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A submillimetre census of star-formation at high-redshift Coppin, Kristen Erin Kathryn 2006

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A Submillimetre Census of Star-Formation at High-Redshift by Kris ten E r i n Ka th ryn Coppin B.Sc. (Physics and Astronomy) University of Vic tor ia , 2000 M.Sc . (Astronomy) University of Br i t i sh Columbia, 2003 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S (Astronomy) T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A October 2006 © Kris ten E r i n Ka th ryn Coppin, 2006 ABSTRACT i i A B S T R A C T Maps, source catalogue and number counts are presented for the largest, most complete and uniform extragalactic submillimetre survey ever undertaken: the 850 fim S C U B A H A l f Degree Extragalactic Survey ( S H A D E S ) . Using the Submillimetre Common-User Bolometer Ar ray ( S C U B A ) on the James Clerk Maxwel l Telescope ( J C M T ) , S H A D E S mapped two separate regions of sky: the Sub&vu/XMM-Newton Deep Fie ld ( S X D F ) and the Lockman Hole East (LH) . These S C U B A maps cover 720arcmin 2 wi th an R M S noise level of about 2 m J y and have uncovered > 100 submillimetre galaxies. Individual source lists from four groups drawn within the S H A D E S team (of which this thesis provides a detailed account of one of the reductions) are compared in terms of source flux densities and positions and combined to produce a 120-object S H A D E S catalogue. This catalogue is an invaluable resource for follow-up campaigns aiming to study the properties of a complete and consistent sample of submillimetre galaxies. For the first time, deboosted flux densities are presented for each submillimetre galaxy using a recipe developed here. S H A D E S has a high enough number of detected sources that meaningful differential counts can be estimated, unlike most submillimetre surveys which have to consider integral counts. Differential and integral source number counts are given and the differential counts are found to be better fit wi th a broken power-law or a Schechter function than wi th a single power-law; the S H A D E S data alone significantly show that a break is required at several mJy, although the precise position of the break is not well constrained. Based on the S H A D E S results, an 850 pm survey complete down to 2 m J y would resolve 20-30 per cent of the Far-IR background into point sources. In order to help constrain spectral energy distributions (SEDs) and hence redshifts for the S H A D E S galaxies, a follow-up effort was undertaken using the Submillimetre High Angular Resolution Camera ( S H A R C - I I ; Dowell 2003) at the Caltech Submillimetre ABSTRACT i i i Observatory (GSO). The maps and 350 / i m flux estimates of a subset of the S H A D E S catalogue are presented. Using available redshift estimates, I attempt to characterise the S E D s i n terms of the dust temperature and far-IR luminosity. Star-formation rates and dust mass estimates for the sample are derived and the S M G population is confirmed to be dominated by very massive (~ 5 x 10 1 0 M©), luminous (~ 10 1 2 L 0 ) star-forming ( S F R ~ 1000 M 0 y r _ 1 ) galaxies wi th intrinsic dust temperatures of ~ 35 K . CONTENTS i v C O N T E N T S Abs t rac t i i Contents iv L i s t of Tables v i i i L i s t of Figures • i x Lis t of A c r o n y m s x i i Preface x iv Acknowledgements x v 1 In t roduct ion 1 1.1 Submillimetre Galaxy Formation and Evolut ion 1 1.1.1 Submillimetre Galaxies 2 1.2 The S C U B A HAlf-Degree Extragalactic Survey 16 1.2.1 Multi-wavelength Follow-up Da ta 19 1.2.2 S H A R C - I I Follow-up of S H A D E S Sources 20 1.3 Guide to This Thesis 23 2 Observations and D a t a Analys i s 25 2.1 Introduction 25 2.1.1 Submillimetre Astronomy: Technical Challenges and Triumphs . . 26 2.2 The 850/nm Submillimetre Survey 26 2.2.1 The Instrument: the J C M T and S C U B A 26 2.2.2 The Observations 31 CONTENTS v 2.2.3 Da ta Reduction 32 2.2.4 Source Extract ion 34 2.2.5 Summary and Comparison of Four Independent S H A D E S Pipelines 35 2.2.6 Tests of the Da ta 37 2.2.7 Maps 40 2.3 350 / i m Follow-up Observations . . . 43 2.3.1 The Instrument: the C S O and S H A R C - I I 43 2.3.2 The Observations 47 2.3.3 Da ta Reduction 50 2.3.4 Source Extract ion 54 2.3.5 Tests of the D a t a 54 2.3.6 Maps 57 3 Flux Density Deboosting and Bias in Submillimetre Surveys 66 3.1 Introduction 66 3.2 M a p Observations and Da ta Reduction 69 3.2.1 F l u x Density Cal ibrat ion 70 3.2.2 Source Detection Method . . 70 3.2.3 Source Robustness 72 3.3 Monte Carlo Simulations , . . . 73 3.4 Candidate Submillimetre Sources 75 3.4.1 Addi t iona l Photometry 75 3.4.2 F lux Density Boosting in the M a p 77 3.4.3 A Revised Source List 81 3.5 A n Attempt at Multi-wavelength Correlations 83 3.6 Summary and Tie- in to Thesis 84 4 S H A D E S Results 86 4.1 Introduction 86 4.1.1 Combining Part ial ly Dependent Da ta 87 CONTENTS v i 4.2 The Catalogue . . . 89 4.2.1 Prel iminary Joint Identification List 89 4.2.2 Deboosted F l u x Densities '. 90 4.2.3 850 fim Catalogue Membership 94 4.2.4 F ina l S H A D E S Catalogue 96 4.2.5 F l u x Density Comparison 104 4.2.6 Astrometry Comparison 106 4.2.7 Source Deblending 110 4.2.8 Analysis of the 450 fxm Da ta 110 4.3 Differential Source Counts 117 4.3.1 Direct Estimate of the Differential Source Counts 119 4.4 Models and Cumulative Source Counts 128 4.4.1 Fi ts to Differential Counts 128 4.4.2 Background Estimate 134 4.4.3 Cumulative Source Counts 134 4.4.4 Comparison of Cumulative Counts to Previous Estimates 135 4.4.5 Bright Source Constraint 137 4.4.6 S M G Evolut ion 137 4.4.7 Comparison of the Two Fields - Evidence for Sampling Variance? 139 4.5 Summary and Future Prospects 140 5 S H A R C - I I R e s u l t s 144 5.1 Introduction 144 5.2 350 nm F l u x Densities of the S H A D E S Galaxies 149 5.2.1 Constraints on 350 fxxn Source Counts 164 5.2.2 Summary of Other S H A R C - I I Da ta of S H A D E S 164 5.3 Trends wi th F l u x Densities at Other Wavelengths 170 5.4 Intrinsic Properties of S M G s 171 5.4.1 Star Formation Rate History 191 CONTENTS v i i 5.5 Summary and Future Prospects 192 6 Epilogue 195 6.1 Future Far- IR/Submil l imetre /Radio Instruments 195 6.1.1 S C U B A - 2 195 6.1.2 L A B O C A o n A P E X 196 6.1.3 A z T E C on the L M T . 196 6.1.4 Herschel 196 6.1.5 Planck 197 6.1.6 A L M A 198 6.1.7 E V L A 198 6.1.8 J W S T 199 6.2 Future Imaging of the S H A D E S Fields 199 Bibliography 202 A Noise Spike Removal Tests 214 B Notes on Individual Sources 218 C Effective Exposure Times 224 D Other Estimates of the Number Counts 226 D . l Another Direct Estimate of the Differential Source Counts 226 D.2 Parametric Mode l Fi ts to Estimate the Differential Source Counts . . . . 228 D.3 Summary of Differences Between the Three Methods 232 LIST OF TABLES viii L I S T O F T A B L E S 2.1 Da ta reduction procedures 38 2.2 Order of signal models in C R U S H 52 2.3 Summary of the S H A R C - I I observations and map properties 53 3.1 G S S 850 yum candidate submillimetre sources wi th follow-up photometry . 75 3.2 G S S 850 fim revised source list 82 4.1 The 850 fim S H A D E S catalogue for the L H and S X D F regions 102 4.2 Astrometry precision 108 4.3 450 fixn stacked flux densities 114 4.4 Methods of accounting for bias 120 4.5 850 lira. S H A D E S differential and integral counts 123 4.6 Covariance matrix for the differential counts 124 4.7 Best-fitting parameters of fits to the differential counts 133 5.1 S H A R C - I I measured 350 / m i flux densities of S H A D E S sources 157 5.2 Multi-wavelength photometry of S H A R C - I I observed sources (this work) 163 5.3 Multi-wavelength photometry of S H A R C - I I observed sources (other work) 169 5.4 Derived properties for the S H A R C - I I observed S H A D E S sources 184 LIST OF FIGURES ix L I S T O F F I G U R E S 1.1 The extragalactic background 4 1.2 S E D o f A r p 2 2 0 8 1.3 Negative K-correction 9 1.4 Evolutionary sequence of Sanders et al . (1988) 14 2.1 S C U B A wideband filter profiles 28 2.2 The S C U B A bolometer arrays 29 2.3 Lockman Hole S C U B A maps 41 2.4 Subaru-XMM Deep Fie ld S C U B A maps 42 2.5 Noise map histograms 44 2.6 Lissajous scan pattern 46 2.7 S / N histograms for the S H A R C - I I maps 56 2.8 R M S versus integration time 58 2.9 S H A R C - I I maps 59 2.9 (continued) 60 2.9 (continued) 61 2.9 (continued) 62 2.9 (continued) 63 2.9 (continued) 64 2.9 (continued) 65 3.1 Gro th Strip S C U B A map 71 3.2 Cumulative number of detected candidate sources 74 3.3 G S S Completeness 76 3.4 G S S flux density deboosting 80 LIST OF FIGURES x 4.1 F l u x density comparison before and after deboosting 91 4.2 Posterior flux probability distributions 93 4.3 Percentage likelihood of zero flux density 95 4.4 Effective cuts in the S H A D E S source catalogue 97 4.5 Distr ibut ion of map-detected S / N ratios 98 4.6 F l u x density comparison between Reductions B and D 105 4.7 Astrometry comparison 109 4.8 Histogram of 450/um stacked flux densities 116 4.9 Effective Area 122 4.10 Differential source count densities in L H 126 4.11 Differential source count densities in S X D F 127 4.12 Test of source count recovery 129 4.13 Differential source count densities in the combined fields 132 4.14 S H A D E S cumulative source counts compared to previous estimates . . . 136 4.15 Are the S X D F and L H counts statistically different? 141 5.1 Dust temperature versus /? 148 5.2 S H A R C - I I thumbnail images of S H A D E S sources 154 5.2 (continued) 155 5.2 (continued) 156 5.3 Cumulative distribution of radial offsets from S H A D E S positions 159 5.4 Stacked signal 350 /xm flux density of non-detections 161 5.5 Composite stacked 350/ im S / N image of non-detections 162 5.6 Cumulative 350 fim source counts 165 5.7 Scatter plot of 24 yum versus radio flux density 172 5.8 Histogram of S H A R C - I I detected radio sources 173 5.9 Histogram of SHARC-II-detected 24 yum sources 174 5.10 Histogram of SHARC-II-detected 850 yum sources 175 5.11 Best-fitting Observed S E D s 180 LIST OF FIGURES x i 5.11 (continued) 181 5.11 (continued) 182 5.11 (continued) 183 5.12 Luminosi ty as a function of rest frequency 186 5.13 Dust temperature versus redshift 188 5.14 Far-IR luminosity versus redshift 189 5.15 Far-IR luminosity versus 850 yum flux density 190 5.16 Star-formation rate history 193 A . l F F T s of jiggle map data 215 D . l The completeness for L H as calculated by Reduction C 233 D.2 The scattering function for Reduction C 234 D.3 Reduction C s observed versus expected source distribution 235 LIST OF ACRONYMS xii L I S T O F A C R O N Y M S A G N - Act ive Galactic Nuclei A L M A - Atacama Large Mill imetre Array A P E X - Atacama Pathfinder Exper iment A z T E C - Astronomical Thermal Emission Camera B H - Black Hole B L A S T - Balloon-borne Large Aperture Submillimeter Telescope C C D - Charge Coupled Device C F H T L S - Canada France Hawaii Telescope Legacy Survey C I B - Cosmic Infrared Background C M B ( R ) - Cosmic Microwave Background (Radiation) C O B E - COsmic Background Explorer ' C R U S H - Comprehensive Reduction Ut i l i ty for S H A R C - I I C S O - Caltech Submillimetre Observatory Dec - Declination D E E P - Deep Extragalactic Evolutionary Probe D I R B E - Diffuse InfraRed Background Experiment D S O S - Dish Surface Optimizat ion System E R O - Extremely Red Object E V L A - Extended Very Large Array F C F - F l u x Conversion Factor F D R - False Detection Rate F I R A S - Far-InfraRed Absolute Spectrophotometer F I R ( B ) - Far-InfraRed (Background) F O V - Fie ld Of View F W H M - Fu l l W i d t h at Half M a x i m u m G A L E X - Galaxy Evolut ion Explorer G M R T - Giant Metre-wave Radio Telescope G O O D S - N - Great Observatories Origins Deep Survey - Nor th G R B - Gamma-Ray Background G S S - G r o t h Strip Survey G T O - Guaranteed Time Observations H D F - Hubble Deep Fie ld H I F I - Heterodyne Instrument for the Far Infrared H S T - Hubble Space Telescope ID - Identification I R A C - InfraRed Ar ray Camera I R A S - InfraRed Astronomical Satellite LIST OF ACRONYMS x i i i ISO - Infrared Space Observatory J C M T - James Clerk Maxwel l Telescope J W S T - James Webb Space Telescope L A B O C A - Large Apex BOlometer C A m e r a L B G - Lyman-Break Galaxy L H - Lockman Hole L I R G - Luminous InfraRed Galaxy L M T - Large Mill imetre Telescope M A M B O - MAx-p lanck Mill imetre BOlometer M I P S - Mul t iband Imaging Photometer for Spitzer M N R A S - Month ly Notices of the Royal Astronomical Society N E F D - Noise Equivalent F l u x Density N I R - Near InfraRed P A C S - Photodetector Array Camera and Spectrometer P A H - Polycyclic Aromat ic Hydrocarbon P I - Pr inc ipa l Investigator P S F - Point Spread Function R A - Right Ascension R M S - Root Mean Square S C U B A - Submillimetre Common-User Bolometer Array S E D - Spectral Energy Distr ibut ion S F R - Star Formation Rate S H A D E S - S C U B A H A l f Degree Extragalactic Survey S H A R C - I I - Submillimetre High Angular Resolution Camera S M A - SubMill imetre Array S M B H - Super Massive Black Hole : S M G - Submillimetre Galaxy S / N - Signal-to-Noise ratio S P I R E - Spectral and Photometric Imaging REceiver S U R F - S C U B A User Reduction Facili ty S W I R E - Spitzer Wide-area Infra Red Extragalactic survey S X D F - S u b a r u - X M M Deep Field U K I D S S - Uni ted Kingdom Infrared Deep Sky Survey U K I R T - Uni ted Kingdom Infra Red Telescope U L I R G - Ultra-Luminous Infra Red Galaxy U V - Ul t ra-Violet V L A - Very Large Array W F C A M - Wide Fie ld C A M e r a WFPC2 - Wide Fie ld Planetary Camera 2 for H S T W M A P - Wi lk inson Microwave Anisotropy Probe W V M - Water Vapour Monitor X R B - X - R a y Background PREFACE xiv P R E F A C E But if there is no solace in the fruits of our research, there is at least some consolation in the research itself. M e n and women are not content to comfort themselves wi th tales of gods and giants or to confine their thoughts to the daily affairs of life; they also bui ld telescopes and satellites and accelerators and sit at their desks for endless hours working out the meaning of the data they gather. The effort to understand the Universe is one of the very few things that lifts human life a little above the level of farce, and gives it some of the grace of tragedy. Excerpt from The First Three Minutes by Steven Weinberg X V Acknowledgements First and foremost, I would like to thank my research supervisor, Dr . Mark Halpern, for his expertise, guidance, patience, enthusiasm and financial support. I would also like to thank N S E R C for awarding me a P G S D 2 award in 2005. I would also like to thank Dr . Douglas Scott for additional guidance and very helpful suggestions along the way that enriched the quality of this work. Also, I am indebted to Dr . J i m Dunlop, the P I of S H A D E S for entrusting me wi th a huge leading role in the main S H A D E S source counts results paper. A n d of course, none of this would have been possible without the hundreds of observing hours put in by members of the S H A D E S team and J A C staff. Addi t iona l funding was received from the National Research Counci l of Canada to-wards 4 trips to the J C M T to collect data for S H A D E S . M u c h thanks also goes out to the staff of the J C M T for their assistance wi th the S C U B A observations, and in particular to T S S J i m Hoge who always kept my spirits up, despite S C U B A being out of order on several occasions. The James Clerk Maxwel l Telescope is operated on behalf of the Par-ticle Physics and Astronomy Research Counci l of the United Kingdom, the Netherlands Organisation for Scientific Research, and the National Research Counci l of Canada. I would also like to thank Drs. Darren Dowell and Co l in Borys from Caltech who provided support and advice during my C S O observing runs and to the C S O crew for keeping the telescope in good working order. Thanks to Dr . Mark Halpern who helped out wi th some of the S H A R C - I I observing and for funding my trips to the C S O . Also thanks to D r . E l i a Batt is tel l i and Jeff Wagg for coming to the C S O as secondary observers. I would also like to thank A t t i l a Kovacs also for answering a plethora of emails regarding his C R U S H reduction code. The Caltech Submillimetre Observatory telescope is operated XVI by Caltech under a contract from the National Science Foundation (NSF) . I have to thank my mom, dad, sisters and grandparents for always supporting my academic pursuits - I would not have made it this far without you. Special thanks to my many fabulous friends throughout the years for constantly reminding me what's important in life and for always being there for me. I cannot possibly name you al l but honourable mentions go to Jessica, Alana , Rob, and Jaymie. C H A P T E R 1 I N T R O D U C T I O N 1 1.1 Submillimetre Galaxy Formation and Evolution Two fundamental unsolved problems in modern cosmology are: How and when did the first galaxies form? and How long did their initial starbursts last? Answering these questions has been extremely difficult due to the challenges of disentangling the complex physical processes involved in forming galaxies during epochs when the Universe was very young, epochs which have only become accessible relatively recently wi th the aid of new observational instrumentation or techniques. Central to this topic is the broad question: How and when did most of the present-day massive galaxies form? The formation of massive spheroids (ellipticals and spiral bulges) is important in the history of structure formation in the Universe as they contain roughly 70 per cent of the stars in the local Universe (Fukugita, Hogan & Peebles 1998). There have historically been two competing theories for depicting how these massive galaxies may have formed: the monolithic collapse and hierarchical merging scenarios. Based on the motions of old stars in our Galaxy, Eggen, Lynden-Bel l & Sandage (1962) conceived the monolithic collapse scenario as a theory of galaxy formation, involving a single rapid collapse of stars at high redshift, producing a violent and short-duration burst of star-formation followed by a quiescent evolution of the stellar population. This theory was questioned by Searle & Zinn (1978) as new and better data became available and they suggested that star formation in our Galaxy was a more prolonged chaotic process. New theories were subsequently developed (see Davis et al . 1985) describing galaxy formation as a 'bottom-up' process, i.e., hierarchical merging, or the gradual formation of a galaxy by the merging of smaller collections of stars at moderate redshifts of z < 1.5 producing moderate and continuous star-formation (e.g., Whi te & Frenk 1991, 1.1. SUBMILLIMETRE GALAXY FORMATION AND EVOLUTION 2 Kauffmann 1996, Baugh, Cole & Frenk 1996). The favoured A - C D M cosmological model (a vacuum-dominated cold dark matter Universe) predicts that the Universe evolved hierarchically at least in terms of the build-up of dark matter haloes. We see plenty of observational evidence of hierarchical merging; for example, our neighbouring satellite, the Sagittarius dwarf galaxy, is being t idally disrupted by our Galaxy 's gravitational field (see Ibata, Gilmore & Irwin 1994). But older stellar populations of galactic spheroids seem to be better explained by a monolithic collapse scenario (e.g., Bruzual & Chariot 1993), this being more recently referred to as 'cosmic downsizing' Cowie et al . (1996). So we appear to see evidence of both processes throughout the history of the Universe but we do not know how to combine hierarchical merging and down-sizing into a complete galaxy formation picture. However, the unique Submillimetre Common-User Bolometer Ar ray ( S C U B A ; Holland et al . 1999) has revealed a population of extremely luminous high-redshift galaxies at submillimetre wavelengths (named submillimetre galaxies or S M G s ) which appear to be forming stars more rapidly than simple theory predicts (Baugh et al . 2005, Somerville 2004). Current semi-analytic models cannot reproduce the substantial population of S M G s at high-redshift without the addition of new ingredients or the adoption of new assumptions (e.g., Kaviani , Haehnelt & Kauffmann 2003; Granato 2004; Baugh et al . 2005; see a discussion later in Section 4.4.6). Submillimetre galaxies are therefore important for constraining models of galaxy formation, and so the study of these rare, dramatic star-formers may help us to understand the formation and evolution of galaxies as a whole. 1.1.1 Submillimetre Galaxies The existence of relatively high-redshift starburst galaxies, a cosmologically significant population, was discovered in the 1980's by a ~ U y all-sky survey at 12, 25, 60 and 100 fxm by the Infrared Astronomical Satellite (IRAS). IRAS revealed a population of previously unseen optically-faint galaxies out to a redshift of « 0.3, hinting that the amount of dust reprocessing increases wi th star production and cannot be measured 1.1. SUBMILLIMETRE GALAXY FORMATION AND EVOLUTION 3 solely wi th optical or U V data and evolves strongly wi th redshift (see Sanders & Mirabe l 1996). The Far-Infrared Background ( F I R B ) was first deduced in 1996 from data taken by the COsmic Background Explorer (COBE). After the dominant cosmic microwave background ( C M B ) emission is accounted for, about half of the remaining energy budget of the extragalactic background is contained in the F I R B and the other half in the o p t i c a l / U V (see F ig . 1.1 and Puget et al. 1996). Therefore, at least half of the energy emitted by galaxies in the Universe (integrated over the life of the Universe) has been absorbed and re-radiated by dust and would be missed by optical observations. What are the objects responsible for producing this background emission and what is their role in galaxy formation?. The Infrared Space Observatory (ISO), sensitive to the low redshift regime, resolved about 10 per cent of the F I R B into discrete galaxies lying at redshifts less than about 1. We are obviously st i l l missing a great deal of the higher-redshift contributors. The discovery of a submillimetre extragalactic background by COBE was an unexpected find and requires the existence of a large population of far-IR emitting galaxies at z > 1 in the early throes of their evolution and producing lots of far-IR emitting dust. This submillimetre background implies a strong cosmological evolution, and the high star-formation rates inferred for the objects which comprise most of this background imply that they must be forming massive galaxies. This is consistent wi th the idea that we are seeing massive early-type galaxies (i.e., elliptical galaxies) at an early stage of their evolution, very different from such galaxies in the local Universe which we know to be predominantly composed of relatively old stars. This progression greatly affects the star formation history, as a large part of the stars being formed are most likely hidden by dust-enshrouded galaxies, eluding optical surveys. Understanding the nature of the objects responsible for producing this F I R B energy is crucial to achieving a complete and unbiased view of galaxy formation. S M G s were first resolved by S C U B A , a state-of-the-art bolometer camera built to find these dusty high-redshift objects, by Hughes et al . (1998) (a blank-field 1 survey of *A 'blank-field' survey is an unbiased study of a population of objects selected solely on their sub-millimetre flux densities. 1.1. SUBMILLIMETRE GALAXY FORMATION AND EVOLUTION 4 energy (keV) 10-9 io- 6 10-3 1 103 IO6 103 1 10-3 10-6 10-9 10- 1 2 wavelength (mm) Figure 1.1: This figure depicts the energetics of the extragalactic background which is comprised of six main components: the Cosmic Microwave Background ( C M B ) , the Cosmic Infrared Background (CIB) or Far-Infrared Background (FIB) , the Near-Infrared (NIR) , the Op t i ca l -UV, the X - R a y Background ( X R B ) and the Gamma-Ray Background ( G R B ) . Use of this figure courtesy of Scott et al . (2002). 1.1. SUBMILLIMETRE GALAXY FORMATION AND EVOLUTION 5 the Hubble Deep Fie ld region) and Smail, Ivison & Bla in (1997) (targetted observations of lensed clusters). Since then, several larger blank-field campaigns to different depths and areal coverage have extended these 'discovery' observations to study the S M G popu-lation in detail and have led to a revolution in our understanding of the importance and diverse nature of heavily enshrouded galaxies at high redshifts (e.g., Barger et al . 2000, B l a i n et al . 2002, Scott et al . 2002, Webb et al . 2003b, Borys et al . 2003). Blank-field surveys have managed to produce source counts at flux densities down to ~ 2 mJy , after which confusion noise (originating from unresolved fainter background sources) starts to become a significant player, effectively preventing blank-field surveys from going much deeper than this (see Condon 1974, Hughes et al . 1998). Despite such progress, the samples being used in any given study are typically quite small, since S C U B A can only detect a couple of S M G s per night in good weather condi-tions. A n d while the total number of sources detected over the lifetime of the instrument (but not including this work) 2 is ~ 300, these are drawn from small ( ^ 100 square ar-cminute) fields spread al l over the sky, each observed, and reduced by different groups using different techniques and source identification criteria. The desire to obtain a well characterised sample of hundreds of S M G s in a large, contiguous area is the motiva-t ion for the S C U B A HAlf-Degree Extragalactic Survey ( S H A D E S ; Mort ier et al . 2005, van Kampen et al . 2005). The importance of having a well characterised sample is ex-plained later. T h e Origin of Submillimetre Emission There are two different mechanisms responsible for submillimetre emission from galaxies: continuum thermal emission from heated dust and molecular line emission 3 . Micron-sized interstellar dust grains, probably primarily composed of silicates and polycyclic 2 S C U B A was operational between 1997 and 2005 3 Approximately 99 per cent of the power output of galaxies at submillimetre and far-IR wavelengths is produced by continuum thermal emission and the rest comes from line emission (Blain et al., 2002). 1.1. SUBMILLIMETRE GALAXY FORMATION AND EVOLUTION 6 aromatic hydrocarbons ( P A H s ) 4 , absorb ha rd-UV photons from regions of intense high mass star-formation or from Active Galactic Nuclei ( A G N ) accretion disks and are heated to temperatures between 20-200 K . The obscuring dust grains re-radiate this absorbed radiation as thermal continuum emission, which peaks in the far-IR and becomes visible at submillimetre wavelengths when the cosmological expansion of the Universe redshifts the far-IR peak into this regime. A t submillimetre wavelengths the dust is optically th in and so one is directly measuring the number of U V photons being re-radiated by the dust; submillimetre observations are therefore a direct tracer of the dust masses and S F R s i n these galaxies. The other emission mechanism involves atomic and molecular transitions in the interstellar gas resulting in spectroscopic lines. P r o b i n g the Highest Redshifts Submillimetre emission may be used as a probe of the high redshift Universe, since it can penetrate dust, and because of a powerful effect called the negative K-correction that accesses far-IR emitting galaxies out to the most distant reaches of the Universe. Redshifting a galaxy results in a decreased observed flux due to the cosmological version of the 1/r 2 distance effect. But at 850 fim, redshifting also means that one is climbing up the Rayleigh-Jeans ta i l of the spectral energy distribution (SED) (see F i g . 1.2) towards the thermal emission peak (100-200 / im, depending on the dust temperature) which rises steeply wi th decreasing rest-frame wavelength (approximately S cx u35). It turns out that the cosmological dimming is essentially cancelled by the increase in emitted flux for 0.5 < z < 8, and causes a galaxy's flux density to remain approximately constant as it is moved to higher redshifts in this range. The negative K-correction is strongest for wavelengths longer than about 250 / im, being the most pronounced at millimetre wavelengths, as seen in F i g . 1.3. This effect is a unique feature of submillimetre cosmology, making it an ideal tool for probing the history of dusty galaxy formation over a large fraction of the lifetime 4 Spectra of nearby stars obscured by dust reveal many absorption features, many of which cannot be explained. Some of the observed features can be attributed to U V photons boosting small silicate grains into highly energetic states; PAHs can be especially prone to this effect. 1.1. SUBMILLIMETRE GALAXY FORMATION AND EVOL UTION 7 of the Universe. Submillimetre galaxies are thus excellent tracers of massive regions of star-formation at high redshifts and they have been found to comprise a large fraction of the power output of al l known galaxies. S M G s are very dusty systems, have typical 850/jm flux densities of 5-10 mJy, and are believed to be mainly powered by star formation (star-formation rates (SFRs) of ~ 100-1000 M Q y r " 1 ; Hughes et al . 1998, Barger et al . 1998, Chapman et al . 2004, Chapman et al . 2005). Studies of the X- ray properties of S M G s indicate a modest (perhaps 10 per cent) contribution to the bolometric luminosity from A G N (e.g., Alexander et al . 2005). The combination of their huge dust content extincting most or al l of the optical light and the low angular resolution and positional uncertainties of S C U B A observations (full width at half maximum ( F W H M ) ~ 15arcsec, A r = 2 -3arcsec) makes identifying these objects wi th populations of distant optical galaxies often impossible or difficult at best; there could be several (~ 10) possibilities wi th in a single S C U B A beam of 15" where a submillimetre source is found, and the correct identification may even be too faint to detect in the deepest optical images. Local Analogues to High-Redshift S M G s ? Resolved submillimetre observations exist only for the lowest redshift galaxies and it is common practice to use the results of these observations as templates for galaxies in the more distant Universe (which may or may not be a reasonable assumption, given the lack of understanding of high redshift galaxies and of the feedback 5 processes involved in star formation). IRAS uncovered a distinct class of extremely luminous objects of ^boi ^ 10 1 1 ! /©, dubbed Luminous Infrared Galaxies or L I R G s . L I R G s appear to almost always be the result of a major merger and emit more energy at far-IR wavelengths than all other wavelengths combined (Lagache, Puget & Dole, 2005). Not-so-distant cousins to L I R G s , U l t r a Luminous Infrared Galaxies (ULIRGs) are probably the most similar 5 T h e star-formation feedback is poorly understood but refers to processes such as stellar or galactic winds or supernovae explosions that are added as ingredients to models of galaxy formation in order to make the radiative cooling of gas less efficient in simulations in order to match observations. 1.1. SUBMILLIMETRE GALAXY FORMATION AND EVOLUTION 8 Figure 1.2: Mode l spectral energy distributions of a nearby U L I R G : the Lagache, Dole & Puget (2003) starburst template (dashed line represents template number 30) fit (solid line) at z = 0.018 to Arp220 photometric data (plus signs) from the N A S A / I P A C Extragalactic Database. The energy output is dominated by a modified blackbody emitting in the far-IR, and the mid-IR emission features seen here are attributed to P A H molecules. 1.1. SUBMILLIMETRE GALAXY FORMATION AND EVOLUTION 9 1000.00 100.00 10.00 b 1.00 0.10 0.01 ~i 1—i—i—\—i i i ~i 1 1—i—i—r T 1 1 — i — i — r r n \ S v 450|i.m j i i 0.1 1.0 10.0 Redshift j i i i i 100.0 Figure 1.3: The effect of 'negative K-correction' on the predicted flux density of a model dusty submillimetre galaxy (see F ig . 1.2) as a function of redshift. The solid, dashed, and dot-dashed lines are for 850 /im, 450 jum, and the near-IR K -band, respectively. The negative K-correction is strongest near millimetre wavelengths, resulting in a nearly constant observed flux density for a galaxy of given luminosity over a redshift range of 0.5 < z < 8. 1.1. SUBMILLIMETRE GALAXY FORMATION AND EVOLUTION 10 to extraordinarily luminous galaxies in the high-redshift world wi th respect to their lu-minosities and physical properties. U L I R G s comprise the most luminous galaxies in the local Universe, having bolometric luminosities in excess of 10l2LQ, the dust emission dominated peak of their spectral energy distribution (SED) lying in the far-IR region of the spectrum (see F i g . 1.2). Local ly U L I R G s are a rare class of special objects, be-lieved to be interacting or merging pairs of spiral galaxies, and make up less than 0.1 per cent of the local Universe, although they may have been more important in the past. In fact, U L I R G s are up to 1000 times more common at z ~ 2.5 than in the present-day (Sanders, 1999)! There is a body of observational and theoretical evidence showing that the end products of these mergers are elliptical galaxies (e.g., Kormendy & Sanders 1992; Genzel et al . 