetic radiation result from the interaction of the shock with the outer material. Large amounts of 5 6 N i are created as the shock wave moves through the shell of silicon that surrounds the iron core. The 5 6 N i isotope is unstable and decays via electron capture with a half life of 6.1 days: 5 6 N i + er -> 5 6 C o + 7 + i / e , E1 = 0.2 - 1.6 MeV. (2.9) The cobalt nucleus decays to iron by electron capture with a half life of 77.3 days: 5 6 C o + e~ -> 5 6 Fe + 7 + ue, E1 = 0.2 - 3.6 MeV (2.10) and, less often, by positron emission: 5 6 C o - > 5 6 Fe + 7 + e+ + zv (2.11) At late times, the supernova light curve is powered by the decay of 5 6 C o . The gamma rays from the decay can begin to escape as the ejecta expands and thins. Chapter 2. Supernova Physics 21 2.4 Expected Frequency of Supernovae 2.4.1 Relative Frequency of Supernova Types Some techniques for estimating the frequency of galactic supernovae only predict the total number for all types. Supernova data from other galaxies can also be used to estimate the ratio of the different types within our own galaxy. Since only supernovae of Type II and Ib/c are expected to generate a substantial neutrino signal, knowing which types of supernovae are more likely is useful information. Galaxies are classified into three general types based on their shapes: elliptical, spiral and irregular. A fourth type of galaxy has been observed to share both elliptical and spiral attributes and is called a "lenticular" galaxy. The Milky Way galaxy is classified as spiral Sbc galaxy. According to Tammann et al. [28], most supernovae occur in spiral and irregular galaxies because of the large population of massive stars in those types of galaxies. Of the few that do occur in elliptical galaxies, essentially all are of Type la with no contribution from any of the other types. Therefore, a neutrino burst due to gravitational collapse is not expected from elliptical galaxies. Narrowing the study to spiral galaxies similar to the Milky Way indicates that Type Il/Ib supernovae are between 5 and 6 times more frequent than those of Type la [28], [16]. In other words, 83-86% of the supernovae in spiral Sbc galaxies belong to the Type Il/Ib designation. For other types of spiral galaxies, the fraction of Type Il /Ib supernovae is estimated to be as high as 91%. 2.4.2 Galactic Supernovae There are a number of different techniques that can be used to estimate the frequency of supernovae within the Milky Way. However, the results of these studies vary quite widely. Chapter 2. Supernova Physics 22 2.4.2.1 Historical Supernovae One method for determining the supernova rate in our galaxy is to rely on observations of supernovae in the past. Over the last one thousand years, 6 supernovae have been observed by early astronomers, which likely constitutes the complete set of supernova events that occurred within 3 kpc of the Sun 7 [29]. However, these observations represent only about 20% of the expected total, since it is likely that many were obscured by dust, especially toward the centre of the galaxy. This is one of the reasons why all of the historically observed supernovae are limited to a sector of the galactic plane which spans only 60°, and in the last millennium, all but the closest one are in the direction away from the galactic centre [30]. The recent known supernovae in our galaxy are listed in Table 2.1. Using historical supernova events, the supernova rate can be calculated in two ways. The most direct way involves assuming that the supernova rate in the entire galaxy is the same as that in the historically observable region. Estimates using this method suggest a galactic supernova mean interval of r <30 yr [30] and 14-25 yr [31]. If the type of supernova in the historical events can be determined accurately then a supernova rate can be determined using detailed models of the population distribution in the galaxy. Calculations performed using this approach estimate one supernova every 6-17 yr [29]. The Crab is almost certainly a Type II supernova based on the observation of the hydrogen spectral lines and of the pulsar remnant. As well, data collected by Tycho Brahe indicates that the supernova of 1572 is of Type I. Unfortunately, the type assignments of other historical supernovae are not as straightforward. Where possible, the type designation for the set of historically observed supernova is also specified in Table 2.1. Distance information8 is compiled from 7The parsec (pc) is denned as the distance at which 1 astronomical unit (AU) perpendicular to an observer's line of sight subtends an angle of 1 arc second. 1 pc = 3.09 x 1013 km = 3.26 light years. 8There are several conflicting reports on the distances to historical supernovae. For instance, in refer-ence [32] the distance to Kepler's supernova of 1604 is quoted as D = 3.4 ± 0.3 kpc, while in reference [33] the distance is D = 10.0 kpc. The author suspects a confusion in units between kpc and kly (3 kpc ss 10 kly). Chapter 2. Supernova Physics van den Bergh [29], Schaeffer [32] and Reed [34]. 23 Name Year Distance (kpc) T y p e Lupus 1006 1.6 la Crab 1054 2.0 II SN1181 1181 3.2 II? Tycho 1572 2.4 I? Kepler 1604 3.4 I/II? Cas A ~1680 3.4 Ib Table 2.1: Recent observed galactic supernovae. The Cas A supernova seems to have gone unnoticed in the records of early astronomers, except possibly by Flamsteed [35]. 2.4.2.2 Supernovae i n Other Galaxies Another technique that is useful in estimating the supernova rate in our galaxy is to measure the supernova rates in other galaxies. However, a number of considerations are required in order to make this comparison. First, the number of supernovae in a given galaxy depends significantly on the type of galaxy and in particular on the luminosity of the galaxy. Therefore, in order to use data from other galaxies to predict the supernova rate in the Milky Way, it is necessary to know both the type and size of our galaxy. Another consideration is the orientation of the galaxy with respect to our own. Due to absorption, supernovae are more difficult to detect when their parent galaxies are viewed "edge-on" rather than from "above". Finally, determination of galactic sizes and therefore luminosity involves determining the distance to the galaxy. Large uncertainties in the Hubble constant mean that these factors are not very well known. Adopting H0 = 50 km s - 1 M p c - 1 for the Hubble constant and assuming that the Milky Way can be classified as a Sbc type galaxy with luminosity L = 2.3 x 10 1 0 L 0 , Tammann et al. [28] estimate a total of 2.0 galactic supernovae per century (or 1 supernova every 49 Chapter 2. Supernova Physics 24 years) with a possible range of 1.6-3.2 supernovae per century (or 1 supernova every 31- 63 years). Roughly 85% of these events are due to supernovae of Type I l /Ib (see Section 2.4.1, from which a substantial neutrino signal is expected. In that case, the best estimate of the rate is 1 every 57 years. Lower values for the galactic supernova rate are obtained by a more recent study. Using the same luminosity as above but a higher value for the Hubble constant (H0 — 65 km s _ 1 M p c - 1 ) , Cappellaro and Turatto [16] suggest that the Type II+Ib/c supernova rate is (1.5 ± 1.0) per century, or one Type II+Ib/c supernova every (67 ± 44) years. Considering all supernova types, the predicted rate is approximately 1/53 yr. Taking into account the uncertainty in the Hubble constant contributes an additional range of 15-20 years. Tammann et al. [28] also report a combined estimate of 1/40 years using both extra-galactic and historical observations. 2.4.2.3 Supernova Remnants Searching for the remains of a supernova explosion is also a crude method used for estimat-ing the supernova rate. After a supernova explosion the expanding shell of ejected material interacts with the interstellar medium, producing radio emission and possibly other types of radiation. Based on the counts and ages of these remnants, an estimate of the supernova rate can be made. However, characteristics of the supernova remnant such as the lifetime depend to a large extent on the interstellar medium surrounding the supernova, which affects the number of observable remnants in different regions of the galaxy. Leahy and Wu [36] provide an estimate of supernova rates based on radio supernova remnant surveys of 1 per / x (18 — 42) yr, where / is some factor less than or of order unity. A different remnant considered by Hartmann et al. [37] is the 7-ray signal from the decay 4 4 T i ->• 4 4 Sc 4 4 C a with a mean life of 78.2 years. The decay of 4 4 T i generates Chapter 2. Supernova Physics 25 a number of gamma-ray photons, of which 1.16 MeV is the highest energy and therefore the easiest to detect. The relatively short mean life implies that this method is sensitive to only very recent or very near supernovae9. In the initial application of this method, no emission was detected after searching almost ten years of data, which when combined with historical supernovae yields a mean interval of r = 10-40 years. The lower end of the estimate range is due to constraints imposed by the 7-ray search. Another type of remnant used to estimate Type Il /Ib supernova rates is the pulsar. Pulsars are thought to be associated only with gravitational collapse supernovae, and are strong sources of highly periodic radio signals which are thought to be rotating magnetic neutron stars. Several pulsars have been associated with supernova remnants (the Crab pulsar, for instance). However, since no conclusive evidence for a pulsar has been found in the remnant of SN1987A, it is possible that not all gravitational collapse events give rise to a pulsar. Therefore, the birthrate of pulsars may represent a lower limit on the Type Il/Ib supernova rate. In order to calculate the supernova rate, it is necessary to know both the number of pulsars in a region and the age of those pulsars. Observations indicate that the rotation period of a pulsar radio signal increases with time as the pulsar "spins down" after the formation of a neutron star. Therefore careful measurements of the rotation period can be used to indicate the age of the pulsar, and from that the rate of formation of pulsars in the galaxy. Sophisticated simulations of pulsars with observational input from from astronomical data suggest a wide range of pulsar birthrates. The lowest estimates are for mean interval times in the range of 1 per 4.4-14 yr [41], while other studies predict a less frequent pulsar 9In fact, according to the authors, none of the known historical supernovae is either close or young enough to produce a detectable signal. However, 7 rays from 4 4Ti have been observed in the Cas A remnant [38] and in the recently discovered young supernova remnant RX J0852.0-4622 / GRO J0852-4642 [39]. There has also been an initial report of observed 4 4Ti emissions associated with a previously unknown galactic supernova [40], but there are some indications that this claim has been withdrawn. Chapter 2. Supernova Physics 26 birthrate: 1 per 100 years [42] and 1 per 125-250 years [43]. 2.4.2.4 Iron Abundances Using estimates of the composition and the age of the universe, predictions of the average supernova rate can be obtained by assuming that a large fraction of the iron in the universe was manufactured and dispersed by supernova explosions [44]. Tammann et al. [28] use this information to argue that the average supernova rate for all types must be 6 supernovae per century. Since approximately 85% of all supernovae are Type Il/Ib, the mean interval time between Type Il/Ib supernovae is ~20 years. However, the present rate of iron production is likely smaller than in earlier epochs, therefore the above rate is an upper limit on current supernova rates. 2.4.2.5 Stellar Evolution Rates The death rate of stars can also be calculated using models of the galaxy that describe the distribution of types of stars and their masses in conjunction with observational data. Ratnatunga and van den Bergh [45] report a supernova mean interval time of 40-250 yr for progenitor masses M > 8 M Q . A more recent application of this methods yields a lower mean interval time of between 28-40 yr for all supernova types [28]. 2.4.2.6 Neutrinos Data from neutrino detectors also places a limit on the rate of supernovae in the galaxy. Early detectors including Baksan, Mont Blanc, 1MB and Kamiokande combine to give an effective search time that is at least 10 years. Using Poisson statistics, the mean interval between Type II and lb supernovae is more than 12 yr at the la level [28]. 2.4.2.7 Summary In the preceding sections, various methods are described that attempt to estimate the supernova rate in our galaxy. From this survey, a wide range of values are suggested Chapter 2. Supernova Physics 27 for the mean interval between supernovae in the Milky Way galaxy. These methods and their associated estimates are summarized in Table 2.2. From these data, Tammann et al. suggest that the combined best estimate for the total galactic supernova rate is 2.5lo!5 supernovae per century. As 85% of these are expected to result from Type Il/Ib supernovae, one neutrino burst is expected every ~47 years. A widely accepted range is 1 supernova per 30-50 years [33]. M e t h o d M e a n Interval (yr) Type II + l b A l l Types Historical Galactic SN 14-25 [31] 6-17 [29] <30 [30] Extragalactic events 34-76 [28] 31-63 [28] 23-111 [16] 20-86 [16] Radio remnants 12-46 [29] < 18-42 [36] Gamma ray remnants > 10-20 [37] Pulsar remnants 4-14 [41] 100 [42] 125-250 [43] Iron abundance >20 [28] >17 [44] Stellar death rates 28-40 [28] 40-250 [45] Neutrinos >12 [28] Table 2.2: Estimates of the mean interval between supernovae in the Milky Way galaxy by various methods. A widely accepted range is 1 supernova per 30-50 years. 2.4.3 Local Group Supernovae Current neutrino detectors are sensitive to a burst of neutrinos from beyond the far edge of the Milky Way galaxy. Therefore, the expected supernova rates for galaxies near to the Milky Way are also of interest. Compared to the massive Milky Way galaxy, the expected frequency of Type Il/Ib Chapter 2. Supernova Physics 28 supernovae in our nearest satellite galaxies, the Large (LMC) and Small (SMC) Magellanic Clouds, is much smaller. The supernova rate in the L M C (where SN1987A originated from) is one supernova on order of every 200 years on average. In the SMC, the supernova rate is even lower at one supernova every 900 years on average [28]. The nearest massive galaxy is Andromeda at a distance of 800 kpc. Studies of Ua line emission and far-infrared fluxes10 in this galaxy indicate that the Type Il/Ib supernova rate is roughly 1/120 years. This is somewhat surprising since this rate is lower than that expected for the Milky Way and yet and the Andromeda galaxy contains more mass. Ta-ble 2.3 summarizes the expected supernova rates in nearby galaxies. These estimates agree with recorded observations. Only one supernova has been observed in the Large Magellanic Cloud (SN1987A) during ^300 years of surveillance, while none has been observed in the Small Magellanic Cloud. Furthermore, roughly 100 years of observation has yielded one supernova in the Andromeda galaxy (SN1885A). G a l a x y M e a n Interval (yr) Type II + l b A l l Types Large Magellanic Cloud (LMC) 222 204 Small Magellanic Cloud (SMC) 909 833 Andromeda (M31) 120 83 Triangulum (M33) 161 147 Table 2.3: Estimates of the mean interval between supernovae in nearby galaxies. Combining the Milky Way together with the Large and Small Magellanic Clouds, Tam-mann et al. [28] estimate that current neutrino detectors are sensitive to 2.7 Type II and lb supernovae per century, or one burst every 37 years. In order to obtain a detection rate on the order of one supernova per year, neutrino 10Ha line emission has been correlated with Type Il/Ib progenitors, since only hot stars with M > 10 M© contribute to the ionization of hydrogen [46]. Similarly, the far-infrared radiation is produced when dust is heated by hot massive stars [28]. Chapter 2. Supernova Physics 29 detectors would need to be sensitive to a much larger volume of space than the current generation, possibly extending as far as the Virgo cluster of galaxies at 15 Mpc, which contains roughly 2000 galaxies and has a total estimated mass of 1.2 x 10 1 5 M 0 [47]. Chapter 3 Supernova Neutrinos 3.1 Introduction The first direct evidence of the role of neutrinos in supernova explosions came on February 23, 1987 with the signal of the brightest supernova in 383 years. Information gathered from that event was sufficient to confirm general aspects of supernova explosion theory, but many details will not be resolved until the next galactic supernova is observed. In the sections that follow, the supernova neutrino signal is described in some detail, from the small number of events recorded in 1987 to general predictions from contemporary supernova models. 3.2 Supernova 1987A Supernova 1987A (SN1987A) was first identified by Ian Shelton at the Las Campanas Observatory in Chile on February 24, 1987 [48]. Shelton had taken a 3-hour exposure photograph starting at 01:20 UT, which later showed the appearance of an extraordinarily bright star in the Large Magellanic Cloud. After the discovery, other observations were used to further define the onset of the optical signal. New Zealand amateur astronomer Albert Jones made a number of observations of SN1987A but perhaps most importantly he did not observe the supernova when monitoring the L M C at 9:22 UT. Later at 10:38 UT, McNaught obtained a photograph of the L M C that showed the supernova at approximately magnitude = 6.0 (barely visible to the naked eye). These two observations would later be 30 Chapter 3. Supernova Neutrinos 31 used to constrain the arrival time of the optical signal. The SN1987A explosion actually took place approximately 165 000 years ago in the Large Magellanic Cloud, an irregular satellite galaxy approximately 51 kpc away from our Sun. The progenitor star was called Sanduleak —69° 202 and had an estimated mass M = 20 M 0 [20]. Somewhat surprisingly, the progenitor was a blue supergiant rather than a red one, and had a lower metallicity and smaller radius than was expected for a typical pre-supernova star. However, the properties of Sanduleak —69° 202 are not inconsistent with models of gravitational collapse. It is assumed that the progenitor star lost several solar masses from its surface during its red giant stage, but still retained much of its hydrogen envelope. There has been recent evidence that a pulsar has been detected in the supernova location. Even though early reports [49] that identified a pulsar associated with SN1987A were withdrawn, new observations [50] suggest that a 2.14 ms pulsar may have been discovered. However, these findings are not yet widely accepted by the astronomical community. 3.2.1 Detected Supernova Neutrinos After the initial discovery of the supernova by optical astronomers, data from various neutrino detectors operating at the time were searched for signs of neutrinos that could be related to the supernova explosion. The results of this intensive search showed that a number of detectors recorded neutrino events in the time preceding the measurements by optical astronomers. These detectors included the Kamiokande II, 1MB, Baksan and LSD detectors. 3.2.1.1 KII Detector The Kamiokande II (KII) detector [51] consisted of 3000 tonnes of purified water (2140 tonnes fiducial volume) surrounded by 948 50-cm diameter photomultiplier tubes capable of detecting Cerenkov radiation. The detection efficiency at the 7.5-MeV energy threshold Chapter 3. Supernova Neutrinos 32 used for analysis was approximately 40% [52]. Unfortunately, little effort was made to synchronize the experiment clock to Universal Coordinated Time (UTC), which contributes a 1 minute error on the time of the first event. The KII detector was sensitive to Cerenkov light from recoil electrons produced by neutrino electron scattering v + e~-n/ + e~, (3.1) and to Cerenkov light from recoil positrons produced by antineutrino absorption on free protons in the water molecules Z7 e+p->-n + e+. (3.2) Eleven events were recorded in the KII detector1 in the energy range of 7.5-50 MeV. The times and energies of these events are shown in Figure 3.1. In the plot, time is taken to be relative to the first event, which was recorded February 23, 1987 at 7:35:35 U T (± 1 min). Since the cross section for the antineutrino reaction is roughly two orders of magnitude higher than for the elastic scattering reaction (see Section 5.4), most, if not all, of the observed events are associated with electron antineutrinos. 3.2.1.2 1 M B Detector Similar to the KII detector, the Irvine-Michigan-Brookhaven (1MB) detector [53] was also a water Cerenkov detector. It consisted of 7000 tonnes of purified water (5000 tonnes fiducial volume) surrounded by 2048 20-cm diameter photomultiplier tubes. For a 7-hour period that included the search for neutrinos from SN1987A, one-quarter of the 1MB photomulti-plier tubes were inoperative, reducing its detection efficiency to 14% at the 20-MeV energy threshold. However, of the four detectors that reported neutrino events from SN1987A, 1MB was one of two detectors that was able to specify the absolute time of their events with an accuracy of less than about 1 minute. The absolute time of each event recorded in *An additional event was also recorded below the nominal analysis threshold. The energy of this event was 6.3 MeV. Chapter 3. Supernova Neutrinos 33 the detector was accurate to 50 ms, whereas the relative time between events was known to better than 1 ms. The 1MB detector was also sensitive to Cerenkov light from recoil electrons and positrons and was able to identify 8 events in the energy range of 20-40 MeV, the first of which was recorded at 7:35:41.37 U T (± 50 ms). The energies and times for these events are shown in Figure 3.1, where the times for the 1MB data are relative to the first 1MB neutrino event. Taking into account the large error associated with the time of the first KII event, the 1MB and KII bursts are essentially simultaneous. 0) 50 40 h 30 h 5 20 10 T • Kamiokande II • 1MB A Baksan II I _L 4 6 8 Relative Time (seconds) 10 12 14 Figure 3.1: Electron/positron energies and relative times for the events identified by the Kamiokande II, 1MB and Baksan detectors during SN1987A. Eleven events were recorded by Kamiokande II, 8 events by 1MB and 5 by Baksan. The time of events recorded by each detector is relative to the first event in that detector. Chapter 3. Supernova Neutrinos 34 3.2.1.3 Baksan Detector The Baksan detector consisted of 330 tonnes of oil-based liquid scintillator (200 tonnes fiducial volume) separated into 3150 units, each of which is viewed by a photomultiplier tube capable of detecting scintillation light. The detection efficiency was approximately 50% for 10 MeV electrons. Initially, the absolute time of each event recorded in the detector was reported to be 2 s [54], but subsequent studies a few weeks after the supernova event showed that the detector clock had shifted forward by 54 seconds [55]. The relative time between events is quoted as being accurate to 1 ms. Scintillator detectors are mainly sensitive to electron antineutrinos through the same reaction that the KII and 1MB water Cerenkov detectors used. Five neutrino events were observed between 11 MeV and 50 MeV in the time range suggested by the KII and 1MB data, with the first event recorded at 7:36:11.818 U T (+54 s). A n additional event is often listed, but is generally attributed to background. The time difference between the first 1MB event and the first Baksan event is 31 seconds. Taking the likely time shift into account, it is not unreasonable to consider the neutrino events recorded in the Baksan detector as belonging to the same burst that was seen in the KII and 1MB detectors. The time and energy data are shown in Figure 3.1, where the times for the Baksan data are relative to the first Baksan event. 3.2.1.4 L S D Detector Another detector that reported observation of neutrino events believed to possibly be as-sociated with SN1987A is the Liquid Scintillator Detector (LSD) in the Mont Blanc Labo-ratory [56]. Instead of water, the LSD detector consisted of 90 tonnes of liquid scintillator as the target material, which was contained in 72 separate counters, each of which was observed by 3 photomultiplier tubes. Different layers of the detector had different energy thresholds. The inner layer had an energy threshold of 5 MeV, while the outer layer was Chapter 3. Supernova Neutrinos 35 less sensitive, having an energy threshold of 7 MeV [57]. As with the other three detectors, LSD was sensitive to electron antineutrinos through the reaction Ve +p —>• n + e + . The positron was detected through the annihilation e + + e~ —> 7 and the neutron was detected through the neutron capture reaction n + p —» d + 7. While the positron detection efficiency is not mentioned, 40-60% of the neutrons are detected in the same counter as the positron. Event T i m e ( U T ) ( ± 2 s) Event Energy ( M e V ) ( ± 2 0 % ) 2:52:36.79 7 40.65 8 41.01 11 42.70 7 43.80 9 Table 3.1: Time and energy information for the events recorded at LSD, possibly associ-ated with SN1987A. While first to announce the detection of neutrinos associated with SN1987A, the results from LSD are the most controversial. The LSD detector recorded 5 events starting at 2:52:36.792 U T (± 2 ms), almost 5 hours earlier than the events observed at the other neutrino detectors [57]. Table 3.1 list the events with their measured time and energy values. Three of the events were observed in the inner layer and 2 were observed in the outer layer. None of the larger water Cerenkov detectors observed a signal near the time of the LSD signal, and the Baksan detector only found a single 11-MeV event, which is near their energy threshold for analysis. As well, based on the signal observed in the KII and 1MB detectors, the most probable signal was less than or of order 1 event in the LSD detector [20], whereas 5 events were recorded. Some also argue [58] that detailed light curve models favour the later time and that the early burst from LSD is not well fit by the standard collapse assumptions. For these reasons, many astrophysicists are skeptical Chapter 3. Supernova Neutrinos 36 of the LSD results. 3.2.1.5 Homestake Detector The Homestake 3 7 C1 detector was also operational immediately preceding SN1987A. The Homestake detector has a fiducial mass consisting of 615 tonnes of C2CI4 and is only sensitive to ue neutrinos. Neutrino interactions are observed using the reaction i / e + 3 7 C l - > e - + 3 7 A r . (3.3) No events were observed that were correlated with SN1987A [20], which is consistent with the number of expected events. 3.2.1.6 Summary A summary of the detectors that reported neutrino events from SN1987A is presented in Table 3.2. A total of 24 events were observed near 7:36 U T on February 23, 1987. An additional signal is claimed by the LSD group near 2:53, but remains unsubstantiated by the other detectors. Although the LSD detector is sensitive to lower energy neutrinos than either the 1MB and Baksan detectors, the KII detector should have registered a significant signal, which it did not. Detector Target Mass (ktonne) Energy ( M e V ) # Events U T T i m e Feb 23, 1987 Tota l F i d . KII 1MB Baksan LSD Homestake H 2 0 H 2 0 ( C H 2 ) n (CH 2 )„ C 2Cl4 3 6.9 0.33 2.1 5.0 0.20 0.09 0.62 7.5-50 20-40 10-50 >5,7 0.8 11 8 5 5 0 7:35:35 (± 1 min) 7:35:41 (± 50 ms) 7:36:12 (t2M s) 2:52:37 (± 2 ms) Table 3.2: Summary of detectors that recorded neutrino events from SN1987A. The exact time of the onset of optical brightening is not known, but constraints from the earliest observations imply that neutrino signal from SN1987A preceded the optical Chapter 3. Supernova Neutrinos 37 signal by at most 3.0 hours. This time delay between the neutrino and optical signals is consistent with predictions from supernova explosion theory. The energies and times of the events observed by the KII , 1MB and Baksan detectors are consistent with the predictions of a simplistic gravitational collapse model. Not only are the neutrino energies in the expected range, but the decrease with time of the average energies and the decrease in event rate with time also agree with general predictions. A l l of the neutrinos observed from SN1987A are believed to be Ve neutrinos, so very little information was gathered regarding the roles that neutrino flavours have in the collapse mechanism. 3.3 Neutrino Signal Having established the general importance of neutrinos to gravitation collapse supernovae through the observation of neutrinos from SN1987A, it is timely to review the current predictions for a more significant neutrino signal. As discussed in Chapter 2, nearly all of the gravitational binding energy in a core collapse supernova is emitted in the form of neutrinos. The gravitational binding energy carried by neutrinos, Eb, is estimated to be: E b ~ : ± p 2 E £ ~ 3 x 1053ergs, (3.4) where G is the gravitational constant, M c o r e ~ 1 M 0 is the mass of the core that collapses (also the mass of the resulting neutron star) and i ? C o r e ~ 10 km is the radius of the proto-neutron star. Of the large amount of energy released, approximately 1% is expected to be carried by electron neutrinos in the prompt neutronization burst, while the remaining en-ergy is imparted equally to the six neutrino flavours through thermal cooling reactions. The properties of supernova neutrinos from various models are discussed at length in Chapter 5, but a few general statements can be made at this point. Chapter 3. Supernova Neutrinos 38 3.3.1 Core Infall and Neutrino Trapping At the onset of collapse, as the temperatures and densities in the core begin to rise, elec-tron neutrinos are produced via electron capture reactions in the neutronization stage. The core is not yet too dense for neutrinos to escape on short time scales. The electron neutrino luminosity (energy radiated per unit time) continues to increase over a period of approximately 100 ms until it reaches its maximum value near the time of core bounce. 3.3.2 Core Bounce and Neutrino Breakout The shock wave that is produced after core bounce takes 1 ms to reach the neutrinospheres located between 50 and 100 km for the various neutrino species, where neutrinos can escape the collapsing star. In the region behind the shock wave, the temperature is sufficiently high that neutrino pairs of all flavours are produced. Neutrinos produced in the core have a hierarchy of energies depending on their type. Electron neutrinos and antineutrinos thermally couple with matter primarily by the fol-lowing charged current processes: ue + n # p + e~, Ve + p =± n + e + . (3.5) The large neutron-to-proton ratio in the core means that for a given neutrino energy, matter has a higher ve opacity than Ve opacity. Hence, electron antineutrinos will tend to thermally decouple from matter deeper in the core where the temperature is hotter. Compared to electron-type neutrinos, muon and tau neutrinos have fewer reaction channels available to them, since they do not possess energy sufficient to interact via charged current reactions. As a consequence, muon and tau neutrinos decouple from the surrounding material earlier than the electron neutrinos and antineutrinos, placing them deepest in the core of the collapsing star and therefore at the highest temperature. Hence, on average, electron neutrinos will have the lowest temperatures, electron antineutrinos will have slightly higher temperatures and and vT neutrinos will have the highest temperatures. Chapter 3. Supernova Neutrinos 39 3.3.3 Explosion The next phase of the neutrino signal depends on whether or not the "prompt" or "delayed" explosion mechanism occurs. If the shock wave is able to propel through the outer layers of material without losing too much energy in the process, a "prompt" explosion may take place. In that case, a relatively small amount of material will fall back onto the core and the neutrino luminosities will decrease as less gravitational energy is available for release. Furthermore, with less mass to traverse, neutrinos tend to emerge from deeper and hotter regions in the core, which is reflected in higher neutrino energies. On the other hand, if the prompt explosion fails, then the luminosity of all neutrino flavours remains high as matter continues to accrete onto the core, contributing more mass to the gravitational energy. With the explosion delayed, additional electron neutrinos are released through electron capture processes behind the shock front. It might also be possible to have subsequent smaller magnitude bounces called "core-ringing". In such a scenario, the changing density and therefore neutrino opacities may be reflected in the emerging neutrino luminosities (for instance, see Figure 5.3). Neutrino heating in the delayed explosion mechanism is expected to cause the neutrino energies to increase suddenly at the time of explosion, similar to the energy increase in the prompt mechanism. 3.3.4 Cooling After the explosion, the newly formed neutron star cools by releasing neutrinos according to the processes described in Section 2.3.6. The cooling phase lasts for some tens of seconds, during which time on the order of 99% of the star's energy is dissipated. Eventually, the densities and temperatures in the core decrease to the point that cooling reactions which produce neutrinos are no longer possible. For the neutrinos that remain trapped, the core will become transparent to neutrinos of different flavours at different times according to the relative opacities. Muon and tau neutrinos and antineutrinos will decouple from the Chapter 3. Supernova Neutrinos 40 material in the core first, followed by the electron neutrinos and antineutrinos. There is also the possibility that a black hole will be formed in the cooling stage. Exceptionally high rates of accretion onto the core may occur in stars with a relatively large amount of mass in the envelope. In such cases, core collapse may proceed beyond the point where nucleon degeneracy pressure is able maintain stability and a black hole may form as a result. Black hole formation is expected to occur 1-2 seconds after core bounce (for example, see the Bruenn 25 M Q model in Section 5.3.5.2). 3.3.5 Supernova Neutrino Summary The supernova neutrino signal is expected to last for tens of seconds. Typical average energies are 12 MeV for electron neutrinos, 15 MeV for electron antineutrinos and 18 MeV for the muon and tau neutrinos and antineutrinos. A l l of the models in Chapter 5 are intended to represent the "delayed" explosion mech-anism. 3.4 Potential Physics The detection of the next galactic supernova will yield important information about the supernova collapse mechanism as well as convey information about the properties of neu-trinos. 3.4.1 Constraints on Supernova Models Electromagnetic waves are unable to convey information about the dense region of the core relevant to the explosion mechanism. Therefore one of the only means to study the inner workings of a supernova explosion is by using the observation of neutrinos. The fundamental role of the neutrino in the process of gravitational collapse was confirmed by the set of neutrinos detected from SN1987A. However, a larger number of events is required Chapter 3. Supernova Neutrinos 41 in order to establish the details of the explosion mechanism and distinguish between the predictions of various supernova models. Many of the signatures of the explosion mechanism are expected to be seen in the time evolution of the neutrino luminosity and energy spectrum. Evidence supporting either the "prompt" or "delayed" explosion hypotheses may be found in a large neutrino data set. In the prompt supernova models, the envelope of the progenitor star is expelled on the timescale of 10 ms, whereas in the delayed scenario, this time is on the order of seconds. Additional support for the delayed explosion hypothesis would be provided were a gradual increase in neutrino energies to be observed during the time before the explosion. It is thought that this corresponds to the gradual decay of mass accretion before the delayed explosion commences [59]. Neutrino flavour information is also extremely valuable. A prompt signal of electron neutrinos provides insight into the neutronization processes in the core of the collapsing star. There is also some indication that the ue neutrinos in the neutronization phase have higher energies in the delayed mechanism as opposed to the prompt mechanism [60]. As well, it remains to be shown that the six neutrino flavours carry off the binding energy of the collapsing star in equal parts. Furthermore, using energy information from the different neutrino flavours, it should be possible to confirm the expected neutrino energy hierarchy. The progression of the neutrino signal over time may also indicate a flux cutoff possibly due to the formation of a black hole. Correlating this observation with information about the progenitor star will provide a more complete picture of the evolution of massive stars. 3.4.2 Neutrino Physics With only the 24 events from SN1987A it was possible to place limits on many properties of the neutrino, including the neutrino mass and lifetime. The number of neutrino events detected in the next galactic supernova should increase this total by more than two orders Chapter 3. Supernova Neutrinos 42 of magnitude. The analysis of such a data set could place limits on neutrino characteristics that could not be achieved any other way. 3.4.2.1 Neutrino Mass Measurement Massive neutrinos arriving from a supernova explosion will have a spread in arrival times based on their energies. That is, higher energy neutrinos will arrive sooner than lower energy neutrinos. The extra time, At, that a neutrino of mass mv and energy Ev requires to travel a distance D compared to a massless neutrino of the same energy is given by: 1 V M(E„) = D(z--) D c 1 / r a „ c 2 \ 2 3 / m „ c 2 \ 4 1 5 / m ^ \ 6 2\~E~ ~8\~E~) + 9 6 l " E W D (mvc2\2 - 2c\Ev) ( 3 - 6 ) in the relativistic limit Ev^> mv, where v is the speed of the neutrino and c is the speed of light. Therefore, even if all neutrinos are emitted simultaneously, the dispersion experienced by massive neutrinos of different energies is expected to stretch the burst in time. In order for a detection signal to be sensitive to neutrino mass in this prescription, it is necessary to make certain assumptions. The most important assumption is that the neutrinos are all emitted from the supernova at the same time, or at least in a much shorter time than the spread of arrival times. Assuming that the electron antineutrinos detected from SN1987A were emitted simultaneously, a conservative upper limit for the mass of the neutrino results in m-y < 30 e V / c 2 [58]. As discussed in Chapter 2, neutrino diffusion from the core is a relatively slow process, lasting on the order of seconds. Therefore, current understanding suggests that neutri-nos produced during core collapse are not emitted simultaneously. However, by making reasonable assumptions about the spread in emission times, slightly lower limits can be obtained using data from SN1987A (mVp < 10-20 eV/c 2 [61]). Recently, Totani [62] has Chapter 3. Supernova Neutrinos 43 suggested that analysis of the initial steep rise in neutrino luminosity may be sensitive to an electron antineutrino mass around 3 eV/c 2 . Unfortunately, even with a nearby super-nova, limits of the electron neutrino mass obtained using supernova neutrinos are higher than current estimates obtained using other methods. The current limit on the mass of the electron antineutrino is inferred from studies of the endpoint region of the tritium beta decay spectrum to be m^e < 3 eV/c 2 [5] ([63], [64]). The masses of the muon and tau neutrinos are not so well constrained. The current mass limits for the muon and tau neutrinos are < 0.19 M e V / c 2 and myr < 18.2 M e V / c 2 , respectively [5]. Therefore the time-of-flight method for determining these neutrino masses may prove useful provided a model-independent method of defining a reference time can be found. Two approaches to this problem have been suggested recently, and are described below. Beacom and Vogel [15] propose that a measurement or limit on the mass of u^tT neutrinos could be obtained by considering the time delay relative to Ve neutrinos. They predict that average delays on the order of 0.1 s could be resolved using the relatively large neutrino data set from a future galactic supernova. The SNO detector (see Chapter 4) is ideal for this measurement because of the high sensitivity to muon and tau neutrinos. Beacom and Vogel determine that the SNO detector would be sensitive to a 35 e V / c 2 muon or tau neutrino in the event of a galactic supernova. Using Ve neutrino data from the SuperKamiokande detector, the upper limit that SNO could place is slightly less at 30 e V / c 2 . Another possible way of defining a reference time is to consider the possibility that a black hole forms after core collapse, as suggested by Beacom et al. [65]. If the rate measured in neutrino detectors remains high at the time of black hole formation, then the neutrino signal will appear to be terminated sharply in time. Time for neutrinos that arrive after the cutoff can then be measured relative to the cutoff time. The expected sensitivity to the mass of the heaviest neutrino using the SNO detector is between 8 and 24 eV/c 2 . Chapter 3. Supernova Neutrinos 44 3.4.2.2 Neutrino Lifetime The fact that neutrinos reached the Earth after having traveled roughly 165 000 light years from the site of SN1987A places a limit on the neutrino lifetime. If neutrinos from SN1987A had decayed in flight, then the flux observed on Earth would have been reduced. Since the measured neutrino luminosity roughly agrees with the expected luminosity based on the binding energy of a neutron star, the minimum neutrino lifetime, r„ can be estimated as [58]: where D is the distance the neutrinos traveled from the supernova and 7 is the relativistic factor. Before evidence was found for solar neutrino oscillations [4], it was thought that neutrinos might decay while en route from the Sun to the Earth. Analysis of the SN1987A data indicated that this was not likely. Note that this limit will likely not be improved for a long time to come. 3.4.3 Early Alert Since neutrinos emerge from the collapsing core of a star sooner than any form of electro-, magnetic radiation, their detection can be used to warn the astronomical community. In the case of SN1987A, the neutrino signal preceded the optical signal by at most 3 hours. For a given supernova event, the time for the shock wave to emerge from the collapsing star depends on the nature of the envelope surrounding the progenitor star. Estimates based on theoretical model calculations indicate that the shock propagation time to the surface of a bare helium core is about 1 minute [66]. According to Shigeyama et al, the propagation time for a standard compact supernova is 35 minutes [67]. For other stars, the propagation time, tpr0p, is given approximately by: 7T„ > D/c = 1.7 x 105 yr, (3.7) = 35 min R M / 7 M ( (3.8) 'prop 21.572©^ E/2.5 x 10 5 1 erg Chapter 3. Supernova Neutrinos 45 where R is the radius of the progenitor, M is the amount of mass ejected and E is the explosion energy. For a supergiant star like Betelgeuse, characteristic parameters of R « 500 R 0 , M « 15 M 0 , E « 10 5 3 ergs yield a shock propagation time of 2 hours. The largest supergiant stars (R « 1500 R 0 ) may experience shock propagation times on the order of 8 hours according to the Shigeyama et al. prescription. Other estimates [68] suggest that the shock wave traversal time in red supergiants may be significantly higher at 17-25 hours for a 15 M 0 star and 58 hours for a 25 M 0 star. Chapter 4 The SNO Detector 4.1 Introduction The Sudbury Neutrino Observatory (SNO) is a heavy water Cerenkov detector situated 2072 m (5996 metres water equivalent) underground in INCO's Creighton Mine near Sud-bury, Ontario, Canada. The cavity that houses the detector is shaped like a barrel with a height of 34 m and a width of 22 m at the widest point. The detector consists of 1000 tonnes of heavy water on loan from Atomic Energy of Canada Limited ( A E C L ) , and is contained within a spherical acrylic vessel. The D 2 0 volume is efficiently viewed by an array of almost 10000 photomultiplier tubes (PMTs). Between the acrylic vessel and the P M T support structure (PSUP) is approximately 1700 tonnes of ultra-pure light water. The volume beyond the support structure contains 5300 tonnes of light water, and is used primarily as a background shield for gamma rays and neutrons originating in the rock and as an anti-coincidence veto. A schematic picture of the Sudbury Neutrino Observatory is provided in Figure 4.1. More specifications and a detailed description of the SNO detector can be found in [69]. 4.2 Detection Mechanisms The SNO detector is able to detect Cerenkov radiation resulting from the passage of charged particles and from the interactions of gamma rays and neutrons. Signatures from each of these particles constitute an important part of the supernova neutrino signal and are 46 Chapter 4. The SNO Detector 47 Figure 4 . 1 : Cross section schematic of the SNO detector, discussed in the sections that follow. 4.2.1 Charged Particle Detection To detect charged particles that are produced by neutrino interactions, the SNO detector relies on the generation of Cerenkov light. The speed of light in a medium of refractive index n is c/n, where c is the speed of light in vacuum. When a charged particle traverses a medium with a speed greater than the speed of light in that medium, a "shock" wave is created and Cerenkov light is emitted as a result. The minimum energy needed to produce Cerenkov light is summarized for various particles in Table 4.1. For the relevant analysis energy thresholds in SNO, all electrons and positrons produce Cerenkov light in both the light- and heavy-water regions. On the other hand, only protons with kinetic energies above ~500 MeV will generate Cerenkov light. Chapter 4. The SNO Detector 48 Charged Particle Particle Total Energy Particle Mass Cerenkov Threshold (MeV/c 2) (MeV) H 2 0 D 2 0 electron/positron, e± muon, p± 0.511 105.658 0.766 158 0.770 159 pion, 7 r ± 139.570 ' 209 210 proton, p+ 938.272 1407 1414 Table 4.1: Cerenkov radiation energy threshold values in H 2 0 and D 2 0 for various charged particles. Cerenkov light is emitted in a cone of half angle 9C with respect to the trajectory of the charged particle: cos0<5 = ^ , (4-1) where f3 = v/c is the particle speed expressed in terms of the speed of light in vacuum. Electrons or positrons that have kinetic energies of 2 MeV have speeds which are already very close to the speed of light, /3 « 1. In the case of heavy water (no 2o = 1-337), charged particles traveling with ft « 1 produce a Cerenkov cone which has an opening angle of 6C = 41.6°. The corresponding angle in light water (n^o = 1.342) is very similar at 9Q — 41.8°. Therefore, the angle 6C « 42° is characteristic of all charged particle events in SNO, and does not distinguish between particle energies or between interactions in either the H 2 0 or D 2 0 volumes. The primary difference between low energy particles and high energy particles lies in the path length. The spectrum of Cerenkov light is a function of both wavelength, A, and path length, x, and is given as [5]: < ™ 2 ™ ' l - ^ , (4.2) dxdX A 2 V P2n2(\) where a « 1/137 is the fine structure constant. In water, the amount of light that a charged particle emits per unit track length is roughly constant over particle energy and Chapter 4. The SNO Detector 49 corresponds to approximately 360 Cerenkov photons for every 1 cm path length in the spectral range to which SNO PMTs are sensitive (A = 300-650 nm) [70]. However, the electron or positron path length depends linearly on energy and is approximately 0.45 cm per MeV [70]. Charged particles with higher energies have longer path lengths and therefore produce more Cerenkov photons, which trigger a larger number of photomultiplier tubes in the detector. The number of PMTs that are hit during a given event is referred to as the "NHIT" of the event and is used in characterizing the energy of the event. Figure 4.2 shows a Monte Carlo simulation of the Cerenkov ring detected when a 10 MeV electron is produced in the SNO detector. For this event, a total of ~1600 Cerenkov photons are produced with wavelengths between 300-650 nm, but only about 6% of those photons are detected due to the low quantum efficiency of the PMTs (17%), attenuation in detector materials (65%) and photocathode coverage (54%). The image of the Cerenkov ring is not filled in because of the short range of 10 MeV electrons and positrons. Due to the 1/A 2 dependence in Equation 4.2, more Cerenkov photons are produced at shorter wavelengths than at longer wavelengths. The SNO photomultiplier tubes are able to detect photons with wavelengths between 300-650 nm, and are therefore mostly sensitive to the blue and ultraviolet end of the Cerenkov spectrum. 