2001; Toomre & Toomre 1972; Barnes & Hernquist 1992). L I R G s and U L I R G s predominantly display r 1 / 4 law elliptical galaxy surface brightness profiles (e.g., Zheng et al . 1999), hinting that U L I R G formation could be just the way to form elliptical galaxies at high redshifts and may be the local analogues of high-z S M G s (see Lonsdale, Farrah & Smith (2006) for a detailed review). The Na tu re of S M G s Obtaining redshifts for these objects is the key to understanding their role i n galaxy formation and evolution. This is challenging though, as they are usually very faint or undetectable in complementary optical observations, making follow-up spectroscopy a difficult and time-consuming task. Some progress has been made by a variety of groups using different techniques to identify optical counterparts to sub-samples of S M G s wi th varying degrees of success. A useful link is to search for 1.4 G H z radio counterparts of S M G s using sub-arcsec resolution wi th the Very Large Ar ray ( V L A ) , exploiting the well-known far-IR/radio correlation (e.g., Car i l l i & Y u n 1999; Car i l l i & Y u n 2000) and the precise positions from the radio to facilitate the identification of optical counterparts. The connection between the far-IR and radio emission stems from the rate at which dust absorbs and re-radiates the radiation from star-forming regions wi th the radio luminos-ity due to synchrotron emission coming from cosmic ray electrons originating from the 1.1. SUBMILLIMETRE GALAXY FORMATION AND EVOLUTION 11 same star-forming regions (see B la in et al . 2002 and references therein). Only approxi-mately half of al l the S M G s have known 1.4 G H z counterparts, so there is a large fraction of S M G s for which we have very little information, creating a hurdle in determining the nature of the S M G population as a whole. Nevertheless, the majority (perhaps 65 per cent) of the bright S M G s are detectable as yuJy radio sources (Ivison et al . 1998; Ivison et al . 2002; Chapman et al . 2001; Chapman et al . 2002; Chapman et al . 2003; Pope et al . 2006), facilitating a reliable identification of faint optical/near-IR counter-parts (Smail et al . , 2004). After a precise location (sub-arcsec radio positional accuracy) and optical ID are known, wide-band spectroscopy can be attempted to try to measure the redshift of the S M G . Chapman et al . (2000) have managed to collect redshifts for S M G s wi th radio IDs brighter than 5 m J y wi th a 75 per cent success rate, finding a median redshift for the sample of 90 S M G s of 2.3, wi th galaxies detected out to redshifts of 3.6. These surveys are biased in several fundamental ways. First of al l , there is a dearth of objects in the Chapman et al . (2000) sample in the 'spectroscopic desert' re-gion of z ~ 1.1-1.6, due to the lack or faintness of spectral emission lines or absorption line systems in that range. Secondly, radio detection is a key requirement for spectro-scopic targetting and means that galaxies too high in redshift (z > 3-4) are too faint for radio observations and are explicitly missed. Pope et al . (2005) find a photometric redshift distribution wi th a peak at z ~ 2.2 for a consistent sample of radio-detected and radio-undetected submillimetre galaxies in the G O O D S - N region and do not find an excess of galaxies at z > 4 (as might have been expected). These redshifts should also be confirmed using interferometric C O studies that trace the dust and gas in these systems, as mis-IDs wi l l give wrong redshifts (e.g., the infamous HDF850.1 ; Downes et al . 1999) which could lead to a comedy of wrong conclusions about luminosities, the population redshift distribution, and in turn the star-formation history of the Universe. Despite the faintness of S M G s in complementary wavelength regimes, l imited progress has been made in determining the relationship of the submillimetre population to other high-redshift galaxy populations through detailed observations. S M G s have often been identified wi th optically obscured faint iC-band extremely red galaxies (EROs; Smai l et al . 1.1. SUBMILLIMETRE GALAXY FORMATION AND EVOLUTION 12 1999). Some S M G s appear to be associated wi th blue optical galaxies wi th weak A G N fea-tures or quasars. Few optically luminous quasars at z ~ 2 have been detected in the sub-millimetre, so the quasar and S M G phases do not show a significant overlap. Bu t the few submillimetre-detected quasars suggest that these particular galaxies could be transition objects on the path from obscured quasar to the unobscured quasar (e.g., Omont et al . 2003, Stevens et al . 2005). There appears to be strong evidence of a direct link between the most active phases of spheroid growth and nuclear accretion (e.g., Borys et al . 2005). These phases can be identified wi th the high-redshift S M G s and quasars, respectively, a l ink which is reinforced by the similarity in their redshift distributions. Supporting evidence for an S M G - U L I R G link include their disturbed irregular mor-phologies and high bolometric luminosities (see Lagache, Puget & Dole 2005 for a de-tailed review). Optical/near-IR/mm-wave spectroscopy has confirmed that the two pop-ulations have similar redshifts, luminosities and dynamical masses and has provided information about the winds and stellar outflows i n S M G s that point to U L I R G - l i k e activity (Swinbank et al . 2004, Greve et al . 2005, Tacconi et al . 2006). Like U L I R G S , S C U B A sources typically appear faint in the rest-frame U V (Chapman et al. , 2005). A difference between the two populations exists in that S C U B A galaxies may also be cooler than local U L I R G s of the same luminosity (e.g., Pope et al . 2006). H S T images of the optical counterparts of S M G s show disturbed irregular morphologies, similar to U L I R G s (Chapman et al . 2003, Smail et al . 2004, Conselice, Chapman & Windhorst 2003). How-ever, S M G s show evidence of extended star-formation over many kpc (Chapman et al. , 2004). The above observations suggest that while high redshift S M G s and local U L I R G s are closely connected in some way, the precise details governing the physics in these two populations are probably somewhat intrinsically different. A r e S M G s s i m p l y a p h a s e i n t h e l i f e o f a l l m a s s i v e g a l a x i e s ? Since S M G s have been found to be connected wi th many types of objects and are found predominantly at high-redshifts, it has been suggested that S M G s are likely an evolu-tionary stage occurring in the life of perhaps every massive galaxy. 1.1. SUBMILLIMETRE GALAXY FORMATION AND EVOLUTION 13 A n important recent astronomical discovery is that a central supermassive black hole ( S M B H ) is housed at the centres of al l massive galaxies, wi th a B H mass proportional to that of its spheroid (e.g., Magorrian et al . 1998; Gebhardt et al . 2000). Therefore it is implied that their B H s grew along wi th the stellar mass. This idea is supported by hydro dynamical simulations of major merging events which demonstrate that feedback from A G N winds and outflows connect the growth of the B H to the host galaxy's growth (e.g., D i Matteo, Springel & Hernquist 2000, Hopkins et al . 2005). These simulations broadly support a general picture where this activity follows the classical evolutionary sequence as first proposed by Sanders et al . (1988): mergers of high-redshift galaxies would induce a burst of star-formation which would be seen as the U L I R G / S M G phase and lasts unt i l the S M B H s merge, which leads into a period of A G N / X - r a y activity after which the system evolves into an obscured quasar, an unobscured luminous quasar, and finally a passive spheroid. See F ig . 1.4 for a summary of this progression. S M G s are also linked to the BH-spheroid mass relation, as seen in G O O D S - N by co-adding their Chandra X - r ay spectra to provide crude estimates of B H mass (Alexander et al. , 2005) and compare these wi th Spitzer IRAC-based stellar mass estimates (Borys et al . , 2005). Spitzer 24 / i m and Chandra X- ray observations of S M G s may be revealing the anticipated presence of underlying A G N in these systems. T h e Cosmic Importance of S M G s The degree of optical extinction present in S M G s has been estimated. Various studies have shown that the contribution to the 850 fj,m submillimetre background of optically-selected starburst galaxies is only about 25 per cent (e.g., Peacock et al . 2000). This result demonstrates that rest-frame U V emission, which traces massive stars and asso-ciated star-formation activity, is often hidden by dust extinction. M u c h progress has been made in observing high-redshift (z < 3) UV-colour selected galaxies, called Lyman-break galaxies ( L B G s ; Steidel et al . 1999). L B G s resemble local UV-br ight starbursting galaxies in many of their spectral properties (Adelberger & Steidel, 2000). L B G s , which are much more common than S M G s , have been argued to be a significant contributor to 1.1. SUBMILLIMETRE GALAXY FORMATION AND EVOLUTION 14 opt ical ly luminous (unobscured) quasar ^ * + passively evolv ing sphero id (massive el l ipt ical) Figure 1.4: The classical evolutionary sequence as first proposed by Sanders et al . (1988): mergers of high-redshift galaxies would induce a burst of star-formation which would be seen as the U L I R G / S M G phase and lasts unti l the S M B H s merge, which leads into a period of A G N / X - r a y activity after which the system evolves into an obscured quasar, an unobscured luminous quasar, and finally a passive spheroid. the stellar production at high-redshifts (Adelberger & Steidel, 2000), though the findings of Chapman et al . (2005) show evidence to the contrary; the z ~ 3 L B G s are typically faint or undetected at submillimetre wavelengths, suggesting that they represent a dis-tinct complementary population to the S M G s (Chapman et al . 2005; Webb et al . 2003a). Schmitt et al . (2006) find that S M G s demonstrate extreme star-forming conditions sim-ilar or greater than those exhibited by local U L I R G s . L B G s on the other hand seem to resemble metal and dust-poor local star-forming galaxies. The most robust optical and IR identifications of S M G s (and hence precise redshifts) provide evidence for no strong decline in the density of star formation at z > 2. The cur-rent belief is that the comoving luminosity density due to active star formation i n galaxies is roughly constant between redshifts of 1-4 (roughly between 8-12 bi l l ion years ago or during 10-45 per cent the history of the Universe, using the cosmological parameters derived from the Wilk inson Microwave Anisotropy Probe, W M A P , data (Spergel et al . , 2003). Before the advent of S C U B A , optical surveys indicated that the star-formation increased by a factor of ~ 5 from redshift 4 to 1 (see e.g., Madau, Pozzett i & Dickinson 1998). These contrasting results can be explained by the S M G s being a distinct popula-U L I R G s merge opt ical ly obscured q u a s a r / A G N gas infal ls and s ta r - f o rma t i on occurs ( S M G / U L I R G phase) BH fo rms at centre of merger ( A G N / X - r a y phase) 1.1. SUBMILLIMETRE GALAXY FORMATION AND EVOLUTION 15 t ion of as well as insufficient correction for dust extinction in the op t ica l -UV estimates of star formation rates. A n y census of star formation is therefore incomplete without the inclusion of S M G s in the big picture. The discovery of massive elliptical galaxies already assembled at high-redshifts of ~ 2 and composed predominantly of ancient stars that are al l around the same age implies that they must have formed co-evally at much earlier times (z > 2). This poses an inter-esting problem of inventing a mechanism to create these galaxies on such relatively short timescales (~ 100 M y r to 1 Gyr , on the order of a starburst timescale). A popular scenario has been to merger-induce the formation of local U L I R G s , resulting in the production of these massive spheroids (see Sanders & Mirabe l 1996 and references therein). S M G s are thought to be the progenitors of these massive elliptical galaxies (Scott et al . 2002; L i l l y et al . 1999), though there only exists very indirect evidence for this link. S M G s have plausible redshifts (1 < z < 3), star-formation rates (~ 100-1000 M © y r _ 1 ) and masses ( 1 0 8 - 1 0 1 0 M Q ) to be assembled on the timescale of a starburt phase (~ 100 M y r to 1 G y r ) . The huge implied S F R s of S M G s are equivalent to that expected from pri-mordial protogalaxies and are sufficient to form the necessary stellar population of an L* galaxy (the characteristic luminosity of local galaxies, similar to our own M i l k y Way; see e.g., Schechter 1976) in only a few dynamical times (Steidel, 1999). If S M G s cluster strongly, then they could represent the progenitors of massive elliptical galaxies since ellipticals are strongly clustered (e.g., Percival et al. 2003). There is some evidence for S M G clustering, though submillimetre surveys up unti l the present were not sufficiently sensitive to measure the expected clustering signals (Scott et al . 2002; Borys et al . 2003; Webb et al . 2003b), although see B la in et al . (2004) who claim to detect strong S M G clustering in redshift space and Greve et al . (2004) who claim a tentative clustering sig-nal. The next step would be to design and carry out a wide medium-deep submillimetre survey which would be sensitive to detecting a clustering signal so that this link could be further investigated since the clustering amplitude tells you about the masses of the host haloes fairly directly. Previous submillimetre surveys have made substantial progress since the discovery of 1.2. THE SCUBA HALF-DEGREE EXTRAGALACTIC SURVEY 16 S M G s : the basic form of the 850 pm source counts is known, we know the basic redshift distribution of S M G s and have managed to establish them as key players in the dusty star formation and galaxy assembly phases of the Universe, while simultaneously discov-ering the best way to perform efficient follow-up observations of S M G s in complementary wavebands. But while many pieces of the puzzle seem to be almost in place, the picture is far from complete. The main factor that has plagued the progress of previous surveys in disentangling the true nature of S M G s as an entire population has been the lack of a statistically significant number (i.e., > 100) of S M G s available from a uniform and unbiased sample. Follow-up studies have been forced to make use of available inhomo-geneous, small and often biased (e.g., lensed or radio-identified) samples of S M G s . To make further strides, we first require a large, robust, unbiased sample of S M G s to study and characterise. 1.2 The SCUBA HAlf-Degree Extragalactic Survey S H A D E S is a wide extragalactic submillimetre survey, split evenly between 2 separate re-gions of sky: the Subaru/XMM-Newton Deep Field ( S X D F ) and the Lockman Hole East ( L H ) . The a im was to map 0.5 deg 2 (~ 7 times the area of its predecessor, the S C U B A 8-mJy Survey) to a comparable depth of a ~ 2 mJy at 850 /xm, which is roughly three times the confusion limit imposed by the underlying sea of fainter unresolved sources in the coarse S C U B A beam (Hogg 2001; Hughes et al . 1998; Cowie, Barger & Kneib 2002). The survey began in late 2002, and finished when S C U B A was decomissioned i n late 2005, having achieved a little over half of its original goal. Nevertheless, S H A D E S is the largest survey in terms of observing time carried out wi th S C U B A . It was proposed by a large team of mainly U K cosmologists, but. wi th some n o n - U K scientists involved, particularly through the inclusion of BLAST (the Balloon-borne Large Aperture Submil-limetre Telescope; Devl in et al . 2004), which may provide shorter wavelength data this winter. The basic a im of S H A D E S is to map 0.5deg 2 to a 4 a detection l imit of 8 m J y at 850nm. in order to address three fundamental outstanding questions:. 1.2. THE SCUBA HALF-DEGREE EXTRAGALACTIC SURVEY 17 1. What is the cosmic history of massive dust-enshrouded star-formation activity? The star-formation history of the S M G population can be derived from a combination of accurate measures of the submillimetre and millimetre source counts and the bolometric luminosities and redshift distribution of these dusty galaxies. This requires a sufficiently large wide area survey to yield a few hundred sources, each wi th a •good redshift estimate (Az < 0.5). Given the large amount of telescope time required to obtain spectroscopic redshifts for the faint optical counterparts, and because currently the spectroscopic approach (described above) only yields redshifts for the brightest, radio-detected submillimetre galaxies in a given survey, it is more efficient and unbiased to obtain photometric redshifts for the entire sample. Several groups (e.g., Ca r i l l i & Y u n 1999; Ca r i l l i & .Yun 2000; Hughes et al . 1998; Aretxaga, Hughes & Dunlop 2005) have developed successful photometric redshift techniques for obtaining robust redshifts for S C U B A or M A M B O (MAx-P lanck Mill imetre BOlometer) detected galaxies accurate to Az « 0.5 or better. We also require deep and unconfused far-IR photometry (from BLAST, Spitzer, or S H A R C - I I ) in order to constrain the bolometric luminosities of the galaxies and to achieve the claimed photometric redshift accuracy. 2. A r e submillimetre sources the progenitors of present-day massive ellip-ticals? To address this question we require only crude redshift estimates and a complete and homogeneous sample of S M G s over a wide enough area (0.5deg 2) in order to statisti-cally detect a clustering signal up to scales of ~ 10 M p c in the rest frame (an angular size of ~ 0.5 deg corresponds to 10 M p c at z = 2). Strong clustering is anticipated if S M G s are the progenitors of massive elliptical galaxies (because ellipticals are clustered), and even crude redshift information substantially reduces the clustering uncertainties. 3. W h a t fraction of submillimetre sources harbour dust-obscured A G N ? It has been shown that some fraction of S M G s may harbour an A G N (e.g., Smail et al . 2002; Alexander et al . 2005). But is accretion a significant contributor to the total far-IR luminosity output of the S M G compared wi th luminosity from star-formation? X -ray signatures are a good way to look for this, but sometimes the S M G s can be so obscuring that even X-rays are a biased indicator of A G N activity. A more powerful way 1.2. THE SCUBA HALF-DEGREE EXTRAGALACTIC SURVEY 18 to disentangle this mystery is to use observations from Spitzer in the mid-IR (24 /xm) band to look for signatures of either dominant star-formation or A G N activity (e.g., Egami 2004; Ivison et al . 2004). A starburst is expected to demonstrate a weak continuum and strong P A H features, whereas A G N activity is revealed by a lack of these emission features and a strong mid-IR continuum component, due to the warmer torus dust (see e.g., Lu tz et al . 2004 and Sajina et al . 2006). The 24pm band wi l l be sensitive to these features at the median redshift of the S M G s and wi l l be the most useful currently available data for discerning between the two scenarios. S H A D E S was therefore designed wi th al l of these requirements in mind. The Lockman Hole and S u b a r u - . X M M Deep Field regions were chosen for the survey because of the min imum contamination from Galactic cirrus emission, for observability throughout the year, and because of the wealth of existing or planned data at other wavelengths. The advantage of S H A D E S over other submillimetre surveys is a bigger and more uniformly-selected sample. Un t i l S H A D E S , which covers a larger area than any previous submillimetre survey to a uniform depth and posesses some of the deepest radio-coverage maps on the market, it has been difficult to determine the redshift distribution and bolo-metric luminosities of the submillimetre and millimetre galaxy population from exisiting S C U B A and M A M B O surveys spanning a range of depths and coverage. These difficul-ties stem from the problems in identifying a unique optical, IR or radio counterpart for each submillimetre galaxy, which in turn prevents a spectroscopic redshift from being ac-quired. Also, rest-frame far-IR luminosities and star formation rates for these galaxies are currently derived from generally poorly contrained rest-frame far-IR thermal peaks 6 The lack of robust redshifts is currently one of the biggest hurdles in understanding the nature of the supposed high-redshift galaxies found in blank-field submillimetre and millimetre wavelength surveys. We wi l l be able to provide a census of the level of obscured star formation i n galaxies at al l redshifts using the wealth of complementary multi-frequency 6 Ground-based rest-frame far-IR observations of these thermal peaks are hindered by the atmosphere's high opacity at these wavelengths, except in a few select atmospheric windows which permit limited access to these wavelengths in good dry weather at high elevations. 1.2. THE SCUBA HALF-DEGREE EXTRAGALACTIC SURVEY 19 data that wi l l be generated as a part of S H A D E S . 1.2.1 Multi-wavelength Follow-up Data The S H A D E S fields are necessarily complemented by observations spanning from the radio to the X-ray. V L A radio data at 1.4 G H z to depths of 4.2 ( L H ; the deepest radio field of its size) and 6.3 / i Jy ( S X D F ) have been obtained. Deep 600 M H z Giant Metre-wave Radio Telescope ( G M R T ) data are also currently being reduced by Ivison et al . (in preparation). M i d - I R data are being provided by the Mul t iband Imaging Photometer for Spitzer (MIPS) at 24 yum to a depth of 47 ^ J y as part of the Spitzer Wide-area InfraRed Extragalactic survey ( S W I R E ; Lonsdale et al . 2004) for the S X D F and to a depth of 11 / i Jy as a guaranteed time ( G T O ) program in the L H (Egami 2004; Huang et al . 2004). There are also some Spitzer M I P S data at 60 and 170 yum. Deep multicolour optical and near-IR imaging of the fields has also been obtained by Subaru and U K I R T . Addi t iona l deep near-infrared imaging of the S H A D E S fields in the J, H, and i\"-bands (down to K ~ 23 in the S X D F and K ~ 21 in the L H ) is underway as part of the on-going United K ingdom Infrared Deep Sky Survey (UKIDSS) using the new U K Infrared Telescope Wide Fie ld Camera ( U K I R T W F C A M ) . Deep optical spectroscopy is being performed at Gemini , Keck and the Very Large Telescope ( V L T ) . M A M B O (Greve et a l , 2004) and Bolocam (Laurent et al. , 2005) data at 1.2 and 1.1mm, respectively, already exist for about half of the S H A D E S coverage of the L H . The newly-commissioned Astronomi-cal Thermal Emission Camera ( A z T E C ; Wi lson et al . 2004) surveyed the full S H A D E S 0.5 deg 2 area at 1.1mm to a depth of less than 1.2 mJy R M S ; these data are presently being analysed by teams at the University of Massachusetts (led by the instrument prin-cipal investigator (PI) G . Wilson) and the University of Br i t i sh Columbia. The S X D F is also the deepest X-ray field covering about a square degree on the sky, wi th several overlapping XMM-Newton frames consisting of one deep lOOksec image in the centre (30 arcmin i n diameter) flanked by 50 ksec images. BLAST w i l l address a similar set of questions as S H A D E S by measuring the flux 1.2. THE SCUBA HALF-DEGREE EXTRAGALACTIC SURVEY 20 of > 1000 sources at shorter wavelengths (250, 350 and 500 /jtm) that cannot easily be surveyed over large areas from the ground (Devlin et al . 2001). The S H A D E S fields form a high priority part of the BLAST survey. BLAST underwent a long-duration flight in June 2005, however focussing problems hindered most of the extragalactic observations and the S H A D E S fields were not observed. The next long-duration flight is planned from Antarc t ica in December 2006, although the S H A D E S fields wi l l be far north and difficult to observe at best. The combination of these rich data-sets wi l l allow a long baseline for photometric redshifts for the bulk of the sources. In order to help address al l of the S H A D E S goals, we have been carrying out an observing programme since mid-2003 wi th the Submillimetre High Angular Resolution Camera ( S H A R C - I I ) at the Caltech Submillimetre Observatory (CSO) to image 850 /um-detected S H A D E S sources at 350 fxm. These data are valuable for constraining S E D shapes and for photometric redshift determination, especially since there is no short-wavelength submillimetre coverage of the fields yet by BLAST. Also, only the 2 4 / i m channel on Spitzer w i l l provide a small enough beamsize and have enough sensitivity to be very useful for redshift determinations of individual S H A D E S sources, leaving a huge gap in the SEDs . 1.2.2 SHARC-II Follow-up of S H A D E S Sources A l l photometric redshift techniques rely on assumed S E D templates, usually derived from libraries of local galaxies, since only a few of the brighter local S M G s have well constrained S E D s (e.g., Ca r i l l i & Y u n 1999; Car i l l i & Y u n 2000; Aretxaga, Hughes & Dunlop 2005; Hughes et al . 1998). However, the assumption that high-redshift galaxy S E D s resemble local ones could be introducing an obvious bias: are local templates representative of those for galaxies in the high-redshift Universe? There is evidence to suggest that local U L I R G s are warmer for a given luminosity than S M G s (e.g., Pope et al . 2006). O n the other hand, Kovacs et al . (2006) have verified that the linear far-IR/radio correlation 1.2. THE SCUBA HALF-DEGREE EXTRAGALACTIC SURVEY 21 holds for high redshifts (z ~ 1-3) and luminosities 1 O 1 1 - 1 O 1 3 L 0 . They provide direct measurements of the far-IR luminosities and dust temperatures for their sample of S M G s , although they note that selection effects could mean that these results cannot be extrap-olated for dusty galaxies selected in different ways. Laurent et al . (2006) also test the far-IR/radio correlation at high redshifts and find that it does not hold, suggesting that galaxies selected at longer wavelengths may possess characteristically different S E D s . Redshifts and S E D s of a large robust sample of S M G s are therefore needed in order to investigate whether dust evolves over cosmic time. Armed wi th spectroscopic redshifts one can make progress on this issue since the dust temperature and emissivity can be constrained independently of the redshift, and one can determine how these properties evolve wi th time (see e.g., Laurent et al . 2006, Pope et al . 2006). Measuring the S E D shapes (and hence accurately constraining the redshifts for a large sample of S M G s ) can only be achieved by obtaining multi-wavelength photometry mea-surements of these submillimetre galaxies. Efficient observations at the shorter submil-limetre wavelengths of 350 and 450 pm were difficult before the advent of S H A R C - I I and S C U B A . Observations at these shorter wavelengths are crucial to constraining the shapes of the S E D s (and hence the dust temperatures and redshifts) (Dunne & Eales 2001; Aretxaga, Hughes & Dunlop 2005). Very little spectral coverage can be obtained since most of the far-IR emission is absorbed by the atmosphere, except for the narrow trans-mission windows at 850 /im and 1.1/1.2 m m that S C U B A , and B o l o c a m / A z T E C / M A M B O have been able to probe. The Spitzer space telescope has also been making steady progress at 24, 60 and 170 pm, albeit wi th much poorer resolution at the longer wave-lengths than either S H A R C - I I or S C U B A . Using the spectroscopic redshifts, the T/(l + z) degeneracy can be broken and the combination of radio, S C U B A and S H A R C - I I observa-tions can provide a means to probe the physical dust properties as a function of redshift. For those sources without high quality short wavelength data, S H A R C - I I at 350 / /m wi l l greatly reduce the dust temperature-redshift degeneracy (Hughes et al. , 2002), and thereby improve both the accuracy and the model-independence of photometric redshifts obtained from combining just S H A D E S and radio data. From currently available red-1.2. THE SCUBA HALF-DEGREE EXTRAGALACTIC SURVEY 22 shifts (Chapman et al. , 2003), and based on simulations wi th a wide range of templates, the majority of the S H A D E S sources should be at 1 < z <3 and therefore potentially detectable at 350/um. Short wavelength data covering a selection of the S H A D E S 850/um sources wi l l allow progress to be made on a number of important questions: 1. It will increase the precision of photometric redshift determinations, allowing us to probe the redshift distribution of these sources. 2. T h e combination of V L A , 850 ^m, 350 /um, and Spitzer M I P S 24 /um data will allow an estimate of the fraction of S H A D E S sources which contain an A G N . The combination of radio, 850 /um and 350 fim data greatly narrows the range of S E D templates which.fit the data. W i t h i n this restricted range, the Spitzer data, par-t icularly at 24 / i m can constrain A G N activity. In particular, the 24 /um band corresponds to P A H features at z ~ 2, and these features trace A G N activity (see e.g., Lu tz et al . 2004 and Sajina et al . 2006). 3. The data will provide a check on the reality of S H A D E S sources which lack V L A counterparts and check whether they comprise a population with a different redshift distribution than the other S H A D E S sources. Prel iminary results show that for the top 20 S H A D E S sources there is a high incidence (75 per cent) of radio cotmterpart identifications wi thin an 8arcsec search radius. This leads to the conclusion that few of the S H A D E S sources lie at redshifts significantly in excess of z ~ 3. 4. The significantly better angular resolution of the 350/um S H A R C - I I data will clarify the effects of confusion on the completeness and bias in the BLAST data, particularly of the highest redshift sources. A t 350 jum, BLAST wi l l have a beam-size of about 40arcsec, and Spitzer w i l l have a beamsize of 45arcsec at 160 /um. Hence confusion noise from extragalactic sources and galactic cirrus wi l l be a significant issue for both instruments. S H A R C - I I data wi l l be less confused than either Spitzer or BLAST because of its significantly smaller beamsize, 9arcsec, at 350 /um. To understand the effects of confusion in the BLAST and Spitzer data and to clarify the completeness and flux bias in their maps, it would be of enormous value to have 1.3. GUIDE TO THIS THESIS 23 350 fxm data at much better resolution than possible wi th BLAST or Spitzer, even if only for a subset of the S H A D E S sources. A modest amount of S H A R C - I I data greatly improves the usefulness of the entire data-set for the S H A D E S and BLAST surveys. In addition, direct comparison of the S H A R C - I I and BLAST flux density measurements for a statistically significant number of S H A D E S sources wi l l help confidently p in the BLAST measurements to a common overall calibration, as well as help to validate the BLAST astromefry, a notoriously difficult problem in balloon-borne observing. It is clear that all of the S H A D E S scientific goals wi l l be greatly aided by inclusion of the S H A R C - I I data, filling a gap in wavelength between the S C U B A data at 850 fim and the Spitzer 24 fim data. 1.3 Guide to This Thesis Because of the large consortium nature of S H A D E S , for the first time in a submillimetre survey the data have been processed by four independent data reduction pipelines in order to increase the robustness of the results (catalogues and number counts). The different groups are based at: the Institute for Astronomy at the University of Edinburgh (Reduction A ) ; the University of Kent (Reduction B ) ; Instituto Nacional de Astrofisica, Opt ica y Electronica (Reduction C ) ; and the University of Br i t i sh Columbia (Reduction D ) . This thesis describes in detail the work done by Reduction D and provides a detailed description and comparison of the methods of the other groups. The observations and al l of the reduction, analysis and comparisons have been performed by the author, except where explicitly stated. The significance of the work contained in this thesis to S H A D E S can be seen in that a U B C recipe for flux deboosting (Coppin et al., 2005) was used to create the source catalogue, and that the U B C number counts were adopted as the S H A D E S number counts for publication. M a n y scientifically powerful results from S H A D E S wi l l come from comparisons of the properties of sources found in the S H A D E S catalogue wi th observations at other wave-lengths. Some of these include radio identifications (Ivison et al. , in preparation), far-IR-1.3. GUIDE TO THIS THESIS 24 radio photometric redshift estimates (Aretxaga et al., in preparation), and submillimetre-Spitzer-based S E D s and photometric redshifts (Clements et al., Dye et al. , Eales et al . and Serjeant et al . , in preparation). In this thesis, new constraints on the numbers of submillimetre sources as a function of 850 pim flux density based on the S H A D E S cata-logues are presented. A complementary analysis effort is also being pursued to constrain the numbers of faint submillimetre sources directly from our maps without the interme-diate step of making a catalogue, a so-called P(D) approach (e.g., Condon 1974, Scheuer 1974). Chapter 2 describes the observations and data analysis of 2 major data-sets: the S H A D E S S C U B A data and the S H A R C - I I follow-up observations of individual S H A D E S sources. Chapter 3 presents the development of a recipe to correct for flux density boosting in maps using an independent data-set which is utilised in Chapter 4 on the S H A D E S data. Chapters 4 and 5 contain the first S H A D E S results (source catalogue and number counts) and the results of the S H A R C - I I follow-up campaign, respectively. A n epilogue provides a glimpse of the future road-map of submillimetre astronomy and of S H A D E S in particular. 25 C H A P T E R 2 O B S E R V A T I O N S A N D D A T A A N A L Y S I S 2.1 Introduction This chapter presents the S C U B A S H A D E S data on which the majority of this thesis is based. The relevant data are those from the S H A D E S survey which were taken by members of the S H A D E S consortium, including myself (10 nights in June 2003, 6 nights in A p r i l 2004, 8 nights in June 2004, and 6 nights in June 2005). Also included here are the short wavelength S H A R C - I I submillimetre follow-up data obtained by myself (as PI) and co-investigators, on behalf of the S H A D E S consortium. Components of this survey and their follow-up data have been or wi l l be published soon by the S H A D E S consortium in the following peer-reviewed papers, of which I am a co-author: Mortier A . et al. (2005) 'The S C U B A H A l f Degree Extragalactic Survey ( S H A D E S ) I - Survey motivation, design and data processing', Monthly Notices of the Royal A s -tronomical Society ( M N R A S ) , 363: 509-520. This paper outlines the survey motivation, observing strategy and design and introduces one of the data reduction pipelines. The only data it contains is a re-analysis of the small older S C U B A 8-mJy Survey (Scott et al. , 2002) region using this pipeline, including the addition of the newer S H A D E S data. I am a co-author on this paper and contributed comments and suggestions for improving the paper. Coppin K . et al. (2006) 'The S C U B A H A l f Degree Extragalactic Survey ( S H A D E S ) II - Maps, source catalogue and number counts', M N R A S , in press (pre-print: astro-ph/0609039). This paper is the 850 and 450/zm S H A D E S Survey paper, highlighting independent reductions of the data undertaken by 4 S H A D E S sub-groups and presenting the S H A D E S 850 [im catalogue that is being used for al l subsequent follow-up work, as well as the S H A D E S number counts. The content of this paper (including text, figures 2.2. THE 850 pm SUBMILLIMETRE SURVEY 26 and tables) has been reprinted in this chapter and Chapter 4 wi th permission from Blackwell Publishing. C o p p i n K . et a l . (2006) '350 observations of S H A D E S galaxies'. This paper is currently in preparation and contains the S H A R C - I I follow-up data of some of the S H A D E S sources and results. I am also a co-author on the radio/Spitzer IDs 'paper IIP which is being led by R . J . Ivison in Edinburgh (I contributed comments to an early draft). I am also a member of the working group for the far-IR photometric redshift estimates 'paper I V , which is being led by I. Aretxaga at I N A O E . 2.1.1 Submillimetre Astronomy: Technical Challenges and Triumphs Advances in detector technology in the 1980's turned dreams of developing sensitive multi-pixel long-wavelength bolometer arrays into a reality. These developements have since allowed astronomers to peer through a new window to the Universe at submillimetre wavelengths. Since then, submillimetre and millimetre continuum studies have been making a significant impact in various astronomical fields, and perhaps most drastically, on our view of star-formation in the early Universe. This has resulted in a whole slew of new and more complex bolometer detectors being built in recent years, including S C U B A , Bolocam, S H A R C , M A M B O , M A M B O - I I , S H A R C - I I , BLAST, A z T E C , B O O M E R A N G , M A X I M A , H A W K , and S C U B A - 2 , to name a few. 2.2 The 850 fim Submillimetre Survey 2.2.1 The Instrument: the J C M T and S C U B A The 15-metre diameter James Clerk Maxwel l Telescope ( J C M T ) is the largest submil-limetre telescope in the world and is situated atop Mauna K e a on the B i g Island of Hawaii . A t this height (approximately 13,400 feet or 4092 metres) one is above most of 2.2. THE 850 fim SUBMILLIMETRE SURVEY 27 the water vapour in our atmosphere. It is very challenging to observe astronomical ob-jects of interest in the submillimetre wavelength regime since there are very few 'windows' where emission can penetrate the water-laden atmosphere, the largest opacity source in the submillimetre regime. The Submillimetre Common-User Bolometer Ar ray ( S C U B A ) (Holland et al., 1999), a continuum detector mounted at the left Nasmyth focus of the J C M T , was built wi th special filters in these windows. Figure 2.1 shows the observed transmission of the S C U B A filters. S C U B A was in operation M a y 1997 unti l Ju ly 2005, and at the time was the premier detector operating in the submillimetre regime, being the most highly cited astronomical instrument in al l of astronomy in 2001. The S C U B A detector has a field of view of 2.3 arcminutes and consists of hexagonal arrays of 37 and 91 bolometers operating at 850 and 450/um, respectively (see F ig . 2.2). It is cooled to about 7 0 m K , making it background-noise l imited. Light collected by the telecope is reflected off of a series of mirrors, decreasing the f-ratio to f/4, where it is then split by a dichroic beam-splitter 1 wi th a 97 per cent transmission efficiency. The beamsizes for the arrays are telescope diffraction-limited and the 850 fj,m beam is well fit by a Gaussian wi th a F W H M of 14.7arcsec. The 450/um beam has a F W H M of 7.5arcsec, although the beamshape is not so simple (it has significant sidelobes), is more prone to surface inaccuracies, and is characteristically less stable over time. Whi le S C U B A does possess a 450 / m i array and obtains these data essentially 'for free' along wi th the 850 / im, the 450 fim array is overall less sensitive in this regime and only really usable in the best weather. The arrangement made for using the J C M T is that S H A D E S would not utilize 'grade 1' weather. This means that the 450/um S C U B A data were expected to be of very limited use, if any. Observing Modes Sky emission dominates the astronomical signal being measured and must be removed. The secondary mirror 'chops', or nutates, at a default frequency of 7.8125 Hz wi th a 1This allows the two bolometer arrays to operate simultaneously 2.2. THE 850 fim SUBMILLIMETRE SURVEY 28 Measured SCUBA filter profiles 250 350 450 550 650 750 850 950 Wavelength (microns) Figure 2.1: The wideband filter profiles measured in 2000 wi th the University of Leth-bridge Fourier Transform Spectrometer. They are plotted over the old nar-rowband filter profiles for comparison. The thin black line (1mm P W V ) traces the submillimetre transmission function assuming a precipitable water vapour content of 1mm. This figure was created by Dav id Naylor and Wayne Holland and is from the J C M T website. 2.2. THE 850 / /m SUBMILLIMETRE SURVEY 29 SHORT WAVE ARRAY (91 de tec tors ) LONG W A V E A R R A Y (3? de tec tors ) 1 3 m m 2,3 a r c r m n u t e s 1,1mm (pho tomet r i c p ixe l ) 111; i j m 1111 M | H111HI !f | 0 S 10 15 20 2S ram 2 m n i Figure 2.2: The arrangement of bolometers in the short wave and long wave S C U B A arrays, which operate simultaneously at 450 and 850 ^ m , respectively. This figure is from the J C M T website. 2.2. THE 850 fj,m SUBMILLIMETRE SURVEY 30 user-defined chop 'throw', or amplitude, and position angle. This produces a differential measurement of the signal from the reference position and another point on the sky, effectively cancelling any slower atmospheric backgound variations. The telescope also 'nods' on and off the source (or 'beam-switches') every 10-20 seconds while chopping i n order to remove effects caused by the movement of the secondary mirror. Astronomical signals are attenuated by absorption in the atmosphere and can be corrected by knowing the airmass of the observation and the sky opacity at zenith. The Caltech Submillimetre Observatory (CSO) has a radiometer operating at 225 G H z which monitors the precipitable water column density by performing sky-dips at a fixed azimuth approximately every 10 minutes. The J C M T also performs hourly sky-dips which involves taking a measurement of the sky brightness temperature as a function of elevation angle (using hot and cold loads as reference values) and then performing a fit to those data to determine the sky opacity at zenith. In general the J C M T sky-dips and C S O tau ( r cso) measurements agree well wi th each other, and usually the TCSO measurements are adopted since they do not require the observing overheads that sky-dips require. The relations for the post-upgrade wide band filters derived by Archibald et al . (2002) are used to translate the rcso atmospheric opacity values to the wavelengths of interest in order to correct the data for sky extinction: 7850 = 4.02rcso + 0.001 (2.1) and T450 = 26.2rcso + 0.014. (2.2) Often, the rcso meter is looking at a completely different part of the sky wi th different humidity and it would be more desirable to measure the atmospheric opacity in the same direction as the astronomical source. In response to this need, since the summer of 2001 the J C M T has been using a cabin-mounted water vapour monitor ( W V M ) which looks at the 183 G H z water vapour line once every 6 seconds using a three channel double side band receiver and the J C M T telescope. In general, the rcso correlates well wi th the 2.2. THE 850 pm SUBMILLIMETRE SURVEY 31 W V M . The W V M is particularly useful during unstable weather conditions, where the rcso meter may be giving unreliable readings. S C U B A has four standard modes of operation: photometry, jiggle-mapping, scan-mapping, and polarimetry. The first two modes are described now since they were the modes used in this thesis. Pho tome t ry Photometry is used for isolated point sources and is done by pointing the central bolome-ter at the target and then making a very small 9-point jiggle around the source position, resulting in an undersampled map. This is the most efficient mode for getting down to the desired signal-to-noise ratio (S /N) level for a point source wi th accurately known coordinates. Each integration takes approximately 18 seconds including the nod. J igg le -Map The jiggle-mapping mode is ideally suited for sources larger than a beam, but less than 2.3 arcminutes in extent. The secondary mirror makes a 16-point jiggle pattern of offset positions from the source's central pointing position. This produces a fully sampled image at 850 / im. In order to get a fully sampled image at 450 fim, the telescope must make a 64-point jiggle pattern, since 3 arcsec spacing between points is required as opposed to the 6 arcsec spacing required at 850 //m. Each integration takes approximately 128 seconds including the nod. In this mode, about 20 minutes of on-source integration time (i.e., not including observing overheads such as calibration and pointing, etc...) is needed in order to reach a noise of l O m J y in good weather (i.e., rcso = 0.05) at an airmass of 1.3, for example. 2.2.2 The Observations The Subaru/XMM-Newton Deep Fie ld ( S X D F ) and Lockman Hole East (LH) regions are centred at (J2000) R A = 2 h 1 7 m 5 7 ! 5 , D e c = - 5 ° 0 0 ' 1 8 " 5 and R A = 1 0 h 5 2 m 2 6 ! 7 , Dec=57°24'12 / . / 6, 2.2. THE 850 fim SUBMILLIMETRE SURVEY 32 respectively. They were observed wi th a resolution of 14.7 arcsec and 7.5 arcsec at 850 and 4.50//m, respectively, wi th S C U B A (Holland et al . 1999) on the 15-m J C M T atop M a u n a K e a in Hawaii. A detailed account of the survey design and observing strategy is given in Mort ier et al . (2005) but is summarised briefly here. The observing strategy consists of making three overlapping jiggle maps for each of six different chop throw (30, 44 and 68 arcsec) and position angle (PA, 0 and 90deg in R A / D e c coordinates) combinations, motivated by the Emerson (1995) approach to map-making 2 . Each set of six observations spans a range of airmass values, while the observations are l imited to a 225 G H z atmospheric opacity range of 0.05 < rcso < 0.1, so as to maintain uniform coverage over the entire survey area. The S H A D E S survey data collection took place between 1998 March and 2005 June (including the epoch of existing data from the L H port ion of the S C U B A 8-mJy Survey, Scott et al . 2002, Fox et al . 2002). After a series of technical problems, S C U B A was officially decommissioned in 2005 July, wi th only a modest amount of S H A D E S data taken in its last year. Only S C U B A data taken up unti l 2004 February 1, covering a total area of 720arcmin 2 down to an R M S noise level of ~ 2.2 mJy, are included here. The sky coverage is approximately evenly distributed between the two S H A D E S fields. Complete S C U B A S H A D E S maps wi l l contain only an additional roughly 7 per cent of the planned area, although these wi l l be complemented wi th 1.1 m m A z T E C data (Wilson et al. , 2004) which wi l l be presented in future work. 2.2.3 Data Reduction The basic reduction steps are de-nodding, flat-fielding, extinction correcting, despiking, removing the sky signal, calibrating, rebinning the data into pixel grids, and finally extracting sources. The de-nodding step combines the individual nods to produce a triple-beam pattern. Flat-fielding involves using the measured response to a known load 2The Emerson-II strategy ensures a minimum loss of Fourier modes smaller than the largest chop-throw and of modes larger than the beam. 2.2. THE 850 / m SUBMILLIMETRE SURVEY 33 at the J C M T to correct the gains of each bolometer on the array relative to the central bolometer. The remaining steps listed above are described in turn below. S U R F scripts are used together wi th locally developed C code (Borys 2002, Borys et al . 2003) to reduce the data. For al l data taken on or after December 6, 2002 the known dead bolometer ' G 9 ' is manually removed from further analysis. Independent checks are made for cases where the azimuth tracking error (see Tilanus 2004) may have affected these data, and no significant effect on the astrometry of the observations are found, consistent wi th the findings of Mortier et al . (2005). The astrometry of the S X D F obser-vations prior to December 26, 2002 are corrected by —6.7 arcsec in declination, in order to account for a J C M T pointing catalogue error for the pointing source oCet i . The data are extinction corrected using the J C M T 183 G H z W V M readings temporally closest to the observations, whenever those data were available, and otherwise the 225 G H z TCSO values closest to or interpolated from the available polynomial fits were used. Occa-sionally, none of these data are available and then J C M T sky-dips were utilised. The software removes cosmic ray hits (i.e., despikes the data) by calculating the R M S a about the mean for each bolometer and removing any signal greater than 4.5 a. The mean sky at each time-step is calculated (based on the mean signal of al l non-excessively noisy or possible source-bearing, i.e., S / N > 3cr, bolometers) and subtracted from the bolometer timestream. The despiking and sky subtraction processes are repeated iteratively unt i l no additional spikes are found. Month ly average flux conversion factors (FCFs) , tabulated on the J C M T website 3 , are used to calibrate the data. For dates prior to January 1999 (the data for the S C U B A 8-m J y Survey, Scott et al . 2002), a 'standard' F C F value of 219 Jy b e a m - 1 V - 1 is used. The calibration uncertainty is not included in the error values, since it is negligible for these low S / N data and has no effect on the source extraction procedure. After calibrating, the final map noise R M S values for the L H and S X D F fields are 2.1 and 2.0 mJy, respectively. The bolometer data are regridded onto an output flux map wi th a pixel size of 3 x 3 arcsec. Every time a bolometer lands on a given pixel, flux is added to this pixel 3http: / / www.jach.hawaii.edu/JCMT/continuum/calibration/sens/gains.html 2.2. THE 850 /xm SUBMILLIMETRE SURVEY 34 by weighting each contributing measurement by the inverse variance in the bolometer's timestream. A n y undersampled pixel (i.e., hit less than 10 times) is cut from the map since it wi l l not be sampled well enough to follow Gaussian statistics or to make useful measurements. Whi le dumping flux into pixels, the flux from the negative off-beams is simultaneously 'folded i n ' to the map 4 in order to increase the overall sensitivity of the sources. Finally, the presence of the 16 sample noise spike (known to have plagued S C U B A observations since ~ 2003) does not warrant any major pipeline alterations, since its effect on these data is found to be almost negligible; an account of the investigation into this issue is presented in Appendix A . Several different checks were performed to test the Gaussianity of the noise and check individual source robustness by examining spatial and temporal fits to point sources in the maps and this analysis is presented in Section 2.2.6. 2.2.4 Source Extraction In order to detect sources, a noise-weighted convolution of the map wi th the point spread function (PSF) was performed, which was assumed to be a 14.7 arcsec F W H M Gaussian beam. This is essentially the same procedure as that of von Hoerner (1967) and is summa-rized by equation (1) in Mortier et al . (2005). The method is mathematically equivalent to fitting the P S F model centred on each pixel and is the minimum variance estimator if the background consists of white noise (see e.g., von Hoerner 1967). Peaks in the map are then deemed to be source candidates if they lie above some S / N threshold. This simple approach is inefficient for distinguishing closely separated sources, and therefore a cut-off is made at 18 arcsec from any already extracted source. This means that to find nearby pairs for a clustering analysis, one would have to revisit each source and perform a simul-taneous fit to a pair of sources. In practice, the S / N was found not to be high enough to enable this to be done. This source extraction method is therefore currently insensitive 4For each timestream sample, the negative flux at the position of the ofFbeams is weighted and added to the flux of the pixel being pointed at. 2.2. THE 850 /.im SUBMILLIMETRE SURVEY 35 to finding sources closer than 18 arcsec, which could be an issue if S M G s are clustered on scales < 18 arcsec. Note, however, that several results indicate that S M G s are clustered on scales larger than 25 arcsec (e.g., Greve et al . 2004, Scott, Dunlop & Serjeant 2005). 2.2.5 Summary and Comparison of Four Independent SHADES Pipelines In order to ensure the utmost robustness of the resulting 850 / i m source catalogue, data reduction was independently carried out by four sub-groups drawn from wi th in the S H A D E S consortium; hereafter referred to as Reductions A , B , C and D , as outlined in Section 1.3. This provides a high degree of reliability wi th respect to other S C U B A source catalogues available from the literature. The reduction of the 450 /um data, which are only of l imited use, is discussed in Section 4.2.8. A major strength of the S H A D E S analysis comes from the concordance of these reductions which have not been modified to bring them into agreement. A l l groups perform the basic reduction steps of combining the nods, flat-fielding, extinction correcting, despiking, removing the sky signal, calibrating, rebinning the data into pixel grids, and finally extracting sources. A l l reduction groups also correct the astrometry of the S X D F observations prior to December 26, 2002 by —6.7 arcsec i n Declination, in order to account for a J C M T pointing catalogue error for oCet i . For al l data taken on or after 2002 December 6 the known dead bolometer ' G 9 ' was manually removed from further analysis. Groups dealt wi th the presence of a 16 sample noise spike in the data in different ways, as first noted by Borys et al . (2004) and Sawicki & Webb (2005) (see also Mortier et al . 2005); this is further discussed in Appendix A . Reduction steps were performed by each group independently using some combina-t ion of S U R F ( S C U B A User Reduction Facility; Jenness & Lightfoot 1998) and their own locally-developed codes. The basic steps of the analysis procedure are described i n Mort ier et al . (2005). Each reduction group made different choices wi th respect to various detailed steps, which are described in Table 2.1. Several of the choices merit 2.2. THE 850 nm SUBMILLIMETRE SURVEY 36 attention and are discussed below. The teams each produce S / N maps convolved with the telescope point spread function. In al l four reductions, flux density measured when bolometers in the 'off-beam chop' of the telescope point at the region in question has essentially been folded in to the likelihood maps in order to increase the sensitivity of the maps. Two approaches have been used here: (1) fitting each pixel in the map to the multi-beam P S F (Reductions A , B and C ) ; or (2) folding in the flux from the off-beams in the timestream data and then fitting each pixel in the map to a single Gaussian (Reduction D ) . Opac i ty The dominant cause of variation in the multiplicative factor between detector voltage and inferred source flux density is temporal variation in the atmospheric opacity. In al l four reductions detector voltages are divided by the atmospheric opacity inferred, using coefficients in Archibald et al . (2002), from either the 225 G H z rcso measurements or the 183 G H z line of sight water vapour monitor ( W V M ; Wiedner 1998) at the J C M T . The differences in strategy described in Table 2.1 do not lead to measurable differences in the data. Largely because of S H A D E S , there is a substantial body of data correlating opacity measured v ia secant scans ('sky dips') for various chop-throws wi th the opacity inferred from measurements of the rcso or the J C M T W V M . Opacity monitors provide a lower noise measurement of opacity than is provided by any single sky-dip and do not cost any observing time (and are therefore preferred). Cal ib r a t i on The flux conversion factor ( F C F ) converts opacity-corrected bolometer voltages to flux densities. It is essentially the receiver responsivity. The F C F is fairly stable on both short and long time scales, but might depart from the long term average as the telescope mirror is distorted by thermal gradients near to sunset and sunrise (Jenness et al. , 2002). Because the F C F at 850 /xm is so stable, the long term average might be a better esti-mator of the F C F at a given moment than any single measurement taken during stable 2.2. THE 850 / /m SUBMILLIMETRE SURVEY 37 conditions. Over-reliance on individual F C F measurements could inject noise into the analysis. However, Reduction B , which makes the most use of measured F C F values, produces maps whose noise is as low as the other reductions. Pixel Size Reductions A and B make 'zero-footprint' maps using an optimal noise-weighted drizzling algorithm (essentially the l imit ing form of the method of Fruchter & Hook 2002) wi th a pixel size of 1 arcsec 2. Reductions C and D use 3 x 3 arcsec pixels. The pressure to use larger pixels is driven by the observation of Borys et al . (2003) that statistical analysis becomes unpredictable when there are too few observations per pixel. The concern that large pixels might lead to larger uncertainty in the positions of the detected sources is not supported i n the data. Reduction D , wi th 3 arcsec pixels, has the lowest positional scatter wi th respect to the mean of the other observations and also demonstrates the lowest positional scatter wi th respect to a subset of radio positions (see Table 4.2). 2.2.6 Tests of the Data Several different checks were performed by the reduction groups in order to examine the noise properties of the maps and test the individual source robustness by examining spatial and temporal fits to point sources in the maps. Tests of Gaussianity in the Maps Reduction C's photometric error distributions were tested for Gaussianity by performing Monte Carlo simulations. A realisation of Gaussian noise was created from the measured detector signal variances for S X D F . The simulated noise signals were reduced and re-binned into pixels using the same procedures as for the real data. Sources were placed into the map one at a time at random locations and their recovery was attempted. The joint probability distribution from the simulations was calculated using the same tech-nique that was used for the real data. The photometric uncertainty is very close to 2.2. TEE 850 SUBMILLIMETRE SURVEY 38 Table 2 .1 : D a t a Reduction Procedures. 'Secondary Ext inct ion M o n i t o r ' refers to the source of the estimation of the sky opacity when the ' P r i m a r y Ext inct ion M o n i t o r ' was unavailable. Step Reduction A Reduction B Reduction C Reduction D Reduction Code Used IDL-based routines used in the S C U B A 8-mJy Survey (Scott et al., 2002). See Serjeant et al. (2003). Reduction A's IDL pipeline altered at the extinction correction, calibration and source extraction phases. See Mortier et al. (2005). SURF scripts for reswitching and flat-fielding and locally developed code from Chapin (2003) thereafter. S U R F scripts for reswitching and flatfield-ing and locally developed C code thereafter (Borys 2002; Borys et al. 2003). Primary Extinction Monitor Polynomial fit to Tcso- Interpolated W V M read-ings. Same as Reduction A. Nearest W V M reading. Secondary Extinction Monitor Linear fit to neighbour-ing sky-dips and inter-polation of neighbouring data points. TCSO, sky-dip values. Interpolated sky-dips. Nearest TCSO reading, linear fit to neighbour-ing sky-dips and interpo-lation. Cosmic Rays Iterative 3 a cuts until no signal is removed. ~ 32 successive 3 a cuts. One 3 cr cut. Iterative 4.5 a cuts until no signal is removed. Baseline Subtrac-tion Subtract the temporal modal sky level obtained from a fit to all bolome-ters in the array itera-tively with cosmic ray re-moval. Subtract mode signal iteratively with cosmic rays. Handle bolometers exhibiting excess 16 sample noise separately. Subtract array median. Subtract mean of non-noisy bolometers from all bolometers iteratively with cosmic ray removal. Calibration Calculate an F C F for each half night and apply to the data. Linearly interpolate be-tween all stable F C F measurements during a night, selected by eye. Mean of measured F C F before and after sun-rise/set (i.e., two aver-ages per shift). Each of 3 chop throw amplitudes handled separately. Monthly average F C F s (single value of 219 J y V - 1 b e a m - 1 for data before January 1999). Flux Den-sity Maps Inverse variance weighted flux density summed in 1 arcsec pixels. Each chop throw mapped sep-arately (six flux density maps) and then combined to produce a single maxi-mum likelihood flux den-sity map. Same as Reduction A. Same as Reduction A, but with 3 arcsec pixels. Inverse variance weighted flux density summed in 3 arcsec pixels to pro-duce a single flux density map. Negative flux den-sity from off-chop posi-tions also summed in at the timestream level(see Borys et al. 2003). Convolution Form maximum likeli-hood point-source flux density and noise maps (and S/N maps) via noise-weighted convolu-tion with the differential PSF that combines 14.5 arcsec Gaussians with the chop pattern. Same as Reduction A. Same as Reduction A, but with 14.7 arcsec Gaussians. Form maximum likeli-hood point-source flux density and noise maps (and hence S /N maps) using noise-weighted convolution with a single 14.7 arcsec Gaussian (i.e., without the chop pattern). Cut Pixels No pixel cuts were made in flux density map. Ig-nore pixels with S/N de-viating more than 4<r from convolved map. No pixel cuts were made in flux density map. Ig-nore pixels with a > 10 mJy in convolved map. Remove pixels with < 10 'hits' in flux density map. Ignore pixels with a > 5 mJy in convolved map. Remove pixels with < 10 'hits' in flux density map. No pixels were ignored in convolved map. Source Ex-traction Positive peaks identified in the convolved signal map above a threshold. A model was constructed by centering a normalised beam-map at the posi-tions of the peaks in the convolved map. Nor-malisation coefficients were calculated simul-taneously, providing a minimum noise-weighted X2 fit to the unconvolved signal map. Peaks identified in the maximum likelihood S/N maps above a 2.5 a threshold. Flux densities identified at those posi-tions in the maximum likelihood point source flux density maps. Same as Reduction B. Same as Reduction B. 2.2. TEE 850 pm SUBMILLIMETRE SURVEY 39 Gaussian, as expected, and the parameter, a that comes out of the source extraction routine is entirely consistent wi th what is expected. General Source Robustness A quick test of source reality is to create the negative of the map and search for sources using the same triple-beam template. Aside from pixels associated wi th the off-beams of positive detections, 3 and 4 > 3.5 a 'detections' and 21 and 25 > 3.0 a 'detections' are found in the inverted Reduction D S X D F and L H maps, respectively. This is consistent wi th the expected number of false positive detections in noisy data. Note that only one of these negative sources (3.9 a, in L H ) has high enough S / N and/or low enough noise to survive the deboosting procedure described in Chapter 3. Spatial and temporal x2 tests are also performed in order to determine how well the raw timestream data fit the final PSF-fi t ted maps. A candidate source may be 'detected' i n the map, but it may not necessarily be well-fit by the P S F , or it may be a poor fit to the set of difference data, or both. Note that these two tests also check for Gaussianity of the noise in the maps, but that they are not a strong test of this distribution. The 'spatial x 2 ' test (see Pope et al . 2005 and Coppin et al . 2005 for more discussion and details) provides a gauge across the map of the goodness-of-fit of the triple-beam differential P S F to the data, and thus indicates if a source is poorly fit by the assumed P S F . Sources greater than 2 .5a wi th x2 values lying outside of the ± 2 a = 2.16 ( L H ) , or 2.05 ( S X D F ) regions of the spatial x2 distribution of the smoothed L H and S X D F maps are picked out. Six such sources are found in Reduction D's L H map, 3 of which correspond to S H A D E S catalogue sources, and 16 such sources are found in Reduction D's S X D F map, 5 of which correspond to S H A D E S catalogue sources. Following the prescription of Pope et al . (2005), the pixel temporal xj and the number of hits for each pixel JVJ i t s is calculated. A S / N map of poorness-of-fit to the model is then constructed by using the quantity X 2 — i V m t s as the 'signal' and y/2N^its as the 'noise' and fitting the P S F to this temporal x2 map. The 'temporal x 2 ' provides a measure of the self-consistency of the raw timestream data which contribute flux density to each 2.2. TEE 850 / m i SUBMILLIMETRE SURVEY 40 map pixel. > 2.5 a sources in the maps lying outside the ± 2 a = 1.60 ( L H and S X D F ) regions of the temporal x2 distribution are selected. In Reduction D's L H map, 17 such sources exist, 5 of which correspond to S H A D E S catalogue sources. In Reduction D's S X D F maps, 16 such sources are found, 6 of which correspond to S H A D E S catalogue sources. Those source candidates wi th relatively poor spatial and/or temporal x2 values are flagged i n Appendix B . A l l of these flagged sources have either temporal or spatial x2 values just outside the 2 a regions of the x2 distributions except for one source that has a spatial x2 value > 3 a (LOCK850.15) . 2 . 2 . 7 M a p s The left panels of Figs. 1 and 2 show the point source S / N maps for the S H A D E S fields from Reduction D . The positive and negative beams are clearly seen in these maps and appear as a result of the differential measurements taken at the different chop throws. Noise maps are also presented (see right panels of Figs. 1 and 2) wi th the positions of the S H A D E S catalogue sources marked by circles. The regular grid pattern in the noise maps corresponds to variation in the effective observing time as a function of location, arising from the triangular pointing pattern in the survey and the decision to chop the telescope along sky coordinates ( R A and D e c ) , rather than allowing field rotation to smooth the observing time over the map. Figure 2.3: The 850 fim S / N map wi th the off-beams folded i n at the timestream stage (i.e., each chop is treated separately in order to optimise S /N) (left) and corresponding noise map (right) of the 485arcmin 2 for the L H are shown. This area only includes 3 arcsec pixels that were sampled more than 10 times. O n the noise map, 15-arcsec diameter circles indicate the positions of the 60 sources i n the L H S H A D E S catalogue. Notice that sources are less often detected in noisier areas of the map; in general they are found in areas corresponding to better weather and on a fine scale sources are preferentially found near the corners of the overlapping triangular rows. The previous S C U B A 8-mJy L H Survey covers approximately one quarter of the map in the lower-right hand corner. W i t h i n that region is a deep rectangular test strip (a ~ l m J y ) that was observed before the rest of the S C U B A 8-mJy Survey. ro bo Figure 2.4: The 850 /urn S / N map (with the off-beams folded in at the timestream level) (left) and corresponding noise map (right) of the 406 arcmin 2 S X D F region are shown. This area only includes 3 arcsec pixels that were sampled more than 10 times. O n the noise map, 15-arcsec diameter circles indicate the positions of the 60 sources in the S X D F S H A D E S catalogue. In general, sources are more often found on a ' r ing ' (avoiding a noisier central region taken i n predominantly poorer weather), while on a finer scale sources are preferentially found near the corners of the overlapping triangular pattern. to 2.3. 