4.2.2 Gamma Ray Detection Gamma rays are detected indirectly through the process of Compton scattering, in which a photon scatters from an atomic electron producing a less energetic photon and a scattered electron: 7 + e" ->-7' + e - . (4.3) In order to be detected, the scattered electron must have enough energy to produce Cerenkov light. In general, because the scattered electron has less energy than the incom-ing gamma ray, fewer Cerenkov photons are generated for a gamma ray event compared to Chapter 4. The SNO Detector 50 SUO Event Display [electron_10MeV.zdab:40] Figure 4.2: Ring of Cerenkov light detected from a 10 MeV electron event simulated in the SNO detector. A total of 100 PMTs register a hit in this event, of which about 10 are from reflected light. In this view, the spherical array of PMTs is unfolded to form a flat map. a charged particle event, and therefore fewer PMTs are hit. 4 . 2 . 3 N e u t r o n D e t e c t i o n Since neutron detection is a crucial aspect of the SNO experiment, three separate running phases are planned. The first phase with pure D 2 0 offers limited sensitivity to neutrons, so two additional methods will also be used to increase the sensitivity. For the ongoing physics programs, the use of these different methods will allow for a comparison of results in which the systematic errors are significantly different. The first phase of running with pure D 2 0 extended from November 2, 1999 to May 28, 2001. Chapter 4. The SNO Detector 51 4.2.3.1 Pure D 2 0 Phase During the initial running stage, no enhanced neutron detection technique is employed, and SNO relies on neutron capture in pure D 2 0 : n + d - > t + 7 ••• - » e - , E1 = 6.3 MeV. (4.4) Free neutrons thermalize and can subsequently capture on a deuteron in the heavy water region to produce an energetic 6.3 MeV gamma ray. The gamma ray then undergoes Compton scattering and the resulting electron often has enough energy to produce Cerenkov light. However, due to the small capture cross section on deuterium, the neutron detection efficiency is relatively low at roughly 37%1. The mean neutron capture time in the pure D 2 0 phase is 40 ms. 4.2.3.2 Salt Phase During the first enhancement phase, NaCl salt is added to the heavy water up to a concen-tration of 0.2%. The sensitivity to neutrons is increased because of the high cross section for neutron capture on 3 5 C1. Neutron capture in 3 5 C1 results in a cascade of gamma rays of energy totaling 8.6 MeV, which are detectable from Cerenkov light produced by Compton scattered electrons: n + 3 5 C1 -> 3 6 C1 + £ 7 >e~, E^ = 8.6 MeV. (4.5) Due to the high neutron capture cross section associated with 3 5 C l , the 83% detection efficiency is significantly higher than for the pure D 2 0 phase. SNO Monte Carlo simulations indicate that it should also be possible to distinguish charged particle events from neutron and gamma-ray events based on the event topology. The distribution of light from Cerenkov light produced by charged particle events is different from that generated during Compton 'For an analysis energy threshold of 5 MeV, the detection efficiency using the only the pure D2O method is even less at approximately 24%. Chapter 4. The SNO Detector 52 scattering interactions in which multiple Cerenkov cones may be produced. Compared to the capture time of 40 ms in the pure D 2 0 phase, the mean neutron capture time with salt in the heavy water is much less at 4 ms. At the end of the salt operation phase, a reverse osmosis filtration system will be used to remove the salt from the heavy water. 4.2.3.3 N C D Phase A second enhancement technique that is planned for the measurement of neutrons involves the introduction of an array of 96 strings of 3 He gas-filled proportional counters into the heavy-water region. The counters have been constructed using ultra pure nickel tubing fab-ricated by a chemical vapour deposition process. Neutrons are detected through energetic protons and tritons produced by the neutron capture on 3 He: n+3Ee^p + t, Ethres = 0.764 MeV. (4.6) The neutron detection efficiency using the neutral current detectors is 37%. However, an additional 18% of neutrons capture on deuterium, bringing the total efficiency during this phase to 55% [69]. With the proposed 1-m spacing of the strings, the mean time to neutron capture in the N C D phase is 16 ms. The N C D neutron signal, which does not depend on Cerenkov light, makes it possible to distinguish neutron events from the charged particle and gamma ray events on an event-by-event basis. During the pure D 2 0 and salt phases, the neutron signature is obtained from Cerenkov radiation just as with electrons, positrons and 7 rays. However, it is possible to distinguish the different types of events based on the event topology. For instance, the distribution of light arising from a single energetic electron is different from a neutron event resulting from a gamma-ray cascade in the salt phase. While the N C D detector array is not as efficient at capturing neutrons as 3 5 C l , it provides a more straightforward means of separating signals from the different event types. Furthermore, the pulse shape of the 3 He capture events will enable them to be distinguished from any alpha particle radioactivity Chapter 4. The SNO Detector 53 from the walls of the ultra pure nickel tubes used as the bodies of the proportional counters. 4.2.3.4 Neutrons i n the H 2 0 Reg ion There is also some sensitivity to neutrons present in the H 2 0 region through the capture reaction with hydrogen: n + p^d + j, £ 7 = 2 .2MeV. (4.7) The 2.2 MeV 7 ray is below the nominal solar neutrino analysis threshold at 5 MeV, but might be observed in the analysis of a supernova signal, where the analysis threshold could be set lower. 4.3 Neutrino Interactions Through the use of both D 2 0 and H 2 0 , the SNO detector is able to rely on a number of reactions in order to observe neutrino interactions. Moreover, the supernova neutrino signal is expected to have significant contributions from all neutrino types, and those neutrinos are expected to have higher energies than solar neutrinos, which further increases the number of available interactions. Reactions in the SNO detector are classified into three groups according to the type of interaction: charged current, neutral current and elastic scattering. In the sections that follow, the relevant reactions from each of these categories are introduced. Further details describing the reaction kinematics and cross sections are provided in Chapter 5. 4.3.1 Charged Current Charged current reactions are identified as such because a charged boson, W±, is exchanged between the interacting particles. Supernova neutrinos, which have energies in the range ~0-100 MeV (see Section 5.3), are unable to produce muon and tau particles in the final state. Therefore, only ue and ue neutrinos participate in charged current reactions. Chapter 4. The SNO Detector 54 4.3.1.1 ue + p —> n + e+ Reaction The Ve inverse beta decay reaction2 is the dominant supernova neutrino reaction in any water Cerenkov detector, including SNO: I 7 e + p - > n + e+ (Ethres - 1-806 MeV) [H 2 0]. (4.8) The Feynman diagram for this process showing the exchange of a charged W+ boson is illustrated in Figure 4.3. The result of the W exchange is that a u quark is converted to a d quark creating a neutron and a positron in the final state. Figure 4.3: Feynman diagram for the Ve + p -> n + e+ charged current reaction. Ex-change of a W+ boson allows one of the u quarks in the proton to change into a d quark, creating a neutron and a positron in the final state. This reaction only occurs in the light water volume, therefore only the relativistic positron in the final state is detected. In principle, it is possible to observe both the positron and the neutron, however the 2.2 MeV 7 ray due to neutron capture on hydrogen is difficult to detect. Therefore, the contribution from the neutron in this reaction is ignored in the studies that follow. Applying weak magnetism and recoil corrections [71], the angle at which the positron is emitted tends to favour the direction of the incoming neutrino (slightly forward peaked), 2The reaction ue +n -» e~ +p will not be directly observed since there are no free neutron targets. Chapter 4. The SNO Detector 55 while the neutron is strongly forward peaked. However, even if the analysis threshold is set low enough to observe the neutron signature in the light water region, the directional information of the neutron is lost during the thermalization process. 4.3.1.2 ue + d Reactions Other important charged current reactions involve neutrino interactions with the deuteron in the heavy water region of the detector: ve + d->p + p + e- (Ethres = 1.442 MeV) [D 20] (4.9) Ve + d->n + n + e+ (Ethres = 4.033 MeV) [D 2 0]. (4.10) In both reactions, the neutrino interacts with a deuteron through the charged-current exchange of a, W boson producing a relativistic charged lepton. Two protons remain in the final state for the reaction in Equation 4.9, while the final state for the reaction in Equation 4.10 has two neutrons. The details of both interactions are illustrated in Figure 4.4. The protons in Equation 4.9 are not detected in SNO because their energies do not ex-ceed the Cerenkov radiation threshold, but Cerenkov radiation from the electron is detected. However, it is possible to detect all three final state particles from the Ve + d-^n + n + e+ reaction. The positron is sufficiently energetic to emit Cerenkov radiation, and the two neu-trons produce a signal due to the neutron capture mechanisms discussed in Section 4.2.3. With three detectable particles in the final state, the signature for this reaction is unique in the SNO detector: the prompt detection of the positron followed by a time-delayed coinci-dence of the two neutrons. In both reactions, the angular distribution is slightly backward peaked, with the neutrino reaction more so than the antineutrino reaction. Chapter 4. The SNO Detector 5G Initial State Final State Initial State Final State Figure 4.4: Feynman diagrams for the ue + d —t p + p + e~ and T>e + d^n + n + e+ charged current reactions. In the case of the electron neutrino, exchange of a W bo-son allows one of the d quarks in the neutron to change into a u quark, creating a proton and an electron in the final state. For the electron antineutrino, one of the u quarks is changed into a d quark, creating a neutron and a positron in the final state. 4.3.1.3 ve + O Reactions Electron neutrinos and antineutrinos also participate in charged current interactions with oxygen in the S N O detector. The principal isotope involved is 1 6 0 : ue + 1 6 0 -> 1 6 F + e~ {Ethres = 15.4 MeV) [D 2 0 , H 2 0 ] (4.11) Vt + 1 6 0 -> 1 6 N + e + {Ethres = 11.4 MeV) [D 2 0 , H 2 0 ] (4.12) (4.13) but the 1 8 0 isotope also contributes, especially at lower energies: ve + 1 8 0 -> 1 8 N + e+ [Ethres = 1.66 MeV) [ D 2 0 , H 2 0 ] . (4.14) In all cases, Cerenkov light from the charged lepton constitutes the detection signal. How-ever, for the energy regime relevant for supernova neutrinos, interactions involving ue tend to have angular distributions that are slightly backward peaked, while the ~Pe reactions involving oxygen are essentially isotropic [72]. Chapter 4. The SNO Detector 57 4.3.2 Neutral Current Instead of a charged boson mediating the process, particles interacting via the neutral current exchange a neutral Z° boson. As a result, neutrinos of all types are able to par-ticipate in neutral current reactions. While both the charged current and neutral current reactions will provide substantial contributions to the total number of neutrinos observed with SNO, the neutral current channels are particularly important because all neutrino types are able to participate in these interactions. This sensitivity is especially important since the majority of the energy in a supernova explosion is carried by the muon and tau neutrino types. No other detector that is currently in operation has the level of sensitivity to i/p and vr neutrinos that SNO offers. 4.3.2.1 vx + d Reactions The main set of neutral current reactions are those involving deuterium: vx + d-t vx+p + n (Ethres = 2.225 MeV) [D 2 0], (4.15) where ux represents all active neutrino flavours (x = e, p, r ) . Exchange of a Z boson means that the deuteron is simply broken apart and the constituent proton and neutron are free particles in the final state. Figure 4.5 shows the details of the interaction. As with previous reactions, the proton does not have sufficient energy to generate Cerenkov radiation, so the neutron is the only particle that is detected. Due to the neutron capture processes, no directional information can be obtained from the final state particles that participate in these interactions. 4.3.2.2 v^r + 1 6 0 Reactions Other neutral current reactions include interactions with oxygen. It is possible that the highest energy supernova neutrinos (v^T neutrinos) will excite resonances in 1 6 0 , which then mainly decay by proton and neutron emission. Although the proton and neutron Chapter 4. The SNO Detector 58 Initial State Final State Figure 4.5: Feynman diagram for the vx + d ->• ux + p + n neutral current reaction. Ex-change of a Z° boson means that the deuteron is simply broken apart and the constituent proton and neutron are free particles in the final state. decays are mainly to the ground states of 1 5 N and 1 6 0 , respectively, in some cases the decays will go to excited states in these nuclei. These excited states will often decay by emitting a 7 ray with energies between 5-10 MeV [73]. The possible reactions are summarized as follows: * V + 1 6 0 -> i v + 1 5 0 + n (Ethrea = 15.0 MeV) [D20] (4.16) * V + 1 6 0 ^ * v + 1 5 0 + n + 7 {Ethres = 15.0 MeV) [D 2 0 ,H 2 0] (4.17) * V + 1 6 0 ^ * V + 1 5 N + p + 7 (Ethres = 15.0 MeV) [D 2 0 ,H 2 0] . (4.18) The detection signal for these reactions arises from either a neutron (Equation 4.16), both a neutron and a 7 ray (Equation 4.17) or a single 7 ray (Equation 4.18). As with the other neutral current reactions, there is no information available concerning the initial neutrino direction. Chapter 4. The SNO Detector 59 4.3.3 Elastic Scattering The elastic scattering process is actually a combination of the charged- and neutral-current processes. The electron neutrino (or antineutrino) and the electron can interact through the exchange of either a charged W boson or a neutral Z° boson. Other neutrino types can only interact through the neutral current channel, which means that their cross sections are lower than those of the ve and Ve neutrinos. 4.3.3.1 v + e~ —, v + e~ Reactions Because of the neutral current component, supernova neutrinos of all flavours can also interact via the neutrino-electron elastic scattering process: ue + e" -)• ve + e~ (Ethres = 0 MeV) [ D 2 0 , H 2 0 ] (4.19) ve + e-^Ve + e- (Ethres = 0MeV) [ D 2 0 , H 2 0 ] (4.20) y^r + e" -> i/„,T + e~ (Ethres = 0 MeV) [ D 2 0 , H 2 0 ] (4.21) F„ i T + e- -)• V^T + e~ (Ethres = 0 MeV) [ D 2 0 , H 2 0 ] . (4.22) Figure 4.6 shows both the charged current and neutral current contributions to the elas-tic scattering reactions involving electron neutrinos (and antineutrinos). Muon and tau neutrinos from a supernova only interact via the neutral current component. Neutrino-electron elastic scattering interactions are important in all water Cerenkov detectors. In the case of SNO, elastic scattering reactions take place in both the D 2 0 and H 2 0 volumes of the detector, and in either region, SNO measures the Cerenkov light emitted by the relativistic recoil electrons. 4.3.3.2 Interaction Summary Table 4.2 lists the interactions that are relevant for supernova neutrinos. Notice that a number of reactions involving oxygen have relatively high interaction energy threshold Chapter 4. The SNO Detector 60 Initial State Final State Initial State Final State »— » ve' ve e * " e t w .0 Charged Current Neutral Current Figure 4.6: Feynman diagrams for the v + e~ —> v + e~ elastic scattering reaction. A l l neutrino flavours ux (x = e, p, r) can interact via the neutral current channel, but only ue and Ve neutrino reactions have contributions from both the charged current and neutral current channels. values compared to the others. The significance of this aspect is discussed in detail in Chapters 5 and 6. SNO observes neutrinos indirectly by detecting final state particles that produce Cerenkov radiation. These particles are listed in Table 4.2 for each interaction, along with any asymmetry in the angular distribution that might be exploited when trying to locate the source of the supernova neutrino signal. 4.4 Detector Backgrounds The SNO detector is designed to provide very low levels of radioactive background for the reactions that are used to detect neutrinos. The entire detector is constructed from materials which have been carefully selected for low 2 3 8 U and 2 3 2 T h content, since gamma rays from the decay of daughter particles from these decay chains can mimic neutrino signals. The most problematic of these daughters are 2 0 8 T1 from the thorium chain and 2 1 4 B i from the uranium chain, which in both cases contribute 7 rays during fission processes that have energies E1 > 2.2 MeV. Gamma rays with such energy are able to photodisintegrate the deuteron and contribute neutrons that are indistinguishable from those produced in neutrino interactions. This is why extraordinary efforts have been made to reduce these backgrounds in the fiducial volume of the detector. Limits on the radiopurity of both the Chapter 4. The SNO Detector 61 Reac t ion Reg ion Energy Detectable Lep ton Threshold Par t ic les Ang le ( M e V ) A s y m Charged Current: F e + p —>• n + e+ H 2 0 1.806 e + , n? ^forward ve + d ^ r p + p-\-e~ D 2 0 1.442 e~ ~forward T7e + d —> n + n + e+ D 2 0 4.033 2n, e~ ^backward ue + 0 -» F + e~ D 2 0 15.4 e~ ^backward F e + 0 -» N+ e+ D 2 0 11.4 e+ none i / e + 0 -» F + e~ H 2 0 15.4 e~ ^backward F e + 0 -> N+ e + H 2 0 11.4 e+ none Neutral Current: ue + d ^ u e + p + n D 2 0 2.225 n N / A Ve + d ^ r V e + p + n D 2 0 2.225 n N / A V^T + d-¥ u ^ T + p + n D 2 0 2.225 n N / A V[iTT + d ->• F ^ ) T + p + n D 2 0 2.225 n N / A + 1 6 0 -»• ^ > T + 1 5 0 + n + 7 D 2 0 15.0 n, 7 N / A »W + 1 6 0 -»• F „ , T + 1 5 0 + n + 7 D 2 0 15.0 n, 7 N / A + 1 6 0 -> i/„,T + 1 5 N + p + 7 D 2 0 15.0 7 N / A » W + 1 6 ° -> ^ . r + 1 5 N + p + 7 D 2 0 15.0 7 N / A ^ , r + 1 6 0 ^ ^ > r + 1 5 0 + n D 2 0 15.0 n N / A ^ , r + 1 6 0 ^ F M > T + 1 5 0 + n D 2 0 15.0 n N / A + 1 6 0 -> + 1 5 0 + n + 7 H 2 0 15.0 n?, 7 N / A + 1 6 0 -> V^T + 1 5 0 + n + 7 H 2 0 15.0 n?, 7 N / A + 1 6 0 -+ + 1 5 N + p + 7 H 2 0 15.0 7 N / A ^ . r + 1 6 0 -> F ^ i T + 1 5 N + p + 7 H 2 0 15.0 7 N / A Elastic Scattering: ue + e~ —>• ^ e + e~ D 2 0 0.0 e~ forward F e + e~ —» F e + e~ D 2 0 0.0 e~ forward + e~ -> i/^r + e~ D 2 0 0.0 e~ forward ^/I,T + e~ - » F p ^ + e" D 2 0 0.0 e~ forward i / e + e~ —> ve + e~ H 2 0 0.0 e~ forward F e + e~ —> F e + e - H 2 0 0.0 e~ forward *W + e~ -> + e~ H 2 0 0.0 e~ forward ^V.T + e~ ->• F M J T + e~ H 2 0 0.0 e~ forward Table 4.2: Summary of supernova neutrino interactions in the SNO detector, including the energy threshold, the final state detectable particles and whether or not there is any asymmetry in the charged lepton angular distribution. It may be possible to detect some of the neutrons in the H 2 0 volume (labeled as "n?") with a sufficiently low analysis threshold. Chapter 4. The SNO Detector 62 light water volume and the heavy water volume are set such that the neutron production rates due to photodisintegration do not exceed one-tenth that of the standard solar model neutral current rate (approximately 1 per day). Sensitive techniques [74] have been developed for the measurement of the principal daughter particles from the 2 3 8 U and 2 3 2 T h decay chains. These techniques include de-gassing (ZnS Lucas cells) and chemical extraction (MnO x , HTiO) from recirculated water to determine the effective levels of 2 3 8 U and 2 3 2 T h . The isotopes 2 2 2 R n and 2 2 6 R a are mon-itored in the case of the uranium chain, while 2 2 4 R a and 2 1 2 P b are used to indicate the levels of thorium daughters. Information on background radiation in the detector can also be gathered from observations of the Cerenkov light patterns on the PMTs . In the case of the 3 He neutron detectors, the materials used in construction have been carefully selected to minimize levels of uranium and thorium and their daughters. Techniques have been developed for the measurement of inherent radioactivity in these detectors which might lead to photodisintegration of the deuteron. Table 4.3 highlights the radioactivity levels in a number of key areas, starting in the surrounding host rock and moving inward to the heavy water region. These limits have been achieved by use of very pure materials and careful manufacture. Furthermore, the detector was constructed under clean-room conditions and continues to be operated in the same manner. The air is filtered using H E P A filters and all personnel wear clean-room clothing to maintain an air quality on the order of Class 2500. A n extensive water purification/recirculation system is used to reduce the radioactivity in both the heavy and light water volumes. The P M T support structure is 99.99% impermeable to water, enabling water flow to be directed outwards from the region between the acrylic vessel and the P M T s into the outer region where it is removed, purified, stripped of radon and radium and re-injected in the inner region. This process maintains a lower level of radioactivity in the light water in the Chapter 4. The SNO Detector 63 Region Radioactivity Radioactivity Goal Level (10-12 g/g) ( lO" 1 2 g/g) 2 3 2 T h 2 3 8 j J 2 3 2 T h 238TJ Norite rock N / A N / A 5.5 x l O 6 1.1 x l O 6 P M T Support Structure 15000 15000 4000 4000 PMTs 90000 120000 6000 9000 Acrylic Vessel 1.1 1.1 < 1.1 < 1.1 H2O (inner) 0.037 0.45 0.0891 0.00233 D 2 0 0.037 0.45 0.00448 0.00157 Table 4.3: Radioactivity levels in various regions of the SNO detector, where the most crucial areas are the heavy water and inner light water regions. In those volumes, the equivalent concentrations of 2 3 8 U and 2 3 2 T h are below the design goals for cleanliness in almost all cases. inner region than in the less critical outer region. 4.5 Detector Components A number of distinct components and systems make up the SNO detector, including the acrylic vessel, the water systems, the P M T array, the readout electronics, the data acqui-sition and the various calibration devices. Each of these components is briefly described in the sections that follow. 4.5.1 Acrylic Vessel The acrylic vessel, which holds the heavy water, is 12 m in diameter and was constructed from 122 ultraviolet-transmitting acrylic panels that were transported underground and bonded together in situ3. These panels are 5.5 cm thick, except for a special set often at the equator that are 11.4 cm thick and were machined to accommodate suspension ropes that support the vessel. 3 The author participated extensively in the construction of the acrylic vessel. Chapter 4. The SNO Detector 64 A n acrylic chimney is attached to the top of the sphere and is made using ultraviolet absorbing acrylic to reduce the "piping" of unwanted Cerenkov light, which could be mis-reconstructed into the fiducial volume. Calibration sources are inserted into the heavy water through the chimney and pipes for the water systems are mounted there as well. Eventually, the 3 He proportional counters will also be deployed through the chimney. 4.5.2 Water Systems The SNO water system consists of three separate systems: the ultrapure light water (H 2 0) system, the heavy water (D 2 0) system and the N 2 cover gas system. 4.5.2.1 Light Water System Light water is supplied from a surface purification plant that produces potable water for the entire mine. The water reaches the 6800-foot level of the mine through a series of pipes and open holding tanks, during which time the water is saturated with air. Before being pro-cessed, the incoming water contains sand and silt particles, bacteria, algae, inorganic salts, organic molecules and many gases (for example, N 2 , 0 2 , C 0 2 , Rn). Just outside the lab, the light water is de-aerated (removing 0 2 and N 2 ) and passed through a multimedia filter consisting of a bed of sand and charcoal to remove large particles. At this stage, a 10 /xm filter is also used to remove finer particles. The water then enters the laboratory, where the water first passes through a pair of activated charcoal filters that convert chlorine into chloride, a form which is easier to remove at later stages. A similar function is performed by the addition of E D T A , which reacts mainly with aluminum leaving it in a form that is more easily removed by reverse osmosis. Zeolite softener is used to remove heavy elements that are present in the water, such as iron, calcium, magnesium and aluminum. In the final stage of pretreatment, the incoming water is passed through a reverse osmosis unit, which removes 99% of ionized salts and organics by using high pressure across a semipermeable membrane. The water is now suitable for injection into the main purification loop. Chapter 4. The SNO Detector 65 The main light water circulation loop continually removes water from outside the PSUP for purification and monitoring and then returns the clean water to the H 2 0 volume inside the PSUP. In the main purification loop, water passes through a 185 nm U V mercury lamp to break up large organic molecules into constituent ions, 12 ion exchange columns, a 1 fj,m filter, a second 254 nm U V lamp to kill any bacteria and a custom process degasser that removes 0 2 and N 2 and Rn gases. Finally, a chiller cools the water to 10°C in order to inhibit organic growth and cool the photomultiplier tubes, and the water is returned to the cavity at 150 litres/minute. 4.5.2.2 Heavy Water System As with the light water system, the heavy water system is used to maintain the high purity levels of the D 2 0 . However, the heavy water system is also responsible for introducing and removing the NaCl salt used during the second phase of detector operation. The D 2 0 is supplied by the Ontario Hydro Bruce heavy water plant and shipped underground in specially designed rail cars. Heavy water delivered to the lab was first passed through ion-exchange columns to reduce the ionic content. The main heavy water circulation loop removes water from the top of the acrylic vessel for purification and monitoring and returns it to the bottom. While the systems are completely separate, many of the same types of purification methods used with the light water are also used with the heavy water. These include a series of reverse osmosis filters, ultrafiltration units and a process degasser. Absorption columns with M n O x beads.are also used to remove radium from the recirculated water. Addition of the NaCl salt into the D 2 0 is done by making a high concentration brine so-lution that is slowly added to the heavy water volume. Later desalination will be performed with two dedicated reverse osmosis units. Chapter 4. The SNO Detector 66 4.5.2.3 Cover Gas System Both the light- and heavy-water volumes are isolated from the laboratory air to prevent radon contamination by using a layer of N 2 gas. The measured concentration of radon in the nitrogen gas is 1 0 - 5 pCi/litre compared with 3 pCi/litre in the laboratory air. 4 . 5 . 3 Photomultiplier Tube Array-Surrounding the acrylic vessel is a geodesic support structure (PSUP) 18 m in diameter, which houses a total of 9529 Hamamatsu R1408 20 cm photomultiplier tubes (PMTs). A photomultiplier tube works by converting photons to electrons at an interface called the photocathode. The photoelectron that is produced is accelerated using a set of plates called dynodes, which have voltage applied such that there is a potential difference at each step. Electrons striking the dynode liberate more electrons, and after several such multiplication steps, the resulting number of electrons constitutes an electronic signal that is measurable. Of the total number of PMTs that make up the detector, 9438 P M T s face inward to the heavy water region. A small subset (49 PMTs) called "low gain" P M T s have a dynode tap and a second signal cable to extend the dynamic range of the charge measurement by a factor of 100. Another 91 PMTs are mounted facing outward to detect light from events such as muon interactions in the outer light water region. It is very likely that the outward looking (OWL) PMTs will also detect events during a burst of supernova neutrinos. An additional 4 PMTs are installed in the A V chimney to veto light from static electric discharge in that area. Finally, a set of 23 PMTs are available for diagnostic studies and are mounted on a sled placed outside the PSUP and facing toward the detector. By itself, the inward facing array of PMTs provides a photocathode coverage of 31%. However, each inward-looking P M T is equipped with a light concentrator to improve the light collection efficiency and increase the effective geometric coverage of the entire array to 54% of 47r. The outward-looking PMTs do not have concentrators. Chapter 4. The SNO Detector 67 The electron cascade in the P M T becomes less efficient in the presence of a magnetic field, as electrons from one dynode are deflected while en route to the successive dynode. Therefore, magnetic field-compensation coils are embedded in the cavity wall that sur-rounds the detector in order to counteract the effect of the Earth's magnetic field. The maximum residual field at the P M T array is 19 pT and the average overall improvement in the gain is 8.6% [75]. The PMTs are operated at high voltages in the range 1700-2100 V , resulting in a gain of 2 x 107 (except for the low gain PMTs) . As specified by the manufacturer, the measured RMS timing resolution of the photomultiplier tubes is 1.5 ns. Average noise rates in the PMTs are relatively low at approximately 500 Hz due in part to the cool 10°C water that surrounds them. 4.6 SNO Electronics The SNO electronics acts as the interface to the P M T array. Each P M T is supplied high voltage and has its signal read out through a single 32 m waterproof coaxial cable that is connected to one channel in an eight channel paddle card. Four paddle cards are seated into one 32-channel P M T interface card (PMTIC), which in turn is connected to both a high voltage distribution plane and a front-end card (FEC), where the P M T signal is processed. One F E C has 4 daughterboards, each of which is responsible for processing the signal from 8 channels for a total of 32 channels per F E C . Signal information is stored in the SNO CMOS chip, which contains a 4 M B on-board memory buffer. There is enough combined memory in all of the FECs to store ~10 6 supernova events4. The PMTICs and FECs are combined in groups of 16 to form a crate and in total there are 9728 possible electronics channels in 19 SNO crates. Each crate also contains a translator card and a crate trigger 4The entire system of readout electronics contains 4 MB x (19 crates x 16 FECs) = 1.2 GB of memory. The average supernova event contains 100 PMT hits, of which each hit requires 12 bytes. Therefore, the event capacity is 1.2 GB / 1.2 kB = 1 million supernova events. Chapter 4. The SNO Detector 68 card. The translator card communicates with a similar card in the data acquisition V M E crate, while the trigger card performs the analog sum the individual channel triggers for a particular crate and sends the sum to a central Master Trigger Card (MTC) . The M T C is responsible for processing the all of the signal sums in the detector and deciding when a set of P M T hits constitutes an interesting event. The SNO electronics is also responsible for measuring P M T time and charge informa-tion. There are three distinct charge values available in the SNO data stream: • QHS: high gain, short integration time (70 ns) • QHL: high gain, long integration time (400 ns) • Q L X : low gain, short or long integration time (the default is 400 ns) The current from each P M T is split into two branches (approximately in the ratio 1:16) and fed into two separate channels of a charge integrator. Low gain charge is measured in the channel with less current, while high gain charge is measured by the channel with more current. Compared to the high gain signal, the Q L X charge is roughly a factor of 10 lower in gain. The low gain charge is useful for events that produce large amounts of light (muon events, for example) where the P M T response is no longer linear in the high gain setting and the associated analog-to-digital converters (ADCs) become saturated and provide no resolution in the measurement. Different charge integration times make it possible to separate charge measured in the prompt signal from the total charge, which may have some contribution from reflected light. Each daughterboard contains level-crossing discriminators5 and charge measurement capacitors. When the discriminator is triggered, the daughterboards begin recording the three charge quantities QHS, QHL and Q L X . The triggering of the discriminator also starts a time-to-amplitude converter (TAC) to measure the charge integration time. 5These thresholds are adjustable in the SNO Data Acquisition software. On average, the discriminator threshold for each electronics channel is set to 0.25 of the mean charge for a single photoelectron. Chapter 4. The SNO Detector 69 4.7 SNO Trigger The trigger for the SNO detector is used to determine which events are interesting and should constitute the data set. Design of the trigger system is dictated by a broad range of physics goals, from observing solar neutrinos to detecting muons and possibly receiving bursts neutrinos originating in supernovae. Other aspects that also need to be considered include a wide range of calibration devices and being able to perform studies of the detector background. After having gathered P M T information from all of the P M T s in the detector, the global trigger is formed at the Master Trigger Card. The primary SNO event trigger uses the number of phototube hits and is called the "NHIT" trigger. SNO P M T hits are counted by performing an analog sum of the signals from the SNO CMOS chips. If the sum is above a programmable threshold, a global trigger causes the data stored on the FECs to be collected by the data acquisition system and built into events. When the global trigger is created, an additional lockout signal prevents any other signal from creating a global trigger while the current trigger cycle is active. The lockout period is set to 400 ns, during which time the M T C writes the trigger related information to its on-board memory. At the end of the lockout period, if any trigger is still above threshold, a new global trigger is generated immediately. Otherwise, the system waits for the next discriminator threshold crossing or external trigger signal to start the cycle again. Therefore, the deadtime per P M T is 400 ns, and the overall trigger deadtime is less than 10 ns. The electronics system is capable of handling trigger rates above 1 MHz and a sustained low energy event rate of better than 1 kHz [76]. The NHIT trigger requires a certain number of photomuliplier tubes (PMTs) to register a Cerenkov photon hit within a certain time window. The nominal setting for the NHIT trigger time window is 100 ns, which is slightly longer than the largest possible difference Chapter 4. The SNO Detector 70 in photon arrival times for an interaction in the D 2 0 (66 ns). A 20 ns NHIT trigger is also available for studies involving a smaller selected fiducial volume of the detector. These two types of NHIT triggers are referred to as the NHIT100 and NHIT20 triggers, respectively. In addition to these discrete analog sums, the SNO detector can also trigger on the analog sum of the 9438 shaped P M T signals, called the " E S U M " trigger. The E S U M trigger is a measure of the total charge in an event (or energy). The NHIT and E S U M triggers complement each other well. An event can have many PMTs hit causing the detector to trigger on NHIT, but the total charge may not be sufficiently high to cause an E S U M trigger. On the other hand, if only a few PMTs are hit in one event, the detector will not trigger on NHIT, but if those few PMTs have very high charge, E S U M will be triggered. It is also possible for the O W L PMTs to generate both an NHIT trigger and an E S U M trigger. To study the P M T noise rates, a built-in pulser is used to provide a global trigger at set intervals. This trigger is called the "pulse-gt" trigger. The pulser rate is programmable, and is typically set to 5 Hz. The trigger system is also responsible for maintaining and recording relative event timing, absolute event time, the global trigger ID number and information regarding which trigger types were satisfied for each event. Two oscillators are used to keep a record of absolute and relative time. Relative timing between events is recording using a 50 MHz counter that relies on a 100 MHz oscillator. The 50 MHz clock resolution allows events times to be latched at 20 ns intervals. Absolute time is maintained for the purpose of correlating events in the SNO data to other experiments by a 10 MHz clock that is synchronized by a commercial GPS unit. Ticks from the 10 MHz clock provide a time resolution of 100 ns, while the absolute accuracy is dictated by the GPS receiver and possible degradation by the military and is thought to be roughly 300 ns 6. 6 Effective midnight on May 1, 2000, the "selective availability" (or degradation) of commercial GPS signals ended. It is unclear how much the absolute timing accuracy is affected. Chapter 4. The SNO Detector 71 4.8 SNO Data Acquisition The SNO data acquisition (DAQ) is designed to read out the P M T data stored in the SNO electronics and sort the individual P M T hits into events. The principal hardware component of the SNO D A Q system is a single V M E crate containing a Motorola 68040 embedded C P U (or eCPU) with 32 M B of on-board memory. Front-end cards in each crate are read out sequentially by the eCPU as is the M T C , and a Sun workstation is responsible for sorting the F E C and M T C data and building them into events. The readout of the electronics is controlled and monitored via a user interface program called "SNO Hardware Acquisition and Readout Control" (SHaRC) running on a Power Computing 250 MHz P P C Macintosh that communicates with the eCPU using a PCIbus-VME interface. The burst capability of the SNO DAQ has not yet been fully investigated. However, the SNO data acquisition system has demonstrated the ability to process data at 450-500 kB/s, which corresponds to an event rate of 38-42 kHz. Real-time processes that subscribe to the data stream, such as the SNO online burst monitor, are able to receive events at a rate of 25-33 kHz with very little loss of information. 4.9 SNO Calibration Accurate measurement of the physics processes in SNO requires a set of calibrations to properly interpret the raw P M T time and charge information. A number of calibration devices are employed to this end, and can be divided into three categories: low level calibration of the detector electronics and photomultipliers, detector optical and energy response and the detector physics response. Chapter 4. The SNO Detector 72 4.9.1 Low Level Calibrations A n electronic charge pulser is used in conjunction with a light source at a known position to convert digitized P M T charge and time values to photoelectrons and nanoseconds. These calibration activities are referred to as electronics calibration (ECA) and the phototube calibration (PCA). 4.9.2 Optical and Energy Calibrations Optical sources are used to measure absorption, scattering and timing, whereas the energy calibration sources are used to determine the correspondence between the energy of a particle and the number of PMTs that receive Cerenkov radiation. The primary optical source employed in SNO is a nitrogen laser connected through fibre optic cable to a diffuser ball (the combined system is referred to as the "laserball"), which produces photons at several discrete wavelengths in the range A = 360-700 nm. The laser generates sharp pulses (600 ps wide) up to a rate of 45 Hz at various intensities and at various locations within both the H 2 0 and D 2 0 volumes. Pulse width is increased slightly by the diffuser ball to about 2 ns. Another optical source that was used during the commissioning of the SNO detector is the sonoluminescence source. This source offers very short pulses (< 100 ps) at a rate of 25 kHz, over a range of frequencies corresponding to a blackbody at a temperature of over 20000 K , which is similar to the Cerenkov spectrum. Energy calibrations are performed using a variety of sources that cover a range of energies. At low energies, the energy response of the SNO detector is determined using a 1 6 N gamma ray source [77]. The 1 6 N is produced in the reaction: n + 1 6 0 - > p + 1 6 N * , (4.23) where 66% of the time the nitrogen excited state decays by beta emission to an excited Chapter 4. The SNO Detector 73 state of oxygen, which returns to the ground state by emitting a gamma ray: i e N * i 6 0 * + e - ; i 6 0 * _> 16O + 7, E1 = 6.13 MeV. (4.24) It is the detector response to the 6.13 MeV gamma ray that is used in the energy calibration. There is no external trigger for this source, so a 3-mm thick scintillator viewed by a 5-cm P M T tags the initial decay electron and is used in the analysis to indicate that a decay took place. The short-lived ( r i / 2 = 7.13 s) 1 6 N * is delivered to the detector fiducial volume through capillary tubes using a gas transport system, during which time some fraction of the isotopes decay in the detector before reaching the decay chamber that houses the scintillator and P M T . Therefore, in addition to the 1 6 N source events that have an associated e~ tag, many events in the data do not, and appear as genuine physics events. To reach energies above 6 MeV, a miniature accelerator [78] is used to produce high energy gamma rays through the proton-tritium (or pt) reaction: p + 3 H - + 4 H e + 7, £ 7 = 19.82 MeV. (4.25) The monoenergetic 19.8 MeV gamma ray is used as the calibration signal, however neu-trons are also produced by side reactions 2 H ( i , n) 4He, 3 H(d, n) 4He and 3 H ( i , nn) 4He due to impurities in the beam and other effects. These events are not tagged in the data. 4.9.3 Physics Calibrations Physics calibrations involve measuring the detector response to various particles that pro-duce Cerenkov light and often have characteristics similar to the principal neutrino inter-actions being measured. A n example of this is the 8 L i beta source. The short-lived ( T I / 2 = 0.84 s) 8 L i isotope is produced through the reaction: n + n F w a + 8 L i , (4.26) and is used to calibrate the detector through the subsequent decay: 8 L i - > e~+ 8Be*, 8Be* -+ 2a. (4.27) Chapter 4. The SNO Detector 74 Unlike the gamma sources which provide monoenergetic particles, the electrons from the 8 L i source have a spectrum of energies similar to that of the 8 B solar neutrino spectrum. As such, it is also possible to use the 13 MeV endpoint energy to study the energy response of the detector. As with the 1 6 N source, a small P M T is installed in the 8 L i decay chamber in order to tag the a particles. However, unlike the 1 6 N source, the scintillation is provided by the He gas that is also used in the transport. The detector response to neutrons is studied using the fission of 2 5 2 Cf, which produces on average 4 neutrons and 20 low energy gamma rays. Two 2 5 2 C f sources of different activities are available: the weak source is 0.001 pCi and the strong source is 0.01 fxCi. Also in this category are calibration sources used to simulate the radioactive back-grounds in the detector, such as 2 3 8 U and 2 3 2 T h . To date, three sources have been used to study these backgrounds in SNO: an encapsulated uranium source, an encapsulated tho-rium source and a proportional counter (PC) source which has thorium plated on the anode wire. As mentioned in Section 4.4, the most serious detector radioactive backgrounds are due to gamma rays produced in the U and Th decay chains that have sufficient energy to photodisintegrate the deuteron. A summary of the calibration sources in use within SNO is provided in Table 4.4. Those sources which are not externally triggered or tagged in the data require special handling by the online burst monitor described in Chapter 9. 4.10 The SNO Monte Carlo Package The official SNO Monte Carlo analysis package is called S N O M A N (SNO Monte Carlo and Analysis) [69] and is written in the F O R T R A N 77 programming language. S N O M A N simulates e, 7, n and p physics in the detector as well as Cerenkov photon propagation to the PMTs . The full geometry and optical properties that are included in the simulation Chapter 4. The SNO Detector 75 Calibration Calibration Triggered/ Source T y p e Tagged? Low Level Calibration: EC A charge triggered P C A discrete A, 360-700 nm triggered Optical Calibration: Laser discrete A, 360-700 nm triggered Sonoluminescence 7, C spectrum none Energy Calibration: 7, E1 = 6.13 MeV some tagged pt 7, E1 = 19.8 MeV none Physics Calibration: 8 L i e~, 8 B spectrum some tagged 2 5 2 C f (strong) n none 2 5 2 C f (weak) n none U 7 —? n none Th 7 —> n none P C 7 —r n some tagged Table 4.4: Summary of sources used to calibrate the SNO detector. package are the result of detailed studies and measurements of the various components and detector calibration. S N O M A N relies on several external software packages. Interactions of the 7 and particles are simulated in SNO using routines from the EGS4 package [79], while routines adopted from M C N P [80] are used to describe the propagation of neutrons. The C E R N L I B software package Z E B R A is used to manage the SNO data structure (and to overcome the lack of dynamic memory allocation in F O R T R A N 77). As well, data from the detector are written to tape in the form of packed Z E B R A banks. A central database (SNODB), which is based on the C E R N L I B package H E P D B , is used to keep track of all constants and time-varying parameters in the SNO detector. Chapter 5 SNO Supernova Monte Carlo 5.1 Introduction Development of the SNO supernova Monte Carlo draws on many different areas of physics— from the description of the supernova signal as it emerges from the collapsing star to the neutrino interactions with the particles in the heavy- and light-water volumes and the many parameters that characterize the SNO detector. These various aspects are described in some detail in the sections that follow. Further details relating to specific calculations are provided in Appendix B . Within the SNO collaboration, the author has been responsible for the development of the current incarnation of the SNO supernova simulation software and for performing Monte Carlo simulations in order to characterize the signal in the detector. Preliminary software developed by Ng [81] for simulating supernova neutrinos in the SNO detector was entirely re-written by the author. 