350 Aim FOLLOW-UP OBSERVATIONS 43 Histograms of the noise maps are given in F ig . 2.5. Several features are worth noting. The L H map has a non-uniform chop strategy, since the earlier S C U B A 8-mJy Survey region (Scott et a l , 2002) was taken only wi th a single 30 arcsec chop (with nod) in Declination. This different chop strategy noticeably changes the character of the flux density map; in the S C U B A 8-mJy Survey region the noise is clearly spatially correlated in the vertical direction, and bright sources only have negative side-lobes above and below them. In the R M S noise map, however, the triangular pattern is repeated across the entire field, since the S C U B A 8-mJy Survey was also built from a mosaic of overlapping jiggle-maps falling on the same grid adopted for S H A D E S . The deepest region of S H A D E S is a small rectangular region at the centre of the S C U B A 8-mJy Survey where additional data were available from a test strip observed before the commencement of the full S C U B A 8-mJy Survey (Scott et al . , 2002). 2.3 350 fim Follow-up Observations 2.3.1 The Instrument: the CSO and SHARC-II The Caltech Submillimetre Observatory (CSO) consists of a 10.4-m diameter 84-hexagonal paneled Leighton primary dish, parabolic in shape, housed i n a protective dome neigh-bouring the J C M T near the 14,000 foot summit of Mauna Kea . It is also one of world's few professional observatories without an operator! The dish has a very low surface error (10.4 / m i R M S at 350 /mi) due to the new Dish Surface Opt imizat ion System (DSOS) installed in 2003 (Leong, 2005) which corrects the primary dish for surface imperfections and gravitational deformations as a function of elevation angle during observations (active optics) to improve the telescope efficiency and pointing. This makes the C S O probably the best telescope in the world at shorter submillimetre wavelengths. The beam size (with good focus and pointing) is 8-9 arcsec F W H M at 350 /mi . S H A R C - I I is the background-limited 350 and 450 / m i common-user continuum camera built for the C S O and commissioned in 2002 (Dowell, 2003). S H A R C - I I also operates 2.3. 350 nm FOLLOW-UP OBSERVATIONS 44 Figure 2.5: Histograms showing the noise distribution of the smoothed noise map (pix-els wi th more than 10 hits) for the L H and S X D F fields in bins of A a = 0.05 m J y b e a m - 1 . The bump in the L H histogram between 1 and 1.5 m J y arises from the deep strip in the S C U B A 8-mJy Survey region. 2.3. 350 Mm FOLLOW- UP OBSERVATIONS 45 at 850 / im, but it is not optimised for use at this particular wavelength and is instead detector noise l imited rather than background noise limited. In August 2004, S H A R C -II moved from the f/4.48 focus of the C S O Cassegrain relay optics to a new Nasmyth platform to allow flexible scheduling wi th visiting instruments. S H A R C - I I is a 'CCD-s ty le ' bare filled 12 x 32 array of 1 m m 2 doped silicon 'pop-up' bolometers. This is a different approach to the S C U B A - l i k e traditional submillimetre de-tector, where conical feedhorns are used to direct the light collected from large apertures onto small bolometers. Approximately 85 per cent of the 384 S H A R C - I I bolometers work well. Each detector has an extent of 4.85 arcsec, resulting in a 2.59' x 0.97' field of view ( F O V ) . This design is advantageous since a filled focal plane wi th instantaneous Nyquist sampling provides an optimal mapping speed when the desired F O V can be completely covered by detectors. But since S H A R C - I I does not cover the entire F O V of the tele-scope, it works best for mapping relatively compact objects. The most efficient map sizes for mapping point sources are on the order of the S H A R C - I I array F O V which is about 2' x 1'. S H A R C - I I is about 4 times faster at detecting known point sources and 30 times faster at mapping larger areas compared to its predecessor S H A R C (a single row of bolometers!). In the best 25 per cent of the winter nights ( rcso = 0 .05) , S H A R C - I I has a typical 350/mi sensitivity, or noise equivalent flux density ( N E F D ) , of about 1 Jy H z - 1 / 2 for a typical airmass of 1.3. A t 850 Aim, an N E F D of about 1-2 J y H z _ 1 / 2 is expected, about 10-20 times worse than S C U B A , and so little observing has been performed at this wavelength. Due to the C S O ' s large aperture and S H A R C - I I ' s optimisation for use at 350 /^m, S H A R C - I I observations are able to provide the most sensitive and highest resolution 350 Ami images currently available, filling a niche in submillimetre coverage. O b s e r v i n g M o d e s Unlike many other bolometer arrays, S H A R C - I I does not employ a chopping strategy to remove the dominant atmospheric signal, and so the primary observing modes wi th S H A R C - I I involve continuous scanning. Instead of chopping, the bolometers are sampled 2.3. 350 fim FOLLOW-UP OBSERVATIONS 46 -EO -10 0 |0 20 ' -00 ' - IB - * 10 B>.- -20 -10 « If £0 Figure 2.6: The progress of a lissajous scan pattern at three different times, providing a uniform coverage of the sky. Axes are in arcsec. This figure is from the C S O website. every 33 msec and the ' total power' measurement is used to estimate the sky contribution, so that it can be removed during the data reduction stage. Two routines were developed by C S O staff to collect data while performing linear and curved controlled scans; they are called ' S W E E P ' and ' B O X S C A N ' . Lissajous or ' S W E E P ' mode, is best suited to making maps comparable to the array size, while the boxscan or ' B O X ' mode is better suited to making much larger maps. The stability timescale of a S H A R C - I I bolometer is approximately 10 seconds; to achieve full sensitiv-ity, one needs to scan from 'off to 'on' source wi thin this time frame. The lissajous S W E E P pattern (see F i g . 2.6) was recommended by the C S O staff to map areas of size on the order of the SHARC - I I array F O V (2' x 1'). Using the centre of the map as the reference point, the telescope modulates its X and Y position, each wi th a different sine wave. X and Y are usually azimuthal coordinates, but equatorial or galactic coordinates can also be used. The user chooses the amplitudes and periods of the sine waves. The offsets, dx, and dy are given by: dx(t) = A X c o s ( 2 7r* /TX) and dy{t) = A Y s i n ( 2 nt/TY), (2.3) where A X and A Y are the respective amplitudes in arcsec and T X and T Y are the respec-tive periods in seconds. Periods were chosen so that one of them is rational number and 2.3. 350 Atm FOLLOW- UP OBSERVATIONS 47 the other is an irrational number to prevent periodic motion, otherwise the scan pattern wi l l be cyclical and repeatable, which makes it inherently impossible to separate the sky noise from the true astronomical signal at those frequencies. Typica l parameters used were 20 arcsec in each of X and Y (mapping a region of 40" x 40", of which approximately the central 20" x 20" is continuously viewed) and 14.142 and 20 seconds in T X and T Y , respectively. Sometimes larger scan patterns of up to 20" x 30" were used i n order to accomodate multiple S H A D E S sources spread much further apart. 2.3.2 The Observations T i m e and Sensitivity Estimates B y design, our strategy was to reach a 3a R M S of 30 mJy at 350 / i m in the best weather (T~CSO < 0.06). The S H A D E S detections have raw flux densities from about 7-12mJy. Since at z ~ 1 the 350 / i m to 850 /um ratio is roughly 10 and at z ~ 3 the ratio decreases to 5 (based on a range of S E D templates drawn from the local U L I R G population), this yields 350 /um flux densities of 70 to 120 mJy and 35 to 60 mJy at z = 1 and z = 3, respectively. This is consistent wi th experience gained from the S C U B A 8-mJy survey (Scott et al . , 2002), the direct precursor for S H A D E S , where two sources were followed up in photometry (and one in deeper mapping) wi th an R M S of ~ 10 m J y and flux densities of 30-40 mJy. Using this as a guide, a la R M S noise of around l O m J y at 350/um is required in order to produce a reasonably high detection rate and a useful signal to noise ratio. Model l ing of S E D s in the relevant redshift range also bears out the importance of good 350 /um data (see Aretxaga et al . 2003). Statistically, the best weather conditions occur 10 per cent of the time i n 'summer' (May-November) and 27 per cent of the time in 'winter' (December-Apri l) . Since good weather is scarce, it is important to be as efficient as possible by only integrating down to the noise needed, maximising the number of fields observed. Whi le at the telescope, Mark Halpern and I developed a more sophisticated and efficient method to calculate the integration time needed to achieve the desired noise levels than a simple integration time 2.3. 350 fj,m FOLLOW-UP OBSERVATIONS 48 calculator (which does not exist for S H A R C - I I ) . We were able to estimate the integration time needed on each field to achieve our noise goals, depending on its instantaneous elevation (sky transmission is worse at low elevation angles) and the sky opacity value at zenith (as reported by the 225 G H z TCSO dipper). Estimated integration times were cross-checked wi th measured N E F D values for S H A R C - I I as a function of Tcso and comparable time estimates were found to wi thin 10 per cent. See Appendix C for details. To reach the desired sensitivity in maps approximately 3' x 1.5' in size, 3-4 hours of on-source observing is required, assuming an average airmass of 1.6 (LH) , and hourly pointing checks. Field Selection 120 submillimetre sources have been identified in the S H A D E S fields, and many of them lie close enough together that multiple galaxies can be found wi th in a single 1.5' x 3' S H A R C - I I field of view. The selected fields contain a large fraction of the S H A D E S close angular-pairs and a deliberate mixture of sources wi th compact and extended radio counterparts, as well as a few sources wi th no identified radio counterpart at a l l . Choosing targets from among sources wi th extended and compact radio counterparts, and including some sources wi th no detected V L A counterpart wi l l help to refine S H A D E S redshift distributions and test if there is a sub-population wi th a high redshift tai l . Summary of the Observations Observations were taken using an altitude-azimuth (alt/az) non-connecting Lissajous scan pattern using the S W E E P command of the telescope control system, wi th small amplitudes of 20 arcsec in both altitude and azimuth and wi th typical periods of 15-20 seconds. Larger amplitudes (30 arcsec) were used in a few cases, where the source separation was larger than usual. Individual scan integration times were 620 seconds (10 minutes) to ensure uniform coverage in individual scans, and several scans were taken 2.3. 350 Aim FOLLOW-UP OBSERVATIONS 49 for each field to reach the required depth. Integration times and the resulting depths of each S H A R C - I I field are given in Table 2.3. 2 fields in the S X D F were observed in September 2004 in very poor weather con-ditions (0.07< rcso < 0.1, S X D F 1 / 1 1 and S X D F 3 / 8 ) . Over the course of 4 superb-weather nights in March 2005 and February 2006 (0.035 < T C S O < 0.06, 10 S H A D E S fields were successfully mapped (containing 2 or more sources each) in the Lockman Hole region wi th S H A R C - I I . 2 of these fields have also been observed by Kovacs et al . (2006) and Laurent et al . (2006) and were chosen for consistency checks ( L O C K 3 / 4 7 and L O C K 1 / 4 1 / 6 3 ) . Before the L H rose during this run, one additional region in the S X D F was observed for about an hour at the start of each of 7 nights ( S X D F 1 7 / 2 6 ) . Another poor weather observing run in 2006 yielded a couple of hours worth of data covering one more region in L H ( L O C K 1 5 ) , though a sufficient depth was not reached in order to make these data very useful. Sky Opac i ty It is crucial to have a good measurement of the sky opacity at the time of an observation, so that the data can be accurately corrected for atmospheric extinction. The atmospheric zenith opacity at 225 G H z and 350 PIRN were monitored every 10 minutes by the rcso sky dippers. This r sampling rate usually results in a noisy r as a function of time, and therefore a single measurement can be a poor representation of what the atmosphere is doing at any instant. Thus, it is recommended that the rcso polynomial fits be used. The fits are provided v ia a web interface as a service by the C S O staff. The reduction software automatically accesses the fits if they are available to obtain a 350 fim sky opacity value to use in the reduction. B y inspection, the 350 fim r fits for each night of S H A R C - I I observations seem to do a better job at describing what the sky was doing than any individual r measurement and so the fits were utilised. 2.3. 350 FOLLOW-UP OBSERVATIONS 50 Po in t i ng and Ca l ib ra t ion Pointing and/or focus checks and calibration were performed hourly on nearby standard sources in close proximity to the science targets using the same scanning strategy as for the science targets, but wi th integration times from 120-160 seconds (as typical flux densities are > 2 Jy . Because the typical pointing rms of 2-3 arcsec at the C S O is a non-negligible fraction of the 9 arcsec beamsize, much care was taken to minimize pointing errors. Observations of point-like galaxies, quasars, protostellar sources, HII regions, and evolved stars were used by the C S O staff for constructing a pointing model for each observing run in order to correct for significant known systematic pointing trends wi th the zenith and azimuthal angles. The model predictions of the calibrators surrounding the science observations were then compared to the actual pointing measurements and small average offsets were calculated and applied to the model pointing predictions of the science observations during the map coaddition stage of the reduction. This procedure tracks the slow time drifts in the pointing, which is the a im of making hourly pointing observations and typically yields a pointing accuracy R M S of ~ 2 arcsec (private communication Darren Dowell). Cal ibrat ion was performed by comparing the known and measured flux densities and beamsizes obtained for standard calibration sources: for S X D F , oCet i (a blazar), and oc-casionally OH231 (an evolved star), were used as pointing and calibration sources; for L H , C I T 6 (an evolved star) was used, or else nearby- asteroids (Pallas and Egeria) were used when C I T 6 was unavailable. The final calibration is expected to be better than 15 per cent, wi th systematic effects being negligible. The standards have well-tabulated known 350/ im flux densities and are available from the C S O / S H A R C - I I calibration webpage. 2.3.3 Data Reduction The primary data reduction package is C R U S H (Comprehensive Reduction Ut i l i t y for S H A R C - I I ) , a java-based tool developed by Kovacs (2006). This software models total 2.3. 350 Mm FOLLOW- UP OBSERVATIONS 51 power detector signals using an iterated sequence of maximum likelihood estimators. It implements a self-consistent least-squares algorithm to solve for the celestial emission, taking into account instrumental and atmospheric contributions to the signal. The code automatically ranks al l of the signal contributions in the pipeline in terms of their flux densities (usually brightest to faintest) and removes a model fit to each contribution one at a .time. The code iteratively removes these signals for a total of 10 times (after which changes to the solution are negligible; private communication A t t i l a Kovacs). The order of the solutions is crucial, as detector artifacts can be bright, and sometimes the default ordering is not correct. The source flux is not in the ordering scheme but is set by the user using special flags (e.g., the 'deep' flag). See Table 2.2 for details of the models. One can see that although the data reduction process is in principle automated, in practice it requires a fair amount of human interaction. The atmospheric opacity is not solved for since this median power contribution swamps al l of the signal, so it is just subtracted. The first contribution to the signal that is fit and removed is the average of the array, leaving just residuals from the array average behind. In this way, each successive parameter estimate is derived from the residuals left by the preceding estimate. Using the 'deep' ut i l i ty for sources fainter than 100 mJy, the maps of each field were coadded. The data are optimally filtered for beam-sized features (9 arcsec) in order to yield maximal S / N on point sources; this is essentially equivalent to fitting the image wi th a slightly wider effective beam of around 9 arcsec. This accounts for the smearing of the 8.5 arcsec beam by pointing and focus variations on long integrations to yield a final image resolution of 12.4arcsec (~ y/2 times worse). The high redshift sources observed are much smaller (< 30kpc 5 ) in extent than 9 arcsec and so the profile of the emission i n the maps is just the P S F of the beam. 5Note that at a z ~ 1-3, a source of about 50kpc in diameter (about the size of the Milky Way including dust, gas, and stars) subtends an angle of < 6.5 arcsec on the sky; so these sources are not likely to be resolved here. 2.3. 350 / i m FOLLOW-UP OBSERVATIONS 52 Table 2.2: Order of signal models in C R U S H . Summary of a table from (Kovacs 2006; reproduced wi th permission). C R U S H places the models in order of decreasing brightness, solves them one at a time, and then iterates. Mode l Name Typica l F l u x Typical T ime Scale Typica l Spatial Scale Residual P ixe l Offsets 10 3 -10 4 Jy scan pixel Correlated Background Noise 10-10 3 Jy 10 min. array G a i n Model l ing scan pixel P ixe l Weights scan pixel Temperature Gradients 1-10 Jy 1 frame array Electronic Row Drifts ~ 1 Jy 1 sec. row Detector 1/f Drifts ~ 1 Jy ~ 30 sec. pixel T ime Weights ~ 1 sec. array Residual Spikes Regional Correlations ~ l O m J y 0.1-1 sec. 4 x 4 - 8 x 6 Acceleration Response ~ 10 3 mJy scan pixel Temporal Features all time scales pixel Spectral Features all time scales pixel to Co Table 2.3: Summary of the S H A R C - I I observations and map properties. R A and Dec. (J2000) coordinates are given for the field pointing centre, each containing one or more S H A D E S sources. The number of 10 minute observation files, total integration time, weather conditions (atmospheric opacity range and mean at 350 fxm) are listed. F ina l flux map R M S and area are also given, but note that they appear to be very high since a large fraction of the maps are comprised of noisier edges, so this is not a representative gauge of the R M S where flux density measurements are made (as a side note, the noise map variance is typically in excess of 5mJy) . Field Name SHADES Sources RA (J2000) Dec. (J2000) Date(s) of observations (UT) No. of Files Int. Time (hrs.) Eff. Int. Time (min.) Mean T350 Map RMS (mJy) Map Ar (arcmin LOCK21/28 21, 28 10h52m57?3 57°30'5470 2005-02-28/03-08/09 23 3.83 8.5 1.30 20.0 3.1 LOCK26/32 26 10h52m39?7 57°23'16"4 2005-02-28 10 1.67 9.3 0.99 12.9 3.1 LOCK4/69 4 10h52m05?5 57°27'06"4 2005-02-28 12 2.00 9.9 0.88 15.8 3.1 LOCK3/47 3, 47 10h52m37f 1 57°24'57"5 2005-02-28 3 0.50 1.1 0.87 34.1 3.0 LOCK33/42 33, 77 10h51m56?5 57°23'05'/5 2005-03-01 12 2.00 8.9 0.90 14.8 3.1 LOCK 10/48/64 10, 48, 64 10h52m52?0 57°32'51'/4 2005-03-01 10 1.67 9.8 0.89 19.0 3.7 LOCK1/41/63 1, 6, 41, 63 10h51m57f9 57° 24' 607 6 2005-03-01 10 1.67 13.7 0.80 32.5 3.9 LOCK16/50 16 10h51m49?3 57°26'4475 2005-03-08 23 3.83 7.5 1.33 23.3 3.8 LOCK22/25 22 10h51m35?2 57°33'26"9 2005-03-08/09 33 5.50 6.0 1.52 26.7 3.5 LOCK44/45 none 10h51m56?8 57°28'37"9 2005-03-09 20 3.33 4.7 1.33 35.3 3.8 LOCK15 15 10h53m19?l 57°21'10"5 2006-02-24 11 1.81 1.1 1.52 73.9 2.8 SXDF1/11 1, 11 02h17m27?9 -04°59'3870 2004-08-30/31/-09-01 39 5.84 6.4 1.83 22.0 3.8 SXDF3/8 3, 8 02h17m43?2 -04°56'12"5 2004-08-30/31/-09-01 51 8.22 5.2 1.81 23.6 4.3 SXDF17/26 17, 119 02h17m55?8 -04°52'5074 2005-03-01/03/05/07/08/09 25 4.17 6.8 1.39 23.9 3.1 CO Cn O O tr-* t-< O O to o CO Cn co 2.3. 350 / im FOLLOW-UP OBSERVATIONS 54 2.3.4 Source Extraction The source extraction employs the same method that was used in this thesis for the S H A D E S data; using an adapted I D L version of the Borys et al . (2003) C code. The code iteratively finds the brightest pixel in the map and then masks a region of 2 abeam = 10.6 arcsec in radius around this pixel and continues the cycle down to a user-defined S / N threshold. In this way, the source extraction algorithm is only sensitive to sources sepa-rated by at least 10.6'arcsec. A preliminary S / N threshold of 2 a was chosen arbitrari ly low so that no genuine sources would be missed in the S H A R C - I I maps. Association and S / N refinement of these candidate 350 pm sources to the S H A D E S catalogue sources are discussed i n Section 5.2. The S / N of the sources are only meaningful if the assumption of Gaussianity holds in the maps, however. This is touched upon briefly in the following section. 2.3.5 Tests of the Data Several different checks were performed in order to examine the noise properties of the maps and to test the overall robustness of detections. Tests of Gaussianity in the Maps Histograms of S / N of the pixels in each map were plotted in order to see if the assumption of Gaussianity holds to first order, see F ig . 2.7. A l l but a few of the S / N maps are consistent wi th a perfect Gaussian of a = 1 and a mean of 0. Note that several rows (4 on each edge) of the maps are clipped out automatically by C R U S H at the map reduction stage, since they are not sampled well enough to follow Gaussian statistics or to make useful measurements. Note that an earlier version of C R U S H did not produce Gaussian looking maps, and Laurent et al . (2006) chose to adopt an additional cut in the maps in order to create a so-called 'uniform coverage map', eliminating pixels that were looked at less than 60 per cent of the maximum integration time in each map. Given that the maps here look sufficiently Gaussian (see F ig . 2.7) and no improvement is seen in the 2.3. 350 fxm FOLLOW-UP OBSERVATIONS 55 maps by cutting out the noisiest edge pixels (in fact, the histograms become noisier and less Gaussian because there are so few pixels in each map!) additional removal of data is not imposed, since C R U S H appears to be doing a sufficient job at edge clipping and producing statistically believable maps. Spl i t t i ng up the D a t a Spli t t ing up the data into two different sets can be useful to answer questions such as as: Does a source persist at lower S/N in both sets of data?; and Does the noise scale down as expected when the 2 data-sets are combined? Each data-set was therefore split into two sub-sets arbitrarily and reduced separately, using the same reduction steps as for the final maps. U p o n examining the split data sets, the sources associated wi th S H A D E S catalogue positions (see later in the thesis) persist in both data-sets, albeit at lower S / N . Since these are low S / N sources even in the final combined maps, this is more of a qualitative test. The split maps were then subtracted from each other. The resulting flux density in the combined map should be ~ 0 (i.e., any real sources should be removed, wi th only noisy features remaining) and the flux density R M S is expected to be about a factor of \/2 higher than in the final maps. For most of the maps the noise did follow this general rule, however, about half the maps showed flux R M S values in the differenced maps which were up to 40 per cent higher than expected (in the worst cases). This is a weak test of the existence of spatially correlated data, which would not be a surprise, given that 350 / i m data are very susceptible to trends and variations in weather, which may have not been completely removed by the filtering timescale of the software. It may be that the noise could be improved by more aggressive filtering, but this was not attempted here. Note that the depths achieved and listed in Table 2.3 are slightly worse than antic-ipated, and this is likely due to higher N E F D s in practice than were used to estimate needed integration times, or due to correlated data. Also, sky variability is difficult for 2.3. 350 fim FOLLOW-UP OBSERVATIONS 56 -4 -2 0 2 4 -4 -2 0 2 4 -4 -2 0 2 4 S/N S/N S/N Figure 2.7: Distr ibut ion of pixel S / N in each SHARC - I I map. The dot-dashed lines are the best-fitting Gaussians. The fit is very close to a perfect normal distribution, wi th the a mean of 0 and variance close to 1. A perfect normal distribution is overplotted in each panel as a solid line. None of the maps show a large excess of positive sources, since the map areas are small and typically only a handful of pixels/sources appear at S / N > 2.5-3. 2.3. 350 nm FOLLOW-UP OBSERVATIONS 57 C R U S H to remove and may be a factor in the higher R M S values than were expected. However, it has been confirmed that the noise in the data scales down wi th integration time among maps of varying depths roughly as \ j\ft as expected. The R M S of the flux density maps versus the effective integration time (see Appendix C) is plotted in F i g . 2.8. The maps a l l seem to follow the expected relation except for map L O C K 1 / 4 1 / 6 3 / 6 , which seems to have an unusually high R M S compared wi th the other maps. Note that the scanning pattern for this map was significantly different than the others because a wider coverage area was mapped to accomodate more sources, at the expense of a shallower map. Source Extraction Tests A reality check was performed by turning the maps upsidedown and extracting sources in the same way as for the positive real maps. In short, an excess of positive sources compared to negative sources is found. Details of the results appear later i n Section 5.2. 2.3.6 Maps The left panels of F i g . 2.9 show the S H A R C - I I point source S / N maps. Noise maps are also presented (see right panels of F i g . 2.9) wi th the positions of the S H A D E S catalogue sources marked by plus signs. Here, noise is calculated as the scatter of the flux density measurements going into each pixel. One can see in these plots that the regions of lowest noise are those areas of the maps that were covered continuously by the Lissajous scan pattern (i.e., the central regions of the maps). S H A R C - I I flux densities of S H A D E S sources are reported in Chapter 5. 2.3. 350 fim FOLLOW- UP OBSERVATIONS 58 0 2 4 6 8 10 12 14 Effective Integration Time [minutes] Figure 2.8: Plot of flux map R M S versus effective integration time (cf. Appendix C ) . The filled circles represent each SHARC - I I map and the solid line is the function R M S oc i _ 1 / / 2 , scaled arbitrarily to show the general trend seen in the data (i.e., it is not a fit). The maps al l seem to follow the relation except for one point, map L O C K 1 / 4 1 / 6 3 / 6 , which seems to have an unusually high R M S compared wi th the other maps; this may be because here a larger scan pattern was adopted to cover a wider area at the expense of map depth. 2.3. 350 nm FOLLOW- UP OBSERVATIONS 59 LOCK21/28 LOCK21/28 30' 32' 00' 30' 3 31'00' 30' 30' 00' 57u 29' 30' 30' 24' 00' 10h 53 m 05s Right Ascension LOCK26/32 30" h 23' 00' 30" h 57° 22'00' 10h 52 m 50s 40 s Right Ascension 32' 00" 30' 00" 57" 29' 30" \-10h 53 m 05 s Right Ascension LOCK26/32 6 o •a 30' 24' 00' 30" 23'00" 30" 57° 22' 00" 10h 52 m 50s 40" Right Ascension Figure 2.9: S H A R C - I I S / N (left) and R M S noise (right) maps of regions of the L H and S X D F containing S H A D E S sources. The images are displayed on the same S / N and noise scales for comparison and the colour bar is given on the last page of the figure. Plus signs indicate the 850/ im positions of S H A D E S catalogue sources. See Table 5.1 for the corresponding flux densities, noise estimates and S / N values. 2.3. 350 nm FOLLOW-UP OBSERVATIONS LOCK4/69 LOCK4/69 28'00 27'00 26'00"h 57" 25' 30 05 s Right Ascension 51 m 55s 57° 25' 30" 28'00"r 27'00 26'00 05 s Right Ascension LOCK3/47 LOCK3/47 26' 00' 30' 25'00' 30' 24' 00' 57° 23'30' 10h 52 m 44s 26' 00' 30' 25' 00" 30' 24' 00" 57°23'30" 10 h 52 m 44 s Right Ascension Right Ascension Figure 2.9: (continued) 2.3. 350 fan FOLLOW-UP OBSERVATIONS 61 LOCK33/42 LOCK33/42 24'00 23 '00 57" 21' 30' 2 2 ' 0 0 " h 10 h 5 2 m 05 s 51'" 55" Right Ascension 30" 24' 00' 30' 23 '00 ' 30" 22' 00" 57° 21' 30' 51'" 55° Right Ascension 34' 00' 30' 3 3 ' 0 0 " 30" 32' 00' 57° 3 1 ' 3 0 " LOCK10/48/64 i 1 1 1 1 i LOCK10/48/64 10 h 5 3 m 00 s 34 '00" 30' 33'00' 30' 32' 00' 57 u 31' 30" h 10 h 5 3 m 00 s Right Ascension Right Ascension Figure 2.9: (continued) .3. 350 nm FOLLOW-UP OBSERVATIONS 62 LOCK 1/41/63 2 4 ' 0 0 " h 57° 2 3 ' 0 0 " h 10 h 5 2 m 10 s 00° Right Ascension 26 '00" 24'00 57° 23' 00" 10 h 5 2 m 10 s 00 s Right Ascension LOCK16/50 LOCK16/50 28' 00 1 52"' 00 51 m 50s Right Ascension 2 8 ' 0 0 " h 57° 25' 00" [ 10 1 52'" 00' Right Ascension Figure 2.9: (continued) 2.3. 350 nm FOLLOW- UP OBSERVATIONS 63 LOCK22/25 LOCK22/25 35'00' 57u 32' 00" 35'00' 57° 32' 00" Right Ascension Right Ascension LOCK15 LOCK15 e ,5 30' 22' 00' 30' 21' 00" h 30" 10h 53 m 30s 20° Right Ascension 22'00"h 21'00 57° 20' 00" 10 h 53 m 30 s Right Ascension Figure 2.9: (continued) 2.3. 350 nra. FOLLOW- UP OBSERVATIONS 64 S X D F l / l l SXDF1/11 00' 58' 30' 00" h •a -04" 59'30" h Q 00" h 00' 30' -05" or oo' 02h 17m 34s 30° 26s Right Ascension 58' 30" 1 -04° 59'30 1 00' 30" -05" or oo" Right Ascension SXDF3/8 SXDF3/8 o 54'30" 00" 55' 30" 00" 56' 30" 00" 57' 30" -04" 58' 00" 02h 17m 50s i i 46s 42s Right Ascension 38* Right Ascension Figure 2.9: (continued) 350fim FOLLOW-UP OBSERVATIONS SXDF 17/26 51'30' 52'30"h 53' 30 00" 54'30 02n 18m02 s '—' • •• 17m 58s 54s 50s Right Ascension I Q 51'30 00" 52' 30" 00" 53'30" 00" -04° 54'30" SXDF 17/26 r i ' •. . . i 02 h 18 m 02 s 17m 58s S/N 54s Right Ascension [mJy beam"1] Figure 2.9: (continued) 66 C H A P T E R 3 F L U X D E N S I T Y D E B O O S T I N G A N D B I A S IN S U B M I L L I M E T R E S U R V E Y S 3.1 Introduction F l u x boosting in maps is a well-known effect in low S / N submillimetre surveys; confusion can either increase or decrease the input flux of a source, but a noisy flux-limited map wi l l preferentially contain sources whose true flux densities have been increased and this effect is exacerbated for steep source counts. F l u x boosting is sometimes referred to as Malmquist or Eddington bias, although flux boosting is distinct from both of these biases (see Section 3.4.2). A simple Bayesian prescription for estimating the unboosted flux distribution is developed here and used to determine the best flux estimates of the sources. This method is easily adapted for any other modest S / N survey in which there is prior knowledge of the source counts, such as S H A D E S . Here, the development of the flux deboosting recipe on an independent data-set is presented and discussed: an 850/im S C U B A map of the Gro th Strip. The data and results discussed here are also presented i n the following paper: Coppin , K . et al. (2005) ' A n 850 /an S C U B A map of the G r o t h Strip and reliable source extraction. ' M N R A S . 357: 1022-1028. The data were collected by C o l i n Borys and Scott Chapman during observing runs in 1999 and 2000 (before I arrived at U B C ) . I reduced and analysed the data and, in addition, was in charge of applying and organising the queued follow-up photometry observations of several of the candidate detections in the reduced maps. The content of this paper (including text, figures and tables) has been reprinted in this chapter wi th permission from Blackwell Publishing. On ly about 300 blank-field S C U B A galaxies have been discovered since S C U B A was commissioned, in contrast to the tens of thousands to millions of objects detected in opti-3.1. INTRODUCTION 67 cal surveys of similar sizes. Nevertheless, the number counts have been well-characterised, and progress is being made in identifying S C U B A galaxies wi th objects in other wave-bands using source positions derived from radio identifications. However, the fact remains that S C U B A sources are difficult to find, and when they are detected they typically have low S / N , bringing into question the reliability of measurements. Using deep radio imag-ing of the S C U B A 8-mJy Survey fields (Scott et al . , 2002), Ivison et al . (2002) have sug-gested that low S / N sources in relatively noisy regions of submillimetre maps which lack radio counterparts are often spurious. Addi t ional evidence that these sources might be spurious comes from the lack of M A M B O counterparts to many of these S C U B A sources (Greve et al . 2004). Mortier et al . (2005) also report not recovering a similar fraction of low S / N sources in the S C U B A 8-mJy Survey region when combined wi th newer S H A D E S data in the same field. Only one region, namely the Hubble Deep Fie ld ( H D F ) region or G O O D S - N field, has been investigated independently by different groups (prior to S H A D E S ) . Reassuringly, Borys et al . (2003, 2004) and Wang, Cowie & Barger (2004) are in close agreement for the higher S / N sources in that region. However, there is some disagreement regarding the reality and the flux densities of several of the noisier sources. The effects of flux boosting (sometimes called Malmquist and/or Eddington bias) are well known for S/N-thresholded maps, and it is worthwhile to investigate whether such discrepancies are to be expected, and when one should be confident about the reality of a source, independent of whether it has a radio identification. It is clear that a careful, un-biased analysis of the robustness of S C U B A detections in shallow maps is called for. In this vein a careful estimate of flux boosting is provided and 5 sources detected in a shallow 850 / i m map of the Gro th Strip have been followed up in photometry mode, in an attempt to quantify the amount of flux boosting present in the map. To interpret the results, a general method to assess the reliability of low S / N sources is developed here. These techniques are applied to a particular S C U B A survey in the 'Gro th Str ip ' . The 'Gro th Strip Survey' (GSS) is a Hubble Space Telescope (HST) programme ( G T O 5090, PI : Groth) consisting of 28 overlapping HST Wide Fie ld Planetary Camera 2 ( W F P C 2 ) medium-deep images, covering an area of 113arcmin 2 , forming a long strip centred on 3.1. INTRODUCTION 68 R A = 1 4 h 1 6 m 3 8 f 8 , Dec=52°16 '52" (J2000), at a Galactic latitude of b ~ 60°. The G S S was the deepest HST cosmological integration before the H D F , reaching a l imi t ing Vega magnitude of ~ 27.5-28 in both the V and I bands (Groth et a l , 1994). The GSS has an enormous legacy value, since extensive multi-wavelength observations centred on this region have been conducted or are planned. Morphological and photometric in-formation from the W F P C 2 images are provided by the Medium Deep Survey ( M D S ) database (Ratnatunga, Griffiths & Ostrander, 1999) and the Deep Extragalactic Evo-lutionary Probe ( D E E P 1 ) survey (Simard et al. , 2002). X-ray sources have also been identified in an 80ks XMM-Newton observation of the G S S (Miyaj i et al . , 2004). The G S S is currently part of the on-going D E E P 2 2 survey and is also targetted to be a major component of upcoming large surveys in the U V (using the Galaxy Evolut ion Explorer, GALEX3), in the optical (as part of the Canada-France-Hawaii Telescope Legacy Survey, C F H T L S 4 ) , and in the IR (the Spitzer G T O I R A C Deep Survey). In this chapter, 850 pm S C U B A observations of about 60 per cent of the original W F P C 2 coverage of the GSS are presented. Confirmation photometry on some of the sources has also been performed. The 850 pm map and source list have been made available to the community so that it may be correlated against existing and future data-sets at other wavelengths 5. No claim is made that this survey is either the deepest or the most extensive performed using S C U B A . However, the observations cover enough integration time that one expects a handful of real sources to be detected, and this survey represents the best set of submillimetre data available in this field unti l the advent of S C U B A - 2 . 1See http://deep.ucolick.org 2See http://deep.berkeley.edu 3See http://www.galex.caltech.edu 4See http: //www.cfht.hawaii.edu/Science/CFHLS 5See http: //cmbr.physics.ubc.ca/groth 3.2. MAP OBSERVATIONS AND DATA REDUCTION 69 3.2 Map Observations and Data Reduction A roughly 70 arcmin 2 portion of the Gro th Strip (GSS) was observed wi th a resolution of 14.7 arcsec and 7.5 arcsec at 850 and 450/um, respectively, wi th the 15-m J C M T in January 1999 and January 2000. The GSS S C U B A map is centred on R A = 14 h 16 m 00 s , Dec = 52°lO'OO" (J2000). 52 overlapping 64-point jiggle maps of the G S S were obtained, providing measure-ments of the continuum emission at both wavelengths simultaneously wi th S C U B A (Holland et a l , 1999). The atmospheric zenith' opacity at 225 G H z was monitored wi th the Caltech Submil-limetre Observatory TCSO monitor. The Tcso ranged from 0.03 to 0.09 in January 1999 and from 0.05 to 0.08 in January 2000. The weather was generally more stable for the latter set of data. The secondary mirror was chopped at a standard frequency of ~ 8 Hz i n azimuth to reduce the effect of rapid sky variations. The telescope was also 'nodded' on and off the source. A 40 arcsec chop-throw was used at a position angle of 54°, almost parallel to the lengthwise orientation of the strip. Pointing checks were performed hourly on blazars and planets and varied by less than 3 arcsec in azimuth and by less than 2 arcsec in elevation. The overlapping jiggle maps were co-added to produce a final map wi th a total integration time of 18 hours and 50 minutes. S U R F ( S C U B A User Reduction Facility; Jenness & Lightfoot 1998) scripts together wi th locally developed code (Borys, 2002) were used to reduce the data (see Section 2.2.3 for details). The S U R F map and our map look similar. The benefit of using our own code to analyse the data is that it makes a map wi th minimally correlated pixels and provides an estimate of the noise in each pixel. 3 arcsec pixels were chosen oriented along R A , Dec. coordinates. This pixel size is slightly too large for 450 / /m studies, but has proven to be adequate at 850/ im (see Borys et al . 2003). 3.2. MAP OBSERVATIONS AND DATA REDUCTION 70 3.2.1 Flux Density Calibration Calibrat ion data of bright submillimetre continuum sources (i.e., planets and blazars) were reduced in the same way as the GSS data. The flux conversion factors (FCFs) over 3 of the 4 nights in January 1999 and al l 3 nights in January 2000 agree wi th the monthly averages to wi thin 10 per cent (see the J C M T calibration web-page). The F C F value for one night in January was 30 per cent higher than the monthly average and this could indicate that the sky was so variable that the rcso w a s n ° t accurately reflecting the opacity along the line of sight to the object. The calibration uncertainty is omitted from our quoted error values, since it is not a major contributor to the global uncertainty of our low S / N data and has no effect on our source detection method. The 850 fim map has a mean consistent wi th zero (none of the handful of detected sources are very bright; cf. Table 3.1), as expected from differential measurements, and an R M S of 3.5 mJy . The final map is shown in F ig . 3.1. The 450 / i m map also has a mean consistent wi th zero and an R M S of 50mJy . 3.2.2 Source Detection Method Given the 14.7 arcsec beam, a high-redshift galaxy wi l l be unresolved and wi l l appear as a positive source flanked by 2 negative sources. The source density at 850/ /m (see e.g., Scott et al . 2002, Borys et al . 2003, Webb et al . 2003b) suggests that only a handful of sources wi l l be recovered in our map. Hence many overlapping sources are not expected, and therefore sources were extracted by fitting the raw rebinned map wi th a three-lobed P S F of an isolated point-source wi th the same chop throw and position angle as the map data. A n accompanying weighted noise map is created simultaneously and provides an estimate of the noise associated wi th the detection of a point source in each pixel. A peak i n the PSF-convolved map which is 3 times the noise i n that pixel constitutes a 3 cr detected point source. 3.2. MAP OBSERVATIONS AND DATA REDUCTION 71 ( • ' « | « I ' | I " I | " " i | i i i | " i i | i i " | i " i | i i " | " H I 1 1 I • • 1 I • 1 1 I • 1 1 I • 1 1 I • 1 1 I • 1 1 I 1 1 • I 1 1 1 I 1 1 1 4 h 1 7 m 0 0 s 1 6 m 3 0 s 0 0 s 1 5 m 3 0 s 0 0 s -2.5 3.5 Figure 3.1: The 850 fxm S / N image of the Groth Strip, smoothed wi th the 3-beam tem-plate (see § 3.2.2). The solid 40-arcsec diameter circles correspond to can-didate sources with S / N > 3.5. Dashed circles indicate the positions of the S / N = 3.0-3.5 candidate sources. The inlay in the top right-hand corner i l -lustrates our field geometry relative to some other surveys in this region, including the original W F P C 2 pointings (jagged squares), the CUDSS - l -14 field, C F R S and ISO survey regions (trio of large squares, listed here in order of increasing size), V L A coverage (large circle) and XMM coverage (smaller circle). 3.2. MAP OBSERVATIONS AND DATA REDUCTION 72 3.2.3 Source Robustness For a list of sources found above a given significance level in a map to be useful, one must address the following questions: 'Are there any statistical anomalies in the data which would cause one to doubt any of the sources?'; 'Given our actual noise and measurement strategy, what fraction of sources present at any given flux level would one expect to detect?', that is, 'How complete is our source list?'; and finally, 'Do the flux densities inferred from the maps form a biased estimator of actual source flux?' Bias and flux boosting are addressed in § 3.4. Quali ty of fit and completeness are addressed here. Source robustness is investigated using several techniques, including spatial and tem-poral x2 tests, searching for negative sources, and Monte Carlo simulations. Spatial and Temporal x2 Tests Even although a candidate source is 'detected' in the map, it may not necessarily be well-fit by the P S F , or it may be a poor fit to the set of difference data, or both. Spatial and temporal x2 tests were performed (see Section 2.2.6 for details) in order to determine how well the raw timestream data fit the final PSF-fi t ted maps. The x2 values for each pixel where a source is detected are wi thin ± 2 a (=2y/2NPix), where Np[x is the of number degrees of freedom or number of pixels included in the fit) in al l cases, except for GSS850.3, a candidate source wi th S/N=3.3 . The poor fit may be the result of its proximity to GSS850.4 (see F ig . 3.1). No pixels at the centres of our candidate sources lie outside the ± 2 a regions of our temporal x2 distribution. A l l of the candidate sources appear to lie in regions of the map wi th self-consistent timestream data and we have no grounds to reject any of our detected candidate sources based on these tests. Note that these two tests also check for Gaussianity of the noise in the map, but they are not a strong test of this distribution. 3.3. MONTE CARLO SIMULATIONS 73 Sources Detected i n the Inverted Map A quick test of source reality is to create the negative of the map and to search for sources using the same triple-beam template. Aside from pixels associated wi th the off-beams of positive detections, 6 'detections' are found in the inverted map, consistent wi th the expected number of false positive detections in noisy data (see § 3.3). 3.3 Monte Carlo Simulations Simulations are required in order to evaluate map completeness and the likely rate of false positive detections, given our non-uniform noise. The procedures described in Borys et al . (2003) are followed for investigating the number of positive sources expected at random, as well as the map completeness. In order to determine how many detections may be spurious, a map is created wi th the same shape and size as the real one, but replaced the 850 fj,m data wi th Gaussian random noise, generated using the R M S of the timestream of each file and each bolometer. The same source detection procedure that was used on the real data was then performed. This sequence of steps was repeated 1000 times and we plot the cumulative number of positive sources detected on average in F ig . 3.2 at each S / N threshold. The simulations suggest that on average one expects 1.6 false positive sources > 3.5 a and a further 4.5 between 3 and 3.5 a. The completeness of a map is the fraction of sources which one expects to detect at each flux level. To measure this fraction, a source of known flux was added into the real map and was extracted using the source extraction method. Input source flux densities were randomly selected in the range 3-20 mJy, and the sources were placed uniformly across the map, and this procedure was repeated 1000 times. A source is considered recovered if it is detected wi th S / N > 3 and located within 7.5 arcsec (the 850 / im beam H W H M ) of the input position. It is estimated that about 60 per cent of the > l O m J y sources are detected above a S / N of 3 a in the map (see F ig . 3.3). The completeness 3.3. MONTE CARLO SIMULATIONS 74 3.0 3.5 4 .0 4 . 5 SNR threshold Figure 3.2: Cumulative number of detected candidate sources. The results are plotted against S / N threshold for the map (dark histogram), the average expected in source-free simulated 850 yum maps containing only Gaussian random noise (light dotted curve), the number of false positives expected on average plus the predicted number of real sources using the source counts of Borys et al . (2003) multiplied by the completeness estimate (dark solid curve), and the confirmed spurious detections (light histogram, see § 3.4). The number of expected detections and the number of actual detections are consistent wi th in the Poisson noise. 3.4. CANDIDATE SUBMILLIMETRE SOURCES 75 Table 3.1: GSS 850/urn candidate submillimetre sources wi th follow-up photometry. Lo-cations of these and the other 6 candidate S C U B A sources are indicated in F i g 3.1. Object 5850° St B 850 (mJy) (mJy) GSS850.1 9.5 ± 2 . 9 (3.3 a) - 1 . 8 ± 3.6 ( -0 .5 a) GSS850.2 8.2 ± 2 . 3 (3.6 a) 5.7 ± 1.1 (5.2 a) GSS850.6 12.3 ± 4 . 1 (3.0 a) 1.2 ± 3.1 (0.4 a) GSS850.7 13.2 ± 3 . 2 (4.1 a) 4.2 ± 1.7 (2.5 a) GSS850.11 11.2 ± 2 . 9 (3.8 a) 0.1 ± 1.6 (0.1 a) a Flux density estimate from the map. 6Flux density measured from follow-up photometry. is slightly higher than it would be in a map wi th uniform noise at the same R M S , as expected (cf. F i g . 3.2). 3.4 Candidate Submillimetre Sources Four candidate sources wi th S / N > 3.5 a and 7 candidate sources wi th S /Ns in the range 3.0-3.5 a are detected. A submillimetre image of the GSS is shown in F i g . 3.1, where each of these 11 candidates are numbered, while in Table 3.1 information on the 5 sources for which follow-up photometry was performed are presented (see § 3.4.1). 3.4.1 Additional Photometry In December 2003 and January 2004, S C U B A photometry observations were performed i n the 2-bolometer chopping mode to check some of our candidate map detections. 2 candidates, GSS850.7 and GSS850.11, near the noisier edge regions of the map and a 'control ' , GSS850.2, in a lower-noise region away from the edges were selected. Also, during one of the observing runs in January 2000, four sources were identified in the map data 'by eye' and selected as targets for follow-up photometry. On ly two of these 3.4. CANDIDATE SUBMILLIMETRE SOURCES 76 100 80 60 40 20 0 _l I I L_ 10 15 Input Flux (mJy) Figure 3.3: Completeness of 850 / m i source recovery at each level of input flux for 3cr detections, as determined from the Monte Carlo simulations of individual sources added to the GSS data described in § 3.3. 3.4. CANDIDATE SUBMILLIMETRE SOURCES 77 pointings correspond to candidate detections in the final map (GSS850.1 and GSS850.6); this is a warning that our eyes often pick out bright outliers in noisy regions of a map. A l l of the photometry observations were reduced in the standard way using S U R F . In order to increase the S / N of sources observed in the 2-bolometer mode by a factor of approximately \ / 3 / 2 , the signal from the off-position bolometers were added to the central bolometer (see Chapman et al . 2000). The results are listed in Table 3.1 for comparison wi th the estimated map flux densities. In al l cases, the photometry pointings were wi thin 3 arcsec of the positions found by the source-detection algorithm in the map. 3 . 4 . 2 F l u x D e n s i t y B o o s t i n g i n t h e M a p It appears that some sources were detected in the map. However none of the candidate sources have very high S/Ns, and so care is needed in interpreting these results. ' F l u x boosting' is a well-known effect in low S / N submillimetre maps and must be quantified so that individual source flux densities can be corrected to represent the best estimate of the true underlying flux density of each source. Weak S / N sources are more often detected when combined wi th positive noise fluctuations, thus leading to a net overestimate of the flux densities and this effect is even more pronounced for steep source counts. This boosting is sometimes referred to as Malmquist bias although more properly that refers to seeing sources more luminous than average in a magnitude-limited survey because of a spread in luminosity, i.e., there is st i l l Malmquist bias even when there is no measurement error. F l u x density boosting is also distinct from Eddington bias, which properly refers to the effect on the number counts rather than the individual source flux densities. There seems to be a great deal of confusion in the astronomical community regarding the meaning of Malmquist and Eddington bias. F lux density boosting is consistent wi th the picture of Eddington bias, but it is really a third kind of bias that manifests itself as the boosting of an individual source flux density due to both the presence of noise in the map and the steepness of the underlying source counts. A set of simulations was performed in order to assess the expected distribution of 3.4. CANDIDATE SUBMILLIMETRE SOURCES 78 pixel brightnesses from triple-beam (i.e., double difference) observations of a noiseless blank-sky. A smooth curve of the form given in Scott et al . (2002) is fit6: dN _ N' a / c \ 0 S'J + \ S ' (3-1) to the number counts of Borys et al . (2003) and constrained by the lensing counts at fainter flux densities as an a priori distribution of flux densities in the range 0.1-40mJy. Three different patches of noiseless sky following a Poisson distribution were populated, and sampled wi th a S C U B A Gaussian beam, taking a double difference each time. This was done one mil l ion times and the anticipated prior distribution of double difference flux measurements, N(SP), is plotted in the first panel of F ig . 3.4. The effects of reasonable excursions from the assumed shape of the source counts were investigated. For example, using the 1 a error bar values at the bright end of the number counts has less than a 10 per cent effect on the resulting flux estimates. The distribution N(SP), which is the prior probability that a pixel i n the map has differential flux Sp, is calculated from noiseless simulations while our actual map contains noise. If M is the statement that flux Sm ± am is measured at some pixel in the map, the probabili ty that the true flux of that pixel is Sp is obtained from Bayes' theorem: P(SP) = P(SP\M,N(SP)) = N ( S p ) p { ^ M l S p \ (3-2) where the probability one would measure Sm when the true flux is Sp is P(M\Sp) = Ae , (3.3) under the assumption that our noise is Gaussian distributed. This assumption has been weakly tested in Section 3.2.3. Because the maps are differential wi th zero mean, and because they contain noise, the expression in Equation 3.2 can have a negative ta i l . The fraction of the posterior distribution P(SP) having Sp < 0 is taken as the probability that 6 In Equation 3.1, N' refers to the normalisation of the differential number counts (dN/dS) at the break location S', and the power-law slopes are given by a and (3. 3.4. CANDIDATE SUBMILLIMETRE SOURCES 79 a given source is falsely detected. P(M) acts as an overall normalisation in Equat ion 3.2, and does not depend upon Sp as long as the noise is not correlated wi th sources on the sky. Str ict ly speaking, P(M\SP) should be altered from the form used here to account for the fact that the probability at a location where a peak is found is being examined. In practice, at Sm — Sp > 3 a the full expression is well approximated by the simpler form used here (e.g., Bond & Efstathiou 1987). Equat ion 3.2 states that the intrinsic flux density distribution of the source is the likelihood of observing the data (right-hand term in the numerator) weighted by the prior distribution of flux densities (left-hand term in the numerator). A n informative prior for pixel flux densities is used and is constructed from existing knowledge of the 850 / i m extra-galactic source counts and the actual observing strategy. This inherently gives more weight to lower flux density sources, since they are more numerous. Each candidate source's flux density is deboosted following this Bayesian recipe, re-sulting in a posterior flux density probability distribution which is altered from the Gaussian probability distribution inferred from the maps. The posterior flux density probabili ty distribution, P(SP)' is shown as a solid histogram in the panels of F i g . 3.4 for each of the 5 sources for which there is also follow-up photometry information. The dot-dashed Gaussian i n each panel is P(M\SP), which is often incorrectly adopted as the flux estimate of a map source. The idea of using Bayes' theorem to find a posterior estimate of the flux density using the source counts as a prior appears to have been first clearly writ ten down by Jauncey (1968), as a way to correct survey-detected radio sources for flux density biasing (as first pointed out by Eddington 1913). Other papers which discuss simi-lar ideas include Murdoch, Crawford & Jauncey (1973), Schmidt & Maccacaro (1986), Hogg & Turner (1998), Wang, Cowie & Barger (2004), and Teerikorpi (2004). In F i g . 3.4 the individual P(SP) plots are placed in order of increasing map S / N . It is clear that one expects to measure a non-zero flux value a significant fraction of the time only for sources wi th relatively high S/Ns. Sources wi th modest S /Ns are much more likely to have non-zero photometry results than lower S / N sources. The peak in the a 3.4. CANDIDATE SUBMILLIMETRE SOURCES 80 0.20 0.15 P(S 0 .10 0.05 0.00 A - 4 0 - 2 0 0 20 40 Flux density S' (mJy) 0.15 0.10 In 0.05 / 0.00 -10 - 5 0 5 10 15 20 Flux density S' (mJy) - 1 0 - 5 0 5 10 15 20 Flux density S' (mJy) 0.20 0.15 0.10 0.05 0.00 -£SS850.2 , i I 1 i u , / \ \ -10 - 5 0 5 10 15 20 Flux density S' (mJy) 0.15 0.10 0.05 0.00 / GSS850.1 1 \ / / \ 0.15 GSS850.7 0.10 / \ In I \ 0.05 0.00 , J3 -10 - 5 0 5 10 15 20 Flux density S' (mJy) -10 - 5 0 5 10 15 20 Flux density S' (mJy) Figure 3.4: The first panel shows the histogram of the one mil l ion noiseless triple-beam simulations described in § 3.4.2. This is the P(D) distribution (e.g., Scheuer 1974, Condon 1974) for a triple-beam experiment, which is strongly peaked around zero and skew positive due to sources. The other panels show the re-sulting flux probability distributions (dark histograms) for the 5 map source candidates which had follow-up photometry observations, given their mea-sured flux densities and errors (assumed to be Gaussian distributions, plotted separately as light dot-dashed lines) and the underlying source count model. Photometry measurements are overplotted for comparison and are also as-sumed to have Gaussian probability distributions (dark dashed lines). A vertical line at ^ = 0 is plotted as a reference wi th which to compare the photometry measurements. One can see that the combination of the intr in-sic distribution of flux densities and the low S / N measurements from the map make the photometry measurements much less inconsistent than they might appear (i.e., the dashed Gaussians compare well wi th the solid histograms, even though the two Gaussians in each panel are usually discrepant). 3.4. CANDIDATE SUBMILLIMETRE SOURCES 81 posteriori distribution at zero flux dominates for S / N < 3.5. This confirms the usual prejudice towards high S / N sources - if a source is bright, it needs to be detected wi th a S / N > 4 a i n order to be deemed a secure detection. Moreover, it is also found that at the same S / N level, apparently brighter sources (with consequently higher flux density uncertainty) are more likely to be spurious (i.e., flux boosted from ~ OmJy) than fainter sources. Thus at a given S / N , low flux density sources are more likely to be real than high flux density sources. Independent photometry observations were performed on 5 sources wi th S /Ns ranging from 3.0-4.1 a and the results are shown i n Table 3.1. Are the photometry measurements consistent wi th the map-detected flux densities? In other words, one wants to answer the question: 'What is the probability that one wi l l measure Sp in photometry mode given the map-detected flux density (Sm) and uncertainty ( a m ) and the underlying source count model?' . The main point is that the a posteriori probability of finding a bright source wi l l be down-weighted by the a priori probability coming from the source counts. A comparison of the dashed curves and solid histograms in F i g . 3.4 shows that the photometry results are consistent wi th P(SP), even though the photometry is often in-consistent wi th the raw (i.e., flux boosted) map readings P(M\SP). 3 . 4 . 3 A R e v i s e d S o u r c e L i s t The probabili ty of obtaining each of the photometry measurements can now be assessed using the distributions in F ig . 3.4. For GSS850.6, a photometry result lower than what was measured is expected 43 per cent of the time. For the remaining sources GSS850.1, GSS850.2, GSS850.11 and GSS850.7, a photometry measurement lower than the one obtained would have occurred 12, 60, 6, and 18 per cent of the time, respectively. A Kolmogorov-Smirnov (KS) test (e.g., see Section 5.4 of W a l l & Jenkins 2004) performed on these results determined that the set of 5 trials is consistent wi th a uniform distribu-tion. The photometry results are thus completely wi thin the realm of what is expected, de-3.4. CANDIDATE SUBMILLIMETRE SOURCES 82 Table 3.2: G S S 850/ im revised source list. The 2 photometry-confirmed sources and an additional > 3.5 candidate source which has a reasonable chance of being real are included. The best 850 / m i flux estimate is given based on the combination of the posterior probability of the map flux given the data together wi th the photometry flux for the sources wi th photometry (2 and 7), and based solely on the posterior probability of the map flux for GSS850.4. The reported flux is the most likely flux in the 68 per cent confidence region, wi th upper and lower error bars shown to indicate the range of that confidence interval. 95 per cent Bayesian upper limits are also given for the 450 / m i flux of each 850 / i m detection. Object Position (2000.0) S850 5 4 5 0 R A Dec (mJy) (mJy) GSS850.2 14 h15m25?0 +52°02 '57" 5.9±?;£ < 170 GSS850.4 14 h15m29?5 +52°04 '48" 6 .9j£? < 48 GSS850.7 1 4 h 1 6 m l r f 6 +52°13 '42" 4 . 8 t ^ < 118 spite the apparently contradictory results presented in Table 3.1. GSS850.2 and GSS850.7 are comfirmed as bona fide 850 /um sources, and GSS850.1, GSS850.6, and GSS850.11 are confidently eliminated from the candidate source list. Note that these eliminated sources are also among the 4 noisiest candidate detections in the map, which makes it even less surprising that they are spurious. The number of detections, expected sources, and spurious detections are tallied up and have been illustrated in F i g . 3.2. Note that the number counts (e.g., Scott et al . 2002, Borys et al . 2003, Webb et al . 2003b) predict the detection of around 3 sources at the flux density l imit of the map (~ l O m J y ) . The revised source list now includes 2 confirmed sources (with coordinates given in Table 3.2) as well as 1 other candidate which is > 3.5 a in the map. Al though not con-firmed by photometry, Figs. 3.2 and 3.4 suggest that S / N > 3.5 sources have a reasonably high chance of being real. The best estimate of the flux density for each of these objects is calculated using the combination of all available information, including the map measure-ments, photometry measurements and the source count prior. To do this, the measured (assumed Gaussian) photometry flux probability distribution, P(SP, cr p), is multiplied by the calculated posterior probability for the map flux density (equation (3.2)), which is 3.5. AN ATTEMPT AT MULTI-WAVELENGTH CORRELATIONS 83 taken as the prior distribution for Sp, and normalised to have unit integral. For the candidate source, GSS850.4, only the a posteriori distribution for the map measurement is known, since there is no photometry measurement for this object. In Table 3.2 the peak of these new distributions is quoted, along wi th the error bars describing the 68 per cent confidence regions. 3.5 An Attempt at Multi-wavelength Correlations The new candidate source list (see Table 3.2) is now used to search for close counter-parts at other wavelengths in other data-sets which overlap wi th our coverage. Stacking analyses are also performed to see if there is any overlap between the catalogues and maps. The 450 pm map of this region is of poor quality; the data are shallow (since the sensitivity at 450 /im is worse) and inhomogeneous (being more prone to changes in the weather). None of the 850 fim sources are detected in the 450 fim map, but 95per cent confidence upper limits to the 450 pro. flux density for each 850 /jm detection are given in Table 3.2. The 450/ im average (or 'stacked') flux density at the 3 850 /im-detected positions is 10 ( ± 2 3 ) mJy . Using an 80 ksec XMM-Newton observation encompassing the northeast part of the GSS , Miya j i et al . (2004) have uncovered about 150 sources down to flux l imits of ~ 1 x 1 0 " 2 0 and ~ 2 x l O ^ W m " 2 in the soft (0.5-2keV) and hard (2-10keV) X- ray bands, respectively. O f these detections, 7 lie within the submillimetre map and the X -ray positional errors are typically about 2-3 arcsec. No X- ray counterparts exist wi th in the anticipated error circle of 4 arcsec, and there are no counterparts even wi th in a full beam of any S C U B A source. However, the stacked 850 pm flux density from the 7 X- ray positions lying wi th in the submillimetre map region is 2.5 (±1 .1 ) mJy, corresponding to a 0.8 m J y 95 per cent confidence lower l imit to the mean flux of these sources. These X- ray sources are therefore brighter than Lyman-break galaxies at 850 pm (e.g., Chapman et al . 2000)! If A G N s do not comprise a large fraction of our sources, 3.6. SUMMARY AND TIE-IN TO THESIS 84 this result indicates that the X- ray emission originates from processes related to star-formation. This result illustrates that this map can, in fact, be used to make statistical remarks about ~ l m J y sources even though individual detections are hopeless, and shows a path to populating the confusion sea in the submillimetre (see also Borys et al . 2004). 3.6 Summary and Tie-in to Thesis Approximately 70 arcmin 2 of the Gro th Strip has been mapped at 850 / i m wi th S C U B A on the J C M T to a 1 a depth of around 3.5 mJy. Using a robust source detection algorithm, 11 candidate sources wi th S / N > 3 a were found. Monte Carlo simulations suggest that most of these wi l l either be spurious or considerably flux boosted. Follow-up photometry observations have confirmed 2 of them and rejected 3. Based on these follow-up photometry data, it has been determined, not surprisingly, that candidate sources in high-noise regions of the map have implausibly high apparent flux densities at S / N > 3 a, and are likely to be spurious false-positive detections. Bright sources detected in a map should have S / N > 3.5 a before they have a reasonable chance of being real, and S / N > 4 a before they should be believed wi th any confidence. The final G S S source list contains 2 confirmed S C U B A sources and 1 further candidate source wi th S / N > 3.5 a. Using a combination of the unboosted map flux posterior probability distributions and the photometry measurements (when available), the best estimates of the flux for these objects are presented. A mi ld statistical detection of low flux density (~ 1 mJy) sources at X- ray wavelengths is measured through a stacking analysis, and it may be that similar comparisons wi th data at other wavebands might also be fruitful. The maps have therefore been made available at http: //cmbr. physics. ubc. ca/groth. This simple Bayesian method should be useful for future surveys carried out wi th S C U B A - 2 , as well as for other instruments which provide data in the low S / N near-confusion regime. This method has been adapted for S H A D E S to find sources, by searching for pixels in a map for which the posterior probability for > 0 is above 3.6. SUMMARY AND TIE-IN TO THESIS 85 some threshold (cf. Chapter 4). A number of additional tests specific to the S H A D E S data have been performed and are discussed in the next chapter. C H A P T E R 4 S H A D E S R E S U L T S 86 4.1 Introduction S C U B A has detected a few hundred S M G s over its lifetime, though the sample is i n h o mogenous in nature since these sources are al l detected at low S / N (using different source identification criteria) in small fields al l over the sky, observed by different groups and to different depths. This often leads to disagreement between groups regarding the reality and the flux densities of several of the noisier sources for the same data sets (cf. 3.1)! The desire to obtain a well characterised sample of hundreds of S M G s in a large, contigu-ous area is the motivation for the S C U B A HAlf-Degree Extragalactic Survey ( S H A D E S ; Mort ier et al . 