5.2 Supernova Signal Formalism For a given neutrino species, the number of neutrinos emitted at the source of the supernova per unit energy per unit time can be written as the product of two components: where U is the time of neutrino emission from the supernova for a given neutrino species and Ev is the specific neutrino energy at time U. 76 Chapter 5. SNO Supernova Monte Carlo 77 The F(ti) factor in Equation 5.1 represents the number of neutrinos emitted per unit time, and has the following general form: F(U) = ^ , (5-2) where hu(ti) is the time-dependent neutrino luminosity, or neutrino energy flux per unit time, and ev(ti) is the time-dependent average neutrino energy. While the details of the luminosity and average energy functions vary between models, there are robust features predicted for the supernova signal. The luminosity spectrum is expected to be sharply peaked at early emission times and the average energy spectrum is expected to exhibit a hierarchical structure in which muon and tau neutrinos have the highest average energies followed by the electron antineutrino and finally the electron neutrino. These two features are discussed further in Section 5.3.2. The total energy carried away by a given neutrino species during a supernova explosion is determined by integrating the source luminosity over all neutrino emission times: roo E^totai = / Lu(ti)dti (5.3) Jo and the total number of neutrinos of a given species emitted during the collapse is given by: K,total = r ^rdU. (5-4) Jo ev{ti) Therefore, the average neutrino energy for a given species is calculated as: 1 *v,total The f(Ev,ti) factor in Equation 5.1 specifies the shape of the neutrino energy distri-bution. In the case of supernova neutrinos, this shape is given by a Fermi-Dirac thermal distribution 1: •1 r T?2 i (5.6) f(Ev,ti)=  NFD(ti) El 1 _|_ EEU/TV(U) 1 While many papers refer to the Fermi-Dirac distribution in the context of supernova neutrino energy spectra, few present the actual form, and those that do are often conflicting. Chapter 5. SNO Supernova Monte Carlo 78 where Eu is the specific neutrino energy (not average), T„(ij) is the time-dependent neutrino temperature and NFD(ti) is the normalization factor such that: roo / f(Ev,U)dEv = l. (5.7) Jo Written explicitly, the expression for the normalization becomes: roo E^ NMU) = JQ 1 + e ^ M d E v . (5.8) For constant neutrino temperatures, the normalization factor simplifies to the following form: = 1.803 Tl, (5.9) where the substitution x = (Ev/Tv) is used to obtain a standard integral form. Monte Carlo studies of neutrino transport within the collapsing star [82] have indicated that the instantaneous neutrino spectra are "pinched", meaning that the low- and high-energy tails of the emergent distribution are suppressed relative to a Maxwell-Boltzmann spectrum of the same average energy. The deficit in low-energy neutrinos is due to the fact that there are fewer low energy neutrinos produced in the core of the proto-neutron star than high energy neutrinos (emission oc E^). On the other hand, the lack of high energy neutrinos is a consequence of the energy dependence in the neutrino interaction cross sections (interaction probability oc El). High energy neutrinos are more likely to scatter than low energy neutrinos, so the high energy tail of the number distribution is shifted to lower energies as higher energy neutrinos are preferentially scattered and lose energy. To address these effects, some models introduce a "degeneracy" or "effective chemical potential" parameter, nv(ti), to better describe the thermal spectrum. Incorporating T}„(ti) Chapter 5. SNO Supernova Monte Carlo 79 into Equation 5.6, f(Eu,ti) then becomes: 1 f(E„,ti) N, FD El (5.10) 1 _|_ eEvITv{ti)-ri»{U) with the corresponding normalization factor modified in the same manner. The neutrinos from the supernova then propagate a distance D to Earth, where they interact in a neutrino detector at time t. The number of such interactions per unit energy per unit time depends on the number of target particles in the detector, Nt, and the interaction cross section, a(E„): J. . 1 (5.11) d2Ndet 1 d2Nt Nto-(Ev) 4 T T £ > 2 dEudU dEvdt Therefore, the number of neutrino interactions that take place in a detector is obtained by integration: 1 roo roo rjz M dEvdti " ^ ^ Including the neutrino mass, m„, in the above treatment, means that the neutrino signal will be delayed relative to its massless counterpart, which travels at the speed of light. The arrival time of a massive neutrino at the detector is t = U + D/c + At(Eu), where (D/c) is the time offset due to the distance traveled by the neutrino, which is usually dropped for convenience. Formally, the supernova neutrino signal at the detector becomes: d2Ndet 1 rd2Ns. dEvdt where the energy-dependent delay, At(E„), is given by Equation 3.6: T r (5.13) L\t{Ev) D D c Eu 3 / mvc 8 l ~ E £ " 2 ^ 4 15 / m , c 2 \ 6 + 96 Ev D ( muc2' 2c \ ~E^ (5.14) in the relativistic limit Ev~>mu, where v is the speed of the particle and c is the speed of light. Chapter 5. SNO Supernova Monte Carlo 80 5.3 Supernova Models 5.3.1 Introduction Beginning with the first numerical simulations performed by Colgate and White [83] in the 1960s, there has been significant progress in the modeling of supernovae. The problem requires understanding the behaviour of matter over extremes of temperature and density that are impossible to reproduce in a laboratory. Failure of the "prompt" mechanism to generate a sustainable shock wave gave way to the "delayed" mechanism, in which the shock wave is reenergized by the intense neutrino flux that is carrying the binding energy of the proto-neutron star. Despite including general relativity in the transport and hydrodynamical equations, simulations of spherically symmetric (1-d) models have so far not resulted in a supernova explosion. The next frontier is to construct axis-symmetric (2-d) models in which it is possible to study the role of convection2, rotation and magnetic fields in the evolution of a collapsing star. Many aspects of the latest two-dimensional models are currently under investigation, and some elements of three-dimensional models are currently being developed [84] to provide even greater insight. A number of supernova models appear in the literature, and are used to predict the expected signal in various neutrino detectors. Some of these models offer a very general supernova signal, glossing over many of the details of the predicted core collapse mechanism, in favour of concentrating on some of the more robust features. Meanwhile, other more sophisticated models are based on the results of detailed calculations over limited regions of the supernova time spectrum. Since there still remains much uncertainty in the supernova community, a survey of five models is presented below for discussion. Descriptions of the most generic models are covered first, followed by the models based on more detailed calculations. In the chapters that follow, these same models will be used to make predictions 2One of the main motivations for considering convection comes from observations of SN1987A, which indicate that extensive mixing occurred throughout much of the ejected material. Chapter 5. SNO Supernova Monte Carlo 81 about the supernova neutrino signal in SNO. 5.3.2 General Predictions According to the description presented in Chapter 3, a number of general features of the supernova neutrino signal are predicted. The first prediction is for a significant enhance-ment in the neutrino signal at the onset of the burst due to electron capture reactions in the core. Only ue neutrinos participate in these interactions, therefore the signal enhancement should be predominantly from ve neutrinos. The second prediction describes the relative energies of the various neutrino species. Neutrinos produced in a supernova explosion are expected to have a hierarchy of tem-peratures depending on their type. Because different neutrinos interact through different reactions, electron neutrinos are thought to have the lowest temperatures, electron antineu-trinos to have slightly higher temperatures and "z/^" neutrinos are predicted to have the highest temperatures. A further prediction of all "delayed" explosion supernova models is that the neutrino luminosity remains fairly high before the explosion. This period of enhanced luminosity may last for hundreds of milliseconds. 5.3.3 Beacom and Vogel Model The most generic supernova model under consideration is one that was recently introduced by Beacom and Vogel [85]. As a basis for their model, Beacom and Vogel use the timing information from the SN1987A data set and cite the numerical simulations of Janka [86] and Woosley et al. [87] for neutrino energy properties. The Beacom and Vogel model has the gravitational binding energy of the star, £ B = 3 x 10 5 3 ergs, released and carried away in equal parts by the 6 neutrino flavours (z/e, Pe, v^, V^, uT, VT). In this scenario, the ve neutrinos are responsible for carrying 17% of the energy, the Ve neutrinos for 17% and the Chapter 5. SNO Supernova Monte Carlo 82 and vT (and their antiparticles), collectively called uiJftn, account for 66%. The Beacom and Vogel model was initially constructed for use in supernova signal timing studies, and as such the detailed shape of the luminosity and average neutrino energy spectra was less important than the general shape of the signal and characteristic durations. Therefore, this model ignores even robust features such as the predicted enhancement to the electron neutrino signal due to the neutronization of the core. The Beacom and Vogel neutrino luminosity is described by two exponential functions3 and is the same for all neutrino species. After core bounce, when the temperature in the core of the proto-neutron star is very high, the luminosity of all neutrino species begins to increase exponentially: where the rise is characterized by the time constant T i = 0.030 s and extends to t0 = 0.090 s. The choice of time constant is related to the shock propagation time across the core of the proto-neutron star. Immediately after the exponential increase phase, a cooling phase begins where the luminosity is described by exponential decay: The decay time constant governing the cooling regime is given as r% = 3 s. Figure 5.1 shows the neutrino luminosity as a function of time. Notice that the neutrino luminosity extends out to a time around 10 s, which is consistent with neutrino data from SN1987A. It should also be noted that the luminosity in the cooling period falls off very slowly compared with other supernova models. In the Beacom and Vogel model, electron neutrinos have the lowest temperature Tye = 3.5 MeV, while electron antineutrinos have a slightly higher temperature Tpe = 5.0 MeV 3In reference [15], the same authors advocate a slightly different model. Instead of an exponential rise, a one-sided Gaussian function is used, which has the same width as the exponential described in the text. The exponential function is used here because it is likely closer in shape to the expected signal and is also easier to normalize. (5.15) (5.16) Chapter 5. SNO Supernova Monte Carlo 83 200 I • 1 1 1 1 1 1 1 ' 1 ' 1 ' 1 1 1 1 1 r I . I . I . l I— l i I i I 1 1 1 1 1 1 2 4 6 8 10 12 14 16 18 20 Time From Core Bounce (seconds) Figure 5.1: Supernova neutrino luminosity as a function of time in the Beacom and Vogel model [85]. The top plot highlights the first 1 s of the burst luminosity signal, showing both the initial exponential rise and the subsequent exponential decay periods. The bottom plot demonstrates that the luminosity spectrum extends out to ~10 s, which is consistent with neutrino observations from SN1987A. In this model, all neutrino species are assumed to have the same luminosity, and no special features relating to the collapse mechanism are included. For the sake of comparison, the luminosity (sum of the V^, vT and VT components) would be four times greater than the individual neutrino signal shown. and V M " neutrinos have the highest temperature T«i/ » = 8.0 MeV. Even though the neutrino flux is decreasing, simulations by Woosley et al. [87] suggest that the average neutrino energies remain high and nearly constant. Beacom and Vogel use this information to argue that there is no compelling reason to introduce a time-dependent temperature, and so they use the temperature values listed above for all times. The average neutrino Chapter 5. SNO Supernova Monte Carlo 84 energies for this model are related to the spectrum temperatures by (Ev) = 3.15 kTv. Since the neutrino temperatures do not vary with time in this model, the average neutrino energies are calculated in a straightforward manner: 11.0 MeV for ve neutrinos, 15.8 MeV for Ve neutrinos and 25.2 MeV for ui/ll" neutrinos. 0.08 100 Neutrino Energy (MeV) Figure 5.2: Fermi-Dirac neutrino energy distribution in the Beacom and Vogel model [85]. Because of the generic nature of this model, the neutrino temperatures are taken to be constant in time and no chemical potential factor is used to modify the distribution. Note that " i ^ " represents any of the following neutrino types: v^, F M , vT or F T , not the sum. The neutrino energy spectra are governed by the Fermi-Dirac distribution, where for this model all neutrino flavours have an associated chemical potential parameter, nv = 0. The resulting Fermi-Dirac spectrum for the various neutrino species is determined using Equations 5.6 and 5.9 with the neutrino temperature values listed above. The energy Chapter 5. SNO Supernova Monte Carlo 85 distributions shown in Figure 5.2 also confirm the relative energies of the different neutrino species. Compared to the other neutrino types, the energy distribution for V M " neutrinos has a peak at higher energies, and also has a long tail extending to nearly 100 MeV. 5.3.4 Burrows et al. Model Although still generic, Burrows et al. [60] provide a model that examines possible structure in the neutrino signal based on details of the core collapse mechanism. The resulting model makes predictions beyond what was identified in the 24 events studied from SN1987A. To construct their model, Burrows et al. draw on the work of several groups who were doing detailed supernova model calculations in the early 1990s, namely Wilson [27], Bruenn [88], Myra and Burrows [89] and Burrows [90]. The total neutrino energy radiated in this model is 2.90 x 10 5 3 ergs, of which 20% is carried by the ue neutrinos, 18% is carried by the Ve neutrinos and 62% is carried collectively by the V M " neutrinos, which is quite similar to that of the Beacom and Vogel model discussed in the previous section. The most relevant features of the model are discussed below. The Burrows neutrino luminosity spectrum has a number of features that reflect various stages of the collapse mechanism, which are highlighted in Figure 5.3. The initial ramp of the ve neutrino signal is the result of neutronization in the core. As the temperature in the core increases, protons and electrons combine to produce ue neutrinos through the p + e~ —» n + ue reaction. This prompt electron neutrino signal is the first signature of collapse and accounts for luminosity values reaching L„ ~ 3 x 10 5 3 ergs/s. Core collapse continues for the first 0.1 s until nuclear density is reached, and the inner core rebounds once further collapse is no longer possible. The shock wave resulting from core bounce is accompanied by both a ue flash as electron capture takes place behind the shock wave front and by the rapid turnon of the Ve and " i ^ " signals made possible by the high temperature of the shock. Figure 5.3 shows the associated contributions to the luminosity spectra shortly Chapter 5. SNO Supernova Monte Carlo 86 after time U = 0. Superimposed on the luminosity peak due to neutronization, the ve flash brings the luminosity to its highest value, Lv — 6 x 10 5 3 ergs/s, after which it then decays over 5 ms. Within ~80 ms of the luminosity peak, the ve and Ve luminosity signals merge. The explosion that ultimately destroys the outer envelopes of the star occurs 460 ms after core bounce, with the potential of a significant increase in the ve and Ve luminosities. In the time between the shock wave breakout and the explosion, Burrows et al. predict that a delayed explosion mechanism may result in modulations to the luminosity spectrum due to pulsations of the outer mantle of the proto-neutron star, possibly lasting for hundreds of milliseconds. A period of cooling follows the explosion for almost 1 minute until the point of transparency where the neutrino luminosities fall dramatically. Unlike Beacom and Vogel, Burrows et al. use a time-dependent spectrum of average neutrino energies for the different neutrino flavours. At the shock breakout, there is a sudden change in the energy spectrum followed by a hardening of the spectrum that cul-minates in the explosion of the star. From that point on, the energy spectra gradually soften. Figure 5.4 shows the average neutrino energy spectrum as a function of time for the various neutrino types. The average energies used in the Burrows et al. model are (EUe) = 9.9 MeV, (E-p^j = 11.6 MeV and (-&<zy ) = 15.4 MeV. Compared to the average neutrino energies found in the Beacom and Vogel model, the values used by Burrows et al. are lower. In particular, the average energy for the Ve and "t^" neutrinos is significantly lower, and this will have a noticeable effect on the supernova signal. In this model, the energy distributions are assumed to have a Fermi-Dirac shape with a time dependent neutrino temperature and a set of non-zero degeneracy parameters. For the prompt ve signal a temperature Tye = 1.7 MeV is used for emission times up until 2 ms after core bounce. A corresponding degeneracy parameter, rjve = 11.0 is used to significantly pinch the tails of the burst ue neutrino thermal spectrum. For all other times, the following degeneracy parameters are used: r\Ve = 1.2,rfp = 2.0, t]^p^ = 3.0 (the Ve and Chapter 5. SNO Supernova Monte Carlo 87 10000 13 c o o 1000 100 10 1 1 1 1 1 1 1 1 I • I • i • = s / I shock breakout explosion v : e - s - ® "v " -- 1/ = <- 1 : 3 <U : q 1 -i i I i I I , I , I , I . I . X -0.1 10000 o c 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 20 30 40 Time From Core Bounce (seconds) 50 Figure 5.3: Supernova neutrino luminosity as a function of time in the Burrows et al. model [60]. The top figure shows the burst evolution in the first second of the neutrino burst, including a sharp prompt peak due to neutronization in the core followed by pulsa-tions leading to an explosion at 460 ms. The bottom figure shows the cooling phase that takes over after the explosion extending to almost 50 seconds. Note that here the " i / ^ " luminosity is the sum of the v^, V^, uT and VT contributions and is therefore a factor of four times greater than either the ve or Ve luminosity signals. "z^" signals are not present prior to tj = 2 ms). The use of non-zero degeneracy parameters means that the neutrino temperature is no longer related to the average neutrino energy by {Ev) = 3.15kTy. Instead, the conversion factors listed in Table 5.1 apply [91]. Using Equation 5.10, the Fermi-Dirac spectra for the various neutrino species are computed and the resulting distributions are shown in Figure 5.5. Chapter 5. SNO Supernova Monte Carlo 88 30 25 20 15 10 5 • 1 1 1 1 1 1 1 1 1 1 1 1 1 1 explosion i i i i i - — -1 1 1 1 1 1 1 i i i I i I i i -0.1 •§ 30 15 10 5 0 10 20 30 40 Time From Core Bounce (seconds) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1 I 1 I 1 1 1 V e • t- \ Is \ V c "v " I , I , I , I , 50 Figure 5.4: Supernova neutrino average energy as a function of time using the Burrows et al. model [60]. According to the top plot, the average energies for all neutrino species rise from the time of core bounce until the explosion. The bottom plot shows that after the explosion, the average energies gradually decrease. V ^ " represents any of the following neutrino types: V^, vT or VT. Neutrino T ime Degeneracy Conversion T y p e Regime Parameter, 7 7 kTv (Ev) ti < 1 ms 11.0 8.90 U > 1 ms 1.2 3.37 Ve ti > 1 ms 2.0 3.61 u " ti > 1 ms 3.0 3.99 Table 5.1: Specifications relating to the degeneracy parameter, 7?, for the Burrows et al. model. Chapter 5. SNO Supernova Monte Carlo 89 0.1 .§ 0.06 i 1 1 1 1 <~ time < 0.002 s V£ (T = 1.7 MeV, TI = 11.0) J i L 80 60 — i — 1 — r time = 1 s V (T = 4.0MeV,Tl, = 1.2) -\ Vfi (T = 4.4 MeV, Tl = 2.0) \ "V " (T = 5.1 MeV, TI = 3.0) - 0.04 —I ' 1 <~ time = 0.460 s V£ (T = 4.7 MeV, TI = 1.2) > v" (T = 5.3 MeV, T) = 2.0) \ " V " (T = 5.9 MeV,Ti = 3.0) ^•r-T.-i i L 60 80 100 0 60 80 100 0 20 Neutrino Energy (MeV) — i — ' — i — time = 10 s V£ (T = 2.5 MeV, TI = 1.2) V (T = 2.7 MeV, T| = 2.0) " v " (T = 3.3 MeV, TI = 3.0) j I i I i_ 40 60 80 100 Figure 5.5: Fermi-Dirac neutrino energy distribution in the Burrows et al. model [60]. Since the neutrino temperatures and degeneracy parameters are a function of time, so are the Fermi-Dirac energy distributions. Four representative times are used to show how the spectral distributions evolve. Notice at t < 0.002 s how the energy distribution at low energies appears shifted toward the peak value, while the high-energy tail of the distribution does not extend as far as the ve distributions at other times. This is due to the relatively large value of r\v used to modify the thermal spectrum. V M " represents any of the following neutrino types: u^, V^, uT or VT. 5.3.5 Bruenn Models In a recent publication [92], Bruenn et al. describe a set of sophisticated calculations used to simulate the supernova collapse mechanism. They consider two sizes of progenitor star, Chapter 5. SNO Supernova Monte Carlo 90 15 M 0 and 25 M 0 , to be representative of small-iron-core and large-iron-core stars, respec-tively. When the core begins to collapse, the iron core mass is 1.278 M 0 for the 15 M 0 model and 1.770 M 0 for the 25 M 0 model. The computer code developed for these simulations is called M G F L D - T R A N S , and it couples the general relativistic multigroup flux-limited diffusion (MGFLD) approximation to the Boltzmann transport equation to Lagrangian general relativistic hydrodynamics. A general relativistic approach is important because of the strong gravitational fields present during core collapse. Compared to Newtonian transport and hydrodynamics, Bruenn et al. find that in most cases the combined effect of including general relativity results in an increase in both the luminosities and average energies of all neutrino flavours during the shock reheating epoch. Some shortcomings of using the M G F L D approximation are discussed by Janka [93]. This model together with the one presented in Section 5.3.6 represent some of the leading edge of supernova collapse modeling to date. However, no group to date has successfully modeled a supernova to the point of explosion. Another drawback of these detailed model calculations is the limited time over which they are performed. However, with faster computers becoming available, many groups are working to add the necessary physics as well as extend the time range in the calculations. 5.3.5.1 Bruenn 15 M 0 Mode l In the case of the 15 M 0 model, core bounce occurs 0.1829 s after the initial collapse. The peak in the ue luminosity shown in Figure 5.6 is due to electron capture in the wake of the shock wave. While the magnitude of the peak is roughly half the value the Burrows et al. use in their generic model, it is still the most striking feature of the distribution. Beginning at 0.4 s after bounce, the electron neutrino and antineutrino luminosities drop abruptly due to a change in the rate of accretion when the interface between the silicon and oxygen shells pass through the neutrinospheres. The drop in density reduces the mass accretion Chapter 5. SNO Supernova Monte Carlo 91 rate and has a significant effect on the ue and Ve luminosities. The V M " luminosity is unaffected by the drop in the mass accretion rate because those neutrinos are produced (and decouple from matter) deeper in the core, where accretion effects are minimal. c o 3000 2000 -Si. \> x 35 o .£ E 1000 h wooh-r= 100 W -0.1 0.1 0.2 0.5 0.3 1 1.5 2 2.5 Time From Core Bounce (seconds) ' I ' I i i i i i i i i i shock breakout v -e ion V e " v " M _ 3 1 - a / i — / i'1 1 , 1 , 1 . 1 , 0.4 0.5 3.5 Figure 5.6: Supernova neutrino luminosity spectrum in the Bruenn 15 M 0 model [92]. The prompt peak due to neutronization is clearly visible. The calculation ends at 3.3 s after core bounce. Note that here the luminosity is the sum of the u^, uT and VT contributions. As with the other models investigated, the hierarchy of neutrino energies exists, in which the ve neutrinos have the lowest average energy and the "z^" neutrinos have the highest average energy. Figure 5.7 presents the average energy spectra for ve, Ve and " i ^ " neutrinos. Starting around 1 s after core bounce, the average energy values for all neutrino types stay roughly constant for the remainder of the burst. This behaviour appears to Chapter 5. SNO Supernova Monte Carlo 92 support the approach adopted by Beacom and Vogel in their model. The data presented in Figure 5.7 differ slightly from those shown by Bruenn et al. in reference [92]. In their paper, Bruenn et al. note that there is a spike in the "z^" average energy at the time of core bounce due to a numerical artifact, and represents an unphysical energy. The data that were made available to the author have the highest energy "z^" neutrinos removed from the calculation of the luminosity and average energy values. Therefore, there is very little evidence of the unphysical energy spike in Figure 5.7. 30 25 20 15 | 1 0 | 5 c ' I 1 , . | . | i | i | . V e -" V " -neutronization I." „/•• i l i I i I . I . I i l i 1 1.5 2 2.5 Time From Core Bounce (seconds) Figure 5.7: Supernova neutrino average energy spectrum using the Bruenn 15 M Q model [92]. From the time of core bounce, the average energies for all neutrino species rise until the onset of accretion effects at 0.42 s. From that point on, the average energies remain relatively constant. The calculation ends at 3.3 s after core bounce. Chapter 5. SNO Supernova Monte Carlo 93 5.3.5.2 Bruenn 25 M 0 Mode l Core bounce for the 25 M Q model occurs 0.2723 s after the initial collapse. Figure 5.8 shows the neutrino luminosity spectrum for ve, Ve and " i ^ " neutrinos. Except for the neutronization peak, the luminosities for all neutrino types in the 25 M Q model are almost twice as large as those in the 15 M 0 calculation. The sizable contribution from the combined " i / ^ " neutrinos immediately following the shock breakout is particularly striking. The difference in the prompt electron neutrino luminosity peak heights in the 15 M 0 and 25 M 0 models is relatively modest at 9%. One other difference between the two models is that there is a small secondary peak in the 25 M 0 model luminosity spectrum for the ue and ~Pe neutrinos. In each case, the spike occurs 15 ms after core bounce and is caused by recollapse of material that in turn heats the ue and F e neutrinospheres increasing the average energy and luminosity for those species. The average energy spectra shown in Figure 5.9 generally resemble the early evolution of the curves shown in Figure 5.7 for the 15 M 0 model. One feature that is different in the 25 M 0 model is the spike in the V M " average energy at the time of core bounce. Bruenn et al. suggest that this feature is a numerical artifact and represents an unphysical energy increase. While this artifact was removed for the 15 M 0 model, it remains for the 25 M 0 model. However, relatively few "z^" neutrinos exist at that time, so the overall effect is small. Another difference is that the average energies in the heavier progenitor model are higher than those in the lighter progenitor model. 5.3.6 Liebendorfer Model Seeking to improve upon previous approaches which use approximations to the transport equations, Liebendorfer et al. [94] developed an exact three-flavour Boltzmann neutrino Chapter 5. SNO Supernova Monte Carlo 94 4000 v-i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 r Time From Core Bounce (seconds) Figure 5.8: Supernova neutrino luminosity spectrum in the Bruenn 25 M 0 model [92]. The luminosity is truncated at 0.73 s after core bounce when a black hole forms. transport program called A G I L E - B O L T Z T R A N . The effect of using a more accurate neu-trino transport is to essentially increase the overall heating efficiency during the core col-lapse. As in the model of Bruenn et a/., general relativity is also included in all transport and hydrodynamics equations. While this approach is more rigorous, it did not yield a supernova explosion4. The results of this model are shown in Figures 5.10 and 5.11. The electron neutrino luminosity rises slowly during the initial period of collapse and infall, and decreases as the core reaches maximum density. It remains suppressed for another ~4 ms while the shock 4 A . Mezzacappa originally reported evidence for a simulated supernova explosion at the Neutrino 2000 conference in Sudbury, O N . This was later found to be an artifact of the computer code. Chapter 5. SNO Supernova Monte Carlo 95 30 r-> 25 shock breakout -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 Time From Core Bounce (seconds) 0.6 0.7 Figure 5.9: Supernova neutrino average energy spectrum using the Bruenn 25 M 0 model [92]. From the time of core bounce, the average energies for all neutrino species rise until the flux is completely cut off at 0.73 s and a black hole forms. wave propagates to the electron neutrinosphere. At that point, the ve luminosity is greatly enhanced due to electron capture behind the shock front. Peak values for the ve luminosity reach 3.5 x 10 5 3 ergs/s at the shock breakout. Generally, the luminosity curves for this 13 M Q model agree quite well with those from the Bruenn 15 M 0 model over the same time range. As with the previous four models, the well-established hierarchy of neutrino energies, in which the ue neutrinos have the lowest average energy and the neutrinos have the highest average energy, also exists in this model. Figure 5.11 presents the average Chapter 5. SNO Supernova Monte Carlo 96 4000 C o o 45 3000 9 ? 2000 '55 o c 1 g 1000 -0.1 shock breakout ' • " V ' VV'v e 'v 0.7 0.2 0.3 Time From Core Bounce (seconds) 0.4 0.5 Figure 5 .10: Supernova neutrino luminosity spectrum in the Liebendorfer 13 M 0 model [94]. The prompt peak due to electron capture in the neutronization phase is clearly visible. The calculation ends at 500 ms after core bounce. Note that the "z^ " luminosity is the sum of the t>M, F^, vT and VT contributions. energy spectra for ve, Ve and V M " neutrinos. In many ways these curves are very similar to those found in the Bruenn 25 M 0 model and not the Bruenn 15 M 0 model, which is more comparable in size. 5.3.7 Supernova Model Summary A general overview of the five models presented in the preceding sections points out a number of robust features. For a supernova explosion that does not result in a black hole, the neutrino signal is predicted to last for several tens of seconds. The formation of a Chapter 5. SNO Supernova Monte Carlo 97 Time From Core Bounce (seconds) Figure 5.11: Supernova neutrino average energy spectrum using the Liebendorfer 13 M Q model [94]. After the initial peak, the average energies for all neutrino species rise until until the calculation ends at 500 ms after core bounce. black hole might limit the flux to only 1-2 seconds. According to the energy distributions specified in the two generic models, supernova neutrinos are expected to have energies in the range 0-100 MeV, with the largest fraction having energies below 50 MeV. Equivalent descriptions of the energy distribution are not available for the detailed model calculations. As expected, the most universal feature that is present in all of the models reviewed is the hierarchy of neutrino energies. Electron neutrinos have the lowest energies, electron antineutrinos have slightly higher energies and muon and tau neutrino and antineutrinos have the highest energies. The exact ratios between these values may differ, but the order Chapter 5. SNO Supernova Monte Carlo 98 SN Model Parameter Beacom Model Burrows Model Bruenn Models Liebendorfer Model Progenitor Mass ( M 0 ) N / A N / A 15 25 13 Burst Duration full full limited full limited Lpeak (x 10 5 3 ergs/s) 0.17 6.00 3.29 3.58 3.52 EvMtai (x 10 5 3 ergs) 3.00 2.90 1.14 1.70 0.68 ve fraction 16.7% 20.2% 27.7% 32.2% 29.5% Ve fraction 16.7% 17.9% 25.6% 27.8% 21.9% "Ufi" fraction 66.7% 61.9% 46.7% 40.0% 48.6% Kjotal (X 10 5 2) 1.56 2.21 0.77 1.05 0.38 ve fraction 29.0% 26.8% 36.0% 38.1% 37.6% Ve fraction 20.3% 20.2% 26.4% 27.7% 22.7% "z^" fraction 50.7% 53.0% 37.5% 34.2% 39.8% (EU) (MeV) 19.2 13.1 14.8 16.2 17.8 (Eue) 11.0 9.9 11.4 13.7 14.0 W ) 15.8 11.6 14.4 16.3 17.2 (E«U») 25.2 15.4 18.5 18.9 21.8 Ratio (ue:Ve:up^) 1:1.4:2.3 1:1.2:1.6 1:1.3:1.6 1:1.2:1.4 1:1.2:1.6 Comments generic generic 1-d G R 1-d G R 1-d G R with details ~trans ~trans exact trans Table 5.2: Summary statistics for various supernova models. is consistently the same. A second feature that appears in all of the models (with the exception of the Beacom and Vogel model) is the enhancement at the onset of the signal due to electron capture in the neutronization phase of collapse. It should be emphasized that the Beacom and Vogel model cannot be used to study features beyond the general time and energy properties of the supernova signal. Of the models under consideration, the Beacom and Vogel model and the Burrows et al. model appear to represent the two extreme cases in supernova models. Comparing average energy values, it is evident that the Beacom and Vogel model uses higher values for all neutrino energies than is found in the Burrows et al. model. The largest difference Chapter 5. SNO Supernova Monte Carlo 99 is in the (^E"U^ values, where the values from the two models are separated by nearly 10 MeV. Higher neutrino energies will lead to a corresponding higher number of counts in certain reaction channels. In some of the studies that follow, results from these two models will be used to indicate the range of possible values. It is difficult to compare values from the generic models, which describe the full duration of the burst, to values from the detailed models because of the limited time over which the calculations for the detailed models are performed. For instance, the fraction of " i ^ " neutrinos is considerably lower for the detailed calculations than for the two generic models. In the case of the Bruenn 25 M Q model, this is due to the formation of a black hole. However, in the Bruenn 15 M 0 model and the Liebendorfer 13 M 0 model, the deficiency is due to the artificially short burst duration. For a full burst, the fraction of V M " neutrinos in these two models would be higher. The relevant parameters from the five models discussed in the preceding sections are summarized in Table 5.2. For much of the discussion of the neutrino signal in Chapter 6 and for all of the sub-sequent analysis, only the two generic models are considered. These models reflect the robust characteristics established from the neutrino events recorded during SN1987A and also contain features predicted from current studies of the core collapse mechanism. As well, both generic models describe the full duration of the neutrino signal, making them more complete examples of potential supernovae. The general predictions offered by the Beacom and Vogel model and the Burrows model make them the most useful models for understanding the detection possibilities of the next galactic supernova. Chapter 5. SNO Supernova Monte Carlo 100 5.4 SNO Supernova Neutrino Kinematics and Cross Sections 5.4.1 Introduction In addition to having more available interactions with heavy water, the interaction cross sections are also higher compared to light water. In the sections that follow, kinematics and cross sections for the main supernova neutrino interactions are presented in some detail. These interactions are grouped into three categories based on the interaction type: charged current, neutral current and elastic scattering. 5.4.2 Charged Current Recall from discussions in Section 4.3 that only ue and Ve neutrinos participate in charged current reactions. Isolating the ue component of the supernova signal is especially important when trying to identify the prompt neutronization peak in the supernova burst. In addi-tion to having higher interaction cross sections than the other interaction types, charged current reactions involving the electron neutrino will give SNO a unique measurement of the neutronization contribution to the supernova signal. 5.4.2.1 /7e + p —> n + e+ Reaction A discussion of the kinematics for this reaction begins with the total positron energy Ee. In the laboratory reference frame, Ee can be expressed as: E, = E„ + f + <f^, (5.17) 2mp 2mp where q2 = (pv — pe)2 is the four-momentum transfer, mn is the neutron mass and mp is the proton mass. The range of positron energies allowed by kinematics is obtained by solving the following quadratic equation: 0 = {[2(Eu + mp)f-4El}E2e Chapter 5. SNO Supernova Monte Carlo 101 +4(E„ + mp)(m2n - m l - m l - 2mpEt/)Ee + (m 2 - m l - m \ - 2mpEv)2 + (2El/me)2. (5.18) The laboratory angle of the positron with respect to the incoming neutrino direction is given by: _ m 2 - m 2 - 2mp{Ev - Ee) + 2EvEe cos 9P m. (5.19) 2Evp2 - m2e In a recent study [71], Vogel and Beacom investigate this reaction and recommend using the Llewellyn Smith cross section formalism [95] in conjunction with modifications they calculate that provide weak magnetism and recoil corrections to order O (1 /M) , where M = {mn + mp)/2 is the nucleon mass. The resulting differential cross section is somewhat reduced, and the formula with corrections is given by: da <ToP = 'E2 d\q A(q2) + B(q2){S'"U) • C(q2)(s-u)2-C(q2)4M2(mn-mp)2 M2 + M 4 (5.20) where the terms A(q2),B(q2) and C(q2) represent the following expressions: Mq2) (m2e - q2) 4M2 Fl \ 1 + h _ r_ M2 9 _ art M2 B(q2) = -^-2FA(Fv + fF2) 4q2FvfF2 M2 ( K + ^ | 2 + i ^ i 2 ) C(q2) = -A \FA\2 + Fy M2 ZFy (5.21) (5.22) (5.23) The form factors used in Equations 5.21, 5.22, 5.23 are assumed to be real in all cases and are given as follows: - l Fy(q2) = 1 - 4 M 2 ; J L V 1 4 M 2 / [GKd2) - GW)} (5.24) (5.25) Chapter 5. SNO Supernova Monte Carlo 102 ^«2> = - ^ ( ' " ( i i r nW) " ' (5'26) and ,2 - 2 G^2) = e-pW) (5-27) G % 2 ) = (5-28) Updated constants used by Llewellyn Smith in Equations 5.24, 5.25, 5.26, 5.27 and 5.28 are provided by Ahrens et al. [96]. In Equation 5.20, s = (pu +pp)2 and u = (p„ - p n ) 2 are Mandelstam variables and the expression (s — u) is given by: (s-u) = AmpEv + q2 - m2e - rn2n + ml (5.29) and <7QP is the normalizing constant defined explicitly as: (hc)2(l + Af n n e r ) Vp M2 cos2 ec 8TT = 1.805 x I O - 3 9 cm 2 , (5.30) where GF is the weak coupling constant, 9C is the Cabibbo angle and A ^ n e r = 0.024 is the energy independent inner radiative correction factor. 5.4.2.2 ue + d Reactions Discrete double differential cross section values, d2N/dE dcosO, for both the ue + d and Ve + d interactions are obtained from tables provided by Kubodera and Nozawa [97]. For the ve + d^p + p + e~ reaction, only the electron is of interest. The electron kinetic energy, T e , is constrained by 7e,mai = Eu -E /^ires) (5.31) where Ethres is the energy threshold for the reaction. Electron kinetic energy and angular distribution quantities are chosen according to the differential cross section values. Chapter 5. SNO Supernova Monte Carlo 103 In the case of the ve + d —> n + n + e+ reaction, all three final state particles can be identified in the SNO detector. The positron energy is determined as above using the differential cross section, and properties of the two neutrons are determined by considering a di-neutron system [98]. In the lab frame, the momentum of the di-neutron system, P2n,iab is determined using conservation of momentum: P2n,iab = \JEl+p\- 2 £ „ p e c o s 0 e , (5.32) where pe is the momentum of the positron (pe = \JE2 — m 2 ) and 8e is the angle of the positron relative to the incoming neutrino direction. The mass of the di-neutron system is given by conservation of energy: ™2n = V^fn "Pin- ( 5- 3 3) The di-neutron system then decays into two neutrons, n x and n 2 . In the centre-of-mass (CM) frame, the momentum of n\ is expressed as: Pnucm = O.Sy/mln - 2ra 2, (5.34) where mn is the mass of the neutron. The corresponding neutron energy in the C M frame is: Enucm = \ M 1 ) C m + ™>l- (5-35) Returning to the lab frame by using the Lorentz transformation along the 2-direction, the energy for ni is given by: Enulab = 7 (Enucm + Ppni,cm,z) (5-36) and the ^-component of the neutron momentum is expressed as: Pni,lab,z — 7 \Pni,cm,z + PEnucm), (5.37) Chapter 5. SNO Supernova Monte Carlo 104 where pnucm,z is the ^-component of the neutron C M momentum, j3 is the speed of the di-neutron system and 7 = 1 / V l - /?2. The angle 9ni of the neutron with respect to the incident neutrino direction is given as: coBfl B l = J ^ ' V (5.38) Having solved for the parameters describing the first neutron, the corresponding quantities for the second neutron are obtained in a straightforward manner using conservation of energy and momentum. The lab energy of the second neutron is given by: En2 =Ev + m d - E e - E n i , (5.39) where rrid is the mass of the deuteron. Finally, the direction of the second neutron is determined by considering the components of pn2/Pn2 obtained using Pn2 = Ep - pp-- pnfi± (5.40) Pv Pe Pm where p is the three-component momentum vector and p is the magnitude of the momentum vector. 5.4.2.3 ve + O Reactions Theorists doing calculations for the charged current interactions involving oxygen combine the contributions from all naturally occurring isotopes of oxygen into one result. Hence-forth, these reactions are referred to as ve + O reactions to indicate that all relevant isotopes are included in the treatment. For the SNO supernova generator, cross section values were obtained from two sources. For neutrino energies Ev < 60 MeV the values published by Haxton [99] were used, while for higher energy neutrinos, values published by Kuramoto et al. [72] were used, as recommended by Kuramoto et al. Chapter 5. SNO Supernova Monte Carlo 105 5.4.3 Neutral Current 5.4.3.1 vx + d Reactions Double differential cross section values for the vx + d—tvx+p + n interactions are ob-tained from tables provided by Kubodera and Nozawa [97]. In all cases, only the neutron is detected in the final state. The maximum momentum of the neutron in the C M frame is given by [100] _\J(s-(mp + mn)2)(s - Amlp) Pn,cm,max — 2^/s ' \ ) where s = m\ + 2Eumd, mp is the mass of the proton, mn is the mass of the neutron and Amnp is the mass difference between the neutron and proton. The maximum total energy of the neutron in the C M frame is En,cm,max — \JPn,cm,max + mn) (5.42) which corresponds to a maximum neutron lab energy of En,max -l(En ,cm,max "h PPn,cm,max) j (5.43) where /3 — Eu//(Ew+rn(i)- A 5% correction factor is applied to the neutron kinetic energy to account for nucleon motion. The neutron energy and direction are then chosen according to the differential cross section values. 5.4.3.2 v^T+ i e O Reactions In order to calculate the number of neutrinos that participate in these reaction, the cross section parameterization suggested by Beacom and Vogel [101] was used in conjunction with branching ratios calculated by Langanke et al. [73]. The gamma rays produced in the final state of Equations 4.17 and 4.18 have energies in the range w 5-10 MeV [73], which is sufficiently high to register as an event in the SNO detector. However, final state energy and direction distributions for these reactions are not currently available5. 5 E . Kolbe has been contacted concerning these calculations. Chapter 5. SNO Supernova Monte Carlo 106 Because of their high energy thresholds, these reactions also serve as a sensitive gauge of neutrino temperatures. Few events produced via these reactions would suggest relatively low " i / ^ " average energies, while on the other hand, a large number of events would would suggest relatively high " i ^ " average energies. 5.4.4 Elastic Scattering The differential cross section for producing a recoil electron with kinetic energy Te by elastic scattering with a neutrino of initial energy, Ev is given by [102]: da d¥e <7n Sfi + SR ( l 9L9Rme^ (5.44) where me is the electron mass and gL and gR are the electron chiral coupling constants to the weak neutral current [103]: gL = +0.5 4- sin 2 0W, gR = sin 2 9W for ue gL = sm26w, gR = +0.5 + sin 2 6W for Ve g^ — —0.5 + sin 2 0\y, gR = sin26 w for v. fl,T gL = sin 2 6W, gR = -0.5 + sin 2 6W for u^7 (5.45) (5.46) (5.47) (5.48) and OQ6 is explicitly given as: an — 2m 7T (hcf (hcf = 8.806 x 1 0 - 4 5 cm (5.49) where Gp is the Fermi coupling constant. The values for all constants used in the elas-tic scattering formalism were obtained from the Particle Data Group [5]. Inspection of the differential cross section given in Equation 5.44 shows that the probability for elastic scattering is highest for events with low recoil electron kinetic energy. Chapter 5. SNO Supernova Monte Carlo 107 The angle 9e, between the direction of the recoil electron and the incoming neutrino is given by: E„ + me I Te , . Expressed in terms of cos 9e, the differential cross section becomes: da A(EV + me)2El cos 9e (da\ dcos9e [(E„ + me)2-E2cos29e}2 \dTeJTe{cosf)e) where T e(cos0 e) is given by: (5.51) r.(M.».)=._ lm°f;coi!!' , . . ( 5 . 5 2 ) (Ev + me)2 - El cos2 6e Using Equations 5.44, 5.51 and 5.52 the spectrum averaged angular distribution of the recoil electrons can be calculated by making use of: / da \ rEv max I d,a \ « > = U ^ H i E " ! ( E " U ) { ^ ) T > r ' ( 5 ' 5 3 ) where for supernova neutrinos f(E„, ti) is taken as the normalized Fermi-Dirac spectrum. In order to simplify the integration over neutrino emission time, the time-independent energy spectra proposed by Beacom and Vogel (see Equation 5.6) is used for the calculations below. Figure 5.12 shows the fraction of cumulative probability for an electron to be scattered to any angle less than or equal to 9e for a series of Tmin values 0, 1.8, 3.8 and 7.7 MeV. As T m ; n approaches the maximum value allowed by energy conservation, more of the recoil electrons are scattered in the forward direction. Since the neutrinos emitted during a supernova explosion have higher average energies than their solar counterparts, the elastic scattering angular distribution for supernova neutrinos is expected to be even more forward peaked than for neutrinos originating from the Sun. Figure 5.12 also shows that at the SNO detector hardware threshold of NHIT = 16 P M T s (Te = 1.8 MeV), there is very little difference between the total width of the distribution (fraction = 1) for ue, Ve, v^r and V^r neutrinos. In fact, at this energy threshold, the recoil electrons from all elastic Chapter 5. SNO Supernova Monte Carlo 108 scattering reactions are expected to fall within 35°. Considering only 0.8 of the cumulative probability at the hardware energy threshold, V ^ " neutrinos have the most forward peaked distribution of the four neutrino classes distinguished in the cross section formalism. At the same energy, Ve neutrinos have the broadest angular distribution. As the energy threshold increases, ue neutrinos become the most forward peaked, whereas neutrinos have the broadest peak. Electron Scattering Angle, 6e (degrees) Figure 5.12: Elastic scattering recoil electron angular distribution for ue,Ve, v^T and V^T supernova neutrinos using energy spectrum of Beacom and Vogel. Shown is the fraction of cumulative probability for a recoil electron to be scattered to any angle less than or equal to 9e. Distributions from four different electron energy thresholds are presented for each neutrino species showing that higher cuts on electron energy produce a more forward peaked distribution. Chapter 5. SNO Supernova Monte Carlo 109 The expression for the total cross section is obtained by integrating Equation 5.44 from the detector energy threshold Tmin to the maximum electron kinetic energy Tmax allowed by energy and momentum conservation: e (n2+n2)(T -T •)-(— + ^ M^l\ (T2 - T2 • ) \ilL < yRJ\-Lmax -Lmtn) \.E IE2 J a x rnin) , 9R (rp3 _ rp3 \ 3E2 m a x rnin) (5.54) where Tmax is expressed as: 2F2 Tmaxm = » . (5.55) 5.4.5 Interaction Summary-According to the supernova models considered in Section 5.3, most of the neutrinos inter-acting in the detector volume will have energies below 50 MeV. Since the charged current reactions have the highest cross section in this energy domain, they will contribute the highest number of interactions to the overall neutrino count total. Having the highest charged-current cross section, the Ve + p —> n + e+ reaction will play a dominant role. The main neutrino interaction cross sections are summarized in Figure 5.13. Depending on the neutrino energy distributions, reactions involving oxygen may also play an important role. For the most part, these reactions have high energy thresholds (see Sections 5.4.2.3 and 5.4.3.2), which means that only high energy neutrinos are able to participate in these channels. Since different supernova models predict different neutrino energy distributions, these reactions will be more important in models that have higher neutrino energies. Figure 5.14 shows the interaction cross sections for the main reactions involving oxygen. As with the previous set of cross sections, the charged current reactions have the highest cross sections. Chapter 5. SNO Supernova Monte Carlo 110 1 1 r Neutrino Energy (MeV) Figure 5.13: Cross sections for the main supernova neutrino interactions in the SNO detector. For the neutral current reactions, ux stands for all active neutrino flavours. Since the Ve + p —> n + e + reaction has the highest cross section at energies below 50 MeV, and because there are a high relative number of targets available for this reaction, it will contribute the highest number of interactions. 5.5 SNO Targets One final ingredient to consider is the number of target particles available to the interactions discussed above. Doe et al. [104] have made a careful study of the mass of the D 2 0 target in the SNO detector, and their values are used for the studies that follow. The number of targets related to the number of H 2 0 molecules is calculated assuming 1700 tonnes of light water between the face of the PMTs and the outer radius of the acrylic vessel. Table 5.3 summarizes the number of targets for each reaction being considered. Even Chapter 5. SNO Supernova Monte Carlo 111 1000000 100000 ] 1 70000 X .§ woo s CO § roo 10 Charged Current: - • F + e I6_ v + O 16 _ v + O—>v + O + n + Y 16,. 15_ v + O — • v + O + p + Y 50 75 100 Neutrino Energy (MeV) Figure 5.14: Cross sections for supernova neutrino interactions involving oxygen in the SNO detector. At low energies, the ve + O —> F + e~ cross section is enhanced by contribu-tions from isotopes 1 7 0 and 1 8 0 . The slight depression in the ve + O —> F + e~ cross section at 70 MeV is the result of joining together cross section data from two different authors. The neutral current cross sections for V^r neutrinos are essentially identical to the ones shown for u^T neutrinos and are not shown. though the elastic scattering reactions have the highest number of target particles, the low cross section means that the total number of events from these channels will still be comparatively low. Chapter 5. SNO Supernova Monte Carlo 112 Reaction Region Number Relative of Targets Number ( x l O 3 1 ) of Targets Charged Current: Ve + p —v n + e+ H 2 0 11.3655 3.783 ve + d-*p + p + e~ D 2 0 6.0086 2.000 Ve + d-Jrn + n + e+ D 2 0 6.0086 2.000 ve + 0 -> F + e~ D 2 0 3.0043 1.000 Ve + 0 -»• N+ e+ D 2 0 3.0043 1.000 ue + 0 -> F + e - H 2 0 5.6827 1.892 I7 e + 0 - ) • N+ e + H 2 0 5.6827 1.892 Neutral Current: ue + d^ue+p + n D 2 0 6.0086 2.000 Ve + d—tVe+p + n D 2 0 6.0086 2.000 D 2 0 6.0086 2.000 "H,T + d -> V^T + p + n D 2 0 6.0086 2.000 Vp,r + 1 6 0 -)• v^T + 1 5 0 + n + 7 D 2 0 3.0043 1.000 F,I ,T + 1 6 0 - 4 T 7 M ) T + 1 5 0 + n + 7 D 2 0 3.0043 1.000 ^ , T + 1 6 0 - > ^ > T + 1 5 N + p + 7 D 2 0 3.0043 1.000 + 1 6 0 -» F ^ , T + 1 5 N + p + 7 D 2 0 3.0043 1.000 iV,r + 1 6 ° "/i,r + 1 5 0 + n D 2 0 3.0043 1.000 D 2 0 3.0043 1.000 ^ , r + 1 6 0 - > ^ > T + 1 5 0 + n + 7 H 2 0 5.6827 1.892 »W + 1 6 0 -> VH,T + 1 5 0 + n + 7 H 2 0 5.6827 1.892 V^T + 1 6 0 ->• v^T + 1 5 N +p + 7 H 2 0 5.6827 1.892 *W + 1 6 0 -)• F M I T + 1 5 N + p + 7 H 2 0 5.6827 1.892 Elastic Scattering: ve + e~ —> ve + e~ D 2 0 30.1730 10.043 ue + e~ —> Ve + e~ D 2 0 30.1730 10.043 " / I , T + e~ ->• i/„ l T + e - D 2 0 30.1730 10.043 ~y~ii,T + e~ -> + e~ D 2 0 30.1730 10.043 f e + e~ —>• i / e 4- e~ H 2 0 56.8275 18.915 z7 e + e~ —» F E + e~ H 2 0 56.8275 18.915 + e" ->• u^r + e~ H 2 0 56.8275 18.915 ~y~n,T + e~ ->• ^ . T + e~ H 2 0 56.8275 18.915 Table 5.3: Number of interaction targets in the SNO detector for the various supernova neutrino reactions. Chapter 5. SNO Supernova Monte Carlo 113 5.6 Event Sampling Once the supernova neutrino events are determined for each reaction, specific neutrino events are produced by sampling the neutrino flux distribution at the detector according to Equation 5.11. The "acceptance-rejection method" [5] for sampling requires that inde-pendent random detection time, tran, and neutrino energy, Eu<ran, values are used to pick a corresponding neutrino flux at the detector, P(tran,Eu^Tan) — d2 N/ dtdE^tran, E^ran). The event is chosen if the neutrino flux, P(tran, £v, r 0 n)> calculated using the random time and energy is less than a detector flux value, Pran, chosen from a comparison distribution function. For these studies, the comparison function was taken to be a flat probability distribution function defined by the maximum and minimum d2N/dtdEu(t, Ev) values. In this way, the boundary of the distribution is preserved by using d2N/dtdEl/{tran,Ev>ran), and the probability of choosing a particular (£, Ev) pair depends on the area under the curve. Therefore, every neutrino event consists of independently chosen detection time and neutrino energy values that are consistent with the cPN/dtdE,, distribution. With this neutrino information, detectable final state particles are sampled according to their differential cross sections. Each final state particle event consists of an interaction time, the total energy of the particle and a set of direction cosines that describe the direction of the particle in the detector coordinate system. The particles are then propagated in the detector volume using the SNO Monte Carlo and Analysis software package. 5.7 SNO Monte Carlo Settings The previous sections describe in detail the parameters and calculations performed by the SNO supernova generator. In the last stage of the simulation, results from the generator are provided to the SNO Monte Carlo and Analysis software package (SNOMAN) that fully describes the detector geometry and response. For each final state particle, the interaction Chapter 5. SNO Supernova Monte Carlo 114 Detector S N O M A N Commen t Character is t ic Set t ing Cerenkov Light Generation: low wavelength cutoff 200 nm high wavelength cutoff 720 nm Cerenkov factor 0.35 individual P M T efficiency PMT: P M T Model 3d P M T full 3d model of P M T P M T efficiency 0.561 P M T array efficiency P M T noise rate 568 Hz Water Specs: H 2 0 fraction in D 2 0 0.000824 1 7 0 fraction in D 2 0 0.000487 neutron capture without 7 cascade Table 5.4: Detector characteristics specified in the supernova neutrino Monte Carlo sim-ulations. time, the total energy of the particle (kinetic energy for neutrons) and a set of direction cosines that describe the direction of the particle in the detector coordinate system are provided. The event position are distributed randomly in the relevant detector volumes. S N O M A N version 4.0186 is used for all Monte Carlo analysis. Characteristics of the SNO detector that are specified in the simulation are summarized in Table 5.4. Chapter 6 SNO Supernova Neutrino Signal 6.1 Introduction In order to study signals in the SNO detector from the possible supernova models suggested in the literature, a set of F O R T R A N routines has been written to implement the supernova signal formalism discussed in Chapter 5. Collectively these routines are called the SNO supernova generator. The supernova generator is used to calculate properties of neutrinos that interact in the SNO detector and the resulting final state particles. Once the final state particles are created, the main SNO Monte Carlo package called S N O M A N is used to correctly describe subsequent scattering and assign the correct detector geometry and collection efficiencies. Results from the SNO supernova generator and the S N O M A N Monte Carlo are presented and discussed in the sections below. 6.2 SNO Supernova Neutrino Interactions The first stage of the supernova signal analysis involves considering the number of neutrino interactions calculated using the SNO supernova generator for the possible reactions in the SNO detector. Since this analysis concerns the number of interactions and not the final detection signal, only the energy threshold associated with a given interaction is imposed at this point. Application of the SNO detection and analysis energy threshold is treated at a later stage. A detailed account of the number of neutrino interactions resulting from each of the five supernova models discussed in Chapter 5 is presented in this section. Where 115 Chapter 6. SNO Supernova Neutrino Signal 116 possible, comparisons between the SNO supernova generator and results published by the authors of the various models are made. Results for the most generic models are presented first, followed by the more detailed models. 6.2.1 Beacom and Vogel Model To compute the total number of counts for each reaction in the SNO detector using the Beacom and Vogel model, Equation 5.12 is used in conjunction with the model parameters outlined in Section 5.3.3. The limits of integration are chosen such that the total energy radiated as neutrinos is in agreement with the total model input energy. In the case of the Beacom and Vogel model, time is integrated from 0 s to 20 s in steps of 5 ms, and energy is integrated from 0.1 MeV to 170 MeV in steps of 0.1 MeV. Before a detector energy threshold is applied, ~1200 neutrinos are expected to interact in the SNO detector for a supernova at 10 kpc according to the Beacom and Vogel model. The largest contribution for a single reaction channel is from the ue + p —> n + e+ reaction due to the high cross section and large number of target molecules. Of the total supernova signal, 49.3% of the neutrinos interact via charged current interactions, 47.1% via neutral current interactions and 3.6% through elastic scattering interactions. The majority of neutrinos interact in the D 2 0 volume, namely 58.6%, while 41.4% of neutrinos are present in the H 2 0 volume. Of the neutrinos interacting in the light water region, the Ve + p —> n + e+ reaction constitutes almost the entire signal at 84.8%. 11.5% of the supernova neutrinos interacting in the SNO detector are ue neutrinos, 47.5% are ue neutrinos and 41.0% are V M " neutrinos. Recall that there is no provision made in the Beacom and Vogel model for electron neutrinos being produced during the neutronization stage of collapse. However, the prompt ue neutrino signal is only expected to contribute 1-2% to the total number of supernova neutrinos that interact in the detector. Table 6.1 summarizes in detail the number of supernova neutrinos expected in the SNO detector using the Beacom and Vogel Chapter 6. SNO Supernova Neutrino Signal 117 Reaction Reaction v Counts v Counts Region (all time) (i < 0.5 s) Charged Current: D20/H20 161.83/428.57 22.03/58.34 Ve + p —> n + e+ H 2 0 419.96 57.17 ve + d^,p + p + e~ D 2 0 79.26 10.79 Ve + d—±n + n + e+ D 2 0 78.01 10.62 z/e + 0 —>• F + e~ D 2 0 1.01 0.14 Ve + 0 ->• N+ e+ D 2 0 3.55 0.48 i / e + 0 - 4 F + e" H 2 0 1.90 0.26 F e + 0 -> N+ e + H 2 0 6.71 0.91 Neutral Current: D20/H20 524.88/38.44 71.47/5.24 ve + d^rVe+p + n D 2 0 34.42 4.69 Ve + d-)Ve+p + n D 2 0 50.94 6.94 "us + d^r u^r +p + n D 2 0 221.21 30.12 V»,T + d^ u^r + p + n D 2 0 178.38 24.28 v^r + 1 6 0 ^ ^ , r + 1 5 0 + n + 7 D 2 0 2.10 0.29 ^ M , T + 1 6 0 ->• F M i T + 1 5 0 + n + 7 D 2 0 2.09 0.28 + 1 6 0 ->• + 1 5 N + p + 7 D 2 0 7.99 1.09 ^ , r + 1 6 0 - ^ F M , r + 1 5 N + p + 7 D 2 0 8.14 1.11 ^ . T + 1 6 0 - » - ^ , r + 1 5 0 + n D 2 0 9.98 1.36 I W + 1 6 0-> F M , T + 1 5 0 + n D 2 0 9.63 1.31 + 1 6 0 -> i / M f T + 1 5 0 + n + 7 H 2 0 3.97 0.54 + 1 6 0 -)• F^, T + 1 5 0 + n + 7 H 2 0 3.95 0.54 ^ , r + 1 6 0 - > ^ , T + 1 5 N + p + 7 H 2 0 15.12 2.06 F ^ r + 1 6 0 - > ^ , T + 1 5 N + p + 7 H 2 0 15.40 2.10 Elastic Scattering: D20/H20 14.90/28.06 2.03/3.81 ve + e~ —»• ve + e" D 2 0 7.27 0.99 F e + e~ - » F e + e~ D 2 0 3.09 0.42 *V,T + e~ i / M ) T + e~ D 2 0 2.44 0.33 + e~ ->• F M ) T + e" D 2 0 2.10 0.29 f e + e~ —, ve + e~ H 2 0 13.69 1.86 F e + e~ —> F e + e~ H 2 0 5.82 0.79 V^T + e~ ->• i / ^ l T + e~ H 2 0 4.59 0.62 v»,r + e~ ->• F M i T + e - H 2 0 3.96 0.54 Total SNO f e Neutrinos 137.55 18.73 Total SNO F e Neutrinos 568.08 77.33 Total SNO ' V Neutrinos 491.05 66.86 Total SNO D 2 0 Neutrinos 701.61 95.53 Total SNO H 2 0 Neutrinos 495.07 67.39 Total SNO Neutrinos 1196.68 162.92 Table 6.1: Neutrino counts for a supernova at 10 kpc calculated for the Beacom and Vogel model using the SNO supernova generator with no detector energy threshold. Chapter 6. SNO Supernova Neutrino Signal 118 model for a supernova at 10 kpc. Notice the relatively large contribution from reactions involving oxygen. A combined total of 92 neutrino interactions (7.6% of the total signal) is expected from charged-current and neutral-current reactions involving oxygen in the SNO detector for a supernova at 10 kpc. Since Beacom and Vogel adopt relatively high neutrino temperatures (especially for " i / ^ " neutrinos), these reaction channels play a prominent role. Other models with lower neutrino temperatures will predict fewer counts from these interactions. Due to the high cross section for the Ve + p —> n + e+ reaction, there exists the potential for a significant contribution to the SNO neutrino signal from neutrinos interacting with H 2 0 molecules in the D 2 0 volume. Careful assays of the water inside the acrylic vessel measure this fraction to be 0.0824%. The consequence in the Beacom and Vogel model is that 0.18 neutrino interactions of the is type (or 0.015% of the total set of neutrino counts in Table 6.1) would arise for a supernova at 10 kpc. This contribution is considered to be insignificant and is therefore ignored in further studies. Once the total number of neutrino interactions is determined for each reaction, neutrino events are sampled from energy and time distributions consistent with the model parame-ters. Final state particle events are then obtained by using appropriate kinematic relations and sampling according to the prescription outlined in Section 5.6. Table 6.2 summarizes the average energies of the sampled neutrino events for each reaction as well as some of the properties of the final state particle events. 50000 neutrino events are produced for each reaction without any energy threshold so that the entire underlying neutrino spectrum can be studied. Notice that average neutrino energy values for the different neutrino types are higher than the emission average energies quoted in Table 5.2. For example, the neutral current reactions involving 1 6 O , which have the highest energy thresholds, also have the highest average energies of neutrinos that interact in the detector. The reason is that in-teractions within the detector do not select neutrinos evenly from the energy distribution. Chapter 6. SNO Supernova Neutrino Signal 119 Reaction Reaction {Eu) (Ee) (cos 0e) Region (MeV) (MeV) Charged Current: 24.92 21.99 -0.0022 Ve + p —> n + e + H 2 0 25.06 23.08 0.0311 ve + d-*p + p + e~ D 2 0 19.42 16.49 -0.1204 T>e + d^rn + n + e+ D 2 0 27.45 21.69 -0.0614 ue + 0 -> F + e - D 2 0 28.68 I7e + 0 ->• N+ e + D 2 0 40.82 i / e + 0 ->• F + e~ H 2 0 28.61 F E + 0 -»• N+ e + H 2 0 40.94 Neutral Current: 42.87 N/A N/A ue + d-^ve+p + n D 2 0 19.68 Ve + d^rVe+p + n D 2 0 26.42 V^T + d-> V^T + p + U D 2 0 42.87 F M l r + d -> F M I T + p + n D 2 0 41.30 + 1 6 0 -» + 1 5 0 + n + 7 D 2 0 67.09 F M ) T + 1 6 0 -»• F M I T + 1 5 0 + n + 7 D 2 0 66.98 + 1 6 0 - » - ^ , r + 1 5 N + p + 7 D 2 0 67.07 + 1 6 0 -»• + 1 5 N + p + 7 D 2 0 67.10 ^ , r + 1 6 0 - > i / M , T + 1 5 0 + n D 2 0 67.10 J?„,T + 1 6 0 - > F M > T + 1 5 0 + n D 2 0 67.04 + 1 6 0 -+ + 1 5 0 + n + 7 H 2 0 67.10 v^r + 1 6 0 ->• F M ) T + 1 5 0 + n + 7 H 2 0 67.07 + 1 6 0 ->• + 1 5 N + p + 7 H 2 0 67.07 * V + 1 6 ° -> * W + 1 5 N + p + 7 H 2 0 67.11 Elastic Scattering: 21.35 9.59 0.9066 ue + e~ ue + e~ D 2 0 14.51 7.53 0.9095 F E + e~ -> F E + e~ D 2 0 20.62 6.76 0.8650 + e" -> + e~ D 2 0 32.84 15.27 0.9349 F )^7- + e" - ) • F M ) T + e - D 2 0 32.80 14.35 0.9281 i>e + e~ —V ve + e~ H 2 0 14.49 7.50 0.9078 Ve + e~ —> F E + e~ H 2 0 20.61 6.74 0.8655 * V , T + e~ + e~ H 2 0 32.84 15.24 0.9351 * V , T + e~ -> F^ ) T + e~ H 2 0 32.79 14.38 0.9284 Total SNO i / e Neutrinos 18.94 14.61 0.0948 Total SNO F E Neutrinos 25.75 22.58 0.0316 Total SNO ' V ' Neutrinos 45.90 14.84 0.9319 Total SNO D 2 0 Neutrinos 36.69 18.25 -0.0048 Total SNO H 2 0 Neutrinos 28.34 22.24 0.0860 Total SNO Neutrinos 33.21 21.13 0.0608 Table 6.2: Average energy and angular distribution values for 50000 sampled neutrinos and their associated final state detectable particles in the Beacom and Vogel model with no detector energy threshold. Chapter 6. SNO Supernova Neutrino Signal 120 However, the energy hierarchy remains present. The " i / ^ " neutrinos that interact in the detector have significantly higher average energies than Ve neutrinos, which in turn have higher average energies than ve neutrinos. As well, the ratio of the average energy values for ue, Ve and "z^" neutrinos stays practically the same at 1:1.4:2.4. The relative changes to the ratio of average neutrino energy values are modest: a 6% decrease in the Ve energy and a 6% increase in the average energy for the "z/^" neutrinos. Because neutrons thermalize in the detector volume and are only detected through indirect capture reactions, much of the energy information carried by the "z/M" neutrinos is lost in the final state. In principle, however, the high threshold energy of the 1 6 0 neutral current reactions can be used to gauge the energies of these neutrinos. A high number of counts from these channels would indicate that a significant fraction of "z^" neutrinos have energies Ev > 15 MeV. According to the Beacom and Vogel model, almost 80 neutrino interactions (or 6.5% of the total number of neutrino events) from these neutral-current channels involving oxygen are expected. Also listed in Table 6.2 are the (cos#e) values for the different reactions, where 9e is the angle between the neutrino and lepton directions in the laboratory. A value of (cos#e) = +1 means that the direction of the outgoing particle is perfectly correlated with the incoming neutrino direction, while (cos#e) = — 1 means that the direction of the outgoing particle is perfectly anticorrelated with the neutrino direction. Reactions in which the final state lepton is emitted isotropically with respect to the neutrino direction have (cos0e) = 0. There is no asymmetry in the angular distribution to exploit in that case. Neutrons thermalize in the detector thereby losing any information about the initial supernova direction; therefore only (cos 8e) values for electrons and positrons are considered. The three charged current reactions, which use either proton or deuteron targets, have only slight asymmetries in the angular distribution. Vogel and Beacom [71] discuss the individual angular distributions for the these reactions, and the (cos 9e) values presented in Table 6.2 Chapter 6. SNO Supernova Neutrino Signal 121 agree with what they present. Together, the results indicate that the asymmetries in the charged current reactions combine to become essentially 0. However, the slight asymmetries can be distinguished by considering the heavy- and light-water signals separately. Elastic scattering reactions, on the other hand, have angular distributions which are very forward peaked (see Section 5.4.4). In those cases, (cos#e) values are very close to being completely aligned with the incoming neutrino direction. While the elastic scattering interactions convey the most useful directional information about the location of the supernova, there are relatively few interactions in those channels. Pointing back to a supernova will involve identifying the forward elastic scattering peak on top of the flat background provided by the other reactions. 6.2.2 Comparison to Beacom and Vogel Published Results To ensure that the supernova signal formalism and models have been implemented correctly and that the SNO supernova generator is yielding valid results, a number of quantities are used as a check. Among these checks are the total supernova energy and the average neutrino energy. However, the most comprehensive comparison is done by comparing integrated neutrino counts and neutrino count rates where possible. Using Equation 5.3, the total neutrino energy calculated by the supernova generator is 3.0 x 10 5 3 ergs, which is identical to the expected result quoted by Beacom and Vogel [15]. The energy fractions are also the same. A comparison of these quantities is listed in Table 6.3. Table 6.4 shows neutrino counts comparing values for reactions published by Beacom and Vogel [15] and count values calculated using the SNO supernova generator. Some important differences need to be taken into account. Beacom and Vogel use 1 ktonne D 2 0 and 1.4 ktonne H 2 0 as the SNO detector volumes and impose a 5 MeV detector threshold on all of the charged-current and elastic scattering reactions. In the case of the Chapter 6. SNO Supernova Neutrino Signal 122 Parameter Beacom Value Th i s W o r k Value Eue,total Eye, total E«ptotal Ev,total 0.5 x l O 5 3 0.5 x l O 5 3 2.0 x l O 5 3 3.0 x l O 5 3 0.499 x l O 5 3 0.499 x l O 5 3 1.996 x l O 5 3 2.995 x l O 5 3 11.0 MeV 15.8 MeV 25.2 MeV 11.025 MeV 15.750 MeV 25.200 MeV Table 6.3: Comparison of supernova source parameters determined using the SNO super-nova generator and Beacom and Vogel published values [15]. Ve + p —> n + e + reaction, an older cross section formula is used by the authors [105] and this is also taken into account. For the sake of comparison, these parameters are employed in the generator to produce the results listed in the last column of Table 6.4. There is excellent agreement between the Beacom and Vogel published values and the generator results, which indicates that the model has been implemented correctly in the generator. 6.2.3 Burrows et al. Model To compute the total number of counts for each reaction in the SNO detector using the Burrows et al. model, Equation 5.12 is used in conjunction with the model parameters outlined in Section 5.3.4. The limits of integration are chosen such that the total energy radiated as neutrinos is in agreement with the total model input energy. For the Burrows model, two time regimes are used for the integration in order to preserve the signal structure at early times and yet cover the long duration of the total signal. Integration over the early burst region is performed from —0.100 s to 1 s in steps of 1 ms, while integration over the cooling region is performed from 1 s to 50 s in 10 ms steps. Neutrino energy is integrated from 0.1 MeV to 100 MeV in steps of 0.1 MeV. Before a detector energy threshold is applied, ~800 neutrino events are expected in the Chapter 6. SNO Supernova Neutrino Signal 123 Reaction Reaction Beacom This Work Region Counts Counts Charged Current: D20/H20 160/365 155.73/363.67 ve + P —> n + e+ H 2 0 365 363.67 ve + d^rP + p + e~ D 2 0 80 78.28 Ve + d-+n-\-n-re+ D 2 0 80 77.45 •Neutral Current: D20/H20 520/30 525.38/31.68 ve-\-d^rve+p-\-n D 2 0 35 34.46 Ve + d—tVe+p + n D 2 0 50 50.99 v^T + d ->• v^T + p + n D 2 0 220 221.42 V~H,T + d -> z7 M i T + p + n D 2 0 180 178.54 v^r + 1 6 0 -> u^T + 1 5 0 + n + 7 D 2 0 20 2.10 V^T + 1 6 0 -> V^r + 1 5 0 + n + 7 D 2 0 2.09 + 1 6 0 ->• i / M | T + 1 5 N + p + 7 D 2 0 8.00 ^M,r + 1 6 0 -> F^, T + 1 5 N + p + 7 D 2 0 8.15 + 1 6 0 - ) • z^,T + 1 5 0 + n D 2 0 15 9.99 I^ ) T + 1 6 0 - > T 7 M i T + 1 5 0 + n D 2 0 9.64 + 1 6 0 - ^ + 1 5 0 + n + 7 H 2 0 30 3.29 F M ) T + 1 6 0 -> I7 M , T + 1 5 0 + n + 7 H 2 0 3.26 ^ , r + 1 6 0 - > ^ , r + 1 5 N + p + 7 H 2 0 12.45 ^ . T + 1 6 0 -> FM,r + 1 5 N + p + 7 H 2 0 12.68 Elastic Scattering: D20/ H20 10/15 8.72/13.52 ve + e~ —> ue + e~ D 2 0 10 3.97 Ve + e~ —7 Ve + e~ D 2 0 1.42 V»,T + e~~ v^r + e~ D 2 0 1.82 V~H,T + e~ ^7 F M ) T + e~ D 2 0 1.51 f e + e~ —> ue + e~ H 2 0 15 6.18 Ve + e~ —> Ve + e~ H 2 0 2.14 Vn,T + e~ -> u^r + e~ H 2 0 2.84 VH,T + er ->• V^T + e" H 2 0 2.36 Total SNO i / e Neutrinos N / A 122.89 Total SNO Ve Neutrinos N / A 495.67 Total SNO ' V Neutrinos N / A 480.14 Total SNO D 2 0 Neutrinos 690 689.83 Total SNO H 2 0 Neutrinos 410 408.87 Total SNO Neutrinos 1100 1098.70 Table 6.4: Comparison of neutrino counts for a supernova at 10 kpc calculated using the SNO supernova generator and values published by Beacom and Vogel [15]. The parameters used by the authors to simulate neutrino interactions in the SNO detector are used to calculate the values in the last column. Instead of specifying the number of neutrino counts for each individual reaction, Beacom and Vogel provide only the count sum for a certain type of interaction in some cases. Chapter 6. SNO Supernova Neutrino Signal 124 SNO detector for a supernova at 10 kpc according to the Burrows model. Of this total, 49.2% of the neutrinos in the supernova signal interact via charged current interactions, 47.2% via neutral current interactions and 3.6% through elastic scattering interactions. The majority of neutrinos interact in the D 2 0 volume, namely 58.8%, while 41.2% are present in the H 2 0 volume. 11.5% of the supernova neutrinos interacting in the SNO detector are ue neutrinos, 47.3% are Ve neutrinos and 41.1% are V M " neutrinos. Table 6.5 summarizes the number of supernova neutrinos expected in the SNO detector using the Burrows model for a supernova at 10 kpc. As with the Beacom and Vogel model, the number of counts expected due to H 2 0 molecules in the D 2 0 volume is considered to be negligible (0.14 counts for a supernova at 10 kpc or 0.018% of the total signal). In contrast to the Beacom and Vogel model, the Burrows model only predicts a total of 13 neutrino interactions (or 1.7% of the entire signal) from charged current and neu-tral current reactions involving oxygen. This is due mainly to the much lower neutrino temperatures used in the Burrows model for the V M " neutrinos. Table 6.6 summarizes the average energies of the sampled neutrino events for each reaction as well as some of the properties of the final state particles. 50000 neutrino events are produced for each reaction without any energy threshold so that the entire underlying neutrino spectrum can be studied. In all cases, the neutrino and corresponding final state particle energies are lower than for the Beacom and Vogel model; however, the energy hierarchy remains. The lower energies also affect the angular distributions. For instance, the (cos 9e) values for the elastic scattering reaction do not correlate with the initial neutrino direction as well as in the Beacom and Vogel model. This is due to the fact that when higher energy neutrinos undergo elastic scattering, the recoil electron maintains the initial direction better than lower energy neutrinos. Chapter 6. SNO Supernova Neutrino Signal 125 Reac t ion Reac t ion v Counts v Counts Reg ion (all t ime) (t < 0.5 s) Charged Current: D20/H20 138.51/333.74 76.14/165.43 Ve + p —» n + e + H 2 0 329.11 162.64 ve + d^p + p + e' D 2 0 82.99 46.23 Ve + d^n + n + e+ D 2 0 53.08 28.44 ue + 0 ->• F + e" D 2 0 1.08 0.61 F e + 0 -+ N+ e + D 2 0 1.36 0.86 + 0 ->• F + e - H 2 0 2.05 1.16 F e + 0 ->• N+ e+ H 2 0 2.58 1.63 Neutral Current: D20/H20 261.24/3.11 120.09/1.69 ve + d^,i>e+p + n D 2 0 35.77 20.11 Ve + d—>I>e+p + n D 2 0 36.27 18.90 y^r + d ^ u^tT + p + n D 2 0 99.22 42.60 + d^> V^T + p + n D 2 0 86.74 36.73 v^r + 1 6 0 -> + 1 5 0 + n + 7 D 2 0 0.17 0.09 F M ) T + 1 6 0 F ^ + 1 5 0 + n + 7 D 2 0 0.17 0.09 + 1 6 0 ^ *V,r + 1 5 N + p + 7 D 2 0 0.65 0.35 * W + 1 6 0 -> + 1 5 N +p + 7 D 2 0 0.66 0.36 + 1 6 0 - > u^T + 150 + n D 2 0 0.81 0.44 ^ , r + 1 6 0 ^ F M ) T + 1 5 0 - r - n D 2 0 0.78 0.42 + 1 6 0 -> + 1 5 0 + n + 7 H 2 0 0.32 0.17 »W + 1 6 0 -> F M , T + 1 5 0 + n + 7 H 2 0 0.32 0.17 J ' / I . T + 1 6 0 - ) • i / M ) T + 1 5 N + p + 7 H 2 0 1.22 0.67 * W + 1 6 0 -> F^ , T + 1 5 N + p + 7 H 2 0 1.25 0.68 Elastic Scattering: D20/H20 15.79/29.74 6.84/12.88 ue + e~ —> ue + e~ D 2 0 8.52 4.13 F e + e~ —> F e + e - D 2 0 3.19 1.32 Vn,r + e~ -> i / M i T + e - D 2 0 2.19 0.75 + e~ -¥ u^T + e~ D 2 0 1.89 0.64 ve + e~ —> ve + e~ H 2 0 16.05 7.77 F e + e~ —> F e + e~ H 2 0 6.01 2.49 VH,T + E ~ ->• + E ~ H 2 0 4.12 1.41 ^ > T + E ~ -* vn,r + e" H 2 0 3.56 1.21 Total SNO i / e Neutrinos 146.46 80.01 Total SNO F e Neutrinos 431.60 216.28 Total SNO ' V Neutrinos 204.07 86.78 Total SNO D 2 0 Neutrinos 415.54 203.07 Total SNO H 2 0 Neutrinos 366.59 180.00 Tota l S N O Neutr inos 782.13 383.07 Table 6.5: Neutrino counts for a supernova at 10 kpc calculated for the Burrows et al. model using the SNO supernova generator with no detector energy threshold. Chapter 6. SNO Supernova Neutrino Signal 126 Reaction Reaction {Eu) (Ee) (cos0e) Region (MeV) (MeV) Charged Current: 20.22 17.65 -0.0196 F e + p —> n 4- e + H 2 0 19.93 18.19 0.0145 ve + d^rP + p + e~ D 2 0 18.70 15.80 -0.1185 F e + d—>n + n + e + D 2 0 22.56 17.21 -0.0760 ue + 0 ->• F + e~ D 2 0 30.00 F e + 0 -r N+ e+ D 2 0 36.68 i / e + 0 -» F + e - H 2 0 29.90 F e + 0 -> N+ e+ H 2 0 36.67 Neutral Current: 25.04 N/A N/A ve + d-)ve-\-p + n D 2 0 18.96 ~Pe + d—7Ve+p + n D 2 0 21.65 VH,T + d ->• u^T + p + n D 2 0 26.40 + d ->• F M , T + p + n D 2 0 25.79 + 1 6 0 -r u^r + 1 5 0 + n + 7 D 2 0 46.83 F M > T + 1 6 0 -» F ^ T + 1 5 0 + n + 7 D 2 0 46.87 + 1 60->- ^,T + 1 5 N + p + 7 D 2 0 46.80 + 1 6 0 -r Vfi,r + 1 5 N + p + 7 D 2 0 46.83 ^ , r + 1 6 0 - > ^ , T + 1 5 0 + n D 2 0 46.81 ^ V , T + 1 6 0 - > F „ , T + 1 5 0 + ra D 2 0 46.87 + 1 6 0 -> + 1 5 0 + n + 7 H 2 0 46.88 F M ) T + 1 6 0 -> F „ , T + 1 5 0 + n + 7 H 2 0 46.86 + 1 6 0 -)• i/„,T + 1 5 N + p + 7 H 2 0 46.89 + 1 6 0 -»• F M , T + 1 5 N + p + 7 H 2 0 46.85 Elastic Scattering: 15.45 7.16 0.8924 ve + e~ —> ^ e + e~ D 2 0 13.36 6.92 0.9022 F e + e~ —> F e + e~ D 2 0 15.55 5.18 0.8420 + e _ -» + e~ D 2 0 19.76 9.35 0.9119 * V , T + e~ ->• F M ) T + e~ D 2 0 19.70 8.82 0.9035 v e + e~ —>• ^ e + e~ H 2 0 13.37 6.97 0.9047 F e + e" —» F e 4- e~ H 2 0 15.61 5.25 0.8420 + e~ -> i / ^ , T + e" H 2 0 19.67 9.32 0.9126 ^ . r + e~ -»• F ^ ) T + e" H 2 0 19.74 8.82 0.9022 Total SNO i / e Neutrinos 18.12 13.78 0.1151 Total SNO F e Neutrinos 20.46 17.75 0.0217 Total SNO "V Neutrinos 26.40 9.09 0.9078 Total SNO D 2 0 Neutrinos 22.97 15.39 0.0014 Total SNO H 2 0 Neutrinos 19.99 17.27 0.0873 Total SNO Neutrinos 21.56 16.71 0.0617 Table 6.6: Average energy and angular distribution values for 50000 sampled neutrinos and their associated final state detectable particles in the Burrows et al. model with no energy threshold. Chapter 6. SNO Supernova Neutrino Signal 127 6.2.4 Comparison to Burrows et al. Published Results The the total neutrino energy as calculated by the SNO Supernova Monte Carlo is 2.90 x 10 5 3 ergs, which is identical to the expected result quoted by Burrows et al. [60]. The aver-age neutrino energies are also in excellent agreement with the published values. Table 6.7 summarizes the comparison of these values. Parameter Bur rows Value Th i s W o r k Value Eue,total Ejye,total E "Up",total EVftotal 0.587 x l O 5 3 0.518 x l O 5 3 1.79 x l O 5 3 2.90 x l O 5 3 0.587 x l O 5 3 0.518 x l O 5 3 1.795 x l O 5 3 2.900 x l O 5 3 (Eue) \ E - U S ) 9.9 MeV 11.6 MeV 15.4 MeV 9.894 MeV 11.620 MeV 15.334 MeV Table 6.7: Comparison of supernova source parameters determined using the SNO super-nova generator and Burrows et al. published values [60]. To characterize the SNO detector, Burrows et al. use 1 ktonne D 2 0 and 1.6 ktonne H 2 0 as the target volumes and also impose a 5 MeV detector threshold on all charged current and elastic scattering reactions. In order to compare to the published values, these parameters as well as the cross sections presented in [60] are used in the supernova generator. Table 6.8 shows neutrino counts comparing count values for reactions published by Burrows et al. [60] and count values calculated using the supernova generator with their parameters. There is very good agreement between the two, which indicates that the model has been implemented correctly in the generator. Chapter 6. SNO Supernova Neutrino Signal 128 Reac t ion Reac t ion Bur rows Th i s W o r k Reg ion Counts Counts Charged Current: D20/H20 151.21/335.70 151.27/335.12 Ve + P —* n + e + H 2 0 331 330.46 ue-\-d^p + p + e~ D 2 0 81.9 82.19 Ve + d —> n + n + e+ D 2 0 66.7 66.46 ue + 0 -> F + e~ D 2 0 1.17 1.18 F e + 0 ->• N+ e + D 2 0 1.44 1.44 i / e + 0 F + e~ H 2 0 2.11 2.10 F e + 0 -> N+ e+ H 2 0 2.59 2.56 Neutral Current: D20/ H20 27240/0.00 272.43/0.00 ve + d-*ve+p-\-n D 2 0 35.2 35.04 ve + d->Ve + p + n D 2 0 37.2 37.24 u^tr + d ->• i / M > T + p + n D 2 0 200 105.69 F M ) T + d -> F M > T + p + n D 2 0 94.46 Elastic Scattering: D20/ H20 7.78/U. 01 7.79/13.85 ve + e~ —» i>e + e~ D 2 0 4.35 4.35 F e + e~ —>• F e + e~ D 2 0 1.07 1.08 V»,T + e~ ->• z^,T + e" D 2 0 2.36 1.18 * V r + e - ->• F^ T + e - D 2 0 1.18 ve + e~ —> ve + e~ H 2 0 7.83 7.73 F e + e~ —» F e + e~ H 2 0 1.93 1.92 . *W + e" ->• ^M, T + e~ H 2 0 4.25 2.10 v^T + e~ -> F M i T + e~ H 2 0 2.10 Total SNO i / e Neutrinos 132.56 132.59 Total SNO F e Neutrinos 441.93 441.15 Total SNO ' V Neutrinos 206.61 206.71 Total SNO D 2 0 Neutrinos 431.39 431.49 Total SNO H 2 0 Neutrinos 349.71 348.97 Tota l S N O Neutr inos 781.10 780.46 Table 6.8: Comparison of neutrino counts for a supernova at 10 kpc calculated using the SNO supernova generator and values published by Burrows et al. [60]. The parameters used by the authors to simulate neutrino interactions in the SNO detector were used to calculate the values in the last column. Instead of specifying the number of neutrino counts for each individual reaction, Burrows et al. provide only the count sum for a certain type of interaction in some cases. Chapter 6. SNO Supernova Neutrino Signal 129 6.2.5 Bruenn Models As the model input data to the SNO supernova generator, supernova source flux values, equivalent to the flux defined by Equation 5.1, are provided for a discrete set of time and energy values [106]. 6.2.5.1 Bruenn 15 M 0 Mode l Before a detector energy threshold is applied, ~340 neutrino events are expected in the SNO detector in the first 3.5 s after core collapse begins for a supernova at 10 kpc according to the Bruenn 15 M 0 model. Of this total, 67.8% of the neutrinos in the supernova signal interact via charged current interactions, 26.4% via neutral current interactions and 5.8% through elastic scattering interactions. Almost half of the neutrinos interact in the D 2 0 volume, namely 46.8%, while 53.2% are present in the H 2 0 volume. 19.4% of the supernova neutrinos interacting in the SNO detector are ue neutrinos, 63.2% are Ve neutrinos and 17.4% are V ^ " neutrinos. Table 6.9 summarizes the number of supernova neutrinos expected in the SNO detector using the Bruenn 15 M 0 model for a supernova at 10 kpc. As with the two generic models considered so far, the number of counts expected due to H 2 0 molecules in the D 2 0 volume is considered to be negligible (0.07 counts for a supernova at 10 kpc or 0.021% of the total signal). Since this signal does not extend for the full expected duration, the fractions quoted above do not necessarily hold for the total burst signal. In particular, the 11 u^' signal is expected to accumulate more counts over time than the corresponding ve and Ve signals. As with the Burrows model, the relative contribution of the reactions involving oxygen is small in the Bruenn 15 M 0 model. In the first 3.5 s after the initiation of core collapse, 4 neutrino interactions are expected, which comprise 1.3% of the calculated signal. Chapter 6. SNO Supernova Neutrino Signal 130 Reaction Reaction v Counts v Counts Region (all time) (t < 0.5 s) Charged Current: D20/H20 63.59/16640 33.30/79.02 F e + p —> n 4- e + H 2 0 164.95 78.23 ve + d^rP + p + e~ D 2 0 36.95 21.76 Ve + d-^n + n + e+ D 2 0 25.88 11.12 ve 4- 0 -r F 4- e~ D 2 0 0.36 0.24 F e + 0 - 4 N+ e + D 2 0 0.40 0.18 i / e + 0 - 4 F + e~ H 2 0 0.69 0.45 F e 4- 0 -» N+ e + H 2 0 0.76 0.34 Neutral Current: D20/ H20 88.41/1.04 39.56/0.40 ve-rd^rve+p + n D 2 0 15.80 9.31 Ve + d^rVe+p + n D 2 0 17.84 7.72 y^r + d - 4 + ? 4 n D 2 0 28.74 11.80 * V T + d - 4 F M ) r 4- p 4- n D 2 0 24.94 10.32 + 1 6 0 - 4 + 1 5 0 4 n 4 7 D 2 0 0.06 0.02 F^, T 4 - 1 6 0 - 4 F „ , T 4 1 5 0 + n 4 7 D 2 0 0.06 0.02 + 1 6 0 + 1 5 N 4 p 4 7 D 2 0 0.22 0.08 Vfi,r + 1 6 0 -> F M ) T 4- 1 5 N + p + 7 D 2 0 0.22 0.09 + 1 6 0 4 v + l s O + n D 2 0 0.27 0.10 F „ , T 4 - 1 6 0 - > v + 1 5 0 + n D 2 0 0.26 0.10 + 1 6 0 - > v + 1 5 ° + n + T H 2 0 0.11 0.04 + 1 6 0 -r F M , T 4 - 1 5 0 4- n + 7 H 2 0 0.11 0.04 ^ M , r + 1 6 0 ^ v + 1 5 N + P + 7 H 2 0 0.41 0.16 F M ) T 4 - 1 6 0 - > F / i ) T 4 - 1 5 N 4 - p 4 - 7 H 2 0 0.41 0.16 Elastic Scattering: D20/ H20 6.87/12.92 3.68/6.94 ve + e~ —> ve + e~ D 2 0 4.19 2.45 F e 4- e - — » F e 4- e~ D 2 0 1.60 0.73 D 2 0 0.58 0.27 Z^.T + E _ ^M.T + E ~ D 2 0 0.50 0.23 ve 4- e~ —r ve 4- e~ H 2 0 7.88 4.62 F e 4- e~ —>• F e 4- e~ H 2 0 3.01 1.37 + e~ -> z^ > r 4- e~ H 2 0 1.09 0.51 + e~ -> F M ; T 4- e~ H 2 0 0.94 0.44 Total SNO i / c Neutrinos 65.87 38.83 Total SNO F e Neutrinos 214.44 99.69 Total SNO ' V Neutrinos 58.92 24.38 Total SNO D 2 0 Neutrinos 158.87 76.54 Total SNO H 2 0 Neutrinos 180.36 86.36 Total SNO Neutrinos 339.23 162.90 Table 6.9: Neutrino counts for a supernova at 10 kpc calculated for the Bruenn 15 M 0 model using the SNO supernova generator with no detector energy threshold. Chapter 6. SNO Supernova Neutrino Signal 131 Reaction Reaction v Counts v Counts Region (all time) (t < 0.5 s) Charged Current: D20/H20 146.43/318.22 95.94/212.84 Ve + p —> n + e+ H 2 0 311.06 209.09 ue + d->p + p + e~ D 2 0 88.65 59.07 Ve + d—>n-hn + e+ D 2 0 53.99 34.89 ue + 0 -> F + e~ D 2 0 2.01 1.05 Ve + 0 ->• N+ e + D 2 0 1.78 0.93 ue + 0 -> F + e~ H 2 0 3.80 1.99 I 7 E + 0 -)• N+ e + H 2 0 3.36 1.76 Neutral Current: D20/ H20 148.12/2.97 104.75/1.77 ve + d—>ve+p + n D 2 0 36.68 25.62 ~Pe + d—>Ve+p + n D 2 0 36.00 23.56 v^T + d -> i / M f T + p + n D 2 0 39.02 28.88 F ^ > r + d F ^ ) T + p + n D 2 0 33.26 24.83 V^T + 1 6 0 -)• u^r + 1 5 0 + n + 7 D 2 0 0.17 0.10 + 1 6 0 -> F P > T + 1 5 0 + n + 7 D 2 0 0.17 0.10 + 1 6 0 - ) - ^ , T + 1 5 N + p - t - 7 D 2 0 0.63 0.37 v^r + 1 6 0 -» F M i T + 1 5 N + p + 7 D 2 0 0.64 0.38 ^ , r + 160-> i / M l T + 1 5 0 + n D 2 0 0.79 0.46 ^ , r + 1 6 0 - 4 I 7 M ) T + 1 5 0 + n D 2 0 0.76 0.45 ",*,T + 1 6 0 ^ , T + 1 5 0 + n + 7 H 2 0 0.31 0.18 + 1 6 0 -> F „ , T + 1 5 0 + n + 7 H 2 0 0.31 0.18 + 1 6 0 -> i ^ , T + 1 5 N + p + 7 H 2 0 1.19 0.70 + 1 6 0 -> F M ( T + 1 5 N + p + 7 H 2 0 1.22 0.71 Elastic Scattering: D20/H20 10.97/20.67 8.24/15.53 ue + e~ —> i / e + e~ D 2 0 7.05 5.32 I 7 E + e~ —>• F e + e~ D 2 0 2.58 1.85 + e~ ->• u^r + e~ D 2 0 0.72 0.57 Vp,T + e~ -)• V^r + e~ D 2 0 0.62 0.50 z^ e + e~ —>• i>e + e - H 2 0 13.28 10.03 77 E + e~ —>• Ve + e~ H 2 0 4.86 3.49 "us + e~ -> + e~ H 2 0 1.36 1.08 *VT + e~ -> + e~ H 2 0 1.17 0.93 Total SNO i / e Neutrinos 151.47 103.08 Total SNO Ve Neutrinos 413.63 275.57 Total SNO ' V Neutrinos 82.28 60.42 Total SNO D 2 0 Neutrinos 305.52 208.93 Total SNO H 2 0 Neutrinos 341.86 230.14 Total SNO Neutrinos 647.38 439.07 Table 6.10: Neutrino counts for a supernova at 10 kpc calculated for the Bruenn 25 M 0 model using the SNO supernova generator with no detector energy threshold. Chapter 6. SNO Supernova Neutrino Signal 132 6.2.5.2 Bruenn 25 M 0 Mode l Before a detector energy threshold is applied, ~650 neutrino events are expected in the SNO detector in the first 1 s after the start of core collapse for a supernova at 10 kpc according to the Bruenn 25 M 0 model. Of this total, 71.8% of the neutrinos in the supernova signal interact via charged current interactions, 23.3% via neutral current interactions and 4.9% through elastic scattering interactions. Almost half of the neutrinos interact in the D 2 0 volume, namely 47.2%, while 52.8% are present in the H 2 0 volume. 23.4% of the supernova neutrinos interacting in the SNO detector are ve neutrinos, 63.9% are Ve neutrinos and 12.7% are V M " neutrinos. Table 6.10 summarizes the number of supernova neutrinos expected in the SNO detector using the Bruenn 25 M 0 model for a supernova at 10 kpc. As with the Beacom and Vogel model, the number of counts expected due to H 2 0 molecules in the D 2 0 volume is considered to be negligible (0.14 counts for a supernova at 10 kpc or 0.022% of the total signal). The higher energies in the Bruenn 25 M 0 model mean that reactions involving oxygen will contribute more neutrino interactions to the overall total. Before the onset of black hole formation at 1 s after core collapse, a total of 17 interactions is expected, which constitutes 2.6% of the entire signal. This is still a much smaller contribution than is predicted in the Beacom and Vogel model. 6.2.6 Liebendorfer Model As the model input data to the SNO supernova generator, supernova source flux values, equivalent to the flux defined by Equation 5.1, are provided for a discrete set of time and energy values [107]. Before a detector energy threshold is applied, ~320 neutrino events are expected in the SNO detector in the first 590 ms from the start of core collapse for a supernova at 10 kpc according to the Liebendorfer 13 M 0 model. Of this total, 61.3% of the neutrinos Chapter 6. SNO Supernova Neutrino Signal 133 Reac t ion Reac t ion v Counts Reg ion (all t ime) Charged Current: D20/H20 67.34/129.21 Ve + p —> n + e + H 2 0 120.84 ve + d-+p + p + e~ D 2 0 40.49 F e + d—»n + n + e + D 2 0 22.42 ue + 0 ->• F + e~ D 2 0 2.65 Ve + 0 -» N+ e+ D 2 0 1.78 i / e + 0 -> F + e - H 2 0 5.01 F e + 0 ->• N+ e + H 2 0 3.36 Neutral Current: D20/H20 96.39/14.38 ve + d-+ve+p + n D 2 0 17.59 Ve + d—7~Pe-rp + n D 2 0 14.74 Vfj.,T + d-^ufi)T+p + n D 2 0 26.42 *VT + d ->• V^T + p + n D 2 0 22.72 "H,T + 1 6 0 -»• + 1 5 0 + n + 7 D 2 0 0.78 zVr + 1 6 0 -> V^T + 1 5 0 + n + 7 D 2 0 0.78 + 1 6 0 -»• + 1 5 N + p + 7 D 2 0 2.99 F M > T + 1 6 0 -> I7M)T + 1 5 N + p + 7 D 2 0 3.04 ^ , T + 1 6 0 - > ^ , T + 1 5 0 + n D 2 0 3.73 FM,T + 1 6 0 ^ F ^ + ^ O + n D 2 0 3.60 + 1 6 0 -r + 1 5 0 + n + 7 H 2 0 1.48 + 1 6 0 -+ F M ) T + 1 5 0 + n + 7 H 2 0 1.48 ^ , r + 1 6 0 - ^ fV,r + 1 5 N + p + 7 H 2 0 5.66 + 1 6 0 -> F„ir + 1 5 N + p + 7 H 2 0 5.76 Elastic Scattering: D20/H20 4.57/8.61 ve + e~ —> ve + e~ D 2 0 2.91 F e + e~ -4i7 e + e~ D 2 0 0.92 + e~ - 4 i / ^ ) T + e' D 2 0 0.40 + e~ -> F / i ,T + e" D 2 0 0.34 i>e + e~ -» i / e + e~ H 2 0 5.49 Ve + e~ —r ue + e~ H 2 0 1.73 V(I,T + e~ -> fM i T + e~ H 2 0 0.75 ' ' / i . T + e~ -» F M ) T + e" H 2 0 0.64 Total SNO i / e Neutrinos 74.14 Total SNO Ve Neutrinos 165.79 Total SNO ' V Neutrinos 80.57 Total SNO D 2 0 Neutrinos 168.30 Total SNO H 2 0 Neutrinos 152.20 To ta l S N O Neutr inos 320.50 Table 6.11: Neutrino counts for a supernova at 10 kpc calculated for the Liebendorfer 13 M 0 model using the SNO supernova generator with no detector energy threshold. Chapter 6. SNO Supernova Neutrino Signal 134 in the supernova signal interact via charged current interactions, 34.6% via neutral current interactions and 4.1% through elastic scattering interactions. The majority of neutrinos interact in the D 2 0 volume, namely 52.5%, while 47.5% are present in the H 2 0 volume. 23.1% of the supernova neutrinos interacting in the SNO detector are ve neutrinos, 51.7% are ve neutrinos and 25.1% are "z/^" neutrinos. Table 6.11 summarizes the number of supernova neutrinos expected in the SNO detector using the Liebendorfer 13 M 0 model for a supernova at 10 kpc. As with the other models, the number of counts expected due to H 2 0 molecules in the D 2 0 volume is considered to be negligible (0.05 counts for a supernova at 10 kpc or 0.016% of the total signal). In their model calculation, Liebendorfer et al. predict relatively high neutrino tem-peratures, which results in a high number of interactions involving oxygen. In the first 590 ms from collapse, results using the Liebendorfer model show 42.1 neutrino interactions or 13.1% of the total signal. Over the same time, results from the Beacom and Vogel model indicate 12 neutrino interactions or 7.7% of the total signal at 500 ms after core bounce. 6.2.7 Neutrino Interaction Summary It is useful to compare the neutrino interaction results discussed in the previous section for the various models. The neutrino interactions that constitute the prompt signal allow for a study of the neutronization peak. Table 6.12 presents the number of neutrino interactions in the first 10 ms after core bounce for a supernova at 10 kpc. In all models except the Beacom and Vogel model, there is a clear indication of ue neutrinos resulting from electron capture reactions in the core of the proto-neutron star. In those models that do contain signal structure information, over 90% of the prompt signal is due to ve neutrinos, with the model resulting in a black hole having the highest fraction at almost 97%. The actual number of prompt electron neutrino interactions varies from 15 in the Burrows model to between 5 and 7 for the detailed model calculations. Results from all models indicate Chapter 6. SNO Supernova Neutrino Signal 135 SN Signal Beacom Burrows Bruenn Liebendorfer Component Model Model Models Model (t < 10 ms) 15 M 0 25 M 0 13 M 0 Neutrino: ve 0.03 14.77 6.27 5.28 7.41 ve 0.11 0.93 0.03 0.03 0.06 u n 0.10 0.70 0.22 0.15 0.50 Region: D 2 0 region 0.14 14.00 5.60 4.62 6.94 H 2 0 region 0.10 2.40 0.92 0.84 1.03 Interaction: charged current 0.12 9.57 3.57 2.94 4.45 neutral current 0.11 4.45 1.67 1.33 2.29 elastic scattering 0.01 2.38 1.28 1.19 1.23 Total Signal: 0.24 16.40 6.52 5.46 7.97 —> ue fraction 12.5% 90.1% 92.8% 96.7% 93.0% Table 6.12: Comparison of the prompt signal between supernova models at 10 kpc for time t < 10 ms from core bounce. In all models where the neutronization peak is included, over 90% of the prompt signal is due to ue neutrinos. that the majority of the prompt signal will be due to the ue charged current reaction ve + d-^p + p + e~ in the heavy water region. It is difficult to compare the total signals from all models because some models only provide results for limited times. However, since all models extend in time to 500 ms, results to that point are compared in Table 6.13. Results show that the Bruenn 25 M 0 model produces the highest number of interactions. Similar values are calculated using the Liebendorfer et al. and Burrows et al. models. The Bruenn 15 M 0 model yields about half the number of interactions compared to the Liebendorfer model. Finally, the simple model of Beacom and Vogel predicts the lowest number of interactions at 500 ms after core bounce. It is also useful to compare the contribution to the supernova signal from reactions Chapter 6. SNO Supernova Neutrino Signal 136 SN Signal Beacom Burrows Bruenn Liebendorfer Component Model Model Models Model (t < 500 ms) 15 M 0 25 M 0 13 M 0 Neutrino: ve 18.73 80.01 38.83 103.08 74.14 Ve 77.33 216.28 99.69 275.57 165.79 u » V\i 66.86 86.78 24.38 60.42 80.57 Region: D2O region 95.53 203.07 76.54 208.93 168.30 H 2 0 region 67.39 180.00 86.36 230.14 152.20 Interaction: charged current 80.37 241.57 112.32 308.78 196.55 neutral current 76.71 121.78 39.96 106.52 110.77 elastic scattering 5.84 19.72 10.62 23.77 13.18 Total Signal: 67.39 383.07 162.90 439.07 320.50 Table 6.13: Comparison of the total signal between supernova models at 10 kpc for time t < 500 ms from core bounce. with oxygen. The high energy threshold for these interactions means that they are very sensitive to the incoming neutrino energy. Fewer events due to reactions with oxygen are expected using models that employ relatively low neutrino temperatures. The numbers of neutrino interactions using oxygen as the target are compared in Table 6.14 for the five models discussed in the previous sections. As expected, the models of Liebendorfer and Beacom and Vogel, which have the highest neutrino temperatures, also have the largest contribution from oxygen reactions. Results from the models of Bruenn and Burrows show that for neutrinos with lower temperatures oxygen reactions contribute only a few percent to the total signal. For many of the studies that follow, only the two generic models are considered, there-fore a comparison of the full duration signals is in order. Both models have signals which Chapter 6. SNO Supernova Neutrino Signal 137 SN Signal Beacom Burrows Bruenn Liebendorfer Component Model Model Models Model (t < 500 ms) 15 M 0 25 M 0 13 M 0 Neutrino: Ve 0.40 1.77 0.69 3.04 7.66 Ve .1.39 2.49 0.52 2.69 5.14 u » M 10.68 3.44 0.81 3.63 29.30 Region: D 2 O region 6.06 3.22 0.83 3.84 19.35 H 2 0 region 6.41 4.48 1.19 5.52 22.75 Interaction: charged current 1.79 4.26 1.21 5.73 12.80 neutral current 10.68 3.44 0.81 3.63 29.30 elastic scattering 0.00 0.00 0.00 0.00 0.00 Total Signal: 12.47 7.70 2.02 9.36 42.10 -» O fraction 7.7% 2.0% 1.2% 2.1% 13.1% Table 6.14: Comparison of the signal due to reactions involving oxygen between supernova models at 10 kpc for time t < 500 ms from core bounce. last for tens of seconds, but the Beacom and Vogel model predicts many more neutral cur-rent events due to the higher neutrino temperatures used. On the other hand, the Burrows model produces a larger fraction of ue neutrinos, due in part to the neutronization signal. 6.3 Supernova Neutrino Interaction Rate In Section 6.2, the total number of neutrino interactions is determined by integrating Equa-tion 5.11 over both time and energy. If instead only the energy integration is performed, the resulting value is the number of neutrino interactions within the detector per unit time, or the interaction rate. This is not a "count" rate as such because SNO does not directly detect neutrinos but rather the detectable final state particles resulting from neutrino in-teractions. In some cases, more than one detectable particle is created for a given neutrino Chapter 6. SNO Supernova Neutrino Signal 138 S N Signal Beacom Bur rows Component M o d e l M o d e l Burst Duration: 0-20 s -0.01-50 s Neutrino: Ve 137.55 146.46 ve 568.08 431.60 "v " 491.05 204.07 Region: D 2 0 region 701.61 415.54 H 2 0 region 495.07 366.59 Interaction: charged current 590.40 472.25 neutral current 563.32 264.35 elastic scattering 42.96 45.53 Tota l Signal: 1196.69 782.13 —> O events 91.54 13.42 Table 6.15: Comparison of the full duration signals for the two generic supernova models at 10 kpc. interaction. 6.3.1 Beacom and Vogel Model There is very little structure to be seen in the interaction rates for the Beacom and Vogel model. The neutrino signal rises quickly to 400 Hz and then slowly falls off to 0 Hz 20 s later. Neutrino interaction rates highlighting various contributions to the signal for the Beacom and Vogel model are shown in Figure 6.1. 6.3.2 Burrows et al. Model Adding contributions from all of the reactions listed in Table 6.5, many of the characteristics of the generic supernova signal described in Section 5.3.4 are preserved in the neutrino interaction rate for a supernova at 10 kpc. The neutronization peak continues to be the Chapter 6. SNO Supernova Neutrino Signal 139 8 10 12 14 16 18 20 — 1 — i — 1 — r all regions D20 region H20 region ~i— 1 —i— '—r~ — all interactions -- charged current neutral current — elastic scattering 20 20 Time From Core Bounce (seconds) Figure 6.1: Neutrino interaction rate for a supernova at 10 kpc according to neutrino type in the SNO detector as a function of time using the model of Beacom and Vogel. Various components of the signal are shown including the contributions from different neutrinos, regions and interactions. Chapter 6. SNO Supernova Neutrino Signal 140 Figure 6.2: Neutrino interaction rate for a supernova at 10 kpc according to neutrino type in the SNO detector as a function of time using the model of Burrows et al. Chapter 6. SNO Supernova Neutrino Signal 141 2000 1500 1000 \-„ 500 c o •a o 2 o I 1 1 1 1 neutronization peak i l l 1 1 1 all regions D 2 0 region - H 2 0 region -— explosion -- / •>-<• \ /•' "A V -/ •• i i i *->.U \/-^^__^ -0.1 100 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 rrr 1 : i \ -1 \ - s \ - \ \ - '- x V , \ X . i 1 i 1 i 1 1 1 : ; " ~ cooling transparency ' i i , i v " . \ \ • \ * A " i , \ \ 10 20 30 Time From Core Bounce (seconds) 40 50 Figure 6.3: Neutrino interaction rate for a supernova at 10 kpc according to region type in the SNO detector as a function of time using the model of Burrows et al. Chapter 6. SNO Supernova Neutrino Signal 142 Figure 6.4: Neutrino interaction rate for a supernova at 10 kpc according to interaction type in the SNO detector as a function of time using the model of Burrows et al. Chapter 6. SNO Supernova Neutrino Signal 143 most dominant feature, and modulations due to ringing of the proto-neutron star mantle as well as the explosion are also clearly distinguishable. When considering the constituents of the neutrino interaction rate, further observations can be made. Figure 6.2 confirms that the neutronization peak is due to the large number of electron neutrinos interacting at the onset of the supernova signal, a sensitivity which is unique to the SNO detector. During the neutronization peak, the total count rate is expected to exceed 1 kHz on a millisecond time scale. Following the prompt peak, the ve signal falls off considerably, yet still remains significant, just below the level of the contribution. Due to the large number of neutrinos that interact via the Ve + p —> n + e+ charged current reaction, elec-tron antineutrinos are the most numerous. On the strength of that contribution, neutrino interaction rates in the light water are comparable to the signal resulting from reactions on deuterium in the heavy water region, as shown in Figure 6.3. Figure 6.4 demonstrates that charged current interactions make up the majority of the neutrino interaction signal, with a substantial contribution also coming from the neutral current reactions. There are relatively few neutrinos produced through elastic scattering reactions, which are important in determining the location of the supernova. 6.3.3 SNO Supernova Neutrino Energy Distribution Integrating Equation 5.11 over time yields the number of neutrino interactions in the detector per unit energy. Since the predictions regarding the neutrino energy for the different neutrino species varies from one supernova model to the other, it is useful to compare the neutrino energy distributions for two generic models. 6.3.3.1 Beacom and Vogel M o d e l As indicated in Table 5.2, the Beacom and Vogel model predicts high average energies for the F e and " i / ^ " neutrinos compared to other models. Since the cross section values increase with neutrino energy, relatively high numbers of interactions are expected for Chapter 6. SNO Supernova Neutrino Signal 144 these neutrino types. Furthermore, since the tails of the Fermi-Dirac supernova neutrino energy distributions extend to high energies (that is, they are not pinched as with the Burrows model), larger contributions to the observed signal from high energy neutrinos are expected. The energy distributions for neutrinos that interact in the SNO detector are shown in Figure 6.5. 6.3.3.2 Burrows et al. M o d e l The neutrino energies in the Burrows model differ from the high neutrino energies predicted by the Beacom and Vogel model. In particular, average energy values for the Ve and " i ^ " neutrinos are lower in the Burrows model, therefore the majority of the signal is shifted to lower energy values. Also, because the Burrows model uses Fermi-Dirac neutrino energies that are pinched, fewer neutrino interactions take place at higher energies. Figure 6.6 shows the distribution for neutrinos that interact in the SNO detector according to the Burrows model 1. 6.4 Modifications to the Neutrino Signal While this work does not consider the effects of neutrino mass on the supernova signal, there is mounting evidence [3],[4] that the neutrino mass is non-zero. Two important consequences of non-zero neutrino mass for the supernova neutrino signal include smearing effects due to time delay and flavour mixing through neutrino oscillations. A few qualitative comments regarding these aspects are included below. 6.4.1 Time Delay As discussed in Section 3.4.2.1, massive neutrinos experience an energy-dependent time delay that affects the observed neutrino signal. Neutrinos with greater masses experience 'Note that coarser integration steps compared to those mentioned in Section 6.2.3 are used for this analysis to limit the computation time. Chapter 6. SNO Supernova Neutrino Signal 145 c o '43 O 2 3 c o .c I 40 30 20 10 0 150 150 ' I ' I ' 1 • 1 i i i all interactions charged current / \ — / ' N \ neutral current / ' v \ /' % elastic scattering - i 1— . i 25 50 75 100 Neutrino Energy (MeV) 125 150 Figure 6 . 5 : Neutrino counts per unit energy as a function of time for a supernova at 1 0 kpc in the SNO detector using the model of Beacom and Vogel. Various contributions are highlighted including neutrino type, region type and interaction type. Chapter 6. SNO Supernova Neutrino Signal 146 Figure 6.6: Neutrino counts per unit energy as a function of time for a supernova at 10 kpc in the SNO detector using the model of Burrows. Various contributions are highlighted including neutrino type, region type and interaction type. Chapter 6. SNO Supernova Neutrino Signal 147 longer time delays, while the time delay is decreased for neutrinos with higher energy. For example, Figure 6.7 shows the expected time delay for neutrinos that interact in the SNO detector according to the Burrows et al. supernova model. Neutrino masses of order 1 eV/c 2 give rise to average time delays of milliseconds for a supernova at 10 kpc. 0.1 1 10 100 Neutrino Mass (eV/c ) Figure 6.7: Energy-dependent time delay as a function of neutrino mass for a supernova at 10 kpc according to the Burrows et al. model. In each of the cases specified, the average energy of neutrinos that interact in the SNO detector is used. For a given neutrino mass, the "I/JJ" neutrinos have the shortest time delay due to their higher average energy. In terms of the observed neutrino signal, the time delay serves to broaden the time distribution of events, as indicated in the study by Burrows et al. [60]. Even though the current upper limit on the mass of the electron neutrino is relatively small (mue < 3 eV/c 2 ) , a neutrino mass of that order of magnitude may still significantly affect the Chapter 6. SNO Supernova Neutrino Signal 148 prompt neutronization signal. 6.4.2 Neutrino Oscillations Neutrinos of all flavours are produced during the collapse of a massive star, and some of these neutrinos may transform into other neutrino flavours through either vacuum oscilla-tion or matter-enhanced (MSW) neutrino oscillation. In either case, the partial or total mixing of neutrino flavours is expected to alter the observed neutrino signal. 6.4.2.1 Vacuum Oscillations Neutrinos of all types are able to participate in vacuum oscillations through z/e-f-> u^r, Fe-f-> F M ) T transitions. Vacuum oscillations do not take place in the high density regions within the supernova and within the Earth, but in the low density region of space while en route to the Earth. Even though both neutrinos and antineutrinos participate in vacuum oscillations, a study performed by Burrows et al. [108] indicates that the observed neutrino signal is only slightly enhanced by these oscillations even at maximal mixing. 6.4.2.2 M S W Oscillations Unlike vacuum oscillations, only certain transitions are available in matter-enhanced M S W neutrino oscillations. Assuming that the vacuum neutrino masses obey the standard mass hierarchy [vnyT > my^ > mue), M S W oscillations are not expected to affect antiparticles such as Ve neutrinos [109], which constitute the bulk of the detected supernova neutrino signal. Therefore, only the matter-enhanced v^T transformations are possible. Neu-trinos produced in the dense core of a collapsing star traverse two resonance layers where flavour conversions are possible. The density of these resonance layers corresponds to the range of allowed atmospheric and solar neutrino M S W A m 2 values. According to Dighe and Smirnov [110], the layer at higher densities (H resonance) corresponds to the larger Chapter 6. SNO Supernova Neutrino Signal 149 mass difference ( A m 2 « 10~3 eV 2 / c 4 ) associated with the atmospheric neutrino mixing parameters and is approximately pH ~ 10 3-10 4 g/cm 3 . The layer at lower densities (L resonance) is characterized by the smaller mass difference ( A m 2 « 1 0 - 5 - 1 0 - 6 e V 2 / c 4 ) in-dicated by solar neutrino MSW investigations, and Dighe and Smirnov estimate that the density of that layer is on the order of pL ~ 5-30 g/cm 3 . Flavour mixing between ve<r> vr is expected to be possible in the high density resonance layer, while ve<-> fM transitions are expected to be possible in the low density resonance layer, as illustrated in Figure 6.8. Since these densities are too low to be found in the central core, flavour transitions are not expected to influence the dynamics of the supernova collapse or the cooling of the core. Matter enhanced oscillations do not occur in the intervening space between the outer envelope of the supernova and the Earth. Earth matter mixing effects are also considered by Dighe and Smirnov [110]. supernova. core r decreasing density, p Figure 6.8: MSW matter neutrino oscillations in the high- and low-density resonance layers of a supernova. The density layers correspond to the allowed atmospheric and solar neutrino MSW A m 2 regimes. Chapter 6. SNO Supernova Neutrino Signal 150 The most significant effect on the supernova neutrinos that arrive at the Earth concerns the ve neutrino signal2. Electron neutrinos are expected to acquire higher energies as a result of mixing with muon and tau neutrinos in the outer layers of the supernova. Therefore, a significant enhancement is predicted [108] for ve signal because the reaction cross sections increase with neutrino energy. In particular, a substantial increase in the number of events produced via interactions involving oxygen targets is expected due to the high energy thresholds for those reactions. At the same time however, the prompt ue neutronization peak becomes less prominent as supernova neutrinos undergo ve<^ u^T flavour mixing. As well, the " i ^ " signal decreases as low-energy ve neutrinos are converted to muon and tau neutrinos. Finally, flavour mixing tends to dilute the effects due to the increased transit time of massive neutrinos. The ve signal is energized at the expense of the "z^" neutrinos, and as a result more electron neutrinos are observed compared with muon and tau neutrinos due to the energy scaling of the cross section. While the time delay increases for lower energy uUfj," neutrinos, fewer of these interactions are detected relative to the more energetic (and less time delayed) electron neutrinos. 2 Muon and tau neutrinos are expected to have identical time and energy spectra because they participate in the same interactions. Therefore evidence of vT flavour mixing is not observable. Chapter 7 SNO Supernova Observed Event Signal In the previous section, neutrino interactions in the SNO detector were studied. The detected signal from S N O M A N simulations is discussed in the sections that follow, in which a detector hardware threshold of NHIT = 16 PMTs is used in all cases. Quantities used to characterize the observed signal include detected counts, time, energy, event position and event direction. While particles from reactions involving oxygen are not simulated in the detector, estimates of the signal contribution from those channels are provided. A detailed discussion of the analysis concerning this estimation can be found in Appendix C. 7.1 SNO Observed Supernova Counts The number of observed counts depends on the particular running phase of the detector. Over its lifetime, the SNO detector will have three separate configurations: pure D 2 0 , salt and the neutral current detectors (NCDs). During each of these running phases, the SNO detector will have different sensitivities to supernova neutrinos, which are discussed in the sections below in terms of two generic supernova models. It should be noted that count values for the N C D phase are not simulated but are calculated using the detection efficiency, t = 0.369 N C D + 0.177 D 2 0 [69]. The reduction in Cerenkov light collection efficiency that is expected while the neutral current detectors are in place is not taken into account. This absorption is estimated to be 15% [69]. 151 Chapter 7. SNO Supernova Observed Event Signal 152 7.1.1 Beacom and Vogel Model In order to investigate the SNO detection efficiencies, neutrinos from two independent sets of 100 supernovae are simulated. Therefore each data set using the Beacom and Vogel model involves simulating 126116 final state detectable particles from supernova neutrinos in the SNO detector. During the pure D 2 0 phase, 66.5% of the total number of possible final state particles are detected. The detection efficiency is much higher for the salt phase, where 90.6% of the particles are detected, and using the neutral current detectors in the heavy-water region, 75.0% of the particles are detected. According to the Monte Carlo results, the neutron detection efficiency is 37.9% in pure D 2 0 for supernova events above the hardware threshold and 85.6% in salt. An additional 75-85 events are expected above the detector hardware energy threshold from reactions involving oxygen using the Beacom and Vogel model. The majority of these events are due to electrons/positrons and gamma rays. During all modes of operation, it is estimated that 13 electron/positron events and 52 7-ray events would be detected above the hardware threshold. In the initial running mode with pure D 2 0 , a further 9 neutron events are expected. While operating with salt in the detector, 20 neutron events are expected and with NCDs in place 13 neutron events are expected. The contribution of events detected above the hardware threshold from oxygen events is between 7-8% of the total signal. Further details of this analysis are available in Appendix C. Besides the 410 positrons produced via the Ve + p —>• n + e+ reaction and the 20 elec-trons produced through elastic scattering, 8 e± events and 33 7-ray events are expected from reactions involving oxygen. Including all of these contributions, electron antineutrinos are expected to constitute 88% of the H 2 0 signal above the detector hardware threshold of 16 PMTs according to the Beacom and Vogel model. Using this information, a large number of the electron antineutrino events can be isolated in the SNO detector volume. Requiring at least 16 PMTs in coincidence imposes an energy threshold on the observed Chapter 7. SNO Supernova Observed Event Signal 153 Reaction Reaction SNO Counts Region (all time D 2 0 Salt NCDs Charged Current: total 623.33 696.96 649.42 Ve + p —>• n + e+ H 2 0 409.71 409.71 409.71 ve-r-d^-p-rP + e~ D 2 0 77.74 77.74 77.74 Ve + d—7n + n + e+ D 2 0 135.88 209.51 161.97 Neutral Current: total 182.74 413.80 264.78 Ve + d-^rVe+p + n D 2 0 12.83 29.41 18.79 Vg + d-^Ve+p + n D 2 0 19.43 43.59 27.81 * V , T + d -r v^T + P + n D 2 0 83.14 188.54 120.78 v~ti,T + d ->• V^T + p + n D 2 0 67.34 152.26 97.40 Elastic Scattering: total 32.21 32.21 32.21 ye + e~ —r ue + e~ D 2 0 5.66 5.66 5.66 Ve + e~ —>• ve + e~ D 2 0 2.18 2.18 2.18 "n,r + e~ -> v^r + e~ D 2 0 2.13 2.13 2.13 F M ) T + e~ ->• 17,,^  + e - D 2 0 1.84 1.84 1.84 z>-e + e~ —>• z>"e + e~ H 2 0 9.64 9.64 9.64 Ve + e~ —> Ve + e~ H 2 0 3.68 3.68 3.68 H 2 0 3.78 3.78 3.78 H 2 0 3.30 3.30 3.30 Total SNO zve Events 105.87 122.45 111.83 Total SNO F e Events 570.88 668.67 605.35 Total SNO ' V ' Events 161.53 351.85 229.23 Total SNO D 2 0 Events 408.17 712.86 516.30 Total SNO H 2 0 Events 430.11 430.11 430.11 Total SNO e± Events 596.44 596.44 596.44 Total SNO n Events 242.91 548.48 349.97 Total SNO Events 838.28 1142.97 946.41 Total SNO Events (with O) 912.24 1228.37 1024.67 Table 7.1: SNO supernova detected particle counts above NHIT = 16 PMTs using the Beacom and Vogel model for a supernova at 10 kpc. Two independent data sets with 100 supernovae at 10 kpc are used to calculate these count values. A n additional ~ 7 5 - 8 5 events above the hardware threshold are expected from reactions involving oxygen. signal. In the case of the elastic scattering events, this means that the angular distribution is more forward peaked than the signal presented in Section 6.2 before the hardware energy Chapter 7. SNO Supernova Observed Event Signal 154 threshold is applied. The energy and angular distribution properties of the final state electron and positron signals are summarized in Table 7.2. Since the detection of electrons and positrons is not affected by the addition of salt, only one set of values is necessary to describe the detector response. Reac t ion Reac t ion ( N H I T e ) (cos 0 e ) Reg ion ( P M T s ) Charged Current: Ve + p —> n 4- e + H 2 0 127 0.0295 ve + d->p + p + e~ D 2 0 136 - 0 . 1 2 1 0 Ve + d—>n + n + e+ D 2 0 177 - 0 . 0 6 2 4 Elastic Scattering: ue + e~ —> ue + e~~ D 2 0 74 0.9615 Ve + e" —> Ve + e~ D 2 0 72 0.9442 "H,T + e~ ->• *V,T + e~ D 2 0 135 0.9668 Vfi,r + e" -)• V^T + e~ D 2 0 130 0.9642 ve + e~ —> ve + e~ H 2 0 58 0.9651 Ve + e~~ —> Ve + e~ H 2 0 57 0.9493 VH,T + e~ ->• fM l T + e" H 2 0 97 0.9697 vfi,r + e~ -)• V^r + e~ H 2 0 93 0.9676 Table 7.2: . Average NHIT. and angular distribution values for final state elec-trons/positrons simulated in the SNO detector above the detector hardware threshold of 16 PMTs according to the model of Beacom and Vogel. 7.1.2 Burrows et al. Model As with the Beacom and Vogel model, two independent data sets using neutrinos from 100 supernovae are used to simulate the detection signal. The final state count values for the reactions used in the simulation are presented in Table 7.3, where the count values have been scaled down by a factor of 100 to reflect the counts of a single supernova a 10 kpc. Of the total 87487 final state detectable particles from supernova neutrinos simulated in the SNO detector, 70.9% are detected during the pure D 2 0 phase, 90.9% during the salt phase and 78.1% during the N C D phase. According to the Monte Carlo results, the neutron Chapter 7. SNO Supernova Observed Event Signal 155 detection efficiency during the pure D 2 0 phase is 37.6% for supernova events above the hardware threshold and 85.6% for the salt phase. Both the Beacom and Vogel and the Burrows models predict that 32 elastic scattering events are observed above the detector hardware threshold for a supernova at 10 kpc. An additional 12-13 events are expected above the detector hardware threshold using the Burrows model from reactions involving oxygen. The majority of these events are due to electrons/positrons and gamma rays. During all modes of operation, it is estimated that 7 electron/positron events and 4 7-ray events would be detected above the hardware threshold. In the initial running mode with pure D 2 0 , a further 0.7 neutron events are expected. While operating with salt in the detector, 2 neutron events are expected and with NCDs in place 1 neutron event is expected. The contribution of events detected above the hardware threshold from oxygen events is of order 2% of the total signal. Further details of this analysis are available in Appendix C. In addition to the 320 positrons produced via the Ve + p —> n + e+ reaction and the 20 electrons produced through elastic scattering, 4 e± events and 3 7-ray events are expected from reactions involving oxygen. Including all of these contributions, electron antineutrinos are expected to constitute 93% of the H 2 0 signal above the detector hardware threshold of 16 PMTs according to the Burrows model. With this knowledge, a large number of the electron antineutrino events can be isolated in the SNO detector volume. As with the Beacom and Vogel model, requiring 16 P M T s means that the angular distribution for the elastic scattering events is more forward peaked than with no detector threshold applied. The energy and angular distribution properties of the final state electron and positron signals are summarized in Table 7.4. Since the detection of electron and positrons is not affected by the addition of salt or NCDs, only one set of values is necessary to describe the detector response. Chapter 7. SNO Supernova Observed Event Signal 156 Reaction Reaction SNO Counts Region (all time D 2 0 Salt NCDs Charged Current: total 492.31 543.07 510.89 Ve + p —)• n + e+ H 2 0 319.81 319.81 319.81 ue + d^p + p + e~ D 2 0 81.03 81.03 81.03 Ve + d^-n + n + e+ D 2 0 91.47 142.23 110.05 Neutral Current: total 96.59 220.30 140.88 Ve + d^Ve+p + n D 2 0 13.34 30.35 19.66 Ve + d^Ve+p + n D 2 0 13.66 30.84 19.66 u^r + d ->• u^r + p + n D 2 0 37.16 84.22 54.60 V/I,T + d -> V^T + p + n D 2 0 32.43 74.89 46.96 Elastic Scattering: total 31.76 31.76 31.76 ve + e~ —> ve + e~ D 2 0 6.50 6.50 6.50 Ve + e~ —> Ve + e~ D 2 0 2.01 2.01 2.01 V^T + e - -> u^r + e~ D 2 0 1.69 1.69 1.69 Vn,T + e~ -t V^T + e~ D 2 0 1.54 1.54 1.54 ve + e~^>-ve + e~ H 2 0 11.09 11.09 11.09 ue + e~ —> Ve + e~ H 2 0 3.25 3.25 3.25 v^r + e~ -> V(I,T + e~ H 2 0 3.16 3.16 3.16 vH,T + e~ -> F M ) T + e~ H 2 0 2.52 2.52 2.52 Total SNO ue Events 111.96 128.97 118.28 Total SNO F e Events 430.20 498.14 454.78 Total SNO ' V Events 78.50 168.02 110.47 Total SNO D 2 0 Events 280.83 455.30 343.70 Total SNO H 2 0 Events 339.83 339.83 339.83 Total SNO e± Events 484.69 484.69 484.69 Total SNO n Events 136.78 311.82 198.84 Total SNO Events 620.66 795.13 683.53 Total SNO Events (with O) 632.48 807.87 695.70 Table 7.3: SNO supernova detected particle counts above NHIT = 16 PMTs using Bur-rows' model for a supernova at 10 kpc. Two independent data sets with 100 supernovae at 10 kpc are used to calculate these count values. An additional ~12-13 events above the hardware threshold are expected from reactions involving oxygen. Chapter 7. SNO Supernova Observed Event Signal 157 Reac t ion Reac t ion ( N H I T e ) (cos 0e) Region ( P M T s ) Charged Current: Ve + p —7 n + e+ H 2 0 104 0.0116 ve + d^rp + p + e~ D 2 0 131 -0.1197 I7e + d—>n + n + e + D 2 0 142 -0.0759 Elastic Scattering: ve 4- e~ —r ve + e~ D 2 0 70 0.9611 Ve + e" —> Ve + e~ D 2 0 60 0.9410 y^r 4- e~ -4 u^T + e~ D 2 0 91 0.9608 * V r + e~ -4 v^r + e~ D 2 0 87 0.9583 ve + e~ —> ve + e~ H 2 0 55 0.9649 Ve + e~ —> Ve + e~ H 2 0 49 0.9464 + e~ v^T + e~ H 2 0 68 0.9645 v^r + e~ 17^ ^ + e~ H 2 0 66 0.9623 Table 7.4: Average NHIT and angular distribution values for final state elec-trons/positrons simulated in the SNO detector above the detector hardware threshold of NHIT = 16 PMTs according to the model of Burrows et al. 7.2 SNO Observed Supernova Counts at Various Dis-tances The number of events observed in the SNO detector will depend very much on the dis-tance to the collapsing star. Scaling the events from a nominal supernova at 10 kpc (see Table 7.3), SNO remains sensitive to bursts of neutrinos from as far away as ~100 kpc. Within our galaxy, SNO should expect to see on average at least 100 events from a super-nova burst, regardless of the neutron detection method being used. For a supernova located at the distance of 1987A, the SNO signal falls to only an average of 26 events during the pure D 2 0 operation phase and 31 events with salt. The Andromeda galaxy is comparable in mass to the Milky Way, but at a distance of approximately 790 kpc, SNO would expect to observe only 0.1 events. However, should the star Betelgeuse end its life in a Type Chapter 7. SNO Supernova Observed Event Signal 158 II supernova explosion, between 8 and 9 million events are expected above the hardware threshold in the SNO detector. Figure 7.1 indicates the number of events expected as a function of distance from the Earth, and summarizes the features discussed above. Notice that for the recent historical galactic supernovae, SNO would have measured a substantial signal in the range of 10000-20000 events. 10' 10° | 10s LU I o o Q) I 70' 103 1<f 101 10° l ' i -::: Betelgeuse i • 1 • i 1 1 1 1 1 ' 1 ' \ Lupi iS (1006) [Type la], Crab (1054) [Type II] — SNO counts pure D 2 0 j - . Tycho (1572) [Type lb?], SN1181 [Type II?] - - - SNO counts salt option '. : ; : Kepi er (1604) [Type ?], Cas A (-1680) [Type lb] _ : : Milky Way Centre _ • Nominal Supernova • : Milky Way Far Edge j _ : L M C "short" -: • SN1987A [Type II] j L M C "long" " : : SMC Near Edge ; SMC Far Edge : ; Andromeda : 890 kpc > I I : • ' , i 1 , , 1 i . i . i . 10 20 30 40 50 60 70 80 Distance of Supernova from Earth (kpc) 90 100 Figure 7.1: SNO supernova detected particle counts as a function of supernova distance from Earth. The dotted lines indicate the distance of a particular feature, and where they cross the plotted lines corresponds to the number of expected counts above the hardware threshold in the SNO detector expected. Another important consideration in determining the number of events to expect for a supernova burst in our galaxy is the spatial distribution of stars. Bahcall and Soneira [111] have constructed a detailed model for the disk and spheroid components of our galaxy. Chapter 7. SNO Supernova Observed Event Signal 159 Fitting tabulated values from this model [112], yields the distribution shown in Figure 7.2. The steepest part of the curve corresponds to the bulge near the centre of the galaxy. The centre of the steep slope of the curve corresponds to 8.4 kpc, which agrees roughly with the measured distance to the centre of the galaxy. The large number of stars in this region means that a larger weighting is placed on those distances. 1 | 1 1 1 1 ' 1 ' 1 ' L Distance From Earth (kpc) Figure 7.2: Fraction of Milky Way stars as a function of distance from the Sun according to the Bahcall and Soneira model of the galaxy [111]. Combining the 1/r2 flux information from Figure 7.1 and the weighting function from Figure 7.2, the number of detected events as a function of the fraction of galactic stars can be determined. Figure 7.3 shows that for a distance that includes 33.4% of the stars in the Milky Way, at least 1000 events would be expected during the pure D 2 0 phase. In the salt Chapter 7. SNO Supernova Observed Event Signal 160 running phase, the expectation of 1000 events would extend to a distance that included 43.5% of the stars. The median number of events expected for a supernova in the galaxy is 663 during the pure D 2 0 phase and 849 during the salt phase. The equivalent distance for the median number of events is 9.7 kpc (recall that the nominal distance is usually quoted as 10 kpc). Notice how practically all of the historical supernovae fall within the 5% of stars closest to us. The fraction of the galaxy visible to the naked-eye is severely limited by interstellar dust. 10' Tycho (1572) [Type lb?], SN1181 [Type II?] 105 Kepler (1604) [Type ?], Cas A (-1680) [Type lb] 0 0.2 0.4 0.6 0.8 1 Fraction of Milky Way Stars Figure 7.3: SNO supernova detected particle counts as a function of supernova distance from the Sun expressed as the fraction of Milky Way stars using the Bahcall and Soneira model of the galaxy [111] and the Burrows supernova model. Chapter 7. SNO Supernova Observed Event Signal 161 7.3 SNO Supernova Time Spectrum One of the key features that distinguishes a burst of supernova neutrinos from other events in the SNO detector is the time spectrum of events. In the generic models under consid-eration, the observed event signal is expected to have a sharp initial rise followed by a decaying count rate that remains distinguishable above background for many seconds. 7.3.1 Beacom and Vogel Model Almost 30% of the observed signal in the Beacom and Vogel model is expected in the first 1 s of the burst, which is rather low compared to other models. The observed signal count rate (without oxygen reactions) reaches a peak value of 300 Hz over millisecond time scales during the pure D 2 0 phase and then falls off to 10 Hz after 10 s. During salt running, the peak count rate reaches 400 Hz over millisecond time scales and falls off to 10 Hz in the same time as the pure D 2 0 signal. For instruments that integrate time over 1 s to compute the event rate, the peak count rate is 225 Hz for pure D 2 0 and 300 Hz for salt. 7.3.2 Burrows et al. Model In contrast to the Beacom and Vogel model, the Burrows model predicts that 60% of the signal will arrive in the first 1 s of the burst. Therefore, the count rates are higher at 800 Hz over millisecond time scales during the pure D 2 0 phase and 1000 Hz during the salt phase. For instruments that integrate time over 1 s to compute the event rate, the peak count rate is 375 Hz for pure D 2 0 and 450 Hz for salt. As with the Beacom and Vogel model, the count rate in both cases falls to 10 Hz after 10 s. Figures 7.4, 7.5, 7.6 and 7.7 show the various contributions to the time spectrum during the pure D 2 0 and salt running phases. Plots of the cumulative counts as a function of time are shown for both running phases in Figures 7.8 and 7.9. The detected particle count rate using only neutrinos from a single supernova at 10 kpc Chapter 7. SNO Supernova Observed Event Signal 162 1000 i § C s LU I 800h 600 400h 200Y Pure D20: Burst (369 particles) all neutrinos (59%) v e ( 19%) v, (70%) 0.4 0.5 0.6 0.7 Event Time (seconds) 0.8 0.9 Pure D20: Cooling (252 particles) all neutrinos (41%) v(, (16%) \/(69%) " v ^ " (15%) 20 25 30 35 Event Time (seconds) 40 45 50 I i *-c 3 c Uj 1200F~ tooor 800 j-600 T 400 7 200 r 0-Salt: Burst (471 particles) all neutrinos (59%) v e (17%) V, (64%) 0.1 0.2 0.3 0.4 0.5 0.6 Event Time (seconds) 0.7 0.8 100\- Salt: Cooling (323 particles) all neutrinos (41%) v c (15%) v|(61%) «V " (24%) 20 25 30 Event Time (seconds) 35 40 45 50 Figure 7.4: SNO supernova detected particle count rate above NHIT = 16 PMTs for the different neutrino types according to Burrows' model. The top two plots show the expected signal using only pure D 2 0 in the detector, while the bottom two plots show the signal with salt added to the D 2 0 volume. In both cases, 100 supernovae at 10 kpc are simulated, and the plots show the signal scaled down to 1 supernova at 10 kpc. Chapter 7. SNO Supernova Observed Event Signal 163 1000[ t 800\ C? 600\ c ^ 4001 | 200| UJ Pure D20; Burs/ (359 particles) all regions (59%) !>,<) region (46%) II,0 region " A * 7 ! / AV region (0%) 0.4 0.5 0.6 Event Time (seconds) I 1 c 2 Pure D20; Cooling (252 particles) all regions (41%) l),() region (44%) IIJO region (56%) AV region (0%) 20 25 30 Event Time (seconds) 35 40 45 Salt: Burst (471 particles) all regions (59%) l)2() region (57%) II 20 region (42%) AV region (0%) 0.4 0.5 0.6 Event Time (seconds) Salt: Cooling (323 particles) all regions (41%) 0 2 O region (56%) II 20 region (44%) AV region (0%) 10 15 20 25 30 Event Time (seconds) 35 40 45 50 50 Figure 7.5: SNO supernova detected particle count rate above NHIT = 16 PMTs accord-ing to Burrows' model for the different region types. The top two plots show the expected signal using only pure D 2 0 in the detector, while the bottom two plots show the signal with salt added to the D 2 0 volume. In both cases, 100 supernovae at 10 kpc are simulated, and the plots show the signal scaled down to 1 supernova at 10 kpc. Chapter 7. SNO Supernova Observed Event Signal 164 1000 i Si i C <s c s I Si c s Ul 800 200 Pure D20: Burst (369 particles) - '~. h 1 :; L r H n all interactions (59%) • '-, :L_rJ , - S r ^ " l H ; charge current (81 %) ;...! • I r neutral current (15%) T , elastic scattering (4%) r M i •" t i f i ' i i i 1 i . . . . r I - i - i . i - l . . . . , , . L . J . , . . . 1 . . . . 1 . . . . c 3 i 2 o o r • 1000 r 800 r 600 7 400-c § 200F-0.1 0.2 0.3 0.4 0.5 0.6 Event Time (seconds) 0.7 0.8 0.9 Pure D20: Cooling (252 particles) all interactions (41%) charge current (77%) neutral current (17%) elastic scattering (6%) 20 25 30 Event Time (seconds) 35 40 45 Salt: Burst (471 particles) all interactions (59%) charge current (70%) neutral current (26%) elastic scattering (4%) 50 0.1 0.2 0.3 0.4 0.5 0.6 Event Time (seconds) 0.7 0.8 0.9 Salt: Cooling (323 particles) all interactions (41%) charge current (66%) neutral current (29%) elastic scattering (5%) 2 & £ 2 20 25 30 Event Time (seconds) 35 40 45 50 Figure 7.6: SNO supernova detected particle count rate above NHIT = 16 PMTs ac-cording to Burrows' model for the different interaction types. The top two plots show the expected signal using only pure D 2 0 in the detector, while the bottom two plots show the signal with salt added to the D 2 0 volume. In both cases, 100 supernovae at 10 kpc are simulated, and the plots show the signal scaled down to 1 supernova at 10 kpc. Chapter 7. SNO Supernova Observed Event Signal 165 1000 800 s QC 600 O 400 o § 200 Pure D20; Burs/ (369 particles) r | i i 1 : | J L rH n n all particles (59%) • 1 ': l—i-1 h J'--I |-! H electrons/positrons (79%) " ''.. ! '.J-i J J neutrons (21%) •. . J , I . . . , 1 • • i . . . . i . . . . i . . . . 0.1 0.2 0.3 0.4 0.5 0.6 Event Time (seconds) 0.7 0.8 0.9 c cS 4M c UJ Pure D20: Cooling (252 particles) all particles (41%) electrons/positrons (77%) neutrons (23%) 20 25 30 35 Event Time (seconds) 40 45 50 1200 1000 & <0 800 QC | 600h P O 4001 C 2 200h Ul Salt: Burst (471 particles) all particles (59%) electrons/positrons (62%) neutrons (38%) 0.1 0.2 0.3 0.4 0.5 0.6 Event Time (seconds) Salt: Cooling (323 particles) all particles (41%) electrons/positrons (60% I neutrons (40%) 20 25 30 Event Time (seconds) 35 40 45 50 Figure 7.7: SNO supernova detected particle count rate above NHIT = 16 PMTs accord-ing to Burrows' model at 10 kpc for the different particle types. The top two plots show the expected signal using only pure D 2 0 in the detector, while the bottom two plots show the signal with salt added to the D 2 0 volume. In both cases, 100 supernovae at 10 kpc are simulated, and the plots show the signal scaled down to 1 supernova at 10 kpc. Chapter 7. SNO Supernova Observed Event Signal 166 400 300 vi | 100 3 <3 ts 0 I 1 I 1 I 1 I 1 I 1 I 1 I 1 1 1 1 1 1 1 Pure D20 all particles electrons/positrons neutrons -i 1 l ST.y 1 , 1 i 1 i 1 i 1 , 1 , 1 i 1 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10 20 30 Relative Event Time (seconds) 40 0.6 H 0.4 0.2 0 1 0.8 0.6 0.4 0.2 Figure 7.8: Cumulative SNO supernova detected particle count rate above the detector hardware threshold of 16 PMTs according to Burrows' model at 10 kpc for the different particle types during the pure D 2 0 phase. The top plot shows the accumulated counts in the first 1 second after core bounce, whereas the bottom plot shows the entire time range of the burst. On each graph, the total number of events is indicated on the left-hand y-axis, while the y-axis on the right-hand side denotes the count fraction of the total burst. is shown in Figure 7.10. Compared to the high-statistics data set that uses neutrinos from 100 supernovae, the underlying distribution is not as clear. However, even with the lower statistics, it is still possible to discern a slight enhancement in the initial signal due to the ue signal from neutronization in the collapsing core of the supernova. As well, the signal is clearly higher before the explosion at 550 ms than after the explosion. Therefore, it should be straightforward for SNO to observe this feature of the delayed supernova Chapter 7. SNO Supernova Observed Event Signal 167 Relative Event Time (seconds) Figure 7.9: Cumulative SNO supernova detected particle count rate above the detector hardware threshold of 16 PMTs according to Burrows' model at 10 kpc for the different particle types during the salt phase. The top plot shows the accumulated counts in the first 1 second after core bounce, whereas the bottom plot shows the entire time range of the burst. On each graph, the total number of events is indicated on the left-hand y-axis, while the y-axis on the right-hand side denotes the count fraction of the total burst. explosion mechanism. Structure in the signal that occurs on timescales of 100 ms, such as the pulsations that are included in the Burrows model, may be difficult to distinguish. 7.3.3 Prompt Signal In addition to the time evolution of the supernova signal, it is also useful to consider the detailed composition of the prompt signal. Information about the neutronization process Chapter 7. SNO Supernova Observed Event Signal 168 Pure D20: Burst (366 particles) all particles (58%) electrons/positrons (80%) neutrons (20%) 0.3 0.4 0.5 0.6 0.7 Event Time (seconds) 0.8 0.9 I cS 4M s <s c UJ 40 r 35 r 30 r 25 r 20\ 15 r 10\ 5-Pure D2Q: Cooling (270 particles) all particles (42%) electrons/positrons (73%) neutrons (27%) 10 15 20 25 30 35 40 45 Event Time (seconds) 50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Event Time (seconds) c 3 8 4M c UJ 50-_ 40 j-30 7 20 r 10-Salt: Cooling (339 particles) all particles (42%) electrons/positrons (58%) neutrons (42%) 10 15 20 25 30 35 40 45 Event Time (seconds) 50 Figure 7.10: SNO supernova detected particle count rate above NHIT = 16 PMTs ac-cording to Burrows' model for the different particle types using only neutrinos from a single supernova at 10 kpc. The top two plots show the expected signal using only pure D 2 0 in the detector, while the bottom two plots show the signal with salt added to the D 2 0 volume. Chapter 7. SNO Supernova Observed Event Signal 169 during core collapse may be contained in the events recorded in the first 100 ms of the burst. According to the Burrows model, 10-12 events from ue neutrino interactions are expected within 100 ms of the onset of the signal for a supernova at 10 kpc. Of the entire signal over that period, 92% of the events above the detector hardware threshold are due to reactions with electron neutrinos in the pure D 2 0 phase, whereas 90% of the events are due to reactions with electron neutrinos in the salt phase. In contrast, the Beacom and Vogel signal does not include any contribution due to the neutronization process and so acts as a baseline prediction. In the scenario where the supernova signal is not enhanced by contributions from the neutronization process, roughly 16% of the signal is due to ue neutrinos during the pure D 2 0 phase and 13% of the signal is due to ve neutrinos during the salt phase. The results for both models are summarized in Table 7.5. 7.4 SNO Supernova NHIT Spectrum The number of PMTs that receive light in a given event is referred to as the "NHIT" of the event, and is directly related to the energy of that event. Regardless of supernova model or whether the detector is being operated with pure D 2 0 or salt, there are two main features prominent in the NHIT spectrum: a peak at low NHIT values superimposed over a broad distribution. The peak at NHIT < 100 PMTs is due mainly to the neutron signal in the D 2 0 volume. The neutron capture signal in SNO does not preserve information about the energy of the parent neutrino, therefore the shape of the neutron peak is not expected to vary significantly between models. In the case of the pure D 2 0 signal, there are actually two peaks at low NHIT. The lowest energy peak is due to neutron capture on the proton in the heavy water molecule, while a second higher energy peak is due to capture on the deuteron. For the salt phase, the first low energy peak is not expected because of the high neutron capture efficiency on chlorine. Chapter 7. SNO Supernova Observed Event Signal 170 SN Signal Beacom Burrows Component Model Model (t < 100 ms) D 2 0 Salt D 2 0 Salt Neutrino: Ue 1.48 1.71 9.55 11.55 Ve 6.69 8.19 0.82 1.00 u n 0.85 3.76 0.07 0.32 Region: D2O region 3.42 8.06 8.84 11.27 H 2 0 region 5.59 5.59 1.58 1.58 A V region 0.01 0.01 0.02 0.02 Interaction: charged current 7.59 8.76 8.50 8.65 neutral current 0.92 4.39 0.38 2.67 elastic scattering 0.51 0.51 1.55 1.55 Particle: electron/positron 7.77 7.77 10.02 10.02 neutron 0.92 4.39 0.41 2.84 Total Signal: 9.02 13.66 10.43 12.86 —> ue fraction 16.4% 12.5% 91.6% 89.8% Table 7.5: Comparison of the signal for relative time t < 100 ms above the detector hardware threshold between two generic supernova models at 10 kpc. Cerenkov light from relativistic electrons and positrons comprise the broad distribution that extends to almost NHIT = 500. The peak of this distribution will vary between models depending on the neutrino temperatures used, and is mainly sensitive to the ue neutrino temperature. Neutral current reactions involving oxygen, which are sensitive to the energy of "1^ " neutrinos, are not included in the SNO detection simulations. However, the most useful signatures of these reactions are the 5-10 MeV 7 rays emitted in both the heavy-and light-water volumes. In terms of the NHIT spectrum, these 7 rays would contribute to Chapter 7. SNO Supernova Observed Event Signal 171 the signal in the NHIT range of 35-70 P M T s 1 , which is the same NHIT range spanned by the neutron peak during both the pure D 2 0 and salt running phases. The neutron NHIT spectrum is fairly well understood, so it is very likely that a significant 7-ray contribution from reactions involving oxygen would be measurable. 7.4.1 Beacom and Vogel Model The expected NHIT distributions using the Beacom and Vogel model are shown in two sets of plots. Figure 7.11 illustrates the characteristics of the NHIT signal for running during the pure D 2 0 phase, while Figure 7.12 shows the same signal during the salt phase. As predicted, the neutron contribution is clearly situated at NHIT < 100 PMTs . Comparing the low NHIT peak in the two figures clearly shows the neutron detection enhancement during the salt phase. The peak of the broad electron/positron distribution is roughly NHIT = 100 in the Beacom and Vogel model, and remains the same in both detector running phases. The bottom graph on both figures indicates the strong ue content of the high NHIT signal. 7.4.2 Burrows et al. Model Compared to the Beacom and Vogel model, the shape of the neutron peaks for the Burrows model in the pure D 2 0 and salt signals is similar. However, since the neutrino temperatures used in this model are lower than those used by Beacom and Vogel, the electron/positron NHIT spectrum will tend to lower values. The peak of the Burrows electron/positron NHIT spectrum is roughly NHIT ~ 80 PMTs, which is located lower than that of the Beacom and Vogel model. The SNO supernova detected particle NHIT distribution above NHIT = 16 PMTs is shown in Figures 7.13 and 7.14. Figure 7.13 describes various components of the signal expected during the pure D 2 0 running phase, while the corresponding plots for 'The correlation between 7-ray energy and NHIT is 1 MeV ~ 7 PMTs. Fewer PMTs are hit for gamma-ray events than for electron/positron events because some energy is lost during Compton scattering. Chapter 7. SNO Supernova Observed Event Signal 172 Pure D20 (839 particles) all particles e l ec t rons /pos i t rons (71 % ) n e u t r o n s ( 2 9 % ) 750 200 250 300 350 NHIT 400 450 500 10\-50 100 150 200 250 300 NHIT all interactions c h a r g e d c u r r e n t ( 74%) n e u t r a l c u r r e n t ( 22%) e las t ic s c a t t e r i n g ( 4 % ) J. 350 400 450 500 • all regions - . . . . D 7 0 r e g i o n ( 4 9 % ) f\ H ~ 0 r e g i o n ( 5 1 % ) - \\ / ' * \ . . . . A V r e g i o n (0%) • I > 1 V - T - ' - V * J ~ ~ 1 L. 1. 1 1 50 100 150 200 250 300 350 400 450 500 NHIT - all neutrinos - . . . . v e ( 1 3 % ) • v ( 6 8 % ) \ i \ " v ^ " ( 1 9 % ) -- • ~ ~ - ~ J . _ . . J . . 1 . 1 , 50 100 150 200 250 300 NHIT 350 400 450 500 Figure 7.11: SNO supernova detected particle NHIT distribution above NHIT = 16 PMTs for the pure D 2 0 phase according to the Beacom and Vogel model. In all cases, 100 supernovae at 10 kpc are simulated, and the plots show the signal scaled down to 1 supernova at 10 kpc. Chapter 7. SNO Supernova Observed Event Signal 173 Salt (1142 particles) all particles electrons/positrons (52%) neutrons (48%) 100 150 200 250 300 350 400 450 500 NHIT all interactions charged current (61 %) neutral current (36%) elastic scattering (3%) ± 100 150 200 250 300 350 400 450 500 NHIT all regions D20 region (62%) H20 region (38%) AV region (0%) ± 150 200 250 300 350 400 450 500 NHIT 1, 150 200 250 300 NHIT all neutrinos v„ (11%) vc (59%) " V ( 1"(31%) J_ 350 400 450 500 Figure 7.12: SNO supernova detected particle NHIT distribution above NHIT = 16 PMTs for the salt phase according to the Beacom and Vogel model. In all cases, 100 supernovae at 10 kpc are simulated, and the plots show the signal scaled down to 1 supernova at 10 kpc. Chapter 7. SNO Supernova Observed Event Signal 174 the salt phase are shown in Figure 7.14. In pure D 2 0 , 46% of the observed signal above the hardware threshold is in the D 2 0 volume, while the remaining 54% of the signal is detected in the H 2 0 region. With the enhanced neutron detection provided by salt, most of the signal, 57%, can be found in the heavy water volume, whereas 43% will be observed in the light water volume. 7.5 SNO Supernova Vertex Position Distribution The distribution of supernova event vertex positions for a supernova at 10 kpc detected during the pure D 2 0 phase is shown in Figure 7.15. In order to simplify the dimensions of the detector volume, the radius of the acrylic vessel, RAV, is used to normalize the radial position, R/RAV, where RAV = 600 cm. This quantity is then cubed, (R/RAV)3, SO that shells of equal volume are plotted. In the pure D 2 0 phase, the vertex position distribution is relatively even across the two detector volumes, with a dip in the number of counts around (R/RAV)3 = 1 due to the presence of the acrylic vessel. On average, there are 1.5 times as many counts per bin in the heavy-water region as compared to the light water region. The slight enhancement inside the AV becomes much more prominent when salt is added to the heavy-water region. Once again the distribution is roughly flat over the D 2 0 volume, but Figure 7.16 shows the number of counts per bin is approximately 2.5 times greater than the counts in the H 2 0 region. Compared to the Burrows model, the ratios of the counts in the two regions is approximately the same with the Beacom and Vogel model. For pure D 2 0 running, the count ratio is about 1.5, but for the salt phase, the ratio is even higher at around 2.7. 7.6 SNO Supernova Angular Distribution The direction of a particle in the SNO detector is defined by a quantity called the direction cosine. Using the momentum vector, p = pxi + pyj + pzk, the components of the direction Chapter 7. SNO Supernova Observed Event Signal 175 1 8 6 4 2 0 A Pure D20 (621 particles) all particles - electrons/positrons (78%) - neutrons (22%) -' 'i I I . I . I ^ - V + U ^ , I , I . I . 50 100 150 200 250 300 350 400 450 500 NHIT all interactions charged current (79%) neutral current (16%) elastic scattering (5%) I 50 100 150 200 250 300 350 400 450 500 NHIT 8 6 4 2 0 I 8 6 4 2 0 - all regions - D , 0 region (45%) - H ~ 0 region (55%) A V region (0%) '-•: *-">."i'.'~V. " . . . i - L -, 1 , 1 . 1 , f < A ^ * t * ^ t W _ _ L . _ . 1 . 1 , 1 , 50 100 150 200 250 300 350 400 450 500 NHIT - — all neutrinos vo(18%) v (69%) " V ( / ' (13%) '-1 , l , 1 . I . 50 100 150 200 250 300 350 400 450 500 NHIT Figure 7.13: SNO supernova detected particle NHIT distribution above NHIT = 16 PMTs for the pure D 2 0 phase according to Burrows' model. In all cases, 100 supernovae at 10 kpc are simulated, and the plots show the signal scaled down to 1 supernova at 10 kpc. Chapter 7. SNO Supernova Observed Event Signal 176 15 10 - A Salt (794 particles) all particles - electrons/positrons (61 %) J neutrons (39%) I , I , i ^ T ^ r - ^ - - . j — . _ . i . 1 . 1 , 1 . 15 10 5 0 i 15 10 50 100 150 200 250 300 NHIT 350 400 450 500 -all interactions 1 \ charged current (68%) I \ neutral current (28%) — / T* J / v.O elastic scattering (4%) . JJ • • h v - - I—, i 1 i —v, J . | . i . l . l . 50 100 150 200 250 300 350 400 450 500 NHIT all regions f t D , 0 region (57%) ),' \ i HJO region (43%) A V region (0%) • F. I ;-..-^„-:.;:, ^ ^ ^ ^ X>U_ 1 , I , l . I . 50 100 150 200 250 300 350 NHIT 400 450 500 JL all neutrinos ve(16%) v|,(63%) "v " (21%) 50 100 150 200 250 300 NHIT 350 400 450 500 Figure 7.14: SNO supernova detected particle NHIT distribution above NHIT = 16 PMTs for the salt phase according to Burrows' model. In all cases, 100 supernovae at 10 kpc are simulated, and the plots show the signal scaled down to 1 supernova at 10 kpc. Chapter 7. SNO Supernova Observed Event Signal 177 vi .c E o c 3 v> .C -S S o si-^. fi c 10 .c •5 E o fi c 3 O o Vt .c fi c 3 8 30 20-10 0 30 2 0 Z. 10-30 Pure D20 (621 particles) all particles electrons/positrons (78%) neutrons (22%) j i i i_ _i i i i i_ 0.5 1 1.5 2.5 Event Vertex Position (R/RAV) all interactions charged current (79%) neutral current (16%) elastic scattering (5%) X i - t- i i_ 0.5 1 1.5 2.5 Event Vertex Position (R/RAV) 0.5 1 1.5 2 Event Vertex Position (R/RAV) 2.5 30 20 10b 0 all neutrinos v c (18%) V (69%) "v " (13%) _ i _ L - • - L . • *. -i—i 1 - - I — 0.5 1.5 2.5 Event Vertex Position (R/RAV) _ all regions - D 2 0 region (45%) - H O region (55%) r L r w ^ — « - ^ _ A V region (0%) i i i i i i i i i . I I I I I I I I i i i i 1 i i i I J I 1_ Figure 7.15: SNO supernova detected particle vertex position distribution above NHIT = 16 PMTs for the pure D 2 0 phase according to the model of Burrows et al. In all cases, 100 supernovae at 10 kpc are simulated, and the plots show the signal scaled down to 1 supernova at 10 kpc. Chapter 7. SNO Supernova Observed Event Signal 178 fi c 5 of .c -5 E o fi c 3 8 CO .c E o fi c 3 3 CO .c S o fi c 3 8 wb 30 Salt (794 particles) all particles electrons/positrons (61 %) neutrons (39%) -I I I L 0.5 1 1.5 2 Event Vertex Position (R/RAVf 2.5 all interactions charged current (68%) neutral current (28%) elastic scattering (4%) Event Vertex Position (R/RAV) Event Vertex Position (R/RAV) all neutrinos v e (16%) v i ( 6 3 % ) V ' (21%) j i i_ 0.5 1 1.5 2 Event Vertex Position (R/RAV) 2.5 Figure 7.16: SNO supernova detected particle vertex position distribution above NHIT = 16 PMTs for the salt phase according to the model of Burrows et al. In all cases, 100 supernovae at 10 kpc are simulated, and the plots show the signal scaled down to 1 supernova at 10 kpc. Chapter 7. SNO Supernova Observed Event Signal cosine vector are defined as: 179 cos a = f^ - cos/? = ^ c o s 7 = f ^ r , (7.1) IPI IPI IPI where \p\ = -dvi+ p\ + pi is the magnitude of the momentum vector and the direction angles a, /3 and 7 are the angles that the momentum vector makes with the positive x-, y-, and z-axes in detector coordinates. Similarly, the direction of the supernova can be defined in terms of a direction cosine vector with components cos O>SN, COS PSN and COS^YSN- The angle 9SN between the event direction and the direction of the supernova is determined by taking the dot product between the individual event direction cosine vector and the direction cosine vector of the supernova: cos 9SN = cos cn cos asN + cos (3 cos @SN + cos 7 cos 7SN (7.2) Events that are observed traveling in the forward direction away from supernova will have COS9SN — +1, while events traveling in the backward direction toward the supernova will have COS9SN = — 1-As outlined in Section 5.4, recoil electrons from elastic scattering interactions are ex-pected to have an angular distribution that is very forward peaked. Figure 7.17 shows the detected particle cos 9SN distribution from reactions that are fully treated in. the SNO supernova generator. As predicted, electrons from elastic scattering reactions above the NHIT = 16 detection energy threshold fall within 35°, or COS9SN = 0.8. The elastic scat-tering signal in the D 2 0 and H 2 0 regions contribute at roughly the same level. Three charged current reactions have slight angular asymmetries, which cancel when summed together in the total signal. Photons resulting from neutron capture are emitted isotropically, therefore the angular distribution for the entire signal is a flat background over which the elastic scattering peak can be identified. Introducing salt in the heavy-water volume serves only to enhance the flat background Chapter 7. SNO Supernova Observed Event Signal 180 without affecting the counts due to elastic scattering. Therefore, the ability to determine the direction of the supernova will be slightly worse during the salt phase due to the decreased signal-to-noise ratio. Chapter 7. SNO Supernova Observed Event Signal 181 15 10 5\-0 Pure D20 (621 particles) all particles electrons/positrons (78%) neutrons (22%) t • I • I l • i 1 V • i i i I • I -1 -0.8 -0.6 -OA -0.2 0 0.2 0.4 0.6 0.8 cos(theta)SN 15 10 5 0 15 10 5 0 _ all interactions - charged current (79%) - neutral current (16%) - elastic scattering (5%) J-— r •0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 cos(theta)SN _ all regions _ 0,O region (45%) H z O region (55%) -AV region (0%) j . " , 1 , I , , , I , , I I 1 1 1 I 1 1 1 I 1 1 1 I 1 1 I I 1 1 1 I 1 1 1 1 L . _ l 1_ -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 cos(theta)SN 15 all neutrinos vt(18%) V (69%) _ l I L •.'•4.- r r .- 4 -.T 1 , . i- < f .^- J . r .- ! l^..^,^ T .-. | . 1 | . , •7 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 cos(theta)SN Figure 7.17: SNO supernova detected particle COS6SN distribution above NHIT = 16 PMTs for the pure D 2 0 phase according to the model of Burrows et al. In all cases, 100 supernovae at 10 kpc are simulated, and the plots show the signal scaled down to 1 supernova at 10 kpc. Chapter 7. SNO Supernova Observed Event Signal 182 15 .c •5 S to fi c O O of 15 .c -S 5 10 cS fi 8 Salt (794 particles) all particles electrons/positrons (61 % ) I • , \ 1 V i i . i " . " i i 1 i i i 1 i i i 1 i neutrons (39%) ij ........... ... .................................... 1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 cos(theta)SN • all interactions charged current (68%) I neutral current (28%) f — elastic scattering (4%) J• - , , . i , , , i . . . I i . . . . . . . . . ; » ; . T f V i . i 1 i i i 1 "I i i 1 J - i ' i •0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 cos(theta)SN of 15 5 w fi 5 c 8 o • all regions : . . . . I ) 2 0 region (57%) 1 H ~ 0 region (43%) \ A V region (0%) j. i i i i i i i i i i i i i . ^•.c<.^:;..:,:i^!r..^^^ i i i i i i i • i i i i i i i • • ' 1 i i i 1 i — i — i — 1 •0.8 -0.6 -0.4 •0.2 0 0.2 cos(theta)SN 0.4 0.6 0.8 0) .c •5 <3 fi c 8 15 10 5 0 all neutrinos v c (16%) v '(63%) - i - •- r - i - r - r - i-T-1- - y-~v •0.8 -0.6 -0.4 -0.2 0 0.2 0.4 cos(theta)SN 0.6 0.8 Figure 7.18: SNO supernova detected particle COS9SN distribution above NHIT = 16 PMTs for the salt phase according to the model of Burrows et al. In all cases, 100 super-novae at 10 kpc are simulated, and the plots show the signal scaled down to 1 supernova at 10 kpc. Chapter 8 SNO Supernova Analysis 8.1 Introduction The Monte Carlo studies presented in Chapter 7 characterize the supernova neutrino sig-nal in the absence of detector background events. Events from a number of sources of instrumental noise must be removed from the raw detector data before the physics signal can be extracted. A discussion of topics related to detector background events and the corresponding analysis energy threshold relevant to supernova neutrinos is presented in the sections that follow. 8.2 SNO Background Events Two classes of background events exist in the SNO detector: instrumental backgrounds and physics backgrounds. Instrumental backgrounds are those events which are induced by the detector itself or the surrounding environment, and are not caused by any physics interaction. The category of physics backgrounds covers those events caused by physics pro-cesses that are not of interest for a particular analysis. For instance, physics backgrounds include the radioactive decay of contaminants in the detector, such as those discussed in Section 4.4. Another form of physics background is due to events that follow muons. Studies of various background events in SNO have led to the development of a stan-dardized set of data reduction cuts, which are made available to all collaboration members by means of the SNO database (see Section 4.10). Background events that fail these cuts 183 Chapter 8. SNO Supernova Analysis 184 are not removed from the data but simply tagged. The SNO event rate is not so high that retaining these events is space prohibitive. 8.2.1 Instrumental Backgrounds Several different sources of instrumental background events persist in the SNO detector. Actual light is produced by P M T flashers, P M T failures, some forms of high voltage break-down and by static electric discharge across insulators in the detector. Other sources of instrumental background trigger the electronics discriminators due to electrical pickup. 8.2.1.1 P M T Flasher Events The most consistent and potentially the most serious SNO background events are known as P M T "flashers". The exact mechanism of these events is not completely understood, but through some process a small amount of light is given off randomly by the P M T , originating possibly somewhere in its dynode structure. On average, each P M T emits light through this process approximately once per week, resulting in a detector-wide P M T flasher rate of one per minute [113]. Bursts of flasher P M T events have also been correlated with mine blasting activity. The number of PMTs that are hit in a flasher event is between 20-500 PMTs , which covers not only the solar neutrino spectrum but closely matches the expected supernova neutrino NHIT range. Fortunately, most P M T flasher events have a distinctive topology. The signal has two identifiable components: a small cluster of PMTs is hit on one side of the detector and a second set of hit PMTs diametrically opposite have a characteristic diffuse elliptical pattern. The small cluster of PMTs often has one hit with very high charge (the flasher P M T ) accompanied by a number of adjacent hits with zero charge consistent with electronic pickup. The separation in time between the early cluster of P M T s and the later hits is of order 70 ns, which corresponds to the transit time for light to travel across from one side of the PSUP to the other. Chapter 8. SNO Supernova Analysis 185 A number of cuts were developed by the collaboration to eliminate flasher events by exploiting the charge and P M T clustering information. The QCluster cut [114] identifies the cluster of pickup hits around the high charge flasher P M T . A second independent cut also examines the event geometry. The F G C cut [115] identifies flasher events by looking for hit clusters and comparing the cluster position to the rest of the P M T s in an event. Flasher events are also tagged by the QvT cut [116] using the fact that light from the flasher event is emitted over a longer period than is expected for a Cerenkov event. Further discrimination is provided by a HIB-9000 hydrophone, which is immersed in the light water to detect pressure waves caused by events such as mine blasting. 8.2.1.2 P M T Failure Events Another class of instrumental background event is thought to be associated with the failure of PMTs. Sometimes when a P M T fails, light is produced in the detector for a relatively long period. These events are also known as "flat T A C " events (where T A C refers to uncalibrated P M T time), and are characterized by a roughly equal number of P M T hits at all times within an event. P M T failure events are relatively rare. The measured P M T failure rate in the SNO detector is 0.7% per year and increasing [117]. Events due to P M T failure are mainly removed by two cuts that examine the time structure of the P M T hits within an event. The two cuts are the ITC cut [118] and the FTS cut [119]. 8.2.1.3 High Voltage Breakdown The underwater (wet end) connection between the P M T base and the high voltage/signal cable does not hold high voltage reliably in the presence of ultra-pure, degassed water. Since the connectors were fastened before the PMTs were submerged in water, some air was trapped in the open volume of the connector. When these connectors were then surrounded by degassed water, the trapped air gradually leaked out, and the lower gas Chapter 8. SNO Supernova Analysis 186 pressure that resulted made the connector more susceptible to high voltage breakdown. The long-term solution to this problem was to regas the water with pure nitrogen gas. Originally, the water was degassed in order to reduce radioactivity and inhibit biological growth, and neither reason is compromised with the introduction of pure nitrogen gas from liquid nitrogen boil-off. While some wet-end breakdown events still occur, they are for the most part relatively rare. High voltage breakdown can also occur where the high voltage/signal cables are con-nected to the electronics P M T I C high voltage cards (dry end). In this case, the breakdown can be due to a damaged high voltage cable or improper connection. When dry-end break-down occurs, a particular channel can often be isolated as the cause and a repair can be made. In the SNO solar neutrino analysis, background events due to both wet- and dry-end breakdown are removed using a series of burst cuts. However, supernova events by their nature are bursts, therefore cuts that remove events based on the relative timing of events cannot be used. Noise events due to dry-end breakdown typically occur within a few electronics cards within a single crate and can be identified using the The Crate Isotropy cut [120]. A large fraction of high voltage breakdown events can be tagged by the A M B cut [121], which examines the shape of the E S U M signal to determine if the number of PMTs hit in the event is consistent with a standard physics event. In fact, the A M B cut has proven to be efficient at tagging almost all instrumental background events. 8.2.1.4 Neck Events Another background in the SNO detector is possibly due to static discharge in the vicinity of the chimney (or neck) region of the acrylic vessel. Since the acrylic used in the construction of the chimney does not transmit U V light, the light produced due to static discharge is directed downward to the PMTs located at the bottom of the detector. To identify events Chapter 8. SNO Supernova Analysis 187 due to this source, four PMTs were installed in the chimney to tag light originating in the neck region. The Neck cut [122] requires that either both neck P M T s register a hit or that one P M T signal has large charge and occurs early in time with respect to the other hits in the event. 8.2.1.5 Electronic Pickup There are several sources of electronic pickup in the SNO detector, including high voltage breakdown, static discharge, and electrical equipment. These cause the channel discrimina-tors to trigger in the absence of light in the detector. The charge of these signals integrates to zero, a feature that is used to tag pickup events. The QvNHIT cut [123] removes events which have anomalously low charge for the number of PMTs participating in the event. The Crate Isotropy cut [120] also makes use of that fact that electronic pickup often induce signal events in just one electronics crate. The R O F cut [124] is able to isolate events in which there is pickup up in the first and last electronic cards in an electronics crate. 8.2.2 Physics Backgrounds Due to the relatively short duration of the expected supernova signal, there are few physics backgrounds to contend with. For instance, the detection rate of solar neutrinos in the SNO detector is on the order of 0.01 events/minute [125] at the proposed supernova analysis threshold. Therefore, solar neutrino events do not constitute a background to the analysis of a supernova burst. However, there is one class of physics events associated with muons that does provide a small background. 8.2.2.1 M u o n Spallation In SNO, spallation occurs when a high energy muon undergoes inelastic scattering with an oxygen, deuterium or hydrogen nucleus in the detector volume, producing free neutrons and radioactive nuclei. For instance, spallation of 1 6 0 may produce 9 L i , which can decay Chapter 8. SNO Supernova Analysis 188 by emitting a neutron and has a relatively long half-life, T i / 2 = 0.178 s. Examples of muon-induced spallation products that decay by /? emission include 1 6 N and n B e , with half-lives of 7.13 s and 13.8 s, respectively [126]. In order to monitor the background due to the presence of muons, a number of pieces of information are used to tag muon events. The first indication of a muon event is provided in the light water region surrounding the PSUP. There, the outward-looking (OWL) PMTs receive Cerenkov light as the muon passes through the light water. At least 5 of the 91 O W L P M T s are required to have a signal by the muon identification algorithm. The muon event signal measured by the main array of PMTs is often quite spectacular, with nearly all of the PMTs registering a hit. However, in some events where the muon travels close to the P M T array through the inner H 2 0 volume, fewer P M T s are hit. A signal from 150 PMTs is sufficient to identify muons when used in conjunction with the O W L P M T information. This then allows the subsequent muon spallation events to be identified. 8.3 SNO Supernova Analysis Threshold Using the set of data reduction cuts deemed appropriate for a burst analysis, the rate of background events is investigated over the period from November 2, 1999 to January 15, 2001. The most meaningful measure of the background is obtained by considering the num-ber of events that pass the data reduction cuts during a set of well-understood running conditions. To this end, 245.61 days of data used for the solar neutrino analysis1 are used to determine the supernova analysis threshold. Figure 8.1 shows the average residual in-strumental background event rate for various analysis threshold NHIT threshold settings. Since a supernova burst is expected to last for approximately 1 minute, the background 'The livetime quoted for the solar neutrino analysis using these same data set is 240.95 days. However, an additional set of burst cuts that are not used in this analysis are employed to further reduce the solar neutrino data set. Chapter 8. SNO Supernova Analysis 189 event data are presented as the number of background events per minute. For subsequent analysis, the NHIT threshold is chosen such that on average one background event or fewer is present in a supernova burst above the NHIT threshold and after the data reduction cuts have been applied. Since the supernova signal has a large contribution due to neutrons at NHIT « 50 PMTs (see Section 7.4), it was felt that one background event was an ac-ceptable compromise to ensure that a substantial portion of the neutron peak remained for analysis. Using an analysis threshold of 34 PMTs , a livetime weighted average background event rate of 0.96 ± 0.09 events/minute is obtained. "Therefore, a value of NHIT=34 is adopted as the supernova analysis threshold setting, and is used in the SNO supernova online burst monitor that is discussed in Chapter 9. This NHIT=34 threshold corresponds roughly to an energy threshold of 3.8 MeV. Having established the analysis NHIT threshold, Figure 8.2 shows the average back-ground event rate above the NHIT=34 analysis threshold as a function of time during the period from November 2, 1999 to January 15, 2000. It appears that after experiencing rela-tively high event rates during the first 50-60 days of running, the detector event rate above NHIT=34 reached an average plateau of approximately 2-3 events/minute. However, a slight downward trend is observed in the event rate above both the NHIT=34 threshold and the data reduction cuts. Occasional periods of high event rates that decrease quickly are due to lab power interruptions, after which the detector is typically noisier. The ab-normally high average event rate on November 26, 1999 (day number 25) is the result of unstable detector conditions in PMTs that are not used for the solar neutrino analysis. This data is not used for the supernova neutrino burst search in Chapter 10. The relatively low average event rate on February 14, 2000 (day number 105) is likely due to the fact that the run was less than 1 hour long. It should also be noted that the analysis threshold for an actual supernova event will likely be determined based on the background event rate experienced at the time of the Chapter 8. SNO Supernova Analysis 190 c s O •c </> 2! (S B o -Cj c UJ 2 15 10 1 eventVminute 1 I 29 T T • Threshold = NHIT Setting • Threshold = NHIT Setting + Data Reduction Cuts II 30 31 32 33 Analysis NHIT Threshold 34 35 Figure 8.1: Average background event rate for various analysis NHIT threshold settings using data chosen for the solar neutrino analysis. The choice of NHIT=34 is adopted for the successive analyses. burst. In many of the more recent data sets analyzed, a threshold of 30-31 PMTs is sufficient to restrict the background event rate to approximately 1 event/minute. Therefore, in many instances an analysis threshold of less than 34 PMTs would be possible. The data used in this background study are taken exclusively during the pure D 2 0 mode of operation, and in the strictest sense may only be applied to studies of the supernova signal in that mode. However, initial studies of the salt data indicate that the analysis threshold determined for analyzing data gathered in the pure D 2 0 phase is also valid for analyzing salt data. Results from background studies performed on a small number of stable salt runs Chapter 8. SNO Supernova Analysis 191 Day Number Figure 8.2: Average background event rate above the NHIT=34 analysis threshold as a function of time during the period from November 2, 1999 to January 15, 2001 using data chosen for the solar neutrino analysis. The abnormally high circle data point on day number 25 is due to detector instabilities. show an average event rate of 1.3 events/minute above NHIT=34 and 0.35 events/minute above NHIT=34 and that pass the data reduction cuts. Events recorded using the neutral current detectors will not experience many of the instrumental backgrounds described above. Therefore, a separate investigation will be necessary in order to characterize the supernova neutrino analysis threshold for data taken using the NCDs. Chapter 8. SNO Supernova Analysis 192 8.4 Supernova Signal Above Analysis Threshold The number of final state particle counts expected above the supernova neutrino analysis threshold of 34 PMTs for both the Beacom and Vogel model and the Burrows model is presented in the sections that follow. Since the analysis threshold to be used during N C D operation cannot be determined at this time, only predictions for the pure D 2 0 and salt running modes are discussed. 8.4.1 Beacom and Vogel Model Above the supernova analysis threshold of 34 PMTs, Monte Carlo simulations of the su-pernova signal indicate that 740 counts are expected during the pure D 2 0 phase and 1060 counts are expected during the salt phase according to the Beacom and Vogel model for a supernova at 10 kpc. The observed counts above the analysis threshold are summarized in Table 8.1. According to the estimates of the observed signal due to reactions involving oxygen (see Appendix C), an average of 53 additional events are expected during the pure D 2 0 phase and 65 events are expected during the salt phase for a supernova at 10 kpc. Therefore, the best estimate for the total signal for a supernova at 10 kpc is 793 counts during pure D 2 0 operation and 1126 counts during salt operation according to the Beacom and Vogel model. These observed count values correspond to 58.5% and 83.0% of the total signal for pure D 2 0 and salt, respectively. As discussed in Chapter 7, the electron antineutrino signal constitutes the majority of the signal in the light-water region. A total of 8 electron/positron events and 20 7-ray events are expected in the H 2 0 region due to reactions with oxygen. Combining those events with the 392 positrons produced via the Ve + p —» n + e+ reaction and the 15 electrons produced through the v + e~ —> v + e~~ reaction yields a total of 398 events in the light water region due to interactions with Ve neutrinos for a supernova at 10 kpc. Therefore, according to the Beacom and Vogel model, approximately 91.5% of the signal in the H 2 0 region is due Chapter 8. SNO Supernova Analysis 193 Reaction Reaction SNO Counts Region (all time) D 2 0 Salt Charged Current: total 586.28 664.26 Ve + p —» n + e+ H 2 0 392.09 392.09 ue + d^-p + p + e~ D 2 0 76.26 76.26 Ve + d^n + n + e+ D 2 0 117.93 195.91 Neutral Current: total 129.44 372.23 Ve + d^Ve+p + U D 2 0 9.46 26.30 T>e + d^l7e+p + n D 2 0 13.67 39.17 VH,T + d^> v^T+p + n D 2 0 58.78 169.83 +d^ V^T + p + Tl D 2 0 47.53 136.93 Elastic Scattering: total 24.68 24.68 ve + e~ -> ue + e~ D 2 0 4.37 4.37 Ve + e~ —v Ve + e~ D 2 0 1.74 1.74 "us + e~ ->• u^T + e~ D 2 0 1.86 1.86 t ' / i . T + e~ -+ F/i.r + e~ D 2 0 1.64 1.64 zve + e~ —>• ue + e~ H 2 0 6.83 6.83 F e + e~ —> X7 e + e~ H 2 0 2.44 2.44 "/X,T + e~ -> JVM)T + e~ H 2 0 3.13 3.13 y^r + e~ -> F M ) T + e~ H 2 0 2.67 2.67 Total SNO jve Events 96.92 113.76 Total SNO F e Events 527:87 631.35 Total SNO ' V Events 115.61 316.06 Total SNO D 2 0 Events 333.24 654.01 Total SNO H 2 0 Events 407.16 407.16 Total SNO e± Events 568.69 568.69 Total SNO n Events 171.72 492.36 Total SNO Events 740.40 1061.17 Total SNO Events (with O) 793.49 1126.17 Table 8.1: SNO supernova detected particle counts above NHIT = 34 PMTs using the Beacom and Vogel model for a supernova at 10 kpc. Two independent data sets with 100 supernovae at 10 kpc are used to calculate these count values. to reactions with ue neutrinos. Setting the supernova analysis threshold at 34 P M T s affects both the observed average energy and the average angular distribution values for the observed signal due to elastic Chapter 8. SNO Supernova Analysis 194 Reac t ion Reac t ion ( N H I T e ) (cos 0e) Region ( P M T s ) Charged Current: Ve + p —> n + e+ H 2 0 132 0.0311 ue + d^p + p-\-e~ D 2 0 139 -0.1214 Ve + d—7n-rn + e+ D 2 0 178 -0.0620 Elastic Scattering: ue + e~ —>• ve + e~ D 2 0 . 88 0.9758 Ve + e~~ —> Ve 4- e~ D 2 0 90 0.9643 * V , T + e~ - 4 /vM>r 4- e~ D 2 0 148 0.9766 Vfi,r 4- e" - 4 F M ) T 4- e~ D 2 0 144 0.9753 z/e 4- e~ - 4 z/e 4- e~ H 2 0 73 0.9791 Z7e 4- e" —> Ve 4- e~ H 2 0 76 0.9692 + e~ ->• v^r 4- e - H 2 0 113 0.9801 4- e~ - 4 V^T + e~ H 2 0 109 0.9789 Table 8.2: Average NHIT and angular distribution values for final state elec-trons/positrons simulated in the SNO detector above the supernova analysis threshold of 34 P M T s according to the model of Beacom and Vogel. scattering in particular. The energy and angular distribution properties of the final state electron and positron signals are summarized in Table 8.2. Since the detection of electrons and positrons is not affected by the addition of salt, only one set of values is necessary to describe the detector response. Results for events observed above the analysis threshold show that on average electrons from elastic scattering reactions are distributed within approximately 9 = 15° of the supernova direction ((cos#e) = 0.96). 8.4.2 Burrows et al. Model Above the supernova analysis threshold of 34 PMTs, Monte Carlo simulations of the su-pernova signal indicate that 545 counts are expected during the pure D 2 0 phase and 727 counts are expected during the salt phase according to the Burrows model for a supernova at 10 kpc. The observed counts above the analysis threshold are summarized in Table 8.3. Chapter 8. SNO Supernova Analysis 195 An estimated 10 additional events are also expected from reactions with oxygen during the pure D 2 0 phase for a supernova at 10 kpc (see Appendix C). The corresponding estimate with salt in the heavy water is that 11 events are expected from reactions with oxygen. Therefore, the total supernova signal for a burst at 10 kpc is 555 counts observed above the supernova analysis threshold during pure D 2 0 operation and 737 counts during salt oper-ation. These observed count values correspond to 62.5% and 83.0% of the total detectable particle signal for pure D 2 0 and salt, respectively Considering the electron antineutrino signal in the H 2 0 region, a total of 4 elec-tron/positron events and 2 7-ray events are expected from reactions with oxygen for a supernova at 10 kpc. Therefore a total of 298 Ve events are expected above the supernova analysis threshold for a supernova at 10 kpc. This corresponds to approximately 94.6% of the signal in the H 2 0 region. The energy and angular distribution properties of the final state electron and positron signals using the Burrows model are summarized in Table 8.4. Results for events observed above the analysis threshold show that on average electrons from elastic scattering reactions are distributed within approximately 9 = 15° of the supernova direction ((cos#e) = 0.96). 8.5 Signal Loss Two analysis factors contribute to the loss of supernova signal. The first is the NHIT analysis threshold and the second is the effect of the data reduction cuts. 8.5.1 Analysis Threshold The amount of supernova signal removed due to the analysis threshold of NHIT=34 PMTs is obtained by comparing the numbers of counts expected above the hardware threshold of NHIT=16 PMTs and the numbers of counts expected above the analysis threshold of NHIT=34 PMTs. Chapter 8. SNO Supernova Analysis 196 Reaction Reaction SNO Counts Region (all time) D 2 0 Salt Charged Current: total 453.30 506.62 Ve + p —> n + e + H 2 0 295.97 295.97 ve + d^p + p + e~ D 2 0 78.83 78.83 Ve + d^n + n + e+ D 2 0 78.50 131.82 Neutral Current: total 69.59 197.55 ue + d^ue+p + n D 2 0 9.62 27.40 Ve-\-d—*Ve+p + n D 2 0 9.83 27.70 VH,T + d-¥ufi)T+p + n D 2 0 26.80 75.77 v^r + d -> V^r +p + n D 2 0 23.34 66.68 Elastic Scattering: total 22.55 22.55 ue + e~ —> ue + e~ D 2 0 5.05 5.05 Ve + e~ —¥ Ve + e _ D 2 0 1.39 1.39 + e~ -»• + e~ D 2 0 1.34 1.34 V»,T + e~ -> * W + e~ D 2 0 1.28 1.28 «ve + e~ —> tve + e~ H 2 0 7.30 7.30 I 7 E + e~ —>• F e + e~ H 2 0 1.95 1.95 + er -»• »vP|T + e~ H 2 0 2.38 2.38 *V,T + e" ->• F ^ ) T + e~ H 2 0 1.86 1.86 Total SNO »ve Events 100.80 118.08 Total SNO ve Events 387.64 458.83 Total SNO ' V Events 57.00 149.31 Total SNO D 2 0 Events 235.98 417.26 Total SNO H 2 0 Events 309.46 309.46 Total SNO e± Events 447.81 447.81 Total SNO n Events 97.64 279.42 Total SNO Events 545.44 726.72 Total SNO Events (with O) 555.14 737.37 Table 8.3: SNO supernova detected particle counts above NHIT = 34 PMTs using the Burrows model for a supernova at 10 kpc. Two independent data sets with 100 supernovae at 10 kpc are used to calculate these count values. For the Beacom and Vogel model, the loss during the pure D 2 0 phase corresponds to 11.7% of the observable supernova signal. In the operation mode with salt, 7.2% of the observable supernova signal is removed with an analysis threshold of 34 PMTs . Fewer Chapter 8. SNO Supernova Analysis 197 Reac t ion Reac t ion < N H I T e ) (cos 0e) Region ( P M T s ) Charged Current: Ve + p — > • n + e + H 2 0 111 0.0141 Ue + d-^-p + p + e' D 2 0 134 - 0 . 1 1 9 5 Ve-r d —7 n + n + e+ D 2 0 145 - 0 . 0 7 4 8 Elastic Scattering: ue + e~ —> ue + e~ D 2 0 84 0.9762 Ve + e~ —7 Ve + e~ D 2 0 78 0.9643 Vn,r + e~ ->• / v M T + e~ D 2 0 105 0.9747 ^ / i ,T + e~ -4 17^ ,- + e' D 2 0 102 0.9732 ue + e~ —> ve + e~ H 2 0 71 0.9791 I7e + e~ —>• I7e + e~ H 2 0 68 0.9688 "us + e~ ->• /vMi7- + e~ H 2 0 84 0.9781 ^ / i ,T + e~ -4 T7MjT + e~ H 2 0 83 0.9769 Table 8.4: Average NHIT and angular distribution values for final state elec-trons/positrons simulated in the SNO detector above the supernova analysis threshold of 34 PMTs according to the Burrows model. events are removed with the salt neutron detection option than for pure D 2 0 because the Compton scattered photons from neutron capture on salt have higher energies than those from neutron capture on deuterium. Slightly higher values for the signal loss are obtained using the model of Burrows et al. since electron/positron events in that model tend to have lower energies that those in the Beacom and Vogel model. Using the Burrows model, the loss during the pure D 2 0 phase corresponds to 12.1% of the observable supernova signal; with salt, the signal loss is 8.6%. 8.5.2 Data Reduction Cuts Relatively little signal loss is expected to be due to the data reduction cuts. Studies using 1 6 N calibration source data indicate that a volume-weighted signal loss of 0.44 ± 0.01% over the D 2 0 volume for the set of data reduction cuts listed in Section 8.2. In the H 2 0 region, Chapter 8. SNO Supernova Analysis 198 the signal loss is higher than in the central D 2 0 region, especially close to the PMTs, as is shown in Figure 8.3. The volume-weighted signal loss in the H 2 0 volume is estimated to be 3.86 ± 0.03%. Combining the results from both regions, the total volume-weighted signal loss for the entire detector is 2.60 ± 0.02%. In all cases, the errors quoted are statistical errors. a c S U J s -O c o •a I 0.001 200 400 600 Distance of Source From Centre (cm) Figure 8.3: Signal loss measured using 1 6 N data as a function of source position in the detector, resulting from the use of the data reduction cuts chosen for the supernova analysis. Chapter 8. SNO Supernova Analysis 199 8.6 Summary Instrumental background is removed from the SNO data by use of a set of data reduc-tion cuts. The cuts adopted for the supernova neutrino analysis do not remove burst events. Naturally occurring physics events (non-calibration events) do not constitute a large background to the supernova analysis. The majority of physics backgrounds are usually associated with a high energy muon event, which is tagged during the supernova analysis. Table 8.5 summarizes the data reduction cuts and physics tags that are used for the SNO supernova neutrino analysis. C u t / T a g Descr ip t ion Background QCluster charge cluster cut P M T flasher QvT charge versus time cut P M T flasher F G C flasher geometry cut P M T flasher ITC in-time channel cut P M T failure electrical pickup FTS fitterless time spread cut P M T failure N E C K uses PMTs installed in chimney neck light QvNHIT charge/NHIT ratio cut electrical pickup R O F pickup in cards 1, 15 electrical pickup ISO crate isotropy cut electrical pickup A M B E S U M pulse shape analysis high voltage breakdown M U O N muon tag muon spallation products Table 8 . 5 : Data reduction cuts used for the supernova analysis. Based on the background event rate experienced during 244 days of stable detector running conditions, a threshold of 34 P M T s is assigned for analysis of the supernova signal. Combining the predictions from both the Beacom and Vogel model and the Burrows model for a supernova at 10 kpc indicates that a total of 550-800 events would be observed above the supernova analysis threshold during the pure D 2 0 phase. During the salt phase, a total of approximately 750-1125 events would be observed for a supernova at 10 kpc. Furthermore, 92-95% of the signal in the light water region is expected to be due to Chapter 8. SNO Supernova Analysis 200 SN Signal Beacom Burrows Component Model Model (t < 100 ms) D 20 Salt D 20 Salt Neutrino: ve 1.36 1.57 8.98 10.81 Ve 6.32 7.78 0.72 0.88 u " M 0.67 3.36 0.05 0.24 Region: D 2 0 region 3.01 7.39 8.46 10.64 H2O region 5.33 5.33 1.27 1.27 A V region 0.01 0.02 0.02 0.02 Interaction: charged current 7.25 8.76 8.27 8.40 neutral current 0.70 3.91 0.24 2.29 elastic scattering 0.40 0.40 1.24 1.24 Particle: electron / positron 7.77 7.77 9.49 9.49 neutron 0.92 4.39 0.26 2.44 Total Signal: 9.02 13.66 9.75 11.93 —> ve fraction 16.4% 12.5% 92.1 % 90.6% Table 8.6: Comparison of the prompt signal above the detector hardware threshold be-tween two generic supernova models at 10 kpc for relative time t < 100 ms. Z7e neutrino interactions, making it possible to essentially isolate that component of the supernova signal for study. The prompt signal (t < 100 ms) above the analysis threshold contains between 9 and 11 events due to ve interactions according to the Burrows model for a supernova at 10 kpc. Therefore, the electron neutrino neutronization burst corresponds to approximately 92% of the total signal during that time period. In the case of the Beacom and Vogel model where no effects due to neutronization are included, 13-16% of the events are due to ue processes. Approximately 12% of the supernova events in pure D 2 0 above the detector hardware Chapter 8. SNO Supernova Analysis 201 threshold are below the supernova analysis threshold of NHIT = 34. The corresponding fraction of the supernova signal that is removed during salt operation is roughly 8% of events. Due to the higher energy photons emitted during neutron capture on 3 5 C1, fewer events are removed during the salt phase than during the pure D 2 0 phase. A comparison of the results in Tables 8.1 and 8.3 with the corresponding results in Tables 7.1 and 7.3, indicates that the main component of the supernova signal that is removed by applying a threshold cut of 34 PMTs is the neutron signal. In the Beacom and Vogel model, the neutron signal decreases by 29% during pure D 2 0 operation and 10% during the salt phase. Results for the Burrows model show a similar decrease in the neutron signal. The decrease in the electron/positron signal when applying a threshold cut of 34 P M T s is 5% using the Beacom and Vogel model and 8% using the Burrows model. A larger number of electron/positron events are below the NHIT = 34 threshold in the Burrows model due to the lower neutrino temperatures used. The effect of the analysis threshold cut during pure D 2 0 and salt operation is illustrated in Figure 8.4 using the Burrows model. The effect of setting an analysis threshold is shown in Figure 8.5, where NHIT as a function of time is shown for the supernova signal expected from Burrows model as well as for stable detector running. Chapter 8. SNO Supernova Analysis 202 Figure 8.4: SNO supernova detected particle NHIT distribution where the shaded area indicates the supernova signal excluded by using an analysis threshold of NHIT = 34 PMTs. Chapter 8. SNO Supernova Analysis 203 400 350 300 250 | 200 150 100 50 0 i 400 350 300 250 | 200 150 100 50 0 Pure D20 detector background supernova burst Analysis NHIT threshold 50 100 150 200 Event Time (seconds) 250 300 I ' I ' I ' I '_ Salt 1 1 ' — i .• s detector background supernova burst Analysis NHIT threshold wSf-V*A'>- V "'.' 50 100 150 200 Event Time (seconds) 250 300 Figure 8.5: NHIT as a function of time showing the expected supernova signal, the detector background and the effect of the analysis NHIT threshold. Chapter 9 SNO Supernova Monitoring Programme 9.1 Introduction A data analysis program to identify neutrinos from a galactic supernova burst was installed on February 23, 20001 as part of the online system at the Sudbury Neutrino Observatory. The system was commissioned after several months of both offline and online testing and development. Some aspects of this development are summarized in Appendix E. The goal of the Supernova Monitor at the Sudbury Neutrino Observatory is to be able to identify neutrinos from a Type Il/Ib galactic supernova in time to provide an alert to the astronomical community. As mentioned in Section 3.4.3, the neutrino emission is expected to precede the optical signal, where the time delay depends on the mass envelope surrounding the collapsing star, and may vary from a few minutes to several hours. To be useful, the alert from the neutrino astronomy community must come as quickly as possible. The SNO supernova monitoring program aims to be able to provide a reliable alert within 20-30 minutes. 9.2 Online Supernova Monitor In order to identify a significant burst of neutrino events in the SNO detector, a data analy-sis program has been installed in the online data stream that automatically analyzes burst 1The fact that this date is the 13th anniversary of SN1987A is purely coincidental. 204, Chapter 9. SNO Supernova Monitoring Programme 205 data. Analysis results for all "interesting" bursts are made available to the SNO Supernova Working Group and to the detector operator on shift. The SNO online supernova monitor is located within the SNO data acquisition system (see Section 4.8). P M T data from the readout electronics is processed by a task called the "event builder", which resides on a Sun Ultra Sparc 1/170 workstation computer. The event builder assembles the individual P M T hits into events. Once built, the event data are written to tape and also transferred along a 2 km ethernet fibre to a Sun Ultra Sparc 1/170 computer on surface, where a second archive copy of the data is made and a process called the "event dispatcher" is responsible for managing all of the processes that subscribe to the online data stream. A n overview of the SNO data flow system is shown in Figure 9.1. PMT Data Event Builder Data Storage Underground Surface Data Storage Event Dispatcher SN Burst Monitor Level 1: Burst Trigger Online Monitoring Tools SN Data Analysis Level 2 : Background Rejection SN Data Level 3: Detai Analysis led Analysis SNEWS Alert Level 4: SNEWS client Figure 9.1: Schematic overview of the SNO data flow system. The connection between underground and surface is via a 2 km ethernet cable. The online supernova monitoring system for SNO can be logically broken up into four Chapter 9. SNO Supernova Monitoring Programme 206 distinct levels, the first three of which are completely automated. The "Level 1" burst trigger monitors the data stream for significant increases in the event rate. In the case of such a burst, events passing the Level 1 trigger are copied out of the data stream and passed to the "Level 2" analysis routine, where events due to instrumental noise are removed. If 35% or more of the events pass the Level 2 stage, the detector operator is notified and the "Level 3" routine is then called to reconstruct a time, energy, location in the detector and direction for each event. Should the burst be identified as having significant physics content, the final stage of SNO's response, "Level 4", would be to manually communicate the details of the burst to the SuperNova Early Warning System (SNEWS) [127] and to issue an alert to the astronomical community. Each of the levels is described below. 9.2.1 Level 1 9.2.1.1 Burst Trigger The Level 1 burst monitor involves looking for a certain number of events (NEVENT) over a certain energy threshold (NHIT) within a certain time window. To this end, one of the existing SNO online data monitoring tools has been modified to hold a circular FIFO buffer and apply the burst criteria to the incoming data on an event-by-event basis [128]. In the current default configuration, the FIFO buffer holds 30 events above the supernova NHIT analysis threshold of 34 PMTs . The burst criteria are met when the time difference between the first and last event in the buffer is less than 2 s. The expected count rate sustained over 2 seconds for events above the NHIT analysis threshold of 34 P M T s is approximately 185 Hz during the pure D 2 0 mode and 275 Hz during the salt mode for a supernova at 10 kpc, regardless of the supernova model. Figure 9.2 indicates the time structure of a supernova burst compared to the typical detector event rate of 15-20 Hz. Once a burst has been identified, the burst events are copied from this circular buffer to a separate file until the events in the FIFO buffer no longer satisfy the burst criteria and Chapter 9. SNO Supernova Monitoring Programme 207 250 200 150 100 50 0 i 300 250 200 150 100 50 0 . i i , 1 Pure DzO - entire signal _ detector l>;nkgrotind -- . -. supernova burst 50 100 150 200 Event Time (seconds) 250 300 I • I ' 1 Salt ' I ' 1 - enliri' signal - detector background - supernova burst 50 100 150 200 Event Time (seconds) 250 300 Figure 9.2: Expected detector count rate in the presence of a supernova burst. The typical detector event rate is 15-20 Hz. the burst ends. In order to ensure a prompt analysis of the events, bursts that last longer than 60 seconds are forced to end prematurely and the remaining events are assigned to a successive burst. The burst monitor currently resides on a Sun Ultra Sparc 1/170 workstation computer; a parallel burst monitor process resides on an Intel Pentium III 600 MHz based computer. Once the parallel system on the faster Intel Pentium computer has been fully commissioned, it will become the official process and the Sun will be used only as a backup. Chapter 9. SNO Supernova Monitoring Programme 208 Run Condition Level 1 Burst Monitor NHIT100 Threshold (PMTs) (MeV) Default 34 3.8 Calibration: • 1 6 N , 8 L i 69 7.7 • 2 5 2 C f (all strengths) 69 7.7 • U , Th 44 4.9 • all other sources 34 3.8 Table 9.1: Level 1 burst monitor NHIT100 trigger thresholds during different detector activities. In all cases, the Level 1 trigger requires 30 events above the appropriate NHIT100 trigger threshold in a 2 second time window. 9.2.1.2 Run-Specific Thresholds In addition to the default settings, several calibration sources require higher thresholds, which are assigned depending on the run type. The 1 6 N and 8 L i calibration sources make use of a gas system to transport radioactive nuclei to the detector, as described in Section 4.9. Although both of these sources have an internal P M T to tag decay events, some of the nuclei decay en route to the decay chamber, causing the detector to register an event without the corresponding internal calibration source tag. The decay products of the 2 5 2 C f , U and Th calibration sources are not tagged and would normally swamp the data stream burst monitor. In order to avoid having physics events from the 1 6 N , 8 L i , 2 5 2 C f , U and Th calibration sources in the data set, the burst monitor sensitivity during these runs is decreased by raising the trigger threshold. Additional instrumental light is observed during the operation of the source manipulator system2. The Level 1 burst monitor parameter settings during various detector activities are presented in Table 9.1. A l l run conditions require 30 events above the appropriate NHIT threshold in a time window of 2 seconds. 2The current online burst monitor uses an NHIT threshold of 124 PMTs during running conditions in which the source manipulator system is in operation. That threshold setting is not used in this analysis. Chapter 9. SNO Supernova Monitoring Programme 209 9.2.1.3 Offline Performance Once the online burst monitor was sufficiently mature, its performance was investigated offline for the period between November 2, 1999 and January 4, 2001, consisting of 391.6 days of live data. To perform the offline study, a set of F O R T R A N routines that provide much of the same functionality as the online monitor was used. The supernova analysis event NHIT threshold of 34 PMTs in conjunction with a time window of 2 seconds were specified in the offline analysis routines. Several N E V E N T settings were employed in order to thoroughly study the response of the monitoring system. In all cases, the run-specific thresholds listed in Table 9.1 were also employed. One slight difference between the online and offline burst monitor software is that a burst is not ended once a duration of 60 seconds is reached, as is the case in the online version. The burst rate observed in the SNO detector depends on the number of events required to form the burst trigger. An average of 44.0 bursts/day are observed during the offline study using the default online burst monitor parameters. For comparison, the total burst rate using NEVENT=50 is approximately 26.5 bursts/day. Results of the offline study for different N E V E N T parameters are shown in Figure 9.3. The increase in the burst rate as a function of the number of events required to form the trigger is mainly due to calibration activity. Before the results of the offline study were available, a conservative trigger setting requiring 50 events was used in the official online monitor. This choice was based on early studies during the development of the trigger and a desire to not overwhelm the detector operators with too many bursts. The current N E V E N T setting is 30 events, but for much of the online operation, N E V E N T = 50 was used. Therefore the N E V E N T = 50 setting is often used for comparison in the offline studies. The bursts identified in the offline study can be classified to first order by considering the three general classes of detector operating conditions: Chapter 9. SNO Supernova Monitoring Programme 210 250 I r n\ I I 1 I I I I I I I 0 10 20 30 40 50 Number of Events Required for Trigger Figure 9.3: Level 1 burst rate as a function of the N E V E N T burst trigger parameter studied offline during the period between November 2, 1999 and January 4, 2001. The online Level 1 burst monitor currently uses N E V E N T = 30, which results in a burst rate of approximately 44 bursts/day. The vast majority of these bursts are due to calibration activity. • neutrino: stable running mode; data used for most physics search analyses come from this class of data; • calibration: running mode associated with detector calibration activities, which in-cludes actual calibration source data as well as data during which the calibration sources are being prepared for use; • maintenance: running mode during which the detector is either unstable or some Chapter 9. SNO Supernova Monitoring Programme 211 N E V E N T = 50 N E V E N T = 30 Burst Cause Rate Fraction of Rate Fraction of (day" 1) Total Bursts (day- 1 ) Total Bursts Calibration 10.1 38.2% 21.8 49.4% Maintenance 9.4 35.5% 11.7 26.6% Neutrino 7.0 26.3% 10.5 23.9% Total 26.5 100% 44.0 100% Table 9.2: Total average Level 1 burst rate experienced during difference detector op-erating conditions. A number of bursts recorded during the neutrino and maintenance operating modes are also due to calibration activity. maintenance or diagnostic procedure is being performed. The burst rates experienced during different detector operating conditions are indicated in Table 9.2. As expected based on experience with the online system, the majority of burst events are due to calibration activities. One factor that significantly skews the burst rate associated with a particular running condition is that of operator error. On numerous occasions, detector activities are not properly reported in the data, in particular calibration activities. As a result, a larger number of bursts are recorded because the run-specific trigger thresholds are not implemented when they should be. This also means that burst rates quoted for the "neutrino" and "maintenance" conditions are higher than warranted for the activities intended for those running conditions. Most of the bursts are grouped closely together in time as shown in Figure 9.4, which suggests that a single source is often responsible for causing more than one burst. Taking this factor into account reduces the Level 1 burst rate to an average of about 7.5 groups of bursts per day at the default N E V E N T setting, most of which are due to calibration activity. During the period where 50 events were required by the online burst monitor, SNO experienced roughly 6 groups of bursts per day. Chapter 9. SNO Supernova Monitoring Programme 212 I 1 4a. OQ 50 40 30 20 10 1 1~~ NEVENT = 30 NEVENT = 50 _L 10 20 30 40 Burst Concatenation Time (seconds) 50 60 Figure 9.4: Level 1 burst rate as a function of the time between bursts, determined offline for the period between November 2, 1999 and January 4, 2001. Most burst events occur within 10 seconds of the preceding burst and are therefore likely due to the same source. The most significant contribution to this effect is from calibration activity. 9.2.2 Level 2 Once a burst has been identified by the Level 1 trigger, the events are analyzed event-by-event using computer software routines developed by the SNO Supernova Working Group, which are linked against the main SNO data analysis software package S N O M A N . This analysis is performed on a Sun Enterprise E450 computer and in parallel on an Intel Pentium III 600 MHz based computer, running the Solaris x86 operating system. The main task of this second-level analysis is to remove instrumental background events Chapter 9. SNO Supernova Monitoring Programme 213 by applying the data reduction cuts outlined in Section 8.2. One drawback to analyzing data online is that the results of the data reduction cuts for the events are not readily available in the SNO database, so the data reduction filters must be applied manually in the S N O M A N routines. As well, it is necessary to provide the latest E C A electronics constants as input to the analysis routines since these values take some time to be included in the SNO database. A l l data in the SNO database has a validity time range, so additional provisions have been made within the database software to apply the latest detector constants in the event that a certain validity range has expired. 9.2.2.1 Burst Classification The Level 2 analysis also attempts to characterize the nature of the burst based on the fraction of events that are tagged by the various data reduction cuts. There are currently 13 categories that exist in the burst classification algorithm, including the category of "Unknown". Six of these categories are associated with the SNO instrumental background sources discussed in Section 8.2: • Flasher: QCluster > 0.50, F G C > 0.45 • Flat T A C : ITC tags higher fraction of events than any other cut • Wet-End Breakdown: A M B > 0.75, QCluster > 0.35, QvT > 0.35, ITC > 0.35, QvNHIT < 0.20, N E C K < 0.35, FTS < 0.35, F G C < 0.45 (veto Flasher) • Dry-End Breakdown: Isotropy > 0.80 • Neck: N E C K > 0.90, A M B > 0.65, FTS > 0.50, QvNHIT < 0.33 • Electrical Pickup: QvNHIT > 0.33 A n additional five burst categories are due to calibration activities and certain water ac-tivities. Light is occasionally produced in the detector during D 2 0 circulation either for Chapter 9. SNO Supernova Monitoring Programme 214 the purpose of purification or for monitoring. Pertinent running conditions are included in the data structure, and this information is used by the burst classification algorithm: • Manipulator Light: Calibration source moving bit, A M B > 0.75, ITC > 0.65, N E C K < 0.20 • P C A Retrigger: Calibration P C A source bit, QvNHIT > 0.33 • D20 Circulation: D20 Circulation bit, either FTS tags higher fraction of events than any other cut or N E C K > 0.75, FTS > 0.50 • D 2 0 Assay: D20 Sample Line Assay bit, A M B > 0.75, N E C K > 0.75. Another burst classification is designed to alert to the detector operator to the possibility of a malfunction of the 10 MHz experiment clock. If the experiment clock is not updating as it should, P M T flasher events accumulate until they trigger the Level 1 burst monitor. This type of burst is identified by comparing the duration of the burst according to the 10 MHz clock and the 50 MHz clock: • Problem Clock: duration (10 MHz) = 0, duration (50 MHz) > 1 second. A l l bursts are also required to have fewer than 35% of the events pass all of the data reduction cuts. The final burst category is that of "Spallation", which is mentioned as a SNO physics background in Section 8.2. Spallation bursts are identified by using information provided by the muon tag and the fraction of events that pass the set of Level 2 data reduction cuts. Bursts in which 35% or more of the events survive the data reduction cuts undergo additional processing in the Level 3 stage (see Section 9.2.3). In order to reduce the contamination due to calibration events, the spallation classification also requires that 90% or fewer of all events pass the data reduction cuts: Chapter 9. SNO Supernova Monitoring Programme 215 Burst Cause N E V E N T = 50 N E V E N T = 30 Rate (day-1) Fraction of Total Bursts Rate (day"1) Fraction of Total Bursts P M T Flasher 0.96 3.6% 1.55 3.5% Flat T A C 1.48 5.6% 1.64 3.7% Wet-End H V Breakdown 0.27 1.0% 0.28 0.6% Dry-End H V Breakdown 0.51 1.9% 0.69 1.6% Neck 0.58 2.2% 1.03 2.3% Electrical Pickup 2.87 10.8% 5.62 12.8% Manipulator Light 1.54 5.8% 1.67 ' 3.9% Retrigger 0.13 0.5% 0.18 0.4% D 2 0 Activity 2.50 9.4% 3.12 7.1% Broken Clock 0.19 0.7% 0.26 0.6% Spallation 0.03 0.1% 0.06 0.1% Unknown 15.46 58.3% 27.85 63.3% Total 26.52 100% 43.95 100% Table 9.3: Burst rate due to various causes as identified by the Level 2 burst classification algorithm. Results are included for two settings of the N E V E N T burst trigger parameter. The majority of "Unknown" bursts are due to calibration activities. • 1 muon tag • 0.35 < fraction passing data reduction cuts < 0.90. To further restrict the number of events incorrectly identified as spallation events due to calibration activity, it is necessary to exclude data in which the source manipulator system is in use. The impact on the livetime is negligible at 1.4% of all NHIT100 live data. The results of the burst classification algorithm for the bursts identified during the offline analysis are summarized in Table 9.3 for the N E V E N T = 30 and N E V E N T = 50 data sets. Analysis of the offline burst data set indicate that the rate of P M T flasher events is about 1 /day. The source of these bursts is almost exclusively due to mine blasting activities, which occur on average once per day (usually at approximately 03:00 Sudbury local time). The P M T flasher rate using the N E V E N T = 30 setting is slightly higher than Chapter 9. SNO Supernova Monitoring Programme 216 the rate with N E V E N T = 50 because the trigger is more sensitive to seismic activity, which also causes bursts of P M T flasher events. Other significant differences in the burst rate are observed for bursts due to neck and electrical pickup events. Within a burst, these events tend to be clustered together at discrete times, and with a lower events required to form the trigger, these bursts are often identified as several smaller bursts. Also, more spallation events are identified with a more sensitive trigger. In this case, high energy muon events that have fewer associated follower events are able to satisfy the burst trigger. On average, 1 spallation event is identified by the burst trigger every 18 days for the N E V E N T = 30 setting and 1/39 days for the N E V E N T = 50 setting. Characteristics for a number of spallation bursts are presented in Table 9.4. Notice that almost all of the P M T channels register a hit due to the muon event. As many as 227 follower events have been observed in the few seconds after the muon event. R u n # M u o n M u o n # Events D u r a t i o n N H I T G T I D (pass cuts) (seconds) 10008 9338 1697058 47 0.23 10946 9578 299141 227 1.71 11038 9473 260531 33 3.27 11291 9491 1017045 129 1.96 11347 9572 92584 37 0.27 11531 9598 3506018 42 1.71 12257 9362 1088642 75 1.68 12568 9554 417782 177 1.96 13401 9427 2674171 54 1.47 14418 9306 7801105 58 0.41 Table 9.4: Characteristics of bursts classified as spallation events when 50 events are required to form the burst trigger. While the current burst classification algorithm often provides useful information, it does not properly classify all bursts. Sometimes, this is due to the fact that bursts from two different sources of instrumental noise coincide. For example, a flasher P M T burst Chapter 9. SNO Supernova Monitoring Programme 217 is occasionally accompanied by wet-end breakdown as a result of mine blasting activities. However, the spallation event identification appears to be robust. 9.2.2.2 Analysis Summaries A text summary of the relevant run conditions and burst characteristics is made available to the detector operator on shift. Included in the summary is information regarding the burst time, number of burst events, the fraction of events that satisfy various triggers (including the hydrophone) and results of the data reduction cuts. A n example summary text message is shown in Figure 9.5 for a Monte Carlo supernova burst at 10 kpc according to the Burrows supernova model. In addition to the Level 2 text summary, a set of histograms showing various relevant distributions are produced, including NHIT, time, trigger types and the number of P M T hits sorted according to electronics crate, card and channel. Two sets of histograms are provided to show the burst data before and after the data reduction cuts are applied. Distri-butions of event NHIT and relative time can be compared to the plots shown in Section 7.1 for the simulated supernova signal. Events from a genuine supernova are expected to have NHIT values in the range 34-500 PMTs spread over tens of seconds. Many bursts due to instrumental noise have events with NHIT > 1000 PMTs and occur over times of less than 1 second. While the supernova signal is expected to have a significant contribution from the O W L PMTs, the majority of the detector triggers will be due to NHIT triggers and not E S U M triggers. The remaining plots in the analysis summary histograms characterize various levels of electronics channel groupings. In each case, the signal due to a supernova is expected to have a roughly equal number of P M T hits in each of the electronics crates, cards and channels. Figures 9.6 and 9.7 show an example of the Level 2 analysis summary histograms for a Monte Carlo supernova burst at 10 kpc according to Chapter 9. SNO Supernova Monitoring Programme 218 Ref . burst_10000_001 A supernova b u r s t candidate has been found by the f i r s t l e v e l t r i g g e r and has been analysed by the second l e v e l t r i g g e r . Burst ZDAB f i l e : burst_10000_001.zdab ( in / s c r a t c h / l t / s s t r e a m / s n w a t c h / z d a b s on SURF) A n a l y s i s summary PDF f i l e : burst_10000_001.pdf ( in / s c r a t c h / l t / s s t r e a m / s n w a t c h / l e v e l 2 / p d f on SURF) A n a l y s i s Info Summary: SNOMAN v e r s i o n 4.0186 SNOMAN a n a l y s i s time 0.58 minutes Run Info Summary: Run type Run f l a g s Run c r a t e f l a g s Run N100_med t h r e s h o l d . . . Supernova Leve l 2 A n a l y s i s Summary: R U N # 3 ( s t a r t i n g at GTID = 1 ) Date / Time 20/01/2000 at 02h 16m 07s (Sudbury l o c a l time) Time d u r a t i o n 47.4995483 s Burst s i z e 572 events NHIT100 t r i g g e r s 100.0% ESUM t r i g g e r s 0.0% OWL t r i g g e r s 0.0% HYDROPHONE t r i g g e r s 0 events Data c l e a n i n g tags: #Passed MUON_TAG 0 Data c l e a n i n g cu t s : %Failed AMB_CUT 0.0% NECK_CUT 0.0% RING_OF_FIRE_CUT 0.0% QvT_CUT 0-2% FTS_CUT 0.3% QvNHIT_CUT 0.0% CRATE-ISOTROPY_CUT 0.0% QCLUSTER_CUT 0.0% ITC_CUT 0.2% FGC_CUT 0.0% ==> Events remaining a f t e r a l l cu t s : 99.3% ( 568 events) ==> Event type: UNKNOWN Neutr ino UC b i t OFF 0-18, Tub ON 16 h i t s Figure 9.5: Level 2 analysis summary text message. Chapter 9. SNO Supernova Monitoring Programme 219 Supernova Trigger Level 2 Analysis Burst Date / Time: 20/01/2000 at 02h 16m 07s (Sudbury local time) Burst Size: 572 events (99.3% remaining after all cuts) Burst Type: UNKNOWN ZDAB File: SN_lxlOkpc_nosalt (Burrows model) 20 h 10 0 i 1 1 1 1 r 10 HI i i . . . . i . . . . i . 0 2500 5000 7500 10000 > 200 400 NHIT spectrum (no cuts) 60 40 20 h 0 10 20 30 40 50 —I L 20 40 Time spectrum (s) (no cuts) 600 h 400 h 200 T — I — I — I — | — i — i — i — i — I — i — i — r j I • i i I i i i_ _i i i i_ 0 10 20 Trigger bits (no cuts) 30 3000 2000 1000 L r i i i i | i i i i | i i i i l i i i _i I i i i i_ 5 10 15 Crate distribution (no cuts) 4000 r 3000 kJ 2000 h 1000 0 T - I — i — i — i — i — i — i — i — I — i — i — i — r • 1 I I I I I I L 5 10 15 Card distribution (no cuts) 2000 1500 h 1000 500 0 i i i i i i i i i i i i i i 10 20 30 Channel distribution (no cuts) Figure 9.6: Level 2 analysis summary histograms showing the raw burst data before the data reduction cuts have been applied. The example shown is a simulated supernova burst at 10 kpc according to the Burrows model. Chapter 9. SNO Supernova Monitoring Programme 220 Supernova Trigger Level 2 Analysis Data Cleaning: AMB_cut= 0% NECK_cut= 0% ROF_cut=0% QvT_cut= 0% FTS_cut= 0% QvNHIT_cut= 100% ISOTROPY_cut= 0% QCLUSTER_cut= 0 % ITC_cut= 0 % FGC_cut= 0 % Events remaining after all cuts: 99.3% (568 events) 20 10 1—r i • • • • i • • • • i * 1 0 2500 5000 7500 10000 kyin,., nm 200 400 NHIT spectrum (cuts) 60 40 20 0 1 T 1 | I , I | , ' -- (1.8 (1.6 L | l l l l | M ^ J ^ M i | > y i l | t W J J --0.4 0.2 C... \ -0 10 20 30 40 50 — - -— — • -20 40 Time spectrum (s) (cuts) 600h' ' ' ' 1 ' ' ' ' 1 ' ' ' ' 400 200 0' ' ' 0 _l I I I I L 10 20 Trigger bits (cuts) 30 3000 2000 1000 -0 H—i—i—i—1—i—i—i—i—I—i i—i—i—i—i—i—r _i i I i i i i_ -I I I I I I I L_ 5 10 15 Crate distribution (cuts) 4000 3000 tJ 2000 '-1000 h 0 nr>—i—i—i—r~i—i—i—i—i—r—i—i—r 1 I 1 I i I I I L I . . . . I 5 10 Card distribution (cuts) 15 2000 1500 1000 500 -0 prr—i—i—i—I—I—I—i—i—I—r j i i i i i i i i_ 10 20 30 Channel distribution (cuts) Figure 9.7: Level 2 analysis summary histograms showing the burst data after the data reduction cuts have been applied. The example shown is a simulated supernova burst at 10 kpc according to the Burrows model. Chapter 9. SNO Supernova Monitoring Programme 221 the Burrows model. The inset plot in the NHIT histogram shows the full NHIT range (0-10000 PMTs) in order to indicate the number of events with NHIT > 1000. An inset plot showing the cumulative time distribution is also provided for the time histogram. These burst characterizations are not only useful for recognizing an actual supernova, but they also allow the detector operator to diagnose bursts due to instrumental noise or detector instability online. The supernova analysis isolates the burst events in a timely manner so that the detector operator can diagnose the problem almost immediately. 9.2.2.3 Communication Analysis results from the Level 2 analysis are saved to a log file and the summary text file and histograms are sent by email to members of the SNO Supernova Working Group, the detector operator email account as well as being posted to an internal website. Detailed procedures [129], [130] are also available at the website outlining how a detector operator on shift is expected to respond to a Level 2 burst alarm and how to interpret the results of the Level 2 analyses. For bursts in which fewer than 35% of the events pass all of the Level 2 data reduction cuts, detector operators are instructed to investigate any burst that is identified by the burst classification algorithm as "Unknown". The popup alert window shown in Figure 9.8 is used to inform the detector operator of such an event. If a burst is identified as one of the known types, no alert is issued other than the log file entry. A burst in which 35% or more of the events pass the all of the Level 2 data reduction cuts also automatically triggers a dial-out computer [131], which currently calls three cell phones carried by members of the SNO Supernova Working Group 3 . A pre-recorded voice message indicating that a significant burst has occurred is stored on the dial-out computer. Text-to-speech software is used to provide additional information in the phone message 3 The author is one of the members of the SNO Supernova Working Group that carries a cell phone for supernova support. Chapter 9. SNO Supernova Monitoring Programme 222 xmessage fllert Posted on: Sep 21 2001 20:38:44 Sudbury local tine ========================== Burst 10000.001 Detected ====================: Rn UNKNOUN burst of events has triggered the Level 1 Supernova Burst Monitor. Mhile the nunber of events passing the data cleaning cuts i s less than the Level 3 threshold, the cause of this burst requires investigation. Proceed according to the "SH0 Supernova Monitoring and Response" checklist and procedure, and investigate this burst using: 1) The results of the Level 2 analysis (sunnary, histograms) 2) Exanination of the burst/clean ZDflB f i l e s with "xsnoed" 3) Your knowledge of the detector's status* Post your findings on 'Manhattan' by using the *Edit* button at the top of the Level 2 posted connent response forn page. < Burst Data Locations > The rau data for these events are available in tuo locations: * Events passing the Level 1 burst Monitor are written to: —> SURF: /scratch/lt/sstrean/snuatch/zdabs/burst_10000_001. zdab • Events passing the Level 2 data cleaning cuts are written to: --> SURF : /scratch/1 t/sstrean/snuatch/clean_zdabs/clean_10000_001 * zdab — < 'Manhattan' Locations >- — — RESPONSE CHECKLIST a PROCEDURE: —> Supernova Logbook:/ Procedures ANALYSIS RESULTS: —> Supernova Logbook;/ Burst Analysis / Level 2 / Rnalysis EXAMPLE BURSTS: —> Supernova Logbook:/ Burst Analysis / Level 2 / Exanples ('Click to close uindou(s) (AG and UO ' ^CLevel 2 Histograws') Figure 9.8: Level 2 popup window alerting the detector operator that a burst has been identified as "Unknown" by the burst classification algorithm. Chapter 9. SNO Supernova Monitoring Programme 223 xmessage fllert Posted on: Oct 1 2001 10:27:32 Sudbury local tine ========================= Burst 10000.001 Detected ===================: R burst of events has passed the Level 3 threshold. The cause of this SIGNIFICANT burst requires investigation. Rs the detector operator, you are expected to initiate a conference call using the conference centre phone nunber and passcode listed on the Supernova Nunbers sheet i n the control roon: Telephone: XXXXXX Chairperson: XXXXXX (press XX to start the call) The available on-call supernova support personnel, the SIC and possibly others u i l l Join the conference call as participants. Proceed according to the "SNO Supernova Monitoring and Response" checklist and procedure, and investigate this burst using: 1) The results of the Level 2 analysis (sunnary, histograns) 2) EKanination of the burst/clean 2DRB files with "xsnoed" 3) Your knowledge of the detector's status. Hatch for the results of the Level 3 analysis to appear shortly in the XXXXXX enail account and on ' M a n h a t t a n ' . Post your findings on 'nanhattan' by using the 'Edit' button at the top of the Level 2 posted connent response form page. < Burst Data Locations > — The raw data for these events are available in tuo locations: • Events passing the Level 1 burst Monitor are written to: --> SURF:/scratch/lt/sstrean/snwatch/zdabs/burst_10000_001.zdab * Events passing the Level 2 data cleaning cuts are written to: —> SURF:/scratch/lt/sstrean/snuatch/clean_zdabs/clean_10000_001.zdab — < 'Manhattan' Locations > RESPONSE CHECKLIST S PROCEDURE: —> Supernova Logbook:/ Procedures RNRLYSIS RESULTS: —> Supernova Logbook:/ Burst Analysis / Level 2 / Analysis —> Supernova Logbook:/ Burst Analysis / Level 3 / Analysis EXAMPLE BURSTS: —> Supernova Logbook:/ Burst Analysis / Level 2 / Exanples —> Supernova Logbook:/ Burst Analysis / Level 3 / Exanples C'Click to close window(s) (RG and UG^X'Level 2 Histograms') Figure 9.9: Level 2 popup window alerting the detector operator that a burst in which 35% or more of the events have passed the data reduction cuts. An appropriate sound also accompanies this alert window. Chapter 9. SNO Supernova Monitoring Programme 224 such as the run type, specific detector conditions and the fraction of events passing the data reduction cuts. The dial-out computer is a Pentium 133 MHz based computer with a Dialogic ProLine/2V dial-out card installed. Tests of the dial-out phone connection are performed once every hour and a test of the full dial-out system, where the cell phones are actually called, is performed once every week. The detector operator on shift is notified by a popup window as well as email that the dial-out has occurred and at that point the operator initiates a conference call to which the cell phone carriers call in and join as participants. The alert window for this scenario is shown in Figure 9.9. 9.2.3 Level 3 Bursts in which 35% or more of the events pass the all of the Level 2 data reduction cuts pass on to the Level 3 analysis where they are analyzed event-by-event using a set of S N O M A N software routines similar to the ones developed for the Level 2 analysis. 9.2.3.1 Threshold The number of bursts removed due to various Level 3 threshold values is shown in Fig-ure 9.10. A large number of bursts are removed for threshold settings less than 35%. How-ever, for threshold values greater than 35%, the number of bursts removed stays roughly constant until calibration events are removed with threshold values greater than 90%. An examination of observed muon-induced spallation events indicates that essentially none of these events are removed with a 35% Level 3 threshold. Therefore, it is felt that 35% represents a conservative threshold for a burst of supernova neutrinos. Note that in Figure 9.10 not all bursts are removed with a Level 3 threshold of 100% because only the bursts in which the fraction of burst events passing the data reduction cuts is strictly less than the threshold value are cut. Chapter 9. SNO Supernova Monitoring Programme 225 0.8 i o E & CC 0.6 0.4 0.2 1 1 1 ! , r-/ / / y 1 * / s 1 / 1 / NEVENT = 50 1 I 11 ' / / / - - NEVENT = 30 Current -Level 3 Threshold 1 i 1 , 1 , 1 0.2 0.4 0.6 Level 3 Threshold 0.8 Figure 9.10: The number of bursts removed using various Level 3 threshold values. The current threshold value of 35% is indicated. 9.2.3.2 Event Reconstruction Unlike in the Level 2 analysis, each event is reconstructed in the Level 3 analysis to de-termine the event time, position and direction cosines (the direction is only meaningful for electron/positron events and for 7-ray events). In water, low energy electrons (and positrons) travel only a few centimetres at relativistic speeds, therefore the Cerenkov light from these particles can be assumed to originate from a point source at one instant in time. The location of the event interaction vertex, Xfit, and the time the interaction took place, t/it, can be reconstructed using the time that each P M T is hit. The time, t{ that P M T i Chapter 9. SNO Supernova Monitoring Programme 226 receives light is given by: U = t f i t + ^ ~ S f U [ (9.1) c/n where %i is the position of P M T % and c/n is the speed of light in a medium of refractive index n. The interaction vertex position and time are then determined by minimizing the time residual, Ri, for each P M T : Ri = k- tfit - I*'"*/*' (9.2) c/n using the x2 quantity X 2 = E ^ - (9-3) The <7j value is the 1-sigma width in the P M T timing resolution, which is determined for each P M T using the laserball calibration source. PMTs that have high residual values ( P M T noise events or events due to reflection) are removed from the x2 a n d the remaining P M T hits are reconstructed. This minimization algorithm is called the "time fitter" in S N O M A N . The direction provided by the time fitter is determined by considering the mean value of the reconstructed vertex xfu values. A more sophisticated reconstruction method employs a simulated annealing algorithm to determine which orientation of a cone best fits the P M T hit data [132]. As mentioned in Section 4.2, Cerenkov light is emitted in a cone of half angle QQ = 42° with respect to the trajectory of the charged particle. The reconstruction is performed by minimizing the residual quantity sin2^>, where 4> is the angle between the axis of the cone and the vector from the event vertex position to the P M T . When performing the summation over P M T hits, weights based on the sin 2 <f> values are assigned to each P M T . Those P M T hits with high residual values are given a lower weight in the fit. The simulated annealing method, which is used to identify the global minimum, essentially weights the weighting factors. Initially, all of the P M T hits are used to reconstruct the cone, and then gradually the selective power of the residuals is increased and P M T hits with high residual values Chapter 9. SNO Supernova Monitoring Programme 227 contribute less pull to the orientation of the cone. This algorithm is called the "elastic fitter" in S N O M A N and is the method used to assign to event reconstruction information for the online supernova analysis. Other reconstruction methods exist, but the algorithms are considerably more compu-tationally intensive than the elastic fitter. Therefore, in the interest of obtaining a reliable result within as short a time as possible, the elastic fitter is adopted as the reconstruction method to be used in the Level 3 analysis stage. Those events which have reconstructed positions within r = 840 cm (the fiducial volume enclosed by the PMTs) are designated as valid events and are the focus of the remaining analysis. 9.2.3.3 Locating the Supernova The direction cosine components of each valid event are used to search for elastic scat-tering events, which are expected to best convey information about the direction of the possible supernova. Without any detector background, the angular resolution obtained by considering only the elastic scattering events is [85] w ^ W T s ( 9 ' 4 ) where NES is the number of electron events due to elastic scattering interactions that are observed above the supernova analysis threshold in SNO. According to the results presented in Section 8.4, approximately 25 elastic scattering events are expected using the Beacom and Vogel model whereas 23 events are expected using the Burrows model. Using this naive prescription, SNO would be able to locate the position of the supernova to within an angle 86 ~ 5°. However, events from other supernova neutrino interactions constitute a background that makes it more difficult to isolate the signal due to elastic scattering. One crude method used to search for the elastic scattering peak is to simply to sum the individual components of the direction cosine values. The idea is that the isotropic back-ground due to the other neutrino reactions cancel, while the forward-peaked contributions Chapter 9. SNO Supernova Monitoring Programme 228 due to elastic scattering reactions sum to a non-zero value. However, this method appears to have limited success. A more sophisticated technique involves binning the direction cosine data. Using an angular bin window of 9 = 24.1° (corresponding to cos# = 0.91), the burst data is exam-ined for a peak in the angular distribution. The elastic scattering peak search algorithm initially considers 234 cardinal directions on a sphere as possible sources of the neutrino burst (corresponding to points on a spherical grid separated by 22.5°). The algorithm then concentrates on the most likely direction from the first stage and searches in a progres-sively finer 8-point grid around that point in order to identify the direction that yields the maximum number of events in the angular bin window [133], [134]. Investigations concerning how well SNO can locate the angular position of the supernova have been carried out with simulated burst data sets produced using the Burrows model. In order to generate the large number of independent data sets needed for this study, ten sets of 100 supernovae at 10 kpc are produced and then sampled randomly to create many smaller data sets. The elastic scattering peak search algorithm is then applied to each of the smaller data sets in order to determine the probability that the algorithm successfully located the supernova within a certain angle, 89. The data shown in Figure 9.11 demonstrate that the current peak search algorithm is able to determine the location of a supernova as far away as 7.4 kpc to within 89 = 20° (probability > 50%) during pure D 2 0 operation and 4.5 kpc during salt operation. With salt in the heavy water, the neutron detection efficiency increases and it becomes more difficult to identify the elastic scattering peak. For the same 20° angular deviation, the peak search algorithm is able to locate the position of a 10 kpc supernova approximately 35% of the time in the pure D 2 0 mode and only approximately 17% of the time in the salt mode. The distribution of angular deviations from the true supernova position are presented for several supernova distances in Figure 9.12. At greater distances, for which the supernova signal contains fewer elastic scattering events, the peak Chapter 9. SNO Supernova Monitoring Programme 229 Figure 9.11: Probability of locating a supernova at various distances as a function of the angular deviation from the true supernova location for both the pure D 2 0 and salt detector modes. Chapter 9. SNO Supernova Monitoring Programme 230 0 45 90 135 180 Angular Deviation (degrees) 0 45 90 135 180 Angular Deviation (degrees) 150r c 3 100Y-0 45 90 135 180 Angular Deviation (degrees) 0 45 90 135 180 Angular Deviation (degrees) 0 45 90 135 180 Angular Deviation (degrees) 0 45 90 135 180 Angular Deviation (degrees) Figure 9.12: The angular difference between the actual supernova position and the posi-tion specified by the Level 3 analysis during pure D 2 0 operation. The angular deviation histograms for the salt mode are similar. Chapter 9. SNO Supernova Monitoring Programme 231 1 0.8 0.6 S 0.4 o E Q) §" 0.2 0) O) 0 8 o - J o a I I . I 1 1 1 1 — • 10 degrees -V r \ v s 20 degrees 40 degrees \ \ \ N V \ s T "V V Pure D 2 0 1 , 1 , 1 1 , 1 8 10 1 • • — 4 k 1 1 1 1 1 1 i > T - - A 10 degrees -i 20 degrees » - - • 40 degrees 0.8 \ \ \ 0.6 " k . 0.4 — _ 0.2 Salt n l i , i , i Tl 1L_ 4 6 8 Supernova Distance (kpc) 10 Figure 9.13: Probability of locating a supernova within various angular areas as a function of supernova distance for both the pure D 2 0 and salt detector modes. Chapter 9. SNO Supernova Monitoring Programme 232 finding algorithm often completely fails to locate the supernova. In some instances, this failure is due to the low number of elastic scattering events in that trial. The random sampling technique used in this analysis does not guarantee that all trials have the same number of elastic scattering events. Figure 9.13 illustrates the probability of locating a supernova as a function of distance for various angular resolution values. For a supernova at 10 kpc, it is possible to locate the supernova to within 42° during the pure D 2 0 mode and 86° during the salt mode. Further studies are required in order to further optimize the peak search algorithm and to investigate means of decreasing the background to the elastic scattering peak. It should be possible to reduce the charged-current contribution by using a high energy cut. The tail of the elastic scattering event NHIT distribution does not extend as far as the charged-current event tail. Therefore, a high energy cut would serve to increase the ratio of elastic scattering events to the events remaining from other interactions. A n energy cut is not an effective method to reduce the neutral-current contribution, however, because those events have the same energies as the majority of the elastic scattering events. 9.2.3.4 Analysis Summaries As with the Level 2 analysis, a text summary of the burst characteristics resulting from the Level 3 analysis is made available to the detector operator on shift. The information provided in the summary includes the number of valid events in each of the D 2 0 and H 2 0 regions as well as the results of the elastic scattering peak finding algorithm. An example summary text message is shown in Figure 9.14 for a Monte Carlo supernova burst at 10 kpc according to the Burrows supernova model. As well, a set of summary histograms is produced for each Level 3 burst. The plots show the NHIT and relative time distributions for the valid events in addition to the volume-weighted distribution of radial positions and the detector (j) and 9 angular distributions. Chapter 9. SNO Supernova Monitoring Programme 233 R e f . b u r s t _ 1 0 0 0 0 _ 0 0 1 A s u p e r n o v a b u r s t c a n d i d a t e h a s p a s s e d t h e l e v e l 2 a n a l y s i s t h r e s h o l d a n d i s now b e i n g a n a l y s e d b y t h e t h i r d l e v e l t r i g g e r . C l e a n e d ZDAB f i l e : b u r s t _ 1 0 0 0 0 _ 0 0 1 . z d a b ( i n / s c r a t c h / l t / s s t r e a m / s n w a t c h / c l e a n _ z d a b o n SURF) A n a l y s i s I n f o Summary: SNOMAN v e r s i o n 4 . 0 1 8 6 SNOMAN a n a l y s i s t i m e 2 . 4 1 m i n u t e s S u p e r n o v a L e v e l 3 A n a l y s i s Summary: RUN # 3 ( s t a r t i n g a t G T I D = 1 ) D a t e / T i m e 2 0 / 0 1 / 2 0 0 0 a t 02h 16m 08s ( S u d b u r y t i m e ) T i m e d u r a t i o n o f c l e a n e v e n t s . . . 4 7 . 4 9 9 5 4 8 3 s (50 MHz) T o t a l number o f c l e a n e v e n t s . . . . 551 e v e n t s F i t t e d D a t a R e s u l t s ( e l a s t i c f i t t e r , v e r t e x w i t h i n PSUP) D a t e / T i m e 2 0 / 0 1 / 2 0 0 0 a t 07h 16m 7 . 3 2 4 5 9 5 8 s ( U n i v e r s a l t i m e ) T i m e d u r a t i o n 4 7 . 4 9 9 5 4 8 3 4 1 s (50 MHz + f i t ) Number o f e v e n t s . . . 420 N H I T 1 0 0 t r i g g e r s . . . 100.0% N H I T < 75 37.9% N H I T >= 75 62.1% ESUM t r i g g e r s 0.0% OWL t r i g g e r s 0.0% Summed d i r c o s 0 . 6 1 4 9 0 4 - 0 . 3 1 5 3 6 3 - 0 . 7 2 2 7 9 9 ( t o w a r d SN) D20 r e g i o n H20 r e g i o n F r a c t i o n o f e v e n t s 50.7% 49.3% F r a c t i o n o f NHIT100 t r i g g e r s . . 50.7% 49.3% F r a c t i o n o f N H I T < 75 26.0% 11.9% F r a c t i o n o f N H I T >= 75 24.8% 37.4% F r a c t i o n o f ESUM t r i g g e r s 0.0% 0.0% Summed d i r c o s ( t o w a r d SN) 0 . 9 1 0 . 00 - 0 . 4 1 - 0 . 9 5 - 0 . 3 2 - 0 . 0 4 S u p e r n o v a D i r e c t i o n A n a l y s i s R e s u l t s D i r e c t i o n c o s i n e s ( t o w a r d SN) . . . 0 . 1 6 9 7 3 - 0 . 6 8 6 4 3 - 0 . 7 0 7 1 1 Z e n i t h , a z i m u t h 1 3 5 . 0 0 0 0 2 d e g r e e s 1 6 6 . 1 1 1 0 9 d e g r e e s E o f N D e c l i n a t i o n , r i g h t a s c e n s i o n . . . . - 4 5 . 3 9 7 2 8 d e g r e e s 1 7 . 3 3 7 9 2 h o u r s Figure 9.14: Level 3 analysis summary text message. Results from the elastic scattering peak finding algorithm are also used to plot a histogram of the cos 6sN distribution, where 6SN is the angle between the event direction and the direction of the supernova, as described in Section 7.6. Events in the D 2 0 and H 2 0 regions are also analyzed separately to ensure the consistency of the burst events. An example of the Level 3 analysis summary histograms are shown in Figure 9.15. The analysis histograms for Chapter 9. SNO Supernova Monitoring Programme 234 the heavy- and light-water regions which are also part of the set, are shown in Figures 9.16 and 9.17 (also see Appendix D). 9.2.3.5 Communication The summary text file and analysis histograms are sent via email to members of the SNO Supernova Working Group, the detector operator email account, as well as being posted to an internal website. By the time that the Level 3 analysis results are available, members of the SNO Supernova Working Group should already have contacted the detector oper-ator and assessed the significance of the burst. The SNO Supernova Working Group, in consultation with the detector operator, will determine whether or not to manually issue an external alert at the Level 4 stage. 9.2.3.6 Burst Causes Despite the application of the data reduction cuts during the Level 2 analysis stage, a number of bursts in which 35% or more of the events remain pass on to be analyzed by the Level 3 stage. Based on the number of bursts experienced at the Level 2 stage, it is not surprising that the vast majority of the bursts that reach the Level 3 stage are due to calibration activities. In any case, the cause of each burst is investigated by reviewing the detector shift reports and by studying the the burst data files and is correctly assigned in Table 9.5. Instances in which the detector operator does not provide information that properly reflected the status of the detector in the case of some calibration activities has been accounted for in the results presented in Table 9.5. Results comparing the Level 3 burst rate using the NEVENT=30 and 50 burst trigger parameter settings are also presented in Table 9.5. The main difference observed between the two settings is the significant increase in the burst rate due to calibration activity, while the burst rates due to the other sources change only slightly. Changing the N E V E N T parameters can sometimes reduce the size of a burst and therefore the fraction of events Chapter 9. SNO Supernova Monitoring Programme 235 Supernova Trigger Level 3 Analysis Clean Burst Date / Time: 20/01/2000 at 02h 16m 08s (Sudbury local time) Clean Burst Size: 417 events fit within PSUP radius (55% D 20,45% H 20) Clean ZDAB File: SN_lxlOkpc_nosalt (Burrows model) -i 1 1 1 1 1 1 1 1—n 200 400 NHIT spectrum within PSUP 0 20 40 Time m (elastic) within PSUP in seconds 15 h -i—i—i—i—i—i—r ~ \ — i — i — r 0 1 2 3 R„, (elastic) within PSUP (AV = 1) 100 200 300 phi m (elastic) within PSUP in degrees •1 -0.5 0 0.5 1 cos(theta)m (elastic) within PSUP 101 i i i i i -1 -0.5 0 0.5 1 cos(theta)SN (elastic) within PSUP Figure 9.15: Level 3 analysis summary histograms showing various distributions for all burst events that are reconstructed within the detector volume. The example shown is a simulated supernova burst at 10 kpc according to the Burrows model. Chapter 9. SNO Supernova Monitoring Programme 236 Supernova Trigger Level 3 Analysis Events fit within D 7 0 volume (R .le. 600 cm): 55% (231 events) 15 10h 5h 0 2500 5000 7500 1000(1" IdilUUuuLlL J L 200 400 NHIT spectrum within D 2 0 0 20 40 Time m (elastic) within D 2 0 in seconds Rn, (elastic) within D 2 0 (AV = 1) -1 -0.5 0 0.5 1 cos(theta)m (elastic) within D 2 0 100 200 300 phi m (elastic) within D 2 0 in degrees 10 h 7.5 l—|—i—i—i—i—|—i—i—i—i—|—i—i—i—r -0.5 0 0.5 cos(theta)SN (elastic) within D 2 0 Figure 9.16: Level 3 analysis summary histograms showing various distributions for burst events that are reconstructed within the D 2 0 region. The example shown is a simulated supernova burst at 10 kpc according to the Burrows model. Chapter 9. SNO Supernova Monitoring Programme 237 Supernova Trigger Level 3 Analysis Events fit within H 2 0 volume (R .le. 840 cm & R .gt. 600 cm): 45% (186 events) 0 T 1 I | 1 I 1 1 Ll ' 1 • • I • ' 1 • P • ' ' ' I 1 0 2500 5000 7500 10000 -I I l_ 0 200 400 NHIT spectrum within H 2 0 Rn, (elastic) within H O (AV = 1) 1—I—I—I—I—I—I—I—I—I—I—I—I—I—I—r fl1-^ 0 100 200 300 phim (elastic) within 11,() in degrees ioo FT—1—1—1—r 75 7 50 -25 -i 1 r J _ 0 20 40 Timen t (elastic) within H 2 0 in seconds 1—I—I—I—I—I—I—I—I—i—i—i—r 111 i i II i in iii i in i L •1 -0.5 0 0.5 1 cos(theta)m (elastic) within H 2 0 10 8 6 4 2 0 i—i—i—I—i—i—i—i—I—i—i—i—i—I—i—r—i—r l i i i k • II- l-l "I.IH1 • -Hi •II- • I'll' • ' -1 -0.5 0 0.5 1 cos(theta)SN (elastic) within H 2 0 Figure 9.17: Level 3 analysis summary histograms showing various distributions for burst events that are reconstructed within the H 2 0 region. The example shown is a simulated supernova burst at 10 kpc according to the Burrows model. Chapter 9. SNO Supernova Monitoring Programme 238 Burst Cause N E V E N T = 50 N E V E N T = 30 Rate (day" 1) Fraction of Total Bursts Rate (day- 1 ) Fraction of Total Bursts Calibration 2.98 86.5% 10.06 93.6% Water Activities 0.41 11.9% 0.61 5.7% Spallation 0.03 0.7% 0.06 0.5% Electronics 0.03 0.9% 0.02 0.2% Neck Static 0.00 0.0% 0.00 0.0% Total 3.45 100% 10.75 100% Table 9.5: Rate of bursts due to various causes in which 35% or more of the events remain after the Level 2 analysis stage. Results are included for two settings of the N E V E N T burst trigger parameter. that pass the Level 2 data reduction cuts. This difference accounts for the decrease in the burst rate due to electronics sources. As discussed in Section 9.2.2.1, the rate of spallation events increases as fewer events are required to form the trigger. Since the majority of the events that reach the Level 3 stage are due to calibration activities, many of the bursts are due to a single cause, as observed with the Level 1 burst monitor. Figure 9.18 shows the rate of Level 3 bursts as a function of the time between bursts, indicating that there are approximately 0.6 bursts/day using the N E V E N T = 30 setting. 9.2.4 Level 4 The final stage in the SNO response is to issue an alert to the astronomical community. Interested parties have already approached the SNO collaboration and asked to be placed on a contact list; however, at the time of this thesis, no formal contact list has been established. In the event of a real supernova, the first alert will likely be issued via the SNEWS network. Chapter 9. SNO Supernova Monitoring Programme 239 50 I 5 1 CQ s Q) 40 h 30 20 ro _L 1 I ' N E V E N T = 30 N E V E N T = 50 10 20 30 40 Burst Concatenation Time (seconds) 50 60 Figure 9.18: Level 3 burst rate as a function of the time between bursts, determined offline for the period between November 2, 1999 and January 4, 2001. The most significant contribution to this effect is from calibration activity. 9.2.4.1 S N E W S The inter-experiment SuperNova Early Warning System (SNEWS) is designed to provide a fast and reliable alert to the astronomical community by requiring a coincidence of burst signals from several operating experiments. Alert signals issued by individual experiments are transmitted as secure encrypted text datagrams via the internet to redundant coinci-dence servers located in Japan and Italy. An alert to the astronomical community would be issued in the event that two or more experiments identified a burst within a coinci-dence time of 10 seconds. Assuming that the individual alerts are distributed according to Chapter 9. SNO Supernova Monitoring Programme 240 Poisson statistics, an alert based on a false coincidence would be issued only once per cen-tury [135]. Experiments that are currently participating in SNEWS include L V D [136] and Super-Kamiokande4 [137]. The M A C R O [138] was also an early SNEWS participant, but that experiment has now been decommissioned. While SNO is not yet officially connected to the SNEWS network, members of the SNO collaboration are part of the working group that constitutes the SNEWS collaboration. 9.2.4.2 Communication In the event of a significant burst, SNO would manually connect to the two SNEWS coincidence servers using a client developed by the SNEWS working group. The client provides a secure means of transmitting the following burst information: • experiment identification number • universal time stamp of first valid event • total number of valid events. Information on the celestial location of the supernova can also be submitted to the coincidence server. It is expected that SNO will begin providing automatic alerts once the monitoring programme is determined to be sufficiently mature. 9.2.5 SNO Supernova Response Time Once a burst is determined to have significant physics content, an alert must be sent as quickly as possible in order to be useful to the astronomical community. The expected time required to send an alert to SNEWS is discussed below. 4As of July 16, 2001, the Super-Kamiokande detector has been taken offline in order to proceed with PMT replacement work. They had expected to be back online in mid-December but an accident on November 12 destroyed over 50% of the detector PMTs. It is not currently known when the detector will be able to resume operation. Chapter 9. SNO Supernova Monitoring Programme 241 The first supernova neutrino interaction starts the response time stopwatch. A small amount of time is required to build the hit P M T information into events and send them to the Level 1 burst monitor computer on the surface. Once the events are in the burst trigger FIFO buffer, it is only a matter of milliseconds before the Level 1 trigger is satisfied. For the following discussions on the analysis stages, Monte Carlo bursts with ~ 500 events were analyzed on the supernova analysis computer. The Level 2 background rejection analysis is expected to take on the order of 2 minutes, which is relatively fast compared to the more detailed analysis at the Level 3 stage. The Level 3 analysis takes the longest time since this is where the events are fit to extract time, position and direction information. During the Level 3 analysis, the three members of the Supernova Working Group with cell phones join a conference call initiated by the detector operator and determine whether or not to send an alert to the SNEWS coincidence computer. A n overview of the predicted response time is presented in Table 9.6. The goal of the Sudbury Neutrino Observatory is to be able to send an alert with an estimate of the supernova direction to SNEWS within approximately 20 minutes from the time of the first event in the detector with essentially zero possibility of false alarm. SNO Supernova Response Stage Individual Cumulative Stage Time Stage Time (minutes) (minutes) First SN neutrino interacts in detector 0 0 Data processing offset 0.5 0.5 Level 1 trigger satisfied 0.003 0.5 Level 2 analysis (based on Monte Carlo) 2 2.5 Level 3 analysis (based on Monte Carlo) 15 17.5 Conference call (during Level 3 analysis) 20 22.5 Alert SNEWS (manually) 1 23.5 Table 9.6: Expected time required to perform the SNO burst analysis and issue an alert to SNEWS. The times for the Level 2 and Level 3 analyses are estimated using Monte Carlo simulations running on the supernova burst analysis computer. Chapter 10 SNO Supernova Sensitivity 10.1 Introduction SNO is considered to be sensitive to neutrinos when the PMTs have nominal high voltage and when the appropriate detector triggers are in use. As mentioned in Section 4.7, the primary trigger used for physics analyses is the NHIT100 trigger, which requires a coin-cidence of a certain number of hit PMTs within 100 ns. Different running modes have different trigger requirements, however the time that the NHIT100 trigger is operative de-fines the detector livetime. A further consideration concerns the degree of sensitivity that SNO possesses during its livetime. Both of these aspects are discussed in the sections that follow. 10.2 SNO Detector Livetime Since a supernova may occur at any time, an effort has been made to maintain supernova sensitivity throughout all types of detector activity. During times when the detector is being triggered externally, such as when the laser calibration light source is in use, the formation of NHIT100 trigger is delayed slightly relative to the calibration signal to allow the detector to remain sensitive to neutrino events. Table 10.1 summarizes the NHIT100 trigger thresholds and associated NHIT100 livetime fractions during different detector running conditions. The livetime statistics span the period beginning November 2, 1999 and ending January 4, 2001. For most of this time, the main "neutrino" NHIT100 trigger required 18 hit PMTs 242 Chapter 10. SNO Supernova Sensitivity 243 Run Condition NHIT100 Threshold Fraction of NHIT100 Livetime Default Monitor (PMTs) (MeV) (PMTs) (MeV) Neutrino 18 2.0 34 3.8 80.0% 16 1.8 34 3.8 3.3% Calibration: • electronics 35 3.9 35 3.9 1.5% • laser (external trigger) 50 5.6 50 5.6 3.0% —> source setup 50 5.6 50 5.6 0.8% • 16N, 8Li, 2 5 2 Cf 18 2.0 69 7.7 2.5% —> source setup 50 5.6 69 7.7 0.5% • U, Th < 44 < 4-9 44 4.9 1.0% 45-60 5.0-6.7 45-60 5.0-6.7 0.1% —>• source setup 50 5.6 50 5.6 0.1% • other < 25 2.8 34 3.8 0.2% 35-50 3.9-5.6 35-50 3.9-5.6 0.1% Maintenance 40 5.0 40 5.0 4.9% Diagnostic 35 3.9 35 3.9 0.1% 55 6.1 55 6.1 0.1% Unstable Conditions 35 3.9 35 3.9 1.6% Other 18 2.0 34 3.8 0.2% Average Threshold 21.0 2.3 36.2 4.0 100% Table 10.1: The 100 ns coincidence trigger thresholds during various detector running conditions and their associated NHIT100 livetime fractions for the period from November 2, 1999 to January 4, 2001. The default threshold values are those implemented by the detector event trigger, whereas the monitor values denote the threshold used in the burst identification algorithm. within 100 ns; however, in December 2000, the neutrino trigger threshold was lowered to 16 PMTs in coincidence. In total, 86.7% of the data collected with the NHIT100 trigger enabled was at a trigger threshold of 2 .MeV or lower. Since November 1999, the SNO detector had high voltage enabled for 92.1% of the time, with the NHIT 100 trigger enabled for 98.7% of that time. Therefore, the fraction of time that SNO has been sensitive to neutrinos is 90.9%, as shown in Figure 10.1. Detector downtime is mainly due to power outages during electrical storms and interruptions in the power arising from Chapter 10. SNO Supernova Sensitivity 244 mining operations. For instance, the significant downtime during the months of August and September 2000 is due to power interruptions resulting from a large number of electrical storms. 50 100 150 200 250 300 350 400 Nov Dec Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Jan Day Number Figure 10.1: SNO supernova livetime as a function of time for the period from November 2, 1999 to January 4, 2001. The average detector NHIT threshold during the time that SNO was sensitive to neu-trinos was approximately 21.1 PMTs or 2.4 MeV. Taking into account the run-specific thresholds discussed in Section 9.2.1.2 for various operating conditions, the average moni-toring NHIT threshold was 36.2 PMTs or 4.0 MeV. Before December 16, 1999, when the global trigger channel was not included in all events, the burst monitoring threshold was Chapter 10. SNO Supernova Sensitivity 245 1 P M T higher (~0.1 MeV) in the cases where the threshold was applied by the burst monitor and not the detector trigger. 10.3 SNO Distance Sensitivity The maximum distance to which SNO is sensitive to a burst of neutrinos from a supernova is determined by considering the minimum supernova signal that satisfies the Level 1 burst trigger. In order to characterize the SNO distance sensitivity, data from two independent simulations of 100 supernovae at 10 kpc using the Burrows model 1 are used to determine the fraction of events that satisfy the NHIT and time window trigger criteria. A time window of 2 seconds is used in all cases. This fraction is then used to scale the minimum number of events required for the trigger to the number of events expected over the course of the full duration of the burst. The scaled number of events corresponds to the total number of events in the burst, which is associated with a standard supernova at a certain distance. For example, of the 545 events that register in the detector above the analysis threshold during the pure D 2 0 phase, approximately 69% of the events in the first 2 seconds have NHIT > 34 PMTs, and are considered by the burst trigger. In the case where 30 such events are required to form the trigger (NEVENT) , the corresponding number of events in the full burst becomes 30/0.69=43 events with NHIT > 34 PMTs . A total burst of 43 events translates into a supernova at a distance of 35 kpc. Hence, the NHIT trigger parameter determines the fraction of the total signal that meets the trigger criteria, while the N E V E N T parameter determines the minimum size of the supernova burst signal. When the number of events in the first 2 seconds with NHIT > 34 P M T s is less than the N E V E N T setting, the burst monitor will not trigger and SNO is no longer sensitive to a supernova using this algorithm. xThe simulated data sets do not contain the contribution due to reactions involving oxygen. For the Burrows model, this contribution is estimated to be less than 2% of the total number of events. Chapter 10. SNO Supernova Sensitivity 246 10.3.1 NHIT Trigger Parameter Fewer events are available to form a burst trigger during periods in which high NHIT thresholds are used, and therefore the detector is less sensitive to neutrinos from a supernova during those times. Figure 10.2 shows how the SNO distance sensitivity is affected as a function of the burst trigger NHIT threshold. The increase in the number of events due to the neutron signal is clearly pronounced in the NHIT region below 100 PMTs . In the unlikely event that the detector trigger threshold (or a future implementation of the burst monitor) is set to NHIT = 215 PMTs, SNO would no longer possess sensitivity to a generic Burrows-like supernova2 using the burst search method that has been described. However, the small fraction of events that are present above this threshold (approximately 5.4% during the pure D 2 0 mode and 4.2% in the salt mode) would still exist in the data and could be identified using other search algorithms. According to the Burrows supernova model, the average distance sensitivity during pure D 2 0 operation is approximately 35 kpc using the supernova analysis threshold of 34 PMTs and requiring 30 events to form the trigger in conjunction with the standard run-specific thresholds. The corresponding distance sensitivity during the salt running mode is approximately 40 kpc. When 50 events are required to form the trigger instead of 30, the average distance sensitivity decreases to 27 kpc and 31 kpc for pure D 2 0 and salt, respectively. Similar results are obtained using the Beacom and Vogel supernova model. Using the default burst monitor parameters and simulated data with the Beacom and Vogel model, the distance sensitivity is 34 kpc during the pure D 2 0 running mode and 41 kpc during the salt running mode. Figure 10.2 also shows that the distance sensitivity does not increase significantly for 2The corresponding upper NHIT threshold limit according to the Beacom and Vogel model is slightly higher because of the higher neutrino temperatures used in that model. Chapter 10. SNO Supernova Sensitivity 247 Burst Trigger NHIT Threshold Figure 1 0 . 2 : SNO supernova distance sensitivity as a function of the online burst trigger NHIT threshold determined using simulated data sets that employ the Burrows supernova model. Various threshold settings are labelled to indicate the corresponding distance sen-sitivity values during the pure D 2 0 and salt detector operation phases for two N E V E N T trigger parameter settings. an NHIT setting below the current analysis threshold of 34 PMTs . Therefore, any consid-erable increase in the sensitivity to distant supernovae will result from adjustments to the N E V E N T parameter rather than the NHIT parameter. 10.3.2 N E V E N T Trigger Parameter Lowering the number of events required for the burst trigger allows the trigger to be more sensitive to smaller bursts, thereby increasing the sensitivity to supernovae located at Chapter 10. SNO Supernova Sensitivity 248 greater distances. Figure 10.3 illustrates the increase in distance sensitivity as fewer events are required to form the trigger. The two NHIT threshold values that are shown indicate the range of threshold settings used during different detector running conditions. Using the default settings, the SNO detector maintains sensitivity to the entire Milky Way galaxy during all running conditions. 100 I ' I \ V \ \ \ ' I ' NHIT = - - NHIT = —- NHIT = I 1 34 (Pure D 20) 34 (Salt) 69 (Pure D 20) (kpc) 80 — \ \ \ \ \ \ \ \ \ N NHIT = 69 (Salt) 8 Y \ \ -ra Distant 60 — V \ ' x v " X ' x -\OUJ 40 _ Supe Milky Way Far Edge ' • • 20 — — n I , I i I 1 I I I I I I I I I 1 1 0 10 20 30 40 50 Number of Events Required for Trigger Figure 10.3: SNO supernova distance sensitivity as a function of the number of events required to form the burst trigger. Two NHIT values are shown to indicate the range of threshold settings used during different detector running conditions. The default parame-ters are NHIT = 34 and N E V E N T = 30. Chapter 10. SNO Supernova Sensitivity 249 ~~i 1 i 1 i 1 i 1 i 1 r Average distance sensitivity over 430 days = 32 kpc 50 100 150 200 250 300 350 400 Nov Dec Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Jan Day Number Figure 10.4: SNO supernova distance sensitivity as a function of time using the default parameters for the period from November 2, 1999 to January 4, 2001. 10.3.3 Detector Livetime As described in Section 10.2, the SNO detector is completely insensitive to neutrinos ap-proximately 8.7% of the time because the detector is not operating. The average distance sensitivity values mentioned above for the Burrows supernova model decrease slightly when the detector livetime is taken into account. During pure D 2 0 operation, the average live-time corrected distance sensitivity is approximately 32 kpc and for salt operation the av-erage livetime corrected distance sensitivity is 37 kpc. From Earth, the distance to the far edge of the Milky Way galaxy is roughly 23 kpc, which means that during both operation Chapter 10. SNO Supernova Sensitivity 250 modes, the SNO distance sensitivity extends beyond the far edge of the Milky Way galaxy. However, the current online mode of operation is not sensitive to bursts originating in the Large or Small Magellanic Clouds (~55 kpc and ~65 kpc, respectively). Figure 10.4 shows the distance sensitivity as a function of time for the offline study in which 30 events are required to form the trigger. The various NHIT conditions outlined in Table 10.1 are also included, as is the small effect of not including due to the global trigger channel in each event as was the case during the initial running conditions (see Section 10.2). Mar 50 Apr May 100 June 150 200 July Aug Sept Day Number 250 Oct Nov 300 Dec Jan Figure 10.5: SNO supernova distance sensitivity as a function of time using the online burst monitor parameters for the period from February 23, 2000 to January 4, 2001. The corresponding plot showing the distance sensitivity as a function of time using the Chapter 10. SNO Supernova Sensitivity 251 actual online parameters over the period from February 23, 2000 to January 4, 2001 is provided in Figure 10.5. The average distance sensitivity achieved with the online burst monitor is approximately 24 kpc (during the pure D 2 0 operating mode), which extends beyond the far edge of the galaxy. 10.4 Burst Identification Efficiency The efficiency of the burst identification algorithm is determined using Monte Carlo data that was generated using the Burrows supernova model. Two independent data sets each containing detected SNO events for 100 supernovae at 10 kpc are separated into many smaller data sets by randomly choosing a certain number of events corresponding to a particular supernova distance. The events in each of the smaller data sets are then subjected to the burst trigger conditions, where n events are required above an NHIT threshold in a certain time window. The burst identification efficiency, e(d), is defined as <d) = (10.1) NtotalW where d is the distance to the supernova, N t r i g is the number of successful triggers and Ntotai is the total number of trials. As the supernova distance increases, the number of events in each trial decreases and therefore so does the number of successful triggers. Figure 10.6 shows the burst identification efficiency as a function of supernova distance during both the pure D 2 0 and salt operating modes. In all cases, the analysis threshold NHIT = 34 and the time window of 2 seconds are used. As the number of events required to form the trigger is lowered, the burst identification algorithm becomes sensitive to a Burrows-like supernova at greater distances away from Earth. For the default setting in which n = 30 events is used, SNO maintains 100% detection efficiency throughout our galaxy in both the pure D 2 0 and salt operating phases. The SNO burst identification algorithm decreases to 50% efficiency at approximately 36 kpc during the pure D 2 0 mode Chapter 10. SNO Supernova Sensitivity 252 0.8 0.6 0.4 .| 0.2 § I 0 .3 C 1 1 1 1 1 \' 1 1 . 1 H " , i 1 i 1 i • i • i • - P u r e D 2 0 \ > \ \ 1 \ \ n = 50 events \ n = 30 events \ n = 20 events — \ n = 10 events \ \ \ \ — \ \ \ \ \ \ Galaxy Far Edge , 1 , 1 i i i \ \ \ \ \ s \ 1 1 , 1 , l l , 1 , 10 20 30 40 50 60 70 80 90 100 8 CQ fe 0.8 0.6 0.4 0.2 Salt Galaxy Far Edge 1 I 1 I 1 I 1 I W0 10 20 30 40 50 60 70 80 90 100 Distance of Supernova from Earth (kpc) Figure 10.6: SNO burst identification efficiency as a function of supernova distance for both the pure D 2 0 and salt operating phases. In all cases, the burst trigger requires n events above the NHIT = 34 threshold in 2 seconds. Chapter 10. SNO Supernova Sensitivity 253 and 41 kpc during the salt mode using the default settings for the burst trigger. The abrupt decrease at the large distance tail of both of the n = 10 event curves occurs when the number of events in the burst falls below the number of events required to form the trigger. The maximum distance sensitivity values discussed in Section 10.3 correspond to burst identification efficiency values of e = 50%. This detection efficiency is taken to be the burst detection threshold. Chapter 1 2 Conclusion Neutrinos are produced in many physical processes, and are known to play a vital role in certain types of supernova explosion mechanisms, where essentially all of the gravitational energy of the collapse is carried away by neutrinos. The SNO detector has unique capabilities that make it very useful as a supernova neutrino detector. The fiducial mass of the detector consists of 1000 tonnes of D 2 0 , which provides sensitivity to all neutrino flavours via reactions where a free neutron is produced from the dissociation of the deuterium nucleus. Over the lifetime of the experiment, three methods for detecting neutrons will be employed: a pure D 2 0 stage, a stage where salt is introduced into the heavy water and finally a stage where 3 He proportional counters are deployed in the D 2 0 region. Neutrino interactions can also be observed in the 1700 tonnes of H 2 0 that surrounds the heavy-water volume. Software has been developed to simulate supernova signals in the SNO detector accord-ing to different supernova models. In this study, the simulated supernova signals from two generic models are used to characterize the detector response. For a core collapse supernova at 10 kpc, 630-910 neutrino events are expected to be observed in the SNO detector over tens of seconds during the pure D 2 0 operation period. Once salt is added to the heavy water, the expected signal observed from supernova neutrinos rises to 810-1230 neutrino events due to the increased neutron detection efficiency. A study of detector performance during the pure D 2 0 operating mode indicates that approximately 1 event/minute or less would be present as background to a supernova 263 Chapter 12. Conclusion 264 signal above an analysis threshold requiring 34 PMTs in coincidence. For a supernova at 10 kpc, the expected signal above this supernova analysis threshold is 555-795 neutrino events during the pure D 2 0 mode and 735-1125 neutrino events during the salt mode. It is possible to isolate various components of the supernova signal by considering events in certain regions of the detector and over certain time intervals. Electron antineutrinos are expected to comprise 92-95% of the signal in the light-water region. Furthermore, approximately 92% of the events in the first 100 ms of the supernova signal are expected to be due to electron neutrinos that are produced in the neutronization process during the early stages of stellar collapse. 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[141] F. James, "MINUIT—Function minimization and error analysis", CERN Program Library D506, 1998. [142] G.J . Feldman and R.D. Cousins, "Unified approach to the classical statistical analysis of small signals", Physical Review D57, 3873-3889 (1998). [143] K . Scholberg, "A search for neutrino from gravitational collapse with the M A C R O experiment", Ph.D. Thesis (unpublished), California Institute of Technology, 1997. [144] J. Ahrens et al., "Search for supernova neutrino-bursts with the A M A N D A detector", astro-ph/0105460, 2001. [145] R.S. Miller et al., "A search for astrophysical sources of low-energy neutrinos using the 1MB detector", Astrophysical Journal 428, 629-632 (1994). [146] Y . Fukuda for the Super-Kamiokande Collaboration, "Observation of supernova neu-trinos at Super-Kamiokande", bound photocopied transparencies of the First In-ternational Workshop of the Supernova Early Alert Network (unpublished), Boston University, 1998. [147] E . N . Alekseev et ai, "Upper bound on the collapse rate of massive stars in the Milky Way given by neutrino observations with the Baksan underground telescope", Journal of Experimental and Theoretical Physics 77, 339-347 (1993). Appendix A The Sudbury Neutrino Observatory Collaboration Below is a complete list of the 227 SNO collaborators that have worked on the project as of June 2001. Since 1983, 16 institutions from 3 countries have been involved with the design and development of the Sudbury Neutrino Observatory. Brookhaven National Laboratory, Upton, NY, USA J. Boger, R .L . Hahn, J .K. Rowley, M . Yeh Carleton University, Ottawa, Ontario, Canada A . L . Carter, B . Hollebone, D. Kessler, N . Starinsky Centre for Research in Particle Physics, Ottawa, Ontario, Canada I. Blevis, F. Dalnoki-Veress, A . DeKok, J . Farine, D.R. Grant, C . K . Hargrove, G. Laberge, I. Levine, K . McFarlane, H. Mes, C. Mifflin, A . T . Noble, V . M . Novikov, M . O'Neill, M . Shatkay, C. Shewchuk, D. Sinclair Chalk River Laboratories, Chalk River, Ontario, Canada E.T .H . Clifford, R. Deal, E.D. Earle, E . Gaudette, G. Milton, B . Sur Laurentian University, Sudbury, Ontario, Canada J. Bigu, M . Braille, J .H .M. Cowan, D.L. Cluff, R . U . Haq, J . Hewett, J .G. Hykawy, G. Jonkmans, S. Luoma, R. Michaud, A . Roberge, J. Roberts, E. Saettler, M . H . Schwendener, H. Seifert, G. Shayer, D. Sweezey, R. Tafirout, C .J . Virtue 275 Appendix A. The Sudbury Neutrino Observatory Collaboration 276 Lawrence Berkeley National Laboratory, Berkeley, CA, USA D. N . Beck, Y . D . Chan, X . Chen, M.R. Dragowsky, F .W. Dycus, J. Gonzalez, M . C . R Isaac, Y . Kajiyama, G.W. Koehler, K . T . Lesko, A . D . Marino, M . C . Moebus, E. B. Norman, C E . Okada, A . W . R Poon, P. Purgalis, A . Schuelke, A .R . Smith, R .G. Stokstad, S. Turner, I. Zlimen Los Alamos National Laboratory, Los Alamos, USA J . M . Anaya, T . J . Bowles, S.J. Brice, E-I. Esch, M . M . Fowler, A . Goldschmidt, A . Hime, K . Kirch, A . F . McGirt, G .G. Miller, W . A . Teasdale, J.B. Wilhelmy, J . M . Wouters National Research Council of Canada, Ottawa, Ontario, Canada J.D. Anglin, M . Bercovitch, W.F . Davidson, R.S. Storey Oxford University, Oxford, UK J . C Barton, S. Biller, R .A . Black, R.J . Boardman, M . G . Bowler, J. Cameron, B. Cleveland, X . Dai, J. Dunmore, G. Doucas, H. Fergani, A.P . Ferraris, K . Frame, H. Heron, C. Howard, N .A. Jelley, A . B . Knox, M . Lay, W. Locke, J . Lyon, S. Majerus, N . McCauley, G. McGregor, M . Moorhead, M . Omori, N .W. Tanner, R . K . Taplin, M . Thorman, P.T. Trent, D.L. Wark, N . West, J . Wilson Princeton University, Princeton, NJ, USA R. Kouzes, M . M . Lowry Queen's University, Kingston, Ontario, Canada A . L. Bell, E. Bonvin, M . Boulay, M . Chen, Y . Dai, M . Dayon, F. Duncan, L.S. Erhardt, H . C Evans, G.T. Ewan, R. Ford, A . Hallin, A . Hamer, P .M. Hart, P.J. Harvey, D. Haslip, C. A . W . Hearns, R. Heaton, J.D. Hepburn, C J . Jillings, E.P. Korpach, H.W. Lee, J.R. Leslie, M.-Q. Liu, H.B. Mak, A . B . McDonald, J.D. MacArthur, W. McLatchie, B. A . Moffat, S. Noel, T . J . Radcliffe, B .C . Robertson, P. Skensved, R .L . Stevenson, X . Zhu Appendix A. The Sudbury Neutrino Observatory Collaboration 277 University of British Columbia, Vancouver, BC, Canada S. Gi l , J . Heise, R .L . Helmer, R.J . Komar, T. Kutter, C.W. Nally, H.S. Ng, Y. I . Tserkovnyak, C E . Waltham University of California at Irvine, Irvine, CA, USA R.C. Allen, G. Buhler, H.H. Chen University of Guelph, Guelph, Ontario, Canada G. Aardsma, T. Andersen, K . Cameron, M.C . Chon, R .H . Hanson, R Jagam, J. Karn, J. Law, I.T. Lawson, R.W. Ollerhead, J.J. Simpson, N . Tagg, J . -X. Wang University of Pennsylvania, Philadelphia, PA, USA C. Alexander, E.W. Beier, J.C. Cook, D.F. Cowen, E.D. Frank, W. Frati, W.J . Heintzelman, P.T. Keener, J.R. Klein, C . C . M . Kyba, G . Mayers, D.S. McDonald, M.S. Neubauer, F . M . Newcomer, S .M. Oser, R . J . Pearce, V . L . Rusu, R . G . Van de Water, R. Van Berg, P. Wittich University of Washington, Seattle, WA, USA Q.R. Ahmad, J . M . Beck, M.C . Browne, T .V . Bullard, T .H . Burritt, G .A. Cox, P.J. Doe, C A . Duba, S.R. Elliott, J .E. Franklin, J .V. Germani, P. Green, A . A . Hamian, R. Hazama, K . M . Heeger, M . Howe, R. Meijer Drees, A . Myers, J .L. Orrell, R .G .H. Robertson, K . K . Schaffer, M . W . E . Smith, T .D. Steiger, T. Van Wechel, J.F. Wilkerson Appendix B Using the Supernova Signal Formalism For illustration purposes, the full calculation for the number of ve neutrinos expected to interact via the elastic scattering reaction in the D 2 0 volume of the detector: ve + e" ->• ve + e- (Ethres = 0 MeV) [D 20] (B.l) at neutrino emission time t,- = 0 s and neutrino energy Ev — 6 MeV will be shown for the supernova model of Burrows et al. [60] at a distance D — 10 kpc. As outlined in Chapter 5, the supernova neutrino signal at the source is described by Equation 5.1: g £ = WW.*)- (B.2) The number of neutrinos leaving the supernova source at ti = 0 is obtained by using the neutrino luminosity and average energy spectra according to Equation 5.2: FiO) - M . (B.S) A ^A^ v in 5 3 2 IE5 v 1 0 ~ 7 J v 1 eV v 1 MeV _ 4-0^0 X 1U s x erg X 1.602xlQ- 1 9J X 106 eV 15.123 MeV = 1.876 x 10 6 8 s _ 1 . According to the Burrows model, the characteristic Fermi-Dirac parameters for ve neutrinos at U = 0 are TUe(0) = 1.7 MeV and 77^(0) = 11.0, indicating that the high-energy tail of this spectrum is very "pinched" relative to a Maxwell-Boltzmann distribution. Using 278 Appendix B. Using the Supernova Signal Formalism 279 Equation 5.10 for a Fermi-Dirac distribution that includes a chemical potential factor, the spectrum at U = 0 is calculated to be: /(6,0) = El NFD(0) [l + e^/^(o)-^(o) 2357.529 M e V 3 0.0153 M e V - 1 , (6.0 MeV) 2 1 _|_ e(6.0 MeV/1.7 MeV-11.0) where the normalization, i V F D ( 0 ) , is determined using Equation 5.8: iW0) = f [r = f JO El El dE„ I _|_ e(E„/1.7 MeV-11.0) dEv = 2357.529 MeV d Hence, the number of neutrinos leaving the collapsing star per unit energy per unit time is: d2N = F(0)/(6,0) Ev = 6 MeV, U = 0 s - (1.876 x 10 5 8s _ 1)(0.0153 M e V " 1 ) = 2.863 x 10 5 6 ( M e V s ) - 1 . dEydti The neutrino flux at the detector is described by Equation 5.11: = Nto(Eu)-d2Ndet „ 1 d2Ns, (B.4) dEydt ""'v AirD2dEudU For the example being considered, the number of neutrino counts in the D 2 0 volume per unit energy per unit time is: d2Ndet dEydt (7(6) Ev = 6 MeV, U = 0 s d iV s r c dEydU E„=6 MeV, U = 0 s (30.173 x 10 3 1 e~ in the D 2 0 volume) 5.418 x ! Q - 4 8 m 2 / 1 kpc N 9 4TT(10 kpc) 2 V3.086 x 1 0 1 9 m y 0.391 ( M e V s ) - 1 . (B.5) 2.863 x 10 5 6 ( M e V s ) - 1 Appendix B. Using the Supernova Signal Formalism 280 Performing the integration over all energies yields the count rate for the time specified in this example: dN, det dt U=0s 1 r°° d iV s r c dEudti U = 0 s = 66.669 s - l (B.6) Finally, the total number of ue neutrinos that interact via the elastic scattering reaction in the D 2 0 volume is determined using Equation 5.12: l r°° r°° , „ , d2N„. 1 rOO roo rl^ V dh = 8.523 counts. (B.7) Appendix C Estimate of the Observed Signal Due to Oxygen Reactions While reactions involving oxygen are not fully specified in the supernova neutrino simu-lations performed, a reasonable estimate can be made. As outlined in Section 4.3, the signal due to interactions with the target oxygen molecules has contributions from both the charged-current channel: ue + 0->F + e~ [ D 2 0 , H 2 0 ] ( C l ) Z7e + 0->N+e+ [ D 2 0 , H 2 0 ] (C.2) and the neutral-current channel: + 1 6 0 -4 i / M > T + 1 5 0 + n + 7 [D 2 0 , H 2 0] (C.3) »W + 1 6 0 -> + 1 5 0 + n + 7 [D 2 0 , H 2 0 ] (C.4) v»,r + 1 6 0 v^T + 1 5 N +p + 7 [D 2 0, H 2 0 ] (C.5) v^r + 1 6 0 -4 F„,T + 1 5 N + p + 7 [D 2 0, H 2 0] (C.6) v^r + 1 6 0 -> ^ i T + 1 5 0 + n [D 20] (C.7) JVr + 1 6 0->. F M , T + 1 5 0 + n [D 2 0]. (C.8) The final state detectable particles from these reactions include electrons, positrons, gamma rays and neutrons. Neutrons in the H 2 0 region are not considered to be detectable because the energy of the 7 ray produced in the neutron capture process is below practical detection thresholds. 281 Appendix C. Estimate of the Observed Signal Due to Oxygen Reactions 282 C l Hardware Threshold Since the energies are relatively high, the probability of detecting electrons and positrons from supernova neutrino charged-current interactions is very high. Monte Carlo simulations of supernova neutrinos show that typically ~97% of the electron and positron events are detected above the detector hardware threshold of 16 PMTs . Due to high energy thresh-old for the 1 6 0 charged-current reactions, the average electron/positron energy is higher than other charged-current reactions1. Therefore the detection efficiency for electrons and positrons from oxygen charged-current reactions is expected to be slightly higher than 97%. However, for the purposes of estimation, the value of 97% is used. Energies for the 7 rays from the neutral-current excitation reactions are predicted to be in the range 5-10 MeV [73]. Monte Carlo simulations show that the detection efficiency for 5 MeV gamma rays is approximately 97% in the D 2 0 region and 80% in the H 2 0 region. For 10 MeV gamma rays, the efficiency is slightly higher at 98% in the D 2 0 region and 91% in the H 2 0 region. Average detection efficiency values of 97% (D 2 0) and 85% (H 2 0) are adopted to estimate the observed 7-ray signal due to interactions with oxygen. As presented in Section 4.2.3, three distinct methods are proposed to detect neutrons in the SNO detector, and each technique has a different detection efficiency. The efficiency values obtained from Monte Carlo study are: e = 37% for pure D 2 0 , e = 85% using NaCl salt and e = 55% with the neutral current detectors in place. The detection efficiencies discussed above are summarized in Table C l . These values are used to estimate the contribution from reactions involving oxygen to the SNO supernova signal above the hardware detector threshold of 16 PMTs . The expected signal in the Beacom and Vogel model and in the Burrows model are discussed in the sections below. 1For average neutrino energy values according to the Beacom and Vogel model and the Burrows model, see Tables 6.2 and 6.6, respectively. Appendix C. Estimate of the Observed Signal Due to Oxygen Reactions 283 Par t ic le Reg ion Detec t ion Efficiency (hardware) e ± D 2 0 0.97 e± H 2 0 0.97 7 D 2 0 0.97 (5 MeV) 0.97 (10 MeV) 0.98 7 H 2 0 0.85 (5 MeV) 0.80 (10 MeV) 0.91 n (D 2 0) D 2 0 0.37 n (Salt) D 2 0 0.85 n (NCDs) D 2 0 0.55 Table C l : SNO particle detection efficiencies above the detector hardware threshold of 16 P M T s for various final state particles. The three entries listed for 7 rays indicate the average efficiency value used in the estimate as well as the efficiency values for the two energies investigated. C . l . l Beacom and Vogel Model Neutrino count values presented in Table 6.1 for the Beacom and Vogel model indicate that 92 neutrino events from reactions with oxygen would yield a total of 13 electron and positron events, 59 7-ray events and 24 neutron events in the final state. The results obtained by applying the detection efficiencies in Table C l indicate that 74 particles would be observed above the detector hardware energy threshold in the pure D 2 0 phase, 85 particles in the salt phase and 78 particles during the time that the neutral current detectors are in place. This corresponds to 13 electron/positron events, 52 gamma-ray events and between 9 and 20 neutron events, depending on the neutron detection method employed. Regardless of the neutron detection method, a total of 8 electron/positron events and 33 7-ray events are expected in the H 2 0 region in addition to the 410 positrons produced Appendix C. Estimate of the Observed Signal Due to Oxygen Reactions 284 via the inverse beta decay reaction and the 20 electrons produced through elastic scatter-ing. Including the estimated contribution due to oxygen reactions, electron antineutrinos constitute 88% of the H 2 0 signal above the detector hardware threshold according to the Beacom and Vogel model. C.1.2 Burrows et al. Model According to Table 6.5, 13 neutrino events are expected from oxygen reactions using the Burrows model, which corresponds to 7 electron and positron events, 5 7-ray events and 2 neutron events in the final state. Applying the particle detection efficiencies listed in Table C l results in the following total numbers of observed final state particles according to the Burrows model: 12 events during pure D 2 0 , 13 events during the salt phase and 12 events with the neutral current detectors. In other words, 7 electron/positron events, 4 gamma-ray events and 1-2 neutron events are expected. Considering the supernova signal in the light-water region alone, a total of 4 elec-tron/positron events and 3 7-ray events are expected in addition to the 320 positrons produced via the Ve + p —> n + e+ reaction and the 20 electrons produced through the v + e~ —>• v + e~ reaction. Including the estimated contribution due to oxygen reactions, electron antineutrinos constitute 93% of the H 2 0 signal above the detector hardware thresh-old of 16 P M T s according to the Burrows model. C.2 Analysis Threshold In Chapter 8, the energy threshold appropriate for the analysis of a supernova burst during the pure D 2 0 and salt phases is determined to be 34 PMTs . The effect of applying this threshold to the signal resulting from interactions with oxygen is discussed below. The probability of detecting electrons and positrons above the supernova analysis Appendix C. Estimate of the Observed Signal Due to Oxygen Reactions 285 threshold due to charged-current interactions remains relatively high. Monte Carlo simula-tions of reactions that do not involve oxygen show that approximately 90% of the electron and positron events are detected above the analysis threshold. As with the signal above the hardware threshold, the high energy threshold value for 1 6 0 reactions means that the signal due to oxygen reactions remains relatively insensitive to an NHIT threshold even as high as 34 PMTs . In order to place a conservative lower limit on the number of counts expected from oxygen reactions an efficiency value of 90% is used. Energies for the 7 rays from the neutral-current excitation reactions are predicted to be in the range 5-10 MeV. In order to characterize the gamma-ray detection efficiency in the energy range 5-10 MeV, Monte Carlo simulations are performed in both the heavy- and light-water regions. The results indicate that the detection efficiency for 5 MeV gamma rays is approximately 48% in the D 2 0 region and only 24% in the H 2 0 region. The detection efficiency for 10 MeV gamma rays is considerably higher in both regions at 98% in the D 2 0 volume and 79% in the H 2 0 volume. In the absence of information regarding the exact distribution of 7-ray energies, average detection efficiency values are used to estimate the signal contribution from oxygen reactions. For the D 2 0 region, the average efficiency value is 73% and for the H 2 0 region the average efficiency value is 52%. The neutron detection efficiency values obtained from Monte Carlo study for events above the analysis threshold are: e = 27% for pure D 2 0 and e = 77% using NaCl salt. The corresponding detection efficiency using the NCDs is not known at this time. The detection efficiencies discussed above are summarized in Table C.2. These values are used to estimate the contribution from reactions involving oxygen to the SNO supernova signal above the supernova analysis threshold of 34 PMTs . Appendix C. Estimate of the Observed Signal Due to Oxygen Reactions 286 Par t ic le Region Detec t ion Efficiency (analysis) e± D 2 0 0.90 e± H 2 0 0.90 7 D 2 0 0.73 (5 MeV) 0.48 (10 MeV) 0.98 7 H 2 0 0.52 (5 MeV) 0.24 (10 MeV) 0.79 n (D 2 0) D 2 0 0.27 n (Salt) D 2 0 0.77 Table C.2: SNO detection efficiencies above the supernova analysis threshold of 34 PMTs for various final state particles. The three entries listed for 7 rays indicate the average efficiency value used in the estimate as well as the efficiency values for the two energies investigated. C.2.1 Beacom and Vogel Model The results obtained by applying the detection efficiencies in Table C.2 indicate that 53 particles would be observed above the supernova analysis threshold in the pure D 2 0 phase and 65 in the salt phase. This corresponds to 12 electron/positron events, 35 gamma-ray events and between 6 and 18 neutron events, depending on whether neutron capture occurs in pure D 2 0 or in salt. Regardless of the neutron detection method, a total of 8 electron/positron events and 20 7-ray events are expected in the H 2 0 region in addition to the 392 positrons produced via the T>e + p —> n + e+ reaction and the 15 electrons produced through the v + e~ —> v + e~ reaction. Including the estimated contribution due to oxygen reactions, electron antineu-trinos constitute 92% of the H 2 0 signal above the supernova analysis threshold according to the Beacom and Vogel model. Appendix C. Estimate of the Observed Signal Due to Oxygen Reactions 287 C.2.2 Burrows et al. Model The results obtained by applying the detection efficiencies in Table C.2 indicate that 10 particles would be observed above the supernova analysis threshold of 34 PMTs in the pure D 2 0 phase and 11 in the salt phase. This corresponds to 6 electron/positron events, 3 gamma-ray events and 1 neutron event (the number of neutrino events is sufficiently low that the neutron method does not make a significant difference). Considering the H 2 0 region, a total of 4 electron/positron events and 2 7-ray events are expected, in addition to the 296 positrons produced via the inverse beta decay reaction and the 13 electrons produced through elastic scattering reactions. Including the estimated contribution due to oxygen reactions, electron antineutrinos constitute 95% of the H 2 0 signal above the supernova analysis threshold according to the Burrows model. C.3 Summary Estimated contributions above both the hardware and analysis thresholds from the various reactions involving oxygen are summarized below for the two generic supernova models. C.3.1 Beacom and Vogel Model Between 75 and 85 events due to supernova neutrino reactions with oxygen are expected above the hardware threshold of 16 PMTs using the Beacom and Vogel model. Once the analysis threshold requiring 34 PMTs in coincidence is applied, the range of total events due to oxygen reactions becomes 53-65. Table C.3 provides a summary of the estimated contributions from the various oxygen reactions above both the hardware and analysis thresholds for the Beacom and Vogel model. Appendix C. Estimate of the Observed Signal Due to Oxygen Reactions 288 Oxygen Reaction Region Counts Counts (hardware) (analysis) D 2 0 Salt NCDs D 2 0 Salt Charged Current: total 12.77 12.77 12.77 11.86 11.86 ue + 0 -> F + e" D 2 0 0.98 0.98 0.98 0.91 0.91 Ve + 0 ->• N+ e + D 2 0 3.44 3.44 3.44 3.20 3.20 z/e + 0 ->• F + e~ H 2 0 1.84 1.84 1.84 1.71 1.71 I7e + 0 -» N+ e+ H 2 0 6.51 6.51 6.51 6.04 6.04 Neutral Current: total 61.19 72.63 65.49 41.23 53.14 V*,T + 1 6 0 - ) • i/„,T + 1 5 0 + n + 7 D 2 0 2.82 3.83 3.20 2.10 3.15 v^r + 1 6 0 F^ > T + 1 5 0 + n + 7 D 2 0 2.80 3.81 3.18 2.09 3.14 ^ , T + 160->- ^ , T + 1 5 N + p + 7 D 2 0 7.75 7.75 7.75 5.83 5.83 » W + 1 6 0 ->• F M , T + 1 5 N +p + 7 D 2 0 7.90 7.90 7.90 5.94 5.94 ^ , T + 1 80-> i / M , r + 1 5 0 + n D 2 0 3.69 8.48 5.49 2.69 7.68 ^ , T + 1 60-> I7M>T + 1 5 0 + n D 2 0 3.56 8.19 5.30 2.60 7.42 y^r + 1 6 0 -»• + 1 5 0 + n + 7 H 2 0 3.37 3.37 3.37 2.06 2.06 + 1 6 0 -> V^r + 1 5 0 + n + 7 H 2 0 3.36 3.36 3.36 2.05 2.05 + 1 6 0 -»• + 1 5 N + p + 7 H 2 0 12.85 12.85 12.85 7.86 7.86 y^r + 1 6 0 -»• F^ l T + 1 5 N+p + 7 H 2 0 13.09 13.09 13.09 8.01 8.01 Total SNO i / e Events 2.82 2.82 2.82 2.62 2.62 Total SNO z7e Events 9.95 9.95 9.95 9.24 9.24 Total SNO ' V Events 61.19 72.63 65.49 41.23 53.14 Total SNO D 2 0 Events 32.94 44.38 37.24 25.36 37.27 Total SNO H 2 0 Events 41.02 41.02 41.02 27.73 27.73 Total SNO e ± Events 12.77 12.77 12.77 11.86 11.86 Total SNO 7 Events 52.39 52.39 52.39 34.81 34.81 Total SNO n Events 8.80 20.24 13.10 6.42 18.33 Total SNO Events 73.96 85.40 78.26 53.09 65.00 Table C.3: Summary of estimated contributions above both the hardware and analysis thresholds from reactions involving oxygen to the supernova signal using the Beacom and Vogel model. C.3.2 Burrows et al. Model Between 12 and 13 events due to supernova neutrino reactions with oxygen are expected above the hardware threshold of 16 PMTs using the Burrows model. Once the analysis threshold of 34 PMTs is applied, the range of total events due to oxygen reactions becomes Appendix C. Estimate of the Observed Signal Due to Oxygen Reactions 289 10-11. Table C.4 provides a summary of the estimated contributions from the various oxygen reactions above both the hardware and analysis thresholds for the Burrows model. Oxygen Reaction Region Counts Counts (hardware) (analysis) D 2 0 Salt NCDs D 2 0 Salt Charged Current: total 6.86 6.86 6.86 6.36 6.36 ve + 0 -»• F + e~ D 2 0 1.05 1.05 1.05 0.97 0.97 Ve + 0 ->• N+ e + D 2 0 1.32 1.32 1.32 1.22 1.22 ve + 0 ->• F + e~ H 2 0 1.99 1.99 1.99 1.85 1.85 Ve + 0 -r N+ e+ H 2 0 2.50 2.50 2.50 2.32 2.32 Neutral Current: total 4.96 5.88 5.31 3.34 4.29 v^r + 1 6 0 -»• + 1 5 0 + n + 7 D 2 0 0.23 0.31 0.26 0.17 0.25 *V, T + 1 6 0 -)• Vfi,r + 1 5 0 + n + 7 D 2 0 0.23 0.31 0.26 0.17 0.25 + 1 6 0 -> z^,T + 1 5 N + p + 7 D 2 0 0.63 0.63 0.63 0.47 0.47 + 1 6 0 -)• F M , r + 1 5 N + p + 7 D 2 0 0.64 0.64 0.64 0.48 0.48 + 1 6 0 - r ^ , T + 1 5 0 + n D 2 0 0.30 0.69 0.45 0.22 0.62 V + 1 6 0 ^ F M , T + 1 5 0 + n D 2 0 0.29 0.66 0.43 0.21 0.60 + 1 6 ° ->• + 1 5 0 + n + 7 H 2 0 0.27 0.27 0.27 0.17 0.17 ^ . r + 1 6 0 - r F M > T + 1 5 0 + n + 7 H 2 0 0.27 0.27 0.27 0.17 0.17 + 1 6 0 - r i / M , T + 1 5 N + p + 7 H 2 0 1.04 1.04 1.04 0.63 0.63 V^r + ^O-r ^ , r + 1 5 N + p + 7 H 2 0 1.06 1.06 1.06 0.65 0.65 Total SNO ue Events 3.04 3.04 3.04 2.82 2.82 Total SNO F e Events 3.82 3.82 3.82 3.54 3.54 Total SNO ' V Events 4.96 5.88 5.31 3.34 4.29 Total SNO D 2 0 Events 4.69 4.95 5.10 3.67 4.62 Total SNO H 2 0 Events 7.13 7.13 7.13 5.79 5.79 Total SNO e± Events 6.86 6.86 6.86 6.36 6.36 Total SNO 7 Events 4.25 4.25 4.25 2.81 2.81 Total SNO n Events 0.71 1.63 1.06 0.53 1.48 Total SNO Events 11.82 12.74 12.17 9.70 10.65 Table C.4: Summary of estimated contributions above both the hardware and analysis thresholds from reactions involving oxygen to the supernova signal using the Burrows model. Appendix D Online Analysis Using 100 Supernovae The Level 3 summary histograms presented in Chapter 9 show a simulated supernova burst at 10 kpc according to the Burrows model. In those plots however, the underlying distribution is not readily apparent, so plots using simulated data from 100 supernovae at 10 kpc are presented in this Appendix. The summary histograms for the events in the entire burst are shown in Figure D . l , whereas the analysis histograms for events in the D 2 0 and H2O regions are shown in Figures D.2 and D.3, respectively. In each of the cos 6SN angular distributions, events from the forward-peaked elastic scattering interactions stand out above events from the other interaction types. 290 Appendix D. Online Analysis Using 100 Supernovae 291 Supernova Trigger Level 3 Analysis Clean Burst Date / Time: 20/01/2000 at 02h 16m 08s (Sudbury local time) Clean Burst Size: 40545 events fit within PSUP radius (50% D 20,50% H 2 0) Clean ZDAB File: SN_100xl0kpc_nosalt (Burrows model) 0 200 400 NHIT spectrum within PSUP _i i i_ 0 20 40 60 Timent (elastic) within PSUP in seconds 1 2 3 Rn, (elastic) within PSUP (A V = 1) 400 200 -i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i— J i i i i I i i i i L J I I L_ •1 -0.5 0 0.5 1 cos(theta)nt (elastic) within PSUP 400 200 h 100 200 300 phint (elastic) within PSUP in degrees 600 400 200 0 !—i—i—i—I—i—I—I—I—I—I—I—I—i—I—n—i—r J i i i i I i_ j i I I I i i L •1 -0.5 0 0.5 1 cos(theta)SN (elastic) within PSUP Figure D . l : Level 3 analysis summary histograms showing various distributions for all burst events that are reconstructed within the detector volume using events from 100 supernovae at 10 kpc simulated according to the Burrows supernova model. Appendix D. Online Analysis Using 100 Supernovae 292 Supernova Trigger Level 3 Analysis Events fit within D,0 volume (R .le. 600 cm): 50% (20408 events) 2500 5000 7500 10000 _L 200 400 NHIT spectrum within D 2 0 10000 r 7500 r 5000 r 2500 r 0 400 200 0 T _] I I I II I I I I I I L 0 1 Rn, (elastic) within D 2 0 (AV = 1) 3001-1 i i i | i i i i | 1 1 1 1 I 1 1 200 100 0 0 100 200 300 phi f i t (elastic) within D 2 0 in degrees T -i p 1 1 1 1 1 1 1 1 r -L ± 0 20 40 60 Time n t (elastic) within D 2 0 in seconds 200 100 h -1 -0.5 0 0.5 1 cos(theta)m (elastic) within D 2 0 -1 -0.5 0 0.5 cos(theta)SN (elastic) within D 2 0 Figure D.2 : Level 3 analysis summary histograms showing various distributions for burst events that are reconstructed within the D 2 0 region using events from 100 supernovae at 10 kpc simulated according to the Burrows supernova model. Appendix D. Online Analysis Using 100 Supernovae 293 Supernova Trigger Level 3 Analysis Events fit within H,0 volume (R .le. 840 cm & R .gt. 600 cm): 50% (20137 events) 300 F 200 lOOh-0 ~\ 1 r j 1 1 200 400 NHIT spectrum within H 2 0 10000 FT 7500 5000 2500 f-0 400 h 200 h 0 I i i i i I i i i i I i i i h-0 1 2 3 Rn, (elastic) within H 2 0 ( A V = 1) 200 100 200 300 phim (elastic) within 11,() in degrees - i — — i — i — r • 1 • i i I L 0 20 40 60 Timem (elastic) within H 2 0 in seconds H 200 100 -i—i—p—i—I—i—i—i—r i I i i i i_ -I i i i I i L_ -1 -0.5 0 0.5 1 cos(theta)fit (elastic) within H 2 0 400 r-i—r—i—i—|—i—i—i—i—|—i—n—i—|—i—i—i—r 300 h . . . . I -1 -0.5 0 0.5 1 cos(theta)SN (elastic) within H 2 0 Figure D.3 : Level 3 analysis summary histograms showing various distributions for burst events that are reconstructed within the H 2 0 region, using events from 100 supernovae at 10 kpc simulated according to the Burrows supernova model. Appendix E Milestones Relevant to SNO Supernova Monitoring Work on the SNO supernova burst monitor began before the detector was filled with water in May 1999. The monitoring software evolved through testing and development stages both offline and online, and the most significant milestones are summarized in Table E . l . Prior to February 23, 2000, some small fraction of bursts were not being identified online due to a software bug in the event storage array. Once this bug was fixed, the online monitoring software was considered to be fully functional. Therefore, February 23, 2000 is taken to be the first day of online monitoring within SNO. 294 Appendix E. Milestones Relevant to SNO Supernova Monitoring 295 Date Significance May 1, 1999 May 19, 1999 August 9, 1999 August 10, 1999 November 2, 1999 December 16, 1999 December 20, 1999 February 17, 2000 February 23, 2000 Apri l 19, 2000 August 8, 2000 October 17, 2000 December 21, 2000 May 28, 2001 May 30, 2001 August 3, 2001 SNO detector online (commissioning stage) Burst monitor installed in online version of S N O S T R E A M (bursts communicated via email to M . H . Schwendener) [30 < NHIT < 800, N E V E N T = 51, T I M E = 2 seconds] Burst information communicated via email to Supernova Working Group [50 < NHIT < 800, N E V E N T = 51, T I M E = 2 seconds] First spallation event seen online by trigger Detector configuration frozen Global trigger channel added to all events [NHIT > 49, N E V E N T = 51, T I M E = 2 seconds] Level 2 analysis installed online Detector operators receive burst email Alert popup window activated for Level 1 bursts Final algorithm bug fixed (burst event numbering) [NHIT > 34, N E V E N T = 51, T I M E = 2 seconds] Change event accounting within S N O S T R E A M [NHIT > 34, N E V E N T = 50, T I M E = 2 seconds] Level 3 event reconstruction activate online Author receives cell phone for supernova on-call support Detector hardware threshold decreased from 18 to 16 PMTs Salt added to D 2 0 region Dial-out system commissioned [NHIT > 34, N E V E N T = 30, T I M E = 2 seconds] Table E . l : Summary of milestones relevant to SNO supernova monitoring. 

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