2005, van Kampen et al . 2005). For the first time in a submillimetre survey the data are processed by four independent data reduction pipelines in order to increase the robustness of the results (see Chapter 2). In order to ensure the reliability of the resulting source catalogue, data reduction was independently carried out by four sub-groups drawn within the S H A D E S team, providing an unprecedented degree of reliability wi th respect to other S C U B A catalogues available from the literature. In Section 4.2, the amalgamation of four source lists into a master 850 / im S H A D E S catalogue is described. Because the source counts have a steep neg-ative slope and the maps are noisy, low S / N source flux densities in the maps wi l l be biased upwards. Pr ior knowledge of the source counts is used to calculate a posterior flux density probability distribution for each S H A D E S source. The posterior probabili ty distributions are also used to compose a catalogue wi th very few spurious sources by effectively removing apparently bright sources lying in noisy map regions that are over-whelmingly likely to be spurious. A discussion of inter-group flux density and position comparisons is also provided. 450 pm data and flux density upper limits for the S H A D E S 4.1. INTRODUCTION 87 sources are also presented here, since it is found that no single 'apparent' 450 / im detec-t ion can be trusted in the maps. In Section 4.3 two different approaches to derive the number counts are described, compared and contrasted. The approaches which are found to produce consistent results are: (1) binning the source catalogue and dividing by the effective survey area; and (2) using the source catalogue as a constraint on parametric fits to the counts. The S H A D E S differential count measurements are provided here, the first time that S M G differential counts have been statistically robust enough to be useful. In Section 4.4, models are fit to the differential counts, and the cumulative source counts are computed in order to compare them with previous data. There is evidence for a break at several m J y and the counts appear low compared to results from cluster lensing studies. Concluding remarks regarding what was learned about data analysis by comparing the different reductions, as well as advice for future surveys, are given in Section 4.5. This chapter presents the S H A D E S results, which also appear in the following paper: C o p p i n K . et a l . (2006) 'The S C U B A H A l f Degree Extragalactic Survey ( S H A D E S ) II - Maps, source catalogue and number counts', M N R A S , in press (pre-print: astro-ph/0609039). The paper focusses on the comparison of four independent reductions, the amalgamation of a robust source catalogue, and the derivation of the number counts. The author led one of the reductions (Reduction D) and much of the comparison among reductions. Whi le the source list is created using the combination of the four reduction source lists, the number counts presented here (and in the paper above) are based solely on the results of this thesis (Reduction D ) . The content of this paper (including text, figures and tables) has been reprinted in this chapter wi th permission from Blackwell Publishing. 4.1.1 C o m b i n i n g P a r t i a l l y D e p e n d e n t D a t a The four data reductions were carried out independently, but since they use the same data, their results are obviously not statistically independent. It is relatively straight-forward to determine if the results of the different reductions are consistent and it is 4.1. INTRODUCTION 8 8 found that the differences between reductions are small compared to the noise in any one reduction (see Sections 4.2.5 and 4.2.6). Given that the reductions are consistent, it is acceptable to choose the result of any single reduction as the final answer, but combining the analyses is likely to lead to slightly higher precision and reliability. The statistics of combining the four reductions is not simple, because the degree of statistical independence is not well characterised. Differences between reductions would arise if systematic errors are present, but might also come from random errors and slight differences in weights of the input data. Differences in the estimated uncertainties would arise if one reduction is genuinely more precise than the others, but also if one reduction over- or under-estimates the uncertainties. In combining the reductions a variety of approaches have been taken, using the mean value, the median or the most precise single reduction, and these choices wi l l be described below in the sections on flux densities, source positions, and source number densities. So how does one go about quoting an uncertainty for combined data which are not statistically independent? Enlarging error bars amounts to losing information, especially if there are genuine differences in the precision of the different reductions. The results should be combined in such a way that reduces the error bars at each step, but not as rapidly as they would be reduced for independent data sets. Therefore, an uncertainty is quoted as the smallest value claimed by a single reduction. In doing so one is taking the conservative position that while combining the reductions does not decrease uncertainties nearly as much as combining fully independent data would, it ought not to increase the uncertainty of our most precise estimate. Here there are only 4 reductions and they are al l similar enough to each other that none of them stand out as outliers. However, if there were instead 100 reductions, one might expect to see some apparent outliers and therefore a different strategy, such as taking the median of the error bars so as to reject obvious large outliers in a set, might be a better approach in that case. 4.2. THE CATALOGUE 89 4.2 The Catalogue The S H A D E S catalogue is compiled using the following steps. First , a preliminary joint identification list is compiled by cross-identifying the four independent source lists. Con-sensus S H A D E S positions and flux densities are then determined. Each source flux den-sity is corrected for flux boosting (see Sections 3.4.2 and 4.2.2), and sources are rejected based on their deboosted flux density distributions (see Section 4.2.3). This t r imming removes from the preliminary list vir tually al l of the sources which appear to be 2.5-3.5 a i n the maps. The catalogue constructed here is a robust list, intended to be a reliable starting point for follow-up observations leading to S E D fitting and photometric redshift estimation for every individual source in the catalogue and for the group. Because it is based on four different analyses the selection criteria are hard to simulate, so this list is not used to derive constraints on 850 / m i source counts. Source count spectra have been determined independently from the provisional source lists arising from each reduction, and those results are presented in Section 4.3. 4.2.1 Preliminary Joint Identification List A n extended source list for each reduction is made of al l points having S / N > 2.5 in the maps. The S / N threshold is kept deliberately low to avoid missing genuine sources at this stage. A preliminary joint list is constructed by identifying sources for the four extended lists which are wi th in 10 arcsec and which are seen wi th S / N > 3 in at least two reductions. This preliminary list contains 94 source candidates in the S X D F and 87 in L H . A S H A D E S map flux density for each source is computed using the following recipe. A raw flux density likelihood distribution is determined by mult iplying the individual Gaussians constructed from the flux and noise in each reduction and normalising the resulting distribution. The S H A D E S map flux density is taken to be the maximum like-l ihood. The lowest quoted error is used as the 1 a S H A D E S map uncertainty. Because the data are common to the four reductions, adding errors as inverse variances is sta-4.2. THE CATALOGUE 90 tistically incorrect and would seriously underestimate the net uncertainty, while simply averaging the uncertainties allows an imprecise single estimate to lower the combined uncertainty, which does not make sense (see Section 4.1.1 for further detail). Reductions B and D agree well on flux densities in both fields and also claim the smallest photometric uncertainty, so data from those two reductions dominate the weighted mean flux density for those sources which they extract. It is found that the deviations between any single reduction and the group flux density are smaller than the adopted measurement noise, as expected. The details are in Section 4.2.5. The ratio of S H A D E S map flux to min imum noise is listed as S / N in Table 4.1. 4 .2 .2 Deboosted Flux Densities The submillimetre source count density in the flux range of the S H A D E S survey falls very rapidly compared to the width of the approximately Gaussian noise distribution of the maps. Therefore one expects to identify an excess of low flux density sources whose locations happen to coincide wi th positive noise and whose apparent flux densities have therefore been increased above the survey's S / N limit (i.e., flux boosting). The simple Bayesian recipe of Coppin et al . (2005) (and described in Section 3.4.2), adapted for the S H A D E S observing strategy, has been employed to correct the preliminary source list for effects of flux density boosting in submillimetre maps. The deboosting recipe has been successfully tested against follow-up photometry for individual sources in Coppin et al . (2005) (see Section 3.4.2). Its performance in returning the input source distribution is tested in Section 4.3.1. Details of how the flux densities from the joint candidate list are deboosted are given below. After deboosting, the catalogue contains 120 robust S H A D E S sources, coincidentally 60 sources per field. O n average, the deboosting reduces the source flux density by ~ 1.8 m J y in both fields (see F i g . 4.1), increases the width of the photometric error distribution by about 10 per cent, and renders the shape of the resulting distribution to be skewed and non-Gaussian. The details of these effects depend both on the observed signal, SQ, and the 4.2. THE CATALOGUE 91 i i i i r i i i i i i i i i i i i i i i r • L H Sources o SXDF Sources a Q 3 -a <D 1/3 O o <D Q (/3 Q 3 < 8 b ° ° « 0 • o 1 • §b o , o • o o o o o o o o 01 8 10 12 14 Map Flux Density [mJy] 16 18 Figure 4.1: M a p flux density minus deboosted flux density versus the map-detected flux density for the L H (filled symbols) and S X D F (open symbols) S H A D E S cata-logue sources. The line y = 0 represents a 1:1 ratio between the flux densities. Map-detected source flux densities are deboosted by an average of 1.8 m J y (the dashed line), although there are a range of deboosting values, because this correction depends on the noise as well as the signal. 4.2. THE CATALOGUE 92 observed noise, aQ, and not just on the S / N . The effects are larger for sources extracted from noisier regions of the maps. Two examples of posterior distributions taken from the L H region are plotted in F ig . 4.2. The first is a bright source and the other is dim; one readily sees that the skew of the distribution is more pronounced i n the d im case. Since some of the L H data were taken originally for the S C U B A 8-mJy Survey (Scott et al . , 2002) using a single chop throw, the effect of using this observing scheme on the reported deboosted flux densities was investigated by recalculating the prior and flux density posterior probability distributions. Reported flux densities were different for less than 10 per cent of the S H A D E S sources, and at most by a negligible ± 0 . 1 mJy . In addition, 3 extra sources near the rejection threshold made it into the final L H source cat-alogue. For simplicity, the prior based on the multiple chop S H A D E S observing scheme is used to deboost a l l of the sources, since it is representative of the majority of the data. Effects of Clustering on Deboosting The possible effects of clustering have not been included in creating the prior distribu-t ion used in deboosting flux densities. It has been checked that clustering at the levels anticipated for S H A D E S sources has a negligible effect on the deboosted flux density dis-tributions. Using 50 realisations of the phenomenological galaxy formation model used in van K a m p e n et al . (2005), wi th a clustering strength of 90 ~ 10 arcsec, a noiseless distri-but ion of map pixel flux densities is created and used to construct a new prior distribution and deboost sources wi th similar flux densities and S / N as the S H A D E S sources. The posterior flux density distributions are compared wi th those calculated using a prior wi th the same input source count model, but wi th randomised positions, i.e., no clustering. Negligible differences are found between the distributions. A larger effect on the shape of the posterior flux density probability distribution comes from using a much steeper source count model at the faint end of the number counts, which has a small but no-ticeable effect on the shape of the posterior flux density probability distribution at flux densities below 1 mJy, making sources more likely to pass the catalogue cut. A most conservative catalogue cut is therefore claimed, as less steep source counts at the faint 4.2. THE CATALOGUE 9 3 5 10 Flux Density [mJy] 5 10 Flux Density [mJy] Figure 4.2: Posterior flux density probability density functions calculated from Reduction D by the method described in Section 4.2.2 are shown as dot-dashed curves for a high S / N source, L O C K 8 5 0 . 5 , and a low S / N one, L O C K 8 5 0 . 5 2 . The thick dashed vertical line indicates the average S H A D E S map flux density before deboosting. Notice how asymmetric the low S / N posterior flux density distribution is. For comparison, distributions calculated by alternate methods from Reductions B and C are shown for the same sources. Each group's map flux density is wi thin 0.5 mJy of this average flux density before deboosting. In these cases, the S H A D E S posterior flux density distribution (not shown) follows closely the shape of Reduction D's posterior flux density distribution. A l l of the distributions shown have been normalised to have unit area. The distributions from Reduction C are lower resolution due to the choice of b in size for the simulations used to determine the posterior distribution and are truncated below 2 m J y (see Section D.2). Posterior distributions from Reduction B are truncated outside the region between 0.5-2 times the map flux density. 4.2. TEE CATALOGUE 94 end are used (a balance between faint lensing and bright blank-field counts). 4.2.3 8 5 0 /im Catalogue Membership The final cut in catalogue membership is the requirement that each accepted source has less than 5 per cent of its posterior probability distribution below OmJy, or P(Si < OmJy) < 5 per cent. This threshold is a good balance between detecting sources while keeping the number of spurious detections to a minimum. One could tune the catalogue membership using the thresholding technique called the False Discovery Rate ( F D R ; see Benjamini & Hochberg 1995 and Mil le r et al . 2001) in order to control the average fraction of spurious sources in the catalogue. In F i g . 4.3 the posterior null probability for each source candidate (i.e., the percentage of the posterior flux density probability distribution which is below 0 mJy) ranked in ascending order is plotted. This plot illustrates how our choice of probability cut-off for individual sources occurs comfortably before the regime where the F D R increases dramatically. It is also coincidentally where the number of sources times the F D R approximately equals 1. These plots show that as one pushes beyond ~ 60, the number of spurious sources becomes significantly greater than 1. Given the number of beams in each map, one expects approximately five 3 a peaks at random. If the null probability cut is relaxed, it would increase the number of sources, but the chances of random noise peaks making it into the catalogue would then become important. The average of the null probabilities is 1.5 (2.0) per cent in the L H ( S X D F ) , and this can be interpreted as an overall F D R for the catalogue. Effective flux density and noise cuts in each catalogue are shown in F i g . 4.4. No sources wi th observed S / N < 3.2 are kept in the final catalogues, wi th the majority of the detections lying above 3.5 a (see F i g . 4.5 for the S / N distribution of the S H A D E S catalogue sources). The flux densities quoted in Table 4.1 are median flux density estimates and the quoted errors correspond to the central 68 per cent of the posterior flux density distri-4.2. THE CATALOGUE 95 Number of Sources Figure 4.3: Percentage likelihood of zero flux density. This plot shows the posterior probability that each source has a flux density < 0 mJy. This probabili ty is plotted for each source candidate in the L H (filled symbols) and S X D F (open symbols) in ascending order. Only those candidate sources for which the null probability is less than 5 per cent (corresponding to locations i n the figure below the horizontal dashed line), are kept in the S H A D E S catalogue. In each of the L H and S X D F there are 60 such sources. Notice the compara-tively small number of sources in the S X D F wi th very low null probabilities compared wi th the L H . Notice also that if a cut below 5 per cent had been chosen there would have been more L H than S X D F sources, while the oppo-site would have been true if a cut above 5 per cent had been chosen. Given the number of beams in each map, one expects typically five 3 a peaks at random, and perhaps three of these survive the deboosting process. The solid line shows the percentage of the catalogue comprised of such sources as a function of the number of sources in the catalogue, P = S/N, which coincidentally crosses in the same place. 4.2. THE CATALOGUE 96 bution. Note that there are substantially more high S / N sources wi th null probabilities below 5 per cent (i.e accepted in the S H A D E S catalogue) in the S H A D E S maps of the L H region than in the S X D F (see F i g . 4.5). 4.2.4 Final SHADES Catalogue The S H A D E S catalogue is given in Table 4.1. Gaps in the source numbering sequence indicate sources that were rejected from the preliminary catalogue because they either failed to be detected by at least two groups wi th S / N > 3, or because P(S[ < OmJy) > 0.05. Comments on particular sources are noted in Appendix B . For the first time in a submillimetre-selected survey, a careful estimate of the unbiased flux density of each source is provided (cf. Sections 3.4.2 and 4.2.2). Table 4.1 also contains 3 a upper limits for the 450 / i m flux densities of each S H A D E S source (see Appendix 4.2.8 for details). 4.2. THE CATALOGUE 97 Figure 4.4: Effective cuts in the L H (left) and S X D F (right) source catalogues are shown. For al l candidate sources, the S H A D E S observed S / N is plotted against ob-served flux density as circles (the size of a circle is proportional to the map noise level where a source was found). The dashed lines show observed noise levels of 2, 3, and 4 m J y . Sources are retained in the catalogue if the total posterior probability that the flux density is zero is less than 5 per cent (filled circles). Only the sources lying above the solid curve satisfy this criterion. The effect of the rapidly falling source count spectrum is visible as the curva-ture of this cut-off, i.e., the rise in the required S / N wi th increasing noise. A 3.5 G source in a noisy region of the map has a higher apparent flux density than a 3.5 a source found in a quiet region; bright sources are rare, so this source is less likely to be genuine than a quieter d im source is. Notice that there are dramatically fewer sources detected at flux densities above 10 m J y in the S X D F as compared to the L H field, even though the number of fainter sources is similar. Also note that essentially none of the detected sources in the S X D F have noise i n the 1-1.5 m J y range, as compared to those i n the L H , which includes the lower noise S C U B A 8-mJy Survey region. 4.2. THE CATALOGUE 98 i i i M i i i i i i i i M i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i 25 < i 20 15 OH 1 0 1 01 ' i l ' I i ' M l 1 |, t i i i I i i i i L H SXDF . U . JJ.JJ.J-4 5 6 7 8 850^im map S/N for the SHADES Sources Figure 4.5: Distr ibut ion of the map-detected S / N ratios ( S H A D E S catalogue values) for the 60 L H and 60 S X D F sources in bins of A S / N = 0.5. Note that a l l of the S H A D E S catalogue sources were ini t ial ly detected above a S / N of 3.2, whereas the preliminary list contained sources > 2.5. Name (IAU) Nickname R A Dec. (J2000) (J2000) SHADES J105201+572443 LOCK850.1 10 h52m01?42 57°24'43'.'0 SHADES J105257+572105 LOCK850.2 10 h52m57f32 57°21'05'/8 SHADES J105238+572436 LOCK850.3 10 h52m38f25 57°24'36"5 SHADES J105204+572658 LOCK850.4 10 h52m04?17 57°26'58"9 SHADES J105302+571827 LOCK850.5 10h53m02?62 57°18'27?0 SHADES J105204+572526 LOCK850.6 10 h52m04?13 57°25'26('3 SHADES J105301+572554 LOCK850.7 10 h53m01?40 57°25'54?2 SHADES J105153+571839 LOCK850.8 10 h51m53?86 57°18'39'.'8 SHADES J105216+572504 LOCK850.9 10 h52m16f09 57°25'04'.'l SHADES J105248+573258 LOCK850.10 10 h52m48f61 57°32'58'/6 SHADES J105129+572405 L O C K 8 5 0 . i l 10 h51m29?53 57° 24' 05? 2 SHADES J105227+572513 LOCK850.12 10h52m27?61 57° 25' 13'.' 1 SHADES J105132+573134 LOCK850.13 10 h51m32f33 57°31'34'.'8 SHADES J105230+572215 LOCK850.14 10 h 52 m 30?l l 57°22'15'.'6 SHADES J105319+572110 LOCK850.15 10 h53m19?20 57°21'10'.'6 SHADES J105151+572637 LOCK850.16 10 h51m51?45 57°26'37'.'0 SHADES J105158+571800 LOCK850.17 10 h51m58?25 57°18'0O'.'8 SHADES J105227+572217 LOCK850.18 10 h52m27f69 57°22'17'/8 SHADES J105235+573119 LOCK850.19 10 h52m35f71 57°31 ' l# ' l SHADES J105256+573038 LOCK850.21 10 h52m56?86 57° 30'38 '^1 SHADES J105137+573323 LOCK850.22 10 h51m37?55 57°33'23"3 SHADES J105213+573154 LOCK850.23 10 h52m13?74 57°31'54?1 SHADES J105200+572038 LOCK850.24 10 h52m00?23 57°20'38"1 SHADES J105240+572312 LOCK850.26 10 h52m40?95 57°23'12"0 SHADES J105203+571813 LOCK850.27 10 h52m03f57 57°18'13'.'5 SHADES J105257+573107 LOCK850.28 10 h52m57?00 57°31'07'.'l SHADES J105130+572036 LOCK850.29 10h52m30?92 57° 20'36? 0 SHADES J105207+571906 LOCK850.30 10 h52m07?79 57°19'06"6 SHADES J105216+571621 LOCK850.31 10 h52m16?06 57°16'21?1 SHADES J105155+572311 LOCK850.33 10 h51m55?98 57°23'11"8 SHADES J105213+573328 LOCK850.34 10 h52m13?50 57° 33'28'.'1 SHADES J105246+572056 LOCK850.35 10h52m46?92 57°20'56'.'3 SHADES J105209+571806 LOCK850.36 10 h52m09?34 57°18'0tf'8 SHADES J105124+572334 LOCK850.37 10 h51m24?13 57°23'34?9 SHADES J105307+572431 LOCK850.38 10 h53m07?10 57°24'31'/4 SHADES J105224+571609 LOCK850.39 10 h52m24?85 57°16'09'.'8 Continued on Next Page. . . 5850 map S /N map <rs50 S450 Other IDs (mJy) (mJy) (mJy) /Notes 8.85 (±l;g) 8.5 1.1 < 47o LE850.1.LE1100 13.45 (±|;J) 6.8 2.1 < 123 LE1100.1.ON 10.95 (±}; |) 6.4 1.9 < 34 LE850.2.LE1100 10.65 (±i;g) 6.4 1.8 < 134o LE850.14,<? 8.15 (±*-°) 4.9 2.0 < 107 6.85 (±i;l) 5.8 1.3 < 77 LE850.4,<? 8.55 (±}; | ) 5.3 1.8 < 85 <? 5.45 (±} ;1) 5.2 1.2 < 31 LE850.27,<?xt 5.95 (±};«) 4.7 1.5 < 68 LE850.29,<? 9.15 ( ± a : J ) 4.5 2.5 < 365 t 6.25 (±\i) 4.5 1.7 < 62 6.15 (±J-7,) 4.6 1.6 < 35 LE850.16,LE110 5.65 (±il) 3.9 2.0 < 109 t* 7.25 (±J-|) 4.8 1.8 < 96 LE850.6,LE1100 13-25 (±*;§) 4.5 3.8 < 149 <?Xt 5.85 (±}; | ) 4.3 1.7 < 67o LE850.7.9 4.75 ( ± } : 3 ) 4.5 1.3 < 55 LE850.3,<? 6.05 (±i;f) 4.3 1.8 < 84 SDS.20,f 5.15 ( ± | : ° ) 3.9 1.8 < 87 <? 4-15 (±I;g) 3.6 1.7 < 70 7.55 (±3;2) 4.0 2.7 < 76 <?N 4.35 (±i;») 3.7 1.7 < 60 2.75 (±}; | ) 3.6 1.1 < 32 LE850.32.C 5.85 ( ± | ; J ) 3.9 2.1 < 48 t 5.05 (±\i) 4.6 1.3 < 32 LE1100.4,t* 6.45 (±\i) 4.7 1.7 < 56 t* 6.75 ( ± a : § ) 4.4 1.9 < 64 LE850.11,<? 4.75 (±J;g) 4.2 1.4 < 86 LE850.12,<? 6.05 (±1;§) 4.3 1.7 < 80 <? 3.85 (±\D 4.4 1.0 < 49 0 LE850.18,f*N 14.05 (±l;i) 5.4 3.0 < 100 t* 6.15 (±U) 4.1 2.0 < 91 t*N 6.35 (±J;|) 4.6 1.7 < 67 t* 7-55 (±1:1) 4.1 2.5 < 20 4.35 (±|-2) 3.6 1.9 < 93 t* 6.55 (±£?) 8.6 2.0 < 9 I O C O Name (IAU) Nickname R A Dec. § 8 5 0 map S/N map CT850 ^450 Other IDs (J2000) (J2000) (mJy) (mJy) (mJy) /Notes SHADES J105202+571915 LOCK850.40 10h52m02?01 57°19'15'.'8 3.05 (±i - i ) 3.8 1.1 < 40 LE850.21,<?Xt SHADES J105159+572423 LOCK850.41 10 h51m59?86 57° 24'23'.'6 3.85 ( ± o . g ) 4.5 1.0 < 16 LE850.8,LE1100.17,txs SHADES J105257+572351 LOCK850.43 10 h52m57?17 57°23'51'.'8 4.95 ( ± | : J ) 3.8 1.8 < 80 t« SHADES J105235+572514 LOCK850.47 10 h52m35?63 57°25'14'.'0 3.55 (±11) 3.5 1.5 < 21 SDS.16,f*K SHADES J105256+573245 LOCK850.48 10 h52m56?24 57°32'4tf'8 5.45 ( ± | ; i ) 3.9 1.9 < 79 t * N SHADES J105245+573121 LOCK850.52 10 h52m45f53 57°31'21"9 3.95 (± | ; 2 7 ) 3.5 1.8 < 106 t* SHADES J105240+571928 LOCK850.53 10 h52m40?49 57°19'28"4 4.45 ( ± ! : D 3.6 1.9 < 90 t SHADES J105143+572446 LOCK850.60 10 h51m43?58 57°24'46^'0 3.15 ( ± J ; J ) 3.4 1.5 < 44 LE850.10,t*K SHADES J105153+572505 LOCK850.63 10 h51m53?91 5 7 ° 2 5 W l 3.65 (±\i) 4.0 1.2 < 50 t SHADES J105251+573242 LOCK850.64 10 h52m51f81 57°32'4#'2 5.85 ( ± 1 ; | ) 3.9 2.2 < 95 t SHADES J105138+572017 LOCK850.66 10 h51m38?69 57°20'17^'2 4.25 ( ± J ; 9 ) 3.7 1.6 < 40 SHADES J105209+572355 LOCK850.67 10 h52m09?00 57°23'55('l 2.55 ( ± i ; | ) 3.3 1.3 < 63 SHADES J105148+573046 LOCK850.70 10h51m48?52 57°30'4tf'7 3.85 ( ± 1 ; | ) 3.5 1.8 < 106 SHADES J105218+571903 LOCK850.71 10h52m18?62 57°19'0#'8 3.95 ( ± J ; § ) 3.7 1.5 < 99 t* SHADES J105141+572217 LOCK850.73 10 h51m41?66 57°22'17^'6 3.55 ( ± i ; | ) 3.5 1.6 < 49 t* SHADES J105315+572645 LOCK850.75 10 h53m15?93 57°26'4#'5 4-45 (±1;I) 3.7 1.8 < 50 t* SHADES J105148+572838 LOCK850.76 10h51m48?52 57°28'3#'7 4.75 (±H) 3.7 2.0 < 90 LE1100.15,<?N SHADES J105157+572210 LOCK850.77 10 h51m57?00 57°22'10"1 3.25 (±};§) 3.8 1.1 < 39 SHADES J105145+571738 LOCK850.78 10 h51m45?33 57° 17' 38? 7 4.55 ( ± | ' 2 ) 3.7 1.8 < 56 t SHADES J105152+572127 LOCK850.79 10 h51m52?10 57°21'27?4 3.15 ( ± 1 - 3 ) 3.7 1.2 < 41 SHADES J105231+571800 LOCK850.81 10 h52m31?99 57°18'00'.'4 5.35 (±H) 4.0 1.8 < 92 t SHADES J105307+572839 LOCK850.83 10 h53m07?94 57°28'39'.'l 3.15 ( ± g - 0 ) 3.4 1.6 < 69 t* SHADES J105153+571733 LOCK850.87 10 h51m53?30 57°17'33'.'4 3.45 (±1^) 3.6 1.3 < 54 t SHADES J105139+571509 LOCK850.100 10 h51m39f06 57°15'09'.'8 11.25 (±f;§) 4.3 3.6 < 75 t* SHADES J021730-045937 SXDF850.1 02h17m3O?53 -04°59'37"0 10.45 ( ± 1 ; | ) 7.3 1.5 < 65 SHADES J021803-045527 SXDF850.2 02 h18m03?51 - 0 4 ° 55'27'.'2 10.15 (±H) 6.6 1.7 < 98 SHADES J021742-045628 SXDF850.3 02 h17m42?14 -04°56'28'.'2 8-75 (±H) 6.0 1.6 < 81 SHADES J021738-050337 SXDF850.4 02 h17m38?62 -05°03'37'.'5 4.45 (±i-7) 3.9 1.6 < 73 SHADES J021802-050032 SXDF850.5 02 h18m02?88 -05°00'32'.'8 8.45 (±11) 5.4 1.8 < 44 o SHADES J021729-050326 SXDF850.6 02 h17m29?77 -05°03'26"8 8.15 ( ± | ; 1 ) 4.7 2.1 < 81 tXs SHADES J021738-050523 SXDF850.7 02 h17m38?92 -05°05'23"7 7-15 ( ± 1 ; | ) 5.2 1.6 < 61 <?Xs SHADES J021744-045554 SXDF850.8 02 h17m44?43 -04°55'54'.'7 6.05 (±\i) 4.4 1.7 < 45 SHADES J021756-045806 SXDF850.9 02 h17m56?42 -04°58'06'.'7 6.45 ( ± 1 ; ? ) 4.3 1.9 < 43 t * N SHADES J021825-045557 SXDF850.10 02 h18m25?25 -04°55'57'.'2 7.75 (+,§;?) 4.2 2.4 < 134 <?Xt SHADES J021725-045937 SXDF850 . i l 02 h17m25?12 -04°59'37?4 4.55 (± i ; l ) 3.8 1.7 < 79 t* SHADES J021759-050503 SXDF850.12 02 h17m59f37 - 0 5 ° 05'03'.'7 5.75 (±\l) 4.3 1.7 < 115 Continued on Next Page. . . Name (IAU) Nickname R A Dec. Ss50 (J2000) (J2000) (mJy) SHADES J021819-050244 SXDF850 14 02 h18m19?26 -05°02'44?2 4.85 f + 1 . 9 1 SHADES J021815-045405 SXDF850 15 02 h18m15?70 -04°54'05?2 6.25 /11.6-, (±1.6) SHADES J021813-045741 SXDF850 16 02 h18m13?89 -04°57'41?7 4.85 ( + 1 • 7 ^ SHADES J021754-045302 SXDF850 17 02 h17m54?98 -04°53'02 //8 7.65 r-t-1-7"! (^1.7) SHADES J021757-050029 SXDF850 18 02 h17m57?79 -05°00'29'.'8 6.45 /-_1_2.0\ (^2.2) SHADES J021828-045839 SXDF850 19 02 h18m28?15 -04°58'39'.'2 4.35 SHADES J021744-050216 SXDF850 20 0 2 h 1 7 m 4 4 f l 8 -05°02'16"0 4.45 SHADES J021742-050427 SXDF850 21 02 h17m42?80 -05°04'27?7 5.25 ^ 2 . 2 . * SHADES J021800-050741 SXDF850 22 02 h18m00?38 -05°07'41?5 6.25 f 4-2.3-1 SHADES J021742-050545 SXDF850 23 02 h17m42?53 -05°05'45?5 5.25 ^2.0) SHADES J021734-050437 SXDF850 24 02 h17m34?58 -05°04'37?7 5.15 f 4.2.0-1 ^2.3) SHADES J021812-050555 SXDF850 25 02 h18m12?12 -05°05'55?7 4.05 ^2.5! SHADES J021807-050148 SXDF850 27 02 h18m07?86 -05°01'48'/5 5.65 SHADES J021807-045915 SXDF850 28 02 h18m07?04 -04°59'15'.'5 4.85 f 4 _ 2 . 2 \ ^2.71 SHADES J021816-045511 SXDF850 29 02 h18m16?47 -04°55 ' l l ' / 8 5.35 (+1.8\ 1*1.9.1 SHADES J021740-050116 SXDF850 30 02h17m4O?31 -05°01'16'/2 5.75 (+2.0\ SHADES J021736-045557 SXDF850 31 02 h17m36?30 -04°55'57'/5 6.05 r + 1 - 7 i ^2.0) SHADES J021722-050038 SXDF850 32 02 h17m22?89 -05°00'38'. 'l 6.05 (4-2.4-1 SHADES J021800-045311 SXDF850 35 02h18m0O?89 - 0 4 ° 53'11'.'2 5.35 /1I.8-, (±2.1) SHADES J021832-045947 SXDF850 36 02 h18m32?27 -04°59'47'/2 5.45 r + 1 - 8 i (^1.9) SHADES J021724-045839 SXDF850 37 02 h17m24?45 -04°58'39'.'9 4.55 [+2.2\ SHADES J021825-045714 SXDF850 38 02 h18m25?43 -04°57'14?7 3.85 t±2.3\ ^2.7) SHADES J021750-045540 SXDF850 39 02 h17m5O?60 -04°55'4ff'2 4.05 SHADES J021729-050059 SXDF850 40 02 h17m29?67 -05°00'59?2 3.65 (±1:1) SHADES J021829-050540 SXDF850 45 02 h18m29?33 -05°05'40"7 21.95 (±1:1 SHADES J021733-045857 SXDF850 47 02 h17m33?89 -04°58'57?7 3.05 (+1.6) SHADES J021724-045717 SXDF850 48 02 h17m24?62 -04°57'17"7 7.65 I -1-2.5-i \^2.9) SHADES J021820-045648 SXDF850 49 02 h18m20?26 -04°56'48?5 3.35 SHADES J021802-045645 SXDF850 50 02 h18m02?86 -04°56'45'.'5 5.35 / -_ |_2.0\ SHADES J021804-050453 SXDF850 52 02 h18m04?90 -05°04'53'.'7 3.25 (^2.1) SHADES J021752-050446 SXDF850 55 02 h17m52?19 -05°04'46'.'5 3.95 / _ l _ 2 . 2 \ ^=•=2.7/ SHADES J021750-050631 SXDF850 56 02h17m5O?68 -05°06'31?8 3.65 V^2.h> SHADES J021745-045750 SXDF850 63 02 h17m45?80 -04°57'5tf '5 4.15 V = t 2 . 1 J SHADES J021807-050403 SXDF850 65 02 h18m07?94 -05°04'03"2 4.35 1 1 1 . 9 \ (^2.3) SHADES J021751-050250 SXDF850 69 02 h17m51?40 -05°02'50'.'8 3.65 (±2.4) SHADES J021811-050247 SXDF850 70 02 h 18 m l l ?20 -05°02'47'.'2 4.05 r-t- 1- 9! (^2.3) SHADES J021821-045903 SXDF850 71 02 h18m21?24 -04°59'03'.'2 4.15 I 4. 1.9-1 Continued on Next Page... ip S /N map <7850 (mJy) S450 (mJy) Other 3.9 1.7 < 121 t* 4.8 1.6 < 42 C 4.1 1.5 < 70 C 5.2 1.7 < 71 t* 4.3 1.9 < 54 CN 3.8 1.6 < 54 C N X s 3.8 1.7 < 82 C 4.0 1.8 < 51 VXs 4.1 2.1 < 172 CN 4.1 1.6 < 59 C 3.9 1.8 < 69 c 3.6 1.8 < 59 t* 4.1 1.8 < 34 C N X s 3.8 1.9 < 75 t*Xt 4.1 1.7 < 135 t* 4.1 1.8 < 85 C 4.4 1.7 < 30 C 4.0 2.1 < 101 t* 4.1 1.7 < 62 C 4.2 1.7 < 76 t* 3.7 1.8 < 63 CN 3.5 1.8 < 76 C 3.7 1.6 < 61 t* 3.8 1.3 < 40 C 4.9 5.6 < 186 t *Xt 3.4 1.4 < 54 <?Xt 4.3 2.3 < 125 t* 3.4 1.6 < 75 1 * * 3.9 1.9 < 74 CN 3.4 1.5 < 84 | * * 3.5 1.8 < 80 t* 3.5 1.8 < 154 fN 3.7 1.6 < 29 CN 3.7 1.7 < 56 t* 3.5 1.7 < 77 J * N 3.6 1.7 < 60 t 3.7 1.7 < 54 C /Notes bo 2 S O Name (IAU) Nickname RA Dec. 5850 map S/N map <T850 5450 Other (J2000) (J2000) (mJy) (mJy) (mJy) SHADES J021758-045428 SXDF850.74 02 h17m58?73 -04°54'28'.'8 3.35 (±l;f) 3.5 1.5 <61 I* SHADES J021755-050621 SXDF850.76 02 h17m55?78 -05°06'21'.'8 4.45 (± | : 0) 3.7 1.7 < 124 tK SHADES J021736-050432 SXDF850.77 02 h17m36?43 -05°04'32 / /2 3.05 ( ± 2 . 0 ) 3.3 1.6 < 50 t SHADES J021817-050404 SXDF850.86 02 h18m17?18 -05°04'04'/7 3.65 (±i-9) 3.5 1.6 < 45 tXt SHADES J021800-050448 SXDF850.88 02 h18m00?99 -05°04'48"5 4.55 ( ± | ; i ) 3.7 1.8 < 99 t SHADES J021734-045723 SXDF850.91 02 h17m34?81 -04°57'23"9 3.55 ( ± l ; i ) 3.4 1.7 < 79 t SHADES J021733-045813 SXDF850.93 02 h17m33?08 -04°58'13?5 3.15 (±1;?) 3.4 1.6 < 70 SHADES J021740-045817 SXDF850.94 02 h17m40?08 -04°58'17?7 4.15 ( ± 1 ; ? ) 3.7 1.6 < 49 t SHADES J021741-045833 SXDF850.95 02 h17m41?72 -04°58'33'/7 3.45 ( ± i ; | ) 3.5 1.6 < 92 SHADES J021800-050212 SXDF850.96 02 h18m00?00 -05°02'12'.'8 4-75 3.8 1.8 < 58 IK SHADES J021756-045255 SXDF850.119 02 h17m56?35 -04°52'55'/2 4.55 (±H) 3.7 1.8 < 70 t /Notes Table 4.1: The 850 ^ m SHADES catalogue for the L H and SXDF regions. Uncertainties in physical positions are 3.2 arcsec in R A and 3.2 arcsec in Dec. (the same uncertainties have been adopted for all SHADES sources in both fields). Estimates of the median true unbiased median flux density of each source is given, with accompanying error bars representing the 68 per cent confidence bounds of the (non-Gaussian) deboosted flux density distribution (cf. Section 4.2.2 for the Bayesian estimate of deboosted flux density). The combined map S/N and noise estimates are also provided (i.e., values prior to deboosting). No 450/im detections of SHADES sources are claimed; 3<r upper limits limits are given in the penultimate column. Corresponding SCUBA 8-mJy Survey IDs (Scott et al. 2002) and new IDs from the reduction of Scott, Dunlop & Serjeant (2005) are listed in the final column for reference, along with an indication of how many groups detected each source. See Appendix B for detailed notes on some of the sources. s O ft L e g e n d : <v> This source was identified by all four groups with a S/N > 3. f This source was identified by three groups with a S/N > 3. | This source was identified by two groups with a S/N > 3. * This source was identified by one additional group with 2.5 < S/N < 3. ** This source was identified by two additional groups with 2.5 < S/N < 3. N This source is mildly affected by the noise spike (cf. Appendix A). Xs, Xt This source has a relatively poor spatial or temporal \ 2 fit. o This source has a hint of flux at 450 fim measured at the SHADES catalogue positions at a significance level > 3cr (see Fig. 4.8). O 4.2. THE CATALOGUE 103 Comparison with the S C U B A 8-mJy Survey The new S H A D E S catalogue was cross-matched wi th the S C U B A 8-mJy Survey > 3.0 a source catalogue (Scott et al . , 2002), which used a subset of our data. S H A D E S fails to re-detect 2/12 of the > 4 a sources (LE850.5 and LE850.9), 5/9 sources wi th published S / N between 3.5 and 4.0 (LE850.13, LE850.15, LE850.17, LE850.19, and LE850.20), and (not surprisingly) 12/15 sources wi th S / N between 3.0 and 3.5 (LE850.22-26, LE850.28, LE850.30, LE850.31, and LE850.33-36). These findings are similar to those given in Ivison et al . (2002), Mortier et al . (2005) and Ivison et al . (2005). Ivison et al . (2002) rejected LE850.9, LE850.10, LE850.15, and LE850.20 due to the lack of associated ra-dio counterparts, combined wi th the fact that they are found in noisy regions of the map (a > 3 mJy) . These sources are also rejected in our analysis, except in the case of LE850.10, since this source is re-detected in the S H A D E S data (LOCK850.60) , albeit wi th a lower S / N than that found in the S C U B A 8-mJy Survey (~ 3.4 a as compared wi th the previous 4 .2a detection). There is less than a 4 per cent chance of LE850.10 having a true flux density of < OmJy and therefore it survives the deboosting cut. This source also has a tentative radio identification (Ivison et al. , in preparation). See Ta-ble 4.1 for the corresponding new S H A D E S measurements of the S C U B A 8-mJy Survey sources. The S H A D E S catalogue was also cross-matched wi th the re-reduction of the S C U B A 8-mJy Survey > 3 . 0 a source catalogue (Scott, Dunlop & Serjeant, 2005), which includes some additional data and improvements made to the reduction methods. In summary, Scott, Dunlop &; Serjeant (2005) re-detected all of the 36 original S C U B A 8-mJy Survey > 3.0 a sources (though 4 sources originally detected above 3.0 a dropped down to below 3.0 a: LE850.25, LE850.29, LE850.30, and LE850.31), and found 8 new 3.0 < S / N < 3.7 sources. S H A D E S re-detects sources SDS.16 (3.7a) and SDS.20 (3.4a), but fails to re-detect SDS.25, SDS.32, SDS.33, SDS.36, SDS.38, and SDS.40 (new < 3 .4a sources). See Table 4.1 for the corresponding S H A D E S measurements of the sources found in the Scott, Dunlop & Serjeant (2005) re-reduction of the S C U B A 8-mJy Survey data. 4.2. THE CATALOGUE 104 4.2.5 Flux Density Comparison Systematic effects between the reduction group flux densities were checked in order to quantify their effect on the adopted S H A D E S map flux density. The discussion that follows is l imited to a subset of sources that all groups find at > 2.5 a: 54 in the L H ; and 58 in the S X D F . Unlike in the astrometry comparison (see later Section 4.2.6), there is no 'true' flux density to compare the mean flux densities against, so only an inter-group comparison can be performed. F l u x density comparison scatter plots were produced, such as F i g . 4.6, for each pair of groups. It was noticed immediately that Reduction C showed a systematically lower flux density than the other groups. This error was traced to improper weighting of the 6 chop throw observations for each S H A D E S pointing. After finding and correcting this error, the scatter in source flux densities between all groups appeared small on average, wi th no systematic offset apparent in any one group compared to another (except at the high flux density end, where the photometric errors are also very large). One might expect the choice of sky opacity correction factors or F C F s (i.e., using monthly F C F s versus nightly measurements) to come into play at about the 2 per cent level for such low S / N data taken in more or less uniform weather conditions. The R M S scatter between flux densities reported for L H sources by Reductions B and D is 0.9 m J y (see F i g . 4.6) and is similar between the other groups. Similar results were found for the S X D F . Photometry errors that might have been introduced through differences in judgment are 1/3 as large as the total uncertainty in flux density, which is noise-based. Therefore it is claimed that the gain differences are small (i.e., less than 5 per cent) and therefore unimportant for these low S / N data (they become important for ~ 10 a sources, of which none are found in this survey). This demonstrates that flux densities are being extracted well. Using monthly averaged F C F s (Reduction D) versus using nightly measurements (Reductions A , B and C) appears to give indistinguishable answers, and therefore the systematic error introduced from the former technique and the instantaneous measurement uncertainty in the latter technique are both insignificant 4.2. TEE CATALOGUE 105 10 15 20 Group B's Observed Flux Density [mJy] 0.5 1.0 1.5 Flux Density Ratio 2.0 Figure 4.6: The difference of the 850 fim flux density as measured by Reductions B and D is plotted against the flux density measured by Reduction B for the L H sources that were found in a l l four reductions (left panel), and a histogram of flux density ratios of Reductions B and D (i.e., B / D ) for the L H (right panel). In the left panel the horizontal solid line indicates a ratio of unity, while the dashed lines show the 1 a scatter expected if each of the two reductions had independent photometry errors corresponding to a S / N of 3.5. The scatter between these two reductions is substantially smaller than photometry er-rors, indicating that systematic errors associated wi th data reduction choices do not substantially influence our final flux density measurement values and uncertainties. Reductions B and D are selected for comparison here because their calibration procedures differ most among the four reductions; any other pair of reductions is likely to demonstrate at least this level of agreement. In the right panel the smooth (dashed) curve is the flux density ratio dis-tr ibution expected for two independent measurements wi th the approximate l imit ing S H A D E S S / N (3.5cr). The narrowness of the histogram compared to the relative width of the Gaussian demonstrates that systematic errors in calibration are small compared to photometric uncertainties for al l sources in the S H A D E S catalogue. The two sets of flux density values are consis-tent wi th each other, while the best fit mean flux density difference is 4 per cent. Since the uncertainty of the mean of all 60 sources in the S H A D E S L H catalogue is also 4 per cent, systematic flux density errors associated wi th differences in data reduction strategy are completely unimportant for individual sources. 4.2. THE CATALOGUE 106 wi th respect to the photometric errors in the survey. 4 . 2 . 6 A s t r o m e t r y C o m p a r i s o n Intercomparing the positions found by the four independent reductions allows one to check for systematic errors and estimate the astrometry uncertainty. W h e n comparing flux densities, differences between reductions can be measured but the 'true' 850 fim flux density is not known, so systematic errors may be difficult to isolate. The situation is much simpler wi th positions. When sources have clearly identified radio counterparts the precision of the positions determined from the radio data is much higher than that available from the 850 JJLYS\ data. Effectively, one knows the 'true underlying position' for these sources and sensitive tests for systematic errors are possible. In this section the positions of a subset of the sources which have clear and compact radio counterparts determined by Ivison et al . (in preparation) and which have been identified at > 2.5 a in al l four reductions are analysed. These criteria, designed to facilitate clear comparison of the four reductions, yield 17 and 24 sources in the L H and S X D F , respectively. The full analysis of the alignment of S H A D E S sources wi th the corresponding radio data is made in Ivison et al . (in preparation). U p o n ini t ia l comparison it was clear that the positions of sources i n the L H determined by Reduction B were displaced to positive R A by just over 2 arcsec (recall that the F W H M of the S C U B A beam is 14.7 arcsec) compared to positions determined by any of the other reductions or compared to the radio positions. This systematic effect was traced to errors in the use of the hastrom routine in i d l - a s t r o l i b and has been corrected. Other than the correction of this small error, nothing has been adjusted to bring the reductions into agreement wi th each other or wi th the radio-determined positions. The positions determined by one reduction (arbitrarily, my reduction 'D ' ) in compar-ison to the mean 850 / im position for al l the sources in the S X D F are plotted i n the left hand panel of F i g . 4.7. The sources wi th compact radio IDs from Ivison et al . (in prepa-ration) are shown as plusses, while other sources in the S X D F are shown as diamonds. 4.2. THE CATALOGUE 107 B o t h sub-samples have similar means and distributions, so the analysis of positions for the restricted sub-sample provides a description of astrometry errors which is valid for the full list. Table 4.2 lists the R M S displacements of source positions determined by each reduction relative to the unweighted mean position determined by the four reductions, separately for each of the two S H A D E S fields. Pixelisation inevitably adds dj\/l2 where d is the pixel size, in quadrature to the R M S astrometry errors 1. This is 0.9 arcsec for 3 arcsec pixels and has not been subtracted from the data in Table 4.2 (since it is close to negligible). Even so, Reductions C and D , wi th 3arcsec pixels, have R M S displace-ments from the 850/xm mean which are, if anything, lower than the displacements of the reductions using smaller pixels. It is perhaps not surprising that using small pixels (smaller than ~ F W 5 H M at least) in reconstructions of the data does not appear to add any astrometric precision (cf. Condon 1997). The left hand panel of F ig . 4.7 shows the deviation of the mean offset of the position determined by the four S H A D E S reductions relative to the presumably correct radio-determined positions from Ivison et al . (in preparation). Notice that the scatter is much larger than the scatter in the right hand panel. Therefore, the four reductions are accurately extracting the location of the peak in the submillimetre flux density from the data, and this peak is displaced from the true source location due to noise i n the 850 fira data. In a careful comparison, Ivison et al . (in preparation) confirm that the offsets scale as expected wi th the submillimetre beam size and S / N . A positional uncertainty is quoted in R A and Dec. offsets of 3.2 arcsec and no evidence is found for an overall mean astrometric error. It is interesting to note that the unweighted mean position from the four reductions is a better predictor of radio position than is obtained from any single reduction. Taken together the panels in Figure 4.7 indicate that the reductions do a good job of determining the positions implied by the submillimetre data, but that those positions have a few arcsec scatter wi th respect to the true underlying source positions. 1The location of a detected source is uniform between - 1 / 2 and 1/2 of the centre of a pixel of size 1. The variance of the error made by quoting the pixel centre is the mean-square error = J^02 x2dx = 1/12. 4.2. TEE CATALOGUE 108 Table 4.2: Astrometry Precision: The submillimetre positions of a subset of S H A D E S sources are compared to each other and to the radio positions found i n Ivison et al . (in preparation). The columns marked 'Variance wrt 850/mi ' show the R M S deviations in arcsec of each reduction wi th respect to the unweighted mean of al l four reductions. The column marked 'Variance wrt Radio ' shows the R M S deviations in arcsec wi th respect to positions determined by Ivison et al . (in preparation). Columns marked 'Net ' list the quadrature sums of the R A and Dec values across both fields. The positions of the radio sources are known to a higher accuracy than is possible using the S C U B A data alone, assuming that al l radio counterpart IDs are correct. The pattern of variances in the table indicates that the peak in the submillimetre data is displaced from the true source position due to noise, but that al l reductions find consistently the same displaced peak location because the submillimetre noise is common to al l four reductions. The unweighted mean position of the four reductions is a better predictor of radio position than any single reduction. Variance wrt 850 Variance wrt Radio S H A D E S Lockman S X D F Net 850 Net Radio Reduction R A Dec. R A Dec. R M S R M S A 2.33 1.94 1.80 2.91 ' 2.29 3.46 B 1.13 1.20 1.40 2.23 1.55 3.06 C 1.26 1.14 1.49 1.71 1.42 2.77 D 0.93 1.43 1.38 1.36 1.29 3.01 4.2. THE CATALOGUE 109 ^ o Q o r \ at °' o o I , , ' , 0 Found by all (no radio) + Found by all (+ radio) i A RA [arcsec] s. o o < I I I I . 1 .1 ! + + i i i i < ++ \ + + + \ i + + | " + 4 i , , , !, + / 0 A RA [arcsec] Figure 4.7: The left panel shows the offset of the source positions inferred by Reduction D from the mean of the positions found by al l four reductions for al l sources in the S X D F which are found in every reduction. The plus signs show those points which are also included in the comparison wi th radio positions (see right panel and Table 4.2). The diamonds are the remaining sources and they do not appear to be distributed very differently than those that were . compared to the radio counterparts. The dashed ellipse indicates y/2 times the one-dimensional variances in R A and D e c ; it contains ~ 2/3 of the sources, as expected. The right panel shows the offset i n position of the mean of the four S H A D E S reductions relative to the radio data of Ivison et al . (in preparation) for a subset of sources which have clear well defined radio positions. The radio data are collected at substantially higher angular resolution and S / N , so the scatter here is presumed to be dominated by scatter in the submillimetre data. A s in the left panel, the semi-major and semi-minor axes of the dashed ellipse are y/2 times the positional variances in R A and Dec. This error ellipse should contain ~ 2/3 of the sources. The vertical and horizontal dashed lines show the mean displacements of S H A D E S locations from the radio; these differences are not statistically significant. Taken together these panels indicate that the reductions do a good job of determining the positions implied by the submillimetre data, but that those positions have a few arcsec scatter wi th respect to the true underlying source positions. See Ivison et al . (in preparation) for a more detailed comparison. 4.2. THE CATALOGUE 110 4.2.7 Source Deblend ing The source extraction methods of Reduction C (D) are insensitive to finding sources closer than 10 (18) arcsec. There is thus a potential problem wi th source blending, since the detection of very near neighbours would be evidence for clustering of S M G s . Motivated by the discovery of two additional sources near two bright S M G s detected i n the G O O D S - N S C U B A map by Pope et al . (2005), double Gaussians wi th variable positions and amplitudes were fitted to the 5 brightest sources in each field found by Reduction D . However, no convincing evidence was found for favouring two sources over one. The x2 was typically lower when fitting double Gaussians, but the second source was never bright enough to be classified as a detection under our criteria. It is noted here (and in Appendix B) that SXDF850 .1 appears quite extended in the NS direction, although the x2 1S n ° t lower for two sources than for one. The deblending check here was performed by Alex Pope of S H A D E S , since the code had already been developed and tested on similar data. 4.2.8 Ana lys i s of the 450 /im D a t a 450 lira data were taken simultaneously wi th those at 850 lira, providing complementary short-wavelength photometry (or flux density limits) over a poorly sampled wavelength regime of the spectral energy distribution of S M G s . For objects in the S H A D E S cata-logue, these data can provide useful constraints for Far-IR-to-mm wavelength photomet-ric redshift estimates, a powerful tool for measuring the star formation history of the submillimetre galaxy population (e.g., Aretxaga et al . 2003). However, 450 / im observa-tions of faint objects wi th S C U B A are of l imited use, as: (1) the J C M T beamshape is non-Gaussian at 450 /ira, due to the non-optimization of the telescope surface for short-wavelength observations; (2) the atmosphere is more opaque at this wavelength and therefore the noise wi l l be more sensitive to small variations in the sky transmission than at longer wavelengths; and (3) atmospheric emission fluctuations are much more severe at 450 /ira, and are not sufficiently reduced by removing the 1 Hz array average (which is 4.2. THE CATALOGUE 111 so successful at 850 jim). A s the S H A D E S survey was conducted throughout a range of weather conditions (rcso > 0.05, mostly unsuitable for sensitive 450pm observations), these data are not expected to add much to our understanding of the 850/um source sample. Nevertheless, for completeness the main results derived from the analysis of these data are described here. The author led this work and put together much of the comparison and results. 450/^m R e d u c t i o n S t r a t eg ie s Reduction methods applied to the 450 /xm data are similar to those described in Sec-t ion 2.2.5, wi th the following minor exceptions. Reduction C uses smaller, 1 arcsec pixels when rebinning, and adopts a 7.5 arcsec Gaussian rather than the full, chopped P S F to extract flux densities. Reduction D also ignores the off-beams in the data and thus does not fold them in when rebinning. Reduction A did not participate in the 450 /mi comparison. The spatial variation in 450 (j,m flux densities across the rebinned maps is more corre-lated between Reductions B and C than between either of these and Reduction D . This is not surprising, given that Reductions B and C follow a similar calibration strategy, i.e., applying F C F s derived from calibration observations taken on the same night as the data, rather than adopting a monthly average F C F as was the strategy for Reduction D (cf. Table 2.1). There are plausible reasons why using frequent measurements of the F C F can either be beneficial, or detrimental, and one cannot use the data to distinguish between these possibilities, as one does not know the true amplitude of the underlying signal. Based on the consistently lower noise in reduction B , one might conclude that the longer, monthly average calibration strategy of Reduction D is introducing noise, and that at 450 yum the more frequent calibration strategy adopted by Reductions B and C is optimal. However, wi thin the large uncertainties of the 450 /im photometry (described below), the reductions are broadly consistent. 4.2. THE CATALOGUE 112 A S e a r c h for 450 / m i B l a n k - F i e l d Sources A s the beamsize at 450/mi is roughly half that at 850 /mi , many more spurious sources are expected to be uncovered in each-map above a given S / N threshold. This translates to a greater number of blank-field source candidates (i.e., those found at random positions in the map), so care must be taken to assess the likelihood of finding spurious sources in each map. A s an in i t ia l test of the data, each group focused on the S X D F data, extracting a list of blank-field, 3 a source candidates. From these source lists, a preliminary cross-identification candidate source list was created using a similar grading scheme to that described in Section 4.2.1. To determine the likely number of spurious objects in this list of 'positive' sources, each group then applied the same source extraction methods to inverted, or 'negative' versions of these same S X D F maps (cf. Section 2.2.6). The result was that in the combined S X D F lists more 'negative' than 'positive' source candidates were identified (142 versus 131). From these lists, those source candidates found in noisier regions of the maps were removed, as these should be less reliable. This resulted in an equal number of 'positive' and 'negative' source candidates in the combined S X D F list (68). Higher S / N threshold cuts (up to 5a) did not yield an excess of 'positive' over 'negative' source candidates. Spatial and temporal x2 tests ( s e e Appendix 2.2.6) were performed on Reduction D's > 3 a source candidates, and it was found that the majority of the sources fit wi thin the allowed 2 a area of the map's x 2 distribution and therefore could not be rejected on these grounds. Based on these analyses, no single 450/um blank-field source candidate can be claimed as a reliable detection in the S H A D E S data. Al though Reductions B and C do agree on the detection of a few 450 / i m counterparts to the 850 / m i sources in the L H field (some of which was observed under excellent weather conditions as part of the S C U B A 8-mJy survey), in no case do al l three reductions agree on a detection wi th a consistent position and significance level. Because of this, the 3 a l imits on the 450 / m i flux densities have been adopted for subsequent analyses, such as the photometric redshift estimates (Aretxaga et al. , in preparation), which benefit from 4.2. TEE CATALOGUE 113 the shorter wavelength data. 450 fim P h o t o m e t r y A s the reductions show broad agreement in the 450/mi flux densities wi th in the un-certainties, and there are no large systematic differences, the 450 / i m flux densities and photometric errors of Reduction B are adopted. Individual 450 / i m detections are not claimed. Equivalent 3 a upper limits are calculated for each source in the following way. A n error distribution is constructed from a histogram of pixel S / N . This error function is nearly Gaussian but has slightly larger wings. For each source, the error distribution is scaled to match the peak and a of the source. Table 4.1 gives the upper l imits to the flux densities bounding 99.73 per cent of the area of the error function (corresponding to the percentage area between the tails of the 3cr region under a Gaussian distribution). 450 pra S t a c k i n g A n a l y s e s Al though 450 /ira detections of 850 / i m S H A D E S sources cannot be claimed, one can attempt to determine if the population as a whole is detected in these data. To do this, a series of stacking analyses are performed on the 450 / i m data at the positions of the 850 / im sources, and also on their proposed 1.4 G H z radio counterparts (Ivison et al . , in preparation). These analyses were performed independently by each group following 2 strategies: (1) pointed 450 fxm photometry at the precise 850 /zm-selected source positions (this result wi l l be biased low since the peak of emission may be offset by an amount as great as the J C M T pointing error of 2-3 arcsec); and (2) a search for the nearest 450/ /m peak wi th in a 7 arcsec radius of the 850 lira, source position, if one exists (an estimate which should be biased high). A 7 arcsec search radius was chosen since the probabili ty of a spurious 450 / i m source lying within this distance of a known 850 lira is very low (see Fox et al . 2002). The results from each reduction are given in columns 2 and 3 of Table 4.3. Table 4.3: 450 / i m stacked flux densities (in mJy) for the B , C and D reductions. The results are for average flux densities measured at the indicated positions, related to those of the 850 / i m S H A D E S catalogue sources. Reduction B has calculated unweighted mean stacked flux densities, while Reductions C and D have calculated mean stacked flux densities wi th inverse noise variance weighting. Reduction 850 / i m position highest S / N detection 850 pm position 850 /xm position radio position wi th in 7 arcsec radius of (all) 850 pm position (all) (radio ID subset) (non-radio ID subset) (radio ID subset) L H B 10.6 ± 3 . 8 38.3 ± 4 . 0 16.9 ± 4 . 3 10.6 ± 4 . 8 19.2 ± 4 . 2 C 12.4 ± 2 . 1 30.6 ± 2 . 1 20.8 ± 3 . 3 7.4 ± 2 . 7 22.0 ± 3 . 3 D 10.5 ± 2 . 3 28.8 ± 2 . 9 19.6 ± 3 . 8 4.9 ± 2 . 9 18.8 ± 3 . 8 S X D F B 5.7 ± 4 . 6 24.3 ± 3 . 7 11.1 ± 4 . 2 14.6 ± 5 . 4 16.6 ± 4 . 2 C 12.5 ± 2 . 4 37.5 ± 2 . 4 14.1 ± 3 . 9 11.4 ± 3 . 1 17.9 ± 3 . 8 D 9.9 ± 2 . 7 36.7 ± 3 . 4 12.1 ± 4 . 3 7.9 ± 3 . 5 14.0 ± 4 . 2 4.2. THE CATALOGUE 115 To determine how frequently the stacked flux density measurements would occur given the number of 850 /urn sources in each field, 10,000 Monte Carlo simulations were performed wi th uniformly-selected random positions in the Reduction D maps. A stacked flux density greater than or equal to the measured value at the 850 /urn-selected positions (strategy 1) occurs < 0.1 percent of the time at random in both fields. The simulations therefore indicate a significant detection of the S H A D E S catalogue of 850 /mi-selected galaxies at 450 /mi . Another indication of a marginal detection of the 850 / m i sources at 450//m, is shown by the slight positive skewness in the distribution of S / N values at the 850 / im S H A D E S catalogue positions (as shown in F i g . 4.8). The simulations were then repeated for strategy 2, searching for the nearest 450 / im peak wi th in 7 arcsec of the S H A D E S catalogue 850 / i m positions. It was found that a value above the measured stacked value occurred 90 (22) per cent of the time in the L H ( S X D F ) field. The stacked 450 / i m flux density obtained using strategy 2 is therefore not high enough compared wi th the Monte Carlos (which pick up 450 / i m noise peaks wi thin the 7 arcsec search radius) to be regarded as statistically significant. The ratio of stacked 450 /am flux density to 850 / im flux density of S H A D E S catalogue sources is around 2-2.5, depending on the precise choice of data and reduction (and including the effect of 850/um flux deboosting). This ratio is low compared to what one would expect, independent of any reasonable choice for a redshifted sample of local S E D templates (which typically yield S450/S850 ^ 4). F i t t ing a range of template galaxies from Aretxaga et al . (2003) yielded redshifts <; 3 for the population, which is higher than that found for S M G s . This result of low stacked 450 / i m flux density is consistent wi th that found for S M G s in the G O O D S - N field (Pope et al., 2005) and suggests a systematic bias when pushing S C U B A data to these faint stacked values. The 450 / i m stacking analysis was also carried out at the positions of the preliminary sub-sample of radio-identified sources (see Section 4.2.6), and compared wi th the results of an analysis at the positions of the. non-radio-identified sub-sample. Note that the radio-detected S M G s are more likely to be detected at 450 / im (since they lie at lower redshifts; e.g., Chapman et al . 2005). The stacked 450/mi flux densities at the 850 / im Figure 4.8: Histogram of stacked flux densities in the 450 / im S / N map at the positions of the 850/im-selected S H A D E S catalogue positions (see Table 4.1). The stacked flux densities for the L H and S X D F are shown by the large-binned thick histograms. The finer-binned histograms represent the 450/um pixel values from the S / N L H and S X D F maps. Notice the appearance of excess positive 450/mi S / N when stacked at the 850/mi positions, indicating that an overlap is detected between these populations. Whi le any single 850 / m i object is not reliably detected, the 850 / i m population as a whole is detected statistically. This plot is specifically for Reduction D (my reduction); the results based on the other two reductions are similar. 4.3. DIFFERENTIAL SOURCE COUNTS 117 positions of the sources wi th radio IDs are similar to the stacked 450 / i m flux densities at the radio positions. This implies that moving to the positions of the proposed radio identifications (which one might expect would provide a more accurate measure of the true source positions) does not actually raise the average 450 /um flux density significantly for the same subset of sources. However, a marked difference was found between the stacked 450 /um flux densities of the radio-identified subset and the non-radio-identified subset. This result may be explained by one of the following: (1) the non-radio-identified subset lies at a higher redshift on average; or (2) there are spurious sources in the non-radio-identified subset, diluting the 450 / i m stacked flux density measurement (Ivison et al . 2002; Greve et al . 2004). Since there is no evidence that the radio-identified S H A D E S sources are more likely to be real, the radio-identified subset is probably biased to lower redshifts (Chapman et al., 2005), yielding a higher S^o/Ss^o ratio. 4.3 Differential Source Counts A n important quantity which can be derived from the data is an estimate of the number of sources as a function of flux density. Using the counts alone, without any details of the individual galaxies comprising these counts, details of the population of S M G s can be inferred. Number counts of S M G s are a measure of how many stars were made in galaxies over a l l time (since the redshift distribution of the S M G s is unknown given the 850 / i m flux densities alone). S H A D E S is a single, uniform survey which has approximately doubled the total area of all SCUBA-observed blank-field surveys. Whi le the dynamic range in flux densities is not as broad as is available from a compilation of data which includes the deepest surveys (particularly those associated wi th foreground gravitational lenses), the results here are the most robust obtained so far in the range of flux densities where S H A D E S is sensitive. In this section reliable estimates of the differential 850 / i m number counts are provided for the first time. Differential counts offer an advantage compared to integral source counts, since each estimate of the number of sources in a flux density b in does 4.3. DIFFERENTIAL SOURCE COUNTS 118 not depend on the counts at brighter flux densities and thus wi l l be much less correlated. This makes fitting the results to models of source counts more straightforward. In the following section, 4.4, the differential counts are integrated to estimate the cumulative source distribution for comparison to previous data. Al though al l of the sources in the S H A D E S catalogue are at least 3 a in the maps, and therefore have raw measured flux densities which are typically above 6 mJy, the well known steep submillimetre source flux density distribution implies that a source which is detected at 6-8 m J y is as likely to be a 3-4 mJy source accidentally observed wi th a positive noise fluctuation as it is to be a genuine 7 m J y source (cf. Section 4.2.2). The number of sources observed depends on the number density of sources down to quite faint flux densities, well below the nominal 6 mJy l imit here. Fi ts of differential source counts to the data wi l l therefore provide constraints on the number of sources per square degree starting at about 3mJy. To obtain estimates of differential source counts one must estimate completeness, flux density bias, survey area, spurious detection rates, and Poisson counting errors. Two analysis approaches have been developed to perform these tasks. One of these is a 'direct estimate', which works wi th a list of sources and their deboosted flux densities and sums the associated probability densities to obtain the parent source density spectrum. The second method, 'parametric fitting', self-consistently estimates the prior source density spectrum, the F D R and the source deboosting. Direct counts use a fixed informative prior to perform the deboosting. This is a maximal use of existing information from past S C U B A surveys. The parametric approach leaves the prior as a free parameter. This second technique is probably more conservative, and the amount of noise in the results strongly depends on how the prior is parameterised. Al though the S H A D E S catalogue is extremely robust in terms of a low expected false detection rate, it has a complicated selection function and is not necessarily optimal for measuring the source counts. Because it is based on four different analyses the selection criteria are hard to simulate, so the S H A D E S catalogue is not used to derive constraints on 850 jim source counts. In particular, one would like to use statistical information 4.3. DIFFERENTIAL SOURCE COUNTS 119 from sources which may not individually be detected wi th high significance. Therefore, source count spectra have been determined independently from the provisional source lists arising from each reduction. Variations of the direct estimation approach have been applied to data from Reductions B and D , while parametric fitting has been applied to Reduction C . The approaches taken by the other Reductions are described in Appendix D . Note that the method and results outlined in this section were adopted as the official S H A D E S results for publication. The fits presented here are al l derived from catalogues of sources detected above at least 2.5 a. Thus, although the number count estimates are statistical they are funda-mentally different from so-called P(D) analyses in which the distribution of pixel flux densities is fit directly to a source count model. If the catalogue was reduced to lower and lower thresholds the P(D) results would effectively be recovered. However, this is left to future work. Table 4.4 highlights the key steps and differences in each reduction's number count estimation. 4 . 3 . 1 D i r e c t E s t i m a t e o f t h e D i f f e r e n t i a l S o u r c e C o u n t s The direct estimate works wi th Reduction D's source list and calculates the differential counts directly using the posterior flux density distributions for individual sources in the list following Coppin et al . (2005). The source list used to calculate the number counts is constructed by identifying a l l 2.5 a peaks in the map, and keeping al l of the peaks likely to be real (i.e., having < 5 per cent deboosted probability of having S\ < 0). For the purposes of measuring the counts the deboosting criterion could be relaxed, but wi th the added complication of statistically taking into account the F D R in the counts (see Section D.2). For this reason, the same criterion that is used to construct the S H A D E S catalogue is applied - the difference being that here only Reduction D's data are used. A n 'effective area' is calculated. It is the area times the completeness,' and these are 4.3. DIFFERENTIAL SOURCE COUNTS 120 Table 4.4: Methods of accounting for bias. Here subscript ' i ' refers to the input or un-biased flux density, subscript 'o' refers to observed quantities in thresholded maps, and subscr ip t 'd ' refers to a true detection. Step Reduction B Reduction C Reduction D Meaning of poste-rior flux density, p(Si\S0,a0) Flux density probability for best fit of flux density to the underlying 'zero-footprint' map distribu-tion. Flux density probability for brightest individual source in a measurement aperture. Total flux density in a mea-surement aperture. Posterior flux density expression p(Si)p(S 0,ffo|Si) p(Si)p d (5 0 |5 i , cr0)pd(ffo|Si) p(Si)p(5o,cTo|5i) p(So,<To) Pd(So,CT0) P(S 0,CT 0) Prior information used Actual S /N map for the given field. Simulated noisy flux den-sity maps, assuming a form of the number counts, and completeness for given field. Simulated noiseless flux density map, assuming a form of the number counts, and Gaussian photometric errors. Source list selection criteria So/<To > 3.5 So/o-o > 2.5 So/o-o > 2.5, p(Si < 0\So, cr0) < 5 per cent Number counts Place sources in bins at peak posterior probability. Fit prior p(S;) by com-paring modelled p(S0,<j0) with data. Place sources in bins by in-tegrating posterior proba-bility. Completeness Add individual sources to real maps, compare input to output catalogue. Completely simulate maps, compare input to output catalogue. Add individual sources to real map, detect nearest peak and compare to input position. Spurious Detections Completely simulate maps, detect nearest peak. Completely simulate maps, compare input to output catalogue. See source list selection cri-teria. Counts Uncertainties Analytic propagation of er-rors. Monte Carlo, using realiza-tions of completely simu-lated data. Monte Carlo, using boot-straps of real data. 4.3. DIFFERENTIAL SOURCE COUNTS 121 estimated together as a function of intrinsic source flux density, ^(S 1;), in order to correct the source counts for incompleteness. Fake sources of known flux density are injected one at a time into the real maps (without worrying if the sources fall entirely wi th in the region that was measured) and then they are extracted using the source extraction method. This procedure is repeated 2000 times each at flux density levels of 4, 6, 8, 10, 12, 14, 16, 40, 60, and 100 mJy . A source is considered recovered if it is found wi th in 7.5 arcsec of its input position and survived the flux density deboosting. fi(S\) is the ratio of the number of sources found to the number put in per square degree (see F i g . 4.9). A smooth best-fitting function of the form (Sa)/(b + cSa) is fitted to the data points and is used in correcting the raw source counts. Here S is the flux density and a, b, c are constants. The values of N(Si) in the bins are estimated using Monte Carlos, which are also used to estimate the errors. In the past, submillimetre survey groups have placed error bars on the counts by simply accounting for the simple 1 a Poisson counting errors (the square root of the raw counts in each bin, scaled to unit solid angle). The estimated number of spurious and confused sources are sometimes added in quadrature to the lower error bar in the corrected number counts (e.g., Scott et al . 2002). Since the deboosting procedure provides a distribution for each S i , rather than just a single value, a modified boot-strapping simulation is used to estimate the differential source counts and uncertainties i n bins of wid th 2 mJy . This simultaneously accounts for the Poisson error, as now described. First , a number of sources is chosen from a Gaussian distribution centred on the number of sources included in the real source list, Ntrue, wi th a standard deviation a = \JNtrue to account for counting errors. This number of sources is then randomly selected from the actual source list and their probability distributions sampled with replacement (i.e., boot-strapping; see Section 6.6 of W a l l & Jenkins 2004); once a flux density is determined at random (using the source's posterior probability distribution), one source per effective area is added into the appropriate flux density bin. This procedure is repeated 10,000 times, in order to make well-sampled histograms of the count distributions for each bin. These histograms are used to estimate the mean counts and the frequentist 68 per cent 4.3. DIFFERENTIAL SOURCE COUNTS 122 Figure 4.9: A fit to f2(5j), the effective area (survey area times completeness) of the 850 / m i source recovery at each level of input flux density for 3 a map detec-tions which have P(S\ < OmJy) < 5 per cent, as determined from Monte Carlo simulations of individual sources added to the S H A D E S maps of Re-duction D (see Section 4.3.1). The curves are fits to the form (Sa)/(b + cSa). 4.3. DIFFERENTIAL SOURCE COUNTS 123 F l u x density 850 / i m differential counts F l u x density 850 / i m integral counts (mJy) dN/dSmJy- ldeg-2 (mJy) N{> S) deg-2 2.77 O O 1+230 o o i - 2 2 7 2.0 25061$ 4.87 240+J} 4.0 8 4 4 ± $ 6.90 1 0 6 l £ 6.0 362lg 8.93 4 i ± i i 8.0 1 5 0 l | 10.94 10.0 6812.} 12.95 12.0 14.96 o n+2.2 ° - y - 3 . 8 14.0 16.96 16.0 7.4^:1 18.96 18.0 3 - 9 l i 9 7 20.97 20.0 2.0±?;i Table 4.5: 850 yum S H A D E S differential (in 2mJy wide bins; quoted per mJy) and inte-gral (in 2mJy bins) source counts of Reduction D . The error bars represent the frequentist 68 per cent confidence intervals of the boot-strapped count distribution in each bin (see text). Each differential count flux density b in is indicated by the midpoint of each bin weighted by S~3, whereas the integral count flux density bins are indicated by the lower flux density bound of each bin. The counts and errors in each of the lowest flux density bins of the differ-ential (integral) estimates have been corrected by a factor of 1.6 (1.33), for the known undercounting in this b in seen in simulations (see Section 4.3.1). Note that a Gaussian approximation to the error bars becomes invalid for high flux densities. confidence intervals in each flux density b in and are given in Table 4.5. Simultaneously, the linear Pearson covariance matrix of the bootstraps across the flux density bins can be calculated to assess the correlation between bins and this can then be used in model fitting procedures; the covariance matrix is given in Table 4.6 for the counts of the combined L H and S X D F fields i n 2 mJy-wide bins. The benefit to calculating binned differential counts in this way is that they can more easily be combined wi th counts from other surveys to constrain models over wider ranges in flux density because the data product that comes out of the procedure are binned counts and a bin-to-bin covariance matrix. Co F l u x density (mJy) 2.77 4.87 6.90 8.93 10.94 12.95 14.96 16.96 18.96 20.97 2.77 19926.5 109.1 -29 .3 - 1 . 5 -12 .5 -14.5 -1 .8 - 2 . 5 -0 .1 1.5 4.87 109.1 2511.9 - 9 . 0 - 3 . 8 0.2 2.4 1.2 0.1 - 1 . 2 0.5 6.90 -29 .3 - 9 . 0 599.4 3.8 - 1 . 2 1.1 -0 .1 0.5 0.1 0.6 8.93 - 1 . 5 -3 .8 3.8 176.5 2.2 0.57 0.5 0.0 0.2 -0 .1 10.94 -12 .5 0.2 - 1 . 2 2.3 62.5 0.27 - 0 . 2 0.1 0.1 0.0 12.95 -14 .5 2.4 1.1 0.6 0.3 28.6 0.0 0.1 -0 .1 0.1 14.96 - 1 . 8 1.2 -0 .1 0.5 - 0 . 2 0.0 11.5 0.0 0.0 0.0 16.96 - 2 . 5 0.1 0.5 0.0 0.1 0.1 0.0 5.2 0.0 0.0 18.96 -0 .1 - 1 . 2 0.1 0.2 0.1 -0 .1 0.0 0.0 2.7 0.0 20.97 1.5 0.5 0.6 -0 .1 0.0 0.1 0.0 0.0 0.0 1.5 s Pa I CO O o Table 4.6: Covariance matr ix for the 850 fim S H A D E S combined differential source counts. This can be used along with Table 4.5 to fit models to the counts using the figure-of-merit \ 2 = (d — m ) T C'1 (d — m), where d is the data, m is the model, and C - 1 is the inverse of the covariance matrix. 4.3. DIFFERENTIAL SOURCE COUNTS 125 For this reason, S H A D E S adopts the counts derived by Reduction D , i.e., the one described in most detail in this thesis, and quotes the combined-field differential number counts and the accompanying bin-to-bin covariance matrix. It is reasonable to select one group's reduction, since one cannot easily combine the three sets of counts like was done for flux densities or positions, and moreover al l of the counts across reductions appear to be consistent wi th each other wi thin the error bar estimation, for al l but the lowest b in (where Reduction B appears to be low). In model tests the best fit parameters are quoted using the counts of Reduction D since that reduction provides the smallest error bars (cf. Section 4.1.1), while using the 68 per cent confidence intervals of Reduction C as a consistency check on the plots. The differential counts for L H and S X D F are shown in Figs. 4.10 and 4.11, respectively. The integral counts are obtained by directly summing over the differential counts and are tabulated in Table 4.5 and shown in F ig . 4.14. See Appendix D for details of the methods used by 2 other teams to estimate the number counts. T e s t s o f D e b o o s t i n g o n S o u r c e C o u n t R e c o v e r y A test for bias i n the recovery of the number counts was carried out in the following way. A fake sky populated wi th the source counts of Borys et al . (2003) was created. This was observed using the actual S X D F observing scheme and a map was made in the same way as for the real data, while simultaneously injecting random Gaussian noise wi th an R M S similar to the real map (~ 2 m J y ) . Sources were then extracted and deboosted according to the prescription described in Section 4.2.2. The recovered cumulative number counts (scaled by the effective area) were found to be consistent wi th the input number count realisation in al l except the lowest flux density bin, where the uncertainty in the com-pleteness estimates dominates (see F i g . 4.12). The differential (integral) counts i n each of the lowest flux density bins have therefore been corrected by a factor of 1.6 (1.33). The input source counts were also recovered when different source count models were used as input to the simulated skies, while keeping the form of the prior distribution of pixel flux 4.3. DIFFERENTIAL SOURCE COUNTS 126 1000 CM 'DO D T3 '>> Hi m 1 100 10 T 1 r 1- ^ - ' V L H \ <k i \ I \ Survey Limit J . \ «H J I I -'-\ : : \ " " \ \ i<3 UN 4 6 8 10 850um Flux Density S [mJy] 20 Figure 4.10: Differential source count densities in the L H region. The number of sources d e g - 2 m J y - 1 at a given flux density is plotted against flux density (with dif-ferent reductions offset horizontally for clarity). A l l error bars are estimates of 1 a uncertainties of the full error distribution including completeness es-timates (see text). The horizontal line marked 'Survey L i m i t ' corresponds to the 68 per cent confidence limit which can be drawn from finding zero sources in 1/8 deg 2 (in a 2mJy-wide bin). The 68 per cent confidence inter-val on the set of best-fitting double power-laws of the form of Equat ion 3.1 (fit to the differential counts of Reduction C) are overplotted as dashed lines; the error bars show that there is little constraint above this level. 4.3. DIFFERENTIAL SOURCE COUNTS 127 1000 - - - . -oo T3 1 4 6 8 10 850um Flux Density S [mJy] 20 Figure 4.11: Differential source count densities in the S X D F region, as for F i g . 4.10. Notice that i n a l l except the lowest two flux density bins for Reduction C, the density of sources inferred in the S X D F is approximately 1 / 4 a lower than for the L H data; see Section 4.4.7 for a discussion of possible field-to-field variations. 4.4. MODELS AND CUMULATIVE SOURCE COUNTS 128 densities fixed. The correction factor hardly changed when different input models were used. A n overall F D R was also calculated in a different manner to that described in Sec-t ion 4.2.2. A noiseless fake sky was populated wi th the Borys et al . (2003) source counts, and the region was sampled using the real observing scheme and map reduction steps for each field, while simultaneously adding Gaussian random noise into the timestream to get the same R M S as the real maps. Sources were extracted in the usual way and then deboosted using the Coppin et al . (2005) prescription to create a final refined catalogue of flux density deboosted sources. More than 90 per cent of sources detected i n the sim-ulated maps corresponded wi th input sources above the faintest deboosted flux densities of the actual S H A D E S catalogue. The interpretation of the remainder is complicated, particularly as one approaches the confusion regime. The overall F D R lies below 10 per cent, but determining the precise F D R from simulations is complicated by source confusion, i.e., interpretation of precisely what the source means. 4.4 Models and Cumulative Source Counts 4.4.1 Fits to Differential Counts In fitting models of the numbers of sources at different flux densities to the data there are different approaches which could be taken. The first choice is whether to fit to the list of sources directly or to count the sources in a series of discrete flux density bins and fit to those numbers. In principle these methods could each be applied to the results of each reduction, but there is little to be gained from generating eight different fits in this way. One approach each was tried on the data of two separate reductions. Starting wi th the catalogue from Reduction C, Monte Carlo techniques are used to compute the maximum-likelihood distribution of models that fit the source catalogue, given the completeness and F D R . The dashed curves in Figs. 4.10 and 4.11, indicate the 68 per cent frequentist interval on the best-fitting models. This procedure requires detailed 4.4. MODELS AND CUMULATIVE SOURCE COUNTS 129 1000 GO A 4 6 8 Flux Density S [mJy] 10 20 Figure 4.12: 850 /mi cumulative source counts recovered from a fake sky populated wi th a known source count model (explicitly for Reduction D ) . The diamonds and error bars are the recovered source counts for these simulated data, observed using the same scheme as for the real S X D F data. The overplotted histogram (solid line) is the actual realisation of the Borys et al . (2003) source counts model that was used (dot-dashed line). This same source count model was used in creating the prior in the Bayesian flux density deboosting method described in Section 4.2.3. 4.4. MODELS AND CUMULATIVE SOURCE COUNTS 130 knowledge of the F D R and completeness as a function of flux density and therefore it is difficult to compare directly wi th published counts. Note that the 68 per cent range on the models fit to Reduction C is about the size of the individual error bars in Reduction D , and that the reductions are al l consistent wi th each other wi thin the error bars i n a l l but the lowest flux density bin. Starting wi th the counts and covariance matrix, based on Reduction D (found in Tables 4.5 and 4.6), a simple power-law of the form is fit using a minimum x2 parametric approach. Here, N' is the normalisation at S' = 5 m j y (the approximate 'pivot ' point for our data). The 'Survey L i m i t ' (as indicated by a dot-dashed line in the figures) corresponds to (in a 2 mJy-wide bin) in each of the two fields. This provides a rule-of-thumb counting l imit to which the S H A D E S fields are sensitive, given the observed areas and depths achieved. Note that the Gaussian error approximation breaks down for the highest flux density bins but these carry little weight in the fits in any case. The approach taken by Reduction C also makes full use of the range of flux densities in which there are no detected objects, and thus provides a consistency check. The best fitting line has parameters: a = 2.9 ± 0.2 and N' — 189 ± 26 in L H ; and a = 3.0 ± 0 . 3 and N' = 136 ± 2 4 in S X D F . Note that a and N' are essentially uncorrelated wi th each other, because the normalisation is chosen to be around S' = 5 mJy, near the centroid of our data. This result, that a is virtually the same in both fields while N' is lower in S X D F , is consistent wi th the data in Figs. 4.10 and 4.11, where every b in in S X D F appears lower than the corresponding bin in L H by about 1/4 a. The slope result agrees wi th previous estimates obtained by other groups (1 a l imits are quoted from the literature): a = 2.8 ± 0 . 7 B la in et al . (1999); a = 2.9 ± 0 . 2 5 Borys et al . (2003); a = 3 . 2 + ° j 5 Barger, Cowie & Sanders (1999); and a = 3.25 ± 0.7 Eales et al . (2000). The total number of sources per square degree in L H versus S X D F differ by less than (4.1) the 68 per cent confidence limit which can be drawn from finding zero sources i n 1 /8 deg 2 4.4. MODELS AND CUMULATIVE SOURCE COUNTS 131 2 a (for purely Poisson scatter) and there is no convincing evidence to suggest that the ratio of the counts between the fields is different from 1. In the rest of the analysis the data for the two fields are combined to improve the statistical power slightly. The combined counts (i.e., for both fields) are plotted in F ig . 4.13. It is clear that a single power-law model for the combined data, shown as the dashed line in F i g . 4.13, is a poor fit to the data. The fit remains poor even if the counts in the lowest bin are arbitrarily doubled, and it is improbable that the completeness has been mis-estimated by this much. Fi ts to broken power-laws, and to a Schechter function (Schechter, 1976) are therefore explored. A full fit to Equation 3.1 involves solving for four parameters: N', S', a, and j3, which are not simultaneously well-constrained by the few data points. The parameter error bars are therefore large and correlated (see Table 4.7). If instead, the break flux density is held fixed at S' = 9, a visually plausible value (and close to the best-fitting value of 5"), the resulting uncertainties in N', a, and (3 are reduced, as also shown in Table 4.7, and the errors become almost uncorrelated. The x2 °f the broken power-law fit is reduced from the single power-law by about 10 for one new parameter (N', a N', a, (5). However, it is noted that the resulting reduced x2 values are unrealistically small (i.e., less than 1.0) in al l but the single power-law fits. This probably reflects the fact that the errors are non-Gaussian or that there are some correlations not taken into account properly in the covariance matrix. But the fact remains that fits to a single power-law do not describe the data well. A broken power-law is also fit and is of the form using the same minimum x2 parametric approach. The best-fitting form of Equat ion 4.2, holding S' fixed at 9 m J y , is plotted in F i g . 4.13 as 2 solid lines. A Schechter function (Schechter, 1976) is also fit to the counts: dN dS j = N'(§) P for S > S' and f = N>(§yaiorS<S>, (4.2) 4.4. MODELS AND CUMULATIVE SOURCE COUNTS 132 850|xm Flux Density S [mJy] Figure 4.13: Differential source counts in the combined fields ( L H + S X D F ) . The number of sources m J y - 1 d e g - 2 at a given flux density is plotted against flux density. A l l error bars are estimates of 1 cr uncertainties of the full error distribution, including completeness estimates (see text). The horizontal line marked 'Survey L i m i t ' corresponds to the 68 per cent confidence l imit which can be drawn from finding zero sources in 1 / 4 deg 2 (in a 2 mJy-wide bin). The best-fitting single power-law (Equation 4.1; dashed line), Schechter function (Equation 4.3; dotted curve), and broken power-law (Equation 4.2; solid lines) to the differential counts of Reduction D are plotted. It is clear that the Schechter function or the broken power-law are a better fit to the data than the single power-law, indicating a break somewhere in the range ~ 5 -13mJy. 4.4. MODELS AND CUMULATIVE SOURCE COUNTS 133 Equat ion S' N' a P 3.1 9.4 ± 4 . 0 647 ± 739 2.0 ± 0 . 6 6.0 ± 2 . 2 3.1 9 735 ± 123 2.0 ± 0 . 2 5.8 ± 0 . 9 4.2 9 49 ± 9 . 3 2.4 ± 0 . 2 5.1 ± 0 . 9 4.3 3.3 ± 1 . 2 1599 ± 1183 - 2 . 0 ± 0.7 -Table 4.7: Best-fitting parameters of Equations 3.1 (smooth double power-law), 4.2 (bro-ken power-laws) and 4.3 (Schechter function) fit to the combined counts. F i x -ing the break location in the source counts, 5", has the effect of reducing the error bars on the other parameters (cf. top 2 rows). 1S = VSW « P ( " ^ ) - (4-3) The parameters N', S' and a of the best-fitting form of Equation 4.3 are tabulated in Table 4.7 (see F i g . 4.13, dotted curve). The Schechter function is an arbitrary fitting formula that seems to describe the optical luminosity function of galaxies and also fits the 850 / i m data as well as the other 2 power-laws fit here. This may not be surprising given that the relationship between 850 / im flux density and rest-frame F I R luminosity is nearly constant and independent of the redshift for 1 < z < 8 (see B l a i n et al . 2002). But there is no evidence to favour an exponential fall off over a steeper power-law at large flux densities. The data clearly favour a change in the slope for the differential counts, although the precise position of this break is not well constrained. This change in slope of the differ-ential counts should be helpful in breaking degeneracies in fitting models of luminosity function evolution. If additional information from low flux density counts is used (particularly from cluster lens fields) the evidence for a break becomes stronger. Also, a shallower slope at low flux densities is required in order not to overproduce the submillimetre background. However, neither of these arguments requires that the break be at a large enough flux density to be seen wi th in the S H A D E S data. It is the direct fits to the differential counts which, for the first time, constrain the power-law break to be at a flux density of several mJy. 4.4. MODELS AND CUMULATIVE SOURCE COUNTS 134 4 . 4 . 2 B a c k g r o u n d E s t i m a t e One can use any of the best-fitting models to estimate the total flux density which has been resolved into discrete sources. Adopt ing Equation 4.2 and using the best-fitting parameters in Table 4.7, wi th S' fixed at 9mJy, the total 850 / m i flux density can be calculated by integrating S N(S)dS. The estimated background of sources brighter than 2 m J y is 9 . 7 l | ; | x 1 0 3 m J y d e g ~ 2 . The background can also be estimated directly from the S H A D E S counts by performing the sum J2 SN(S) over the bins, which gives l.OOig;!! x 1 0 4 m J y d e g - 2 . B y comparison, the total F I R 850 /um background inferred from COBE-FIRAS is 3 .1-4.4 x 1 0 4 m J y d e g " 2 (Puget et al . 1996; Fixsen et al . 1998; Lagache, Puget & Dole 2005). Based on the S H A D E S counts, a survey complete down to 2 mJy at 850 yum would resolve between 20 and 30 per cent of the F I R background into point sources. The uncertainty in this fraction is dominated by uncertainty in the unresolved background, rather than uncertainty in the S H A D E S sources. This result is consistent wi th values quoted by other groups (e.g., Barger, Cowie & Sanders 1999, Eales et al . 2000, Borys et al . 2003). A significant fraction of the submillimetre emission lies below the detection l imit of blank-field S C U B A surveys at 850 /um. Therefore, knowing the number counts accurately down to much fainter flux density l imits (~ 0.1 mJy) is essential in order to constrain models that predict the evolution of luminous IR galaxies. 4 . 4 . 3 C u m u l a t i v e S o u r c e C o u n t s Previous S C U B A surveys wi th fewer sources have reported source densities i n the form of cumulative counts rather than differential counts, since the latter are somewhat sensitive to the b in choice for small source catalogues. The S H A D E S integral counts are obtained by directly summing over the differential counts of Reduction D . The best-fitting double power-law model and Schechter function (cf. Equations 4.2 and 4.3 and Table 4.7) of the differential counts have been integrated to produce models of the cumulative counts. The cumulative counts and these models are plotted in F i g . 4.14 and given in Table 4.5. 4.4. MODELS AND CUMULATIVE SOURCE COUNTS 135 Note that the models are not fit in the cumulative counts domain. These should be the most accurate 850 / i m number counts in the flux density range 2-15 m J y achieved so far by any single survey. 4.4.4 Comparison of Cumulative Counts to Previous Estimates Previous measurements of the cumulative number counts have differed by factors of ~ 2.5-3 among groups observing various small (10s to ~ 200arcmin 2 ) patches of sky, espe-cially at flux densities between 2-6 mJy (e.g., Barger, Cowie & Sanders 1999, B l a i n et al . 1999, Eales et al . 2000, Scott et al . 2002, Borys et al . 2003, Webb et al . 2003b; see dis-cussion in Scott et al . 2002). The culprits are most likely sampling variance, clustering and/or low number statistics, due to the small-area surveys, as well as different ways of treating flux density boosting in the low S / N regime. In F i g . 4.14, the S H A D E S counts are plotted i n comparison wi th previous work in order to assess the level of agreement. Gravi ta t ional lensing amplification by clusters of galaxies has been used as a tool to study the faintest S M G s (e.g., B la in et al . 1999; Cowie, Barger & Kneib 2002; Smai l et al . 2002; Chapman et al . 2002; Webb et al . 2005; and Knudsen et al . 2006). The agreement between these independent surveys is very good below about 2 m J y . Note that there is a smooth transition also at 3 m J y between the cluster surveys and this work. However, Borys et al . (2003), Webb et al . (2005) and others noted that the lensing number counts above 4 m J y (where the cluster and blank-field counts overlap) appear higher than the combined blank-field survey counts, and the results here support this statement. This is most likely due to the fact that the quoted error bars in the literature do not contain a variance component or a contribution from uncertainties i n the lens modelling, and that the flux density boosting bias has been treated differently by different groups. In particular, note that the brightest point at 5 mJy from Cowie, Barger & Kneib (2002) is many a above the S H A D E S data. The best agreement may be expected at the bright end of the source counts (among 4.4. MODELS AND CUMULATIVE SOURCE COUNTS 136 IO 3 T3 00 A 0.2 1 2 4 6 8 10 20 850|xm Flux Density S [mJy] Figure 4.14: Cumulative combined S H A D E S source counts (solid points) compared to previous estimates. The 68 per cent confidence interval in Reduction C 's model fits is indicated by the dashed lines. The 95 per cent Poisson upper confidence l imit to the surface density of sources brighter than 2 2 m J y i n S H A D E S from Section 4.4.5 is shown by the downward arrow. The source counts determined from various other blank-field and cluster lensing sur-veys (corrected for lensing) are indicated using different symbols, wi th the Scott, Dunlop & Serjeant (2005) compiled counts being represented by the hatched region. The best fitting form of Equation 4.2 (dark solid curve), holding S' fixed at 9 m J y , and Equation 4.3 (dark dotted curve) to the differential counts are integrated and plotted here. See Table 4.7 for the best-fitting parameter values for these functions. The data confirm a break in the power-law somewhere in the middle of the flux density range. The lensing data are consistently high, which could have a number of explana-tions (see text). 4.4. MODELS AND CUMULATIVE SOURCE COUNTS 137 previous wide-area blank-field surveys to varying depths), since only the brightest sources would have prevailed in shallower data. However, the largest disagreement may be ex-pected to be wi th small area blank-field surveys, since very bright sources are rare and a large degree of sampling variance may therefore come into play, particularly if S M G s cluster on arcminute scales. A t the bright end, the Borys et al . (2003) blank-field counts follow an approximately power-law decline wi th increasing flux density, and although the S H A D E S counts appear to steepen more dramatically, they are well wi th in 1 a of the Borys et al . (2003) counts and are therefore not statistically different. Similarly, the counts of Scott, Dunlop & Serjeant (2005), which is a compilation of data covering a similar area to each of the two S H A D E S fields (the 'band' in F ig . 4.14), appear lower on average than the S H A D E S counts, however, there is no discernable statistical difference between the two. 4.4.5 Bright Source Constraint A limit to the surface density of the brightest S M G s can also be estimated. There are various ways to do this, but the simplest is just to take the fact that S H A D E S contains no sources brighter than 22mJy in the entire surveyed area to constrain the bright counts using Poisson statistics. A^(>22mJy) < 17 d e g - 2 is found at 95 per cent confidence. This estimate is probably more robust than previous upper l imits at similar flux densities (e.g., Borys et al . 2003; Scott et al . 2002) and can be compared wi th the even brighter Barnard et al . (2004) l imit of iV(>100mJy) < 2.9 d e g - 2 . 4.4.6 S M G Evolution S M G s are believed to be an important population of luminous objects at high redshifts responsible for producing a substantial fraction of present-day stars in galaxies. E x -trapolating from the IRAS 60 /um counts (out to z < 0.3) has always underpredicted the observed S M G 850 / /m number counts. This is direct evidence that the number of 850 /um sources per comoving volume is hundreds of times higher than i n the local Universe and 4.4. MODELS AND CUMULATIVE SOURCE COUNTS 138 implies significant evolution (see fig. 11 in L i l l y et al . 1999). A s a direct consequence of the observed S M G number counts, modelling this evolu-t ion has been a major challenge for theories of galaxy formation and evolution. Current semi-analytic models (e.g Baugh et al . 2005; Somerville 2004) cannot reproduce this sub-stantial population of dusty starburst galaxies at high redshift without the addition of new ingredients or assumptions. For example, Kaviani , Haehnelt & Kauffmann (2003) find that the observed number of S C U B A galaxies can only be reproduced wi th the presence of extended cold dust in roughly normal galaxies. A G N feedback is the main new ingredient added to semi-analytic models of Granato (2004) to explain the high redshift massive star bursts observed by S C U B A . A n d the main modification required to the semi-analytic model of Baugh et al . (2005) to reproduce the observed number of high redshift S C U B A galaxies is to assume a very top-heavy ini t ia l mass function ( IMF) during starbursts induced by galaxy mergers. In general, it is difficult to find a unique (non-degenerate) set of parameters matching overvations for current galaxy formation models (van Kampen et al. , 2005). This prob-lem can be overcome by comparing model predictions at high redshifts to observations, since many of the model parameters are constrained by low redshift observations. The S H A D E S differential number counts are better fit wi th a parametric function wi th an intrinsic break. This could indicate an intrinsic turn-over in the underlying luminosity function, which is interesting for several reasons: it can place an interesting upper l imit on the luminosity (and mass) of a high-redshift galaxy, which would in turn help constrain galaxy formation scenarios and help to break any underlying degeneracies in the model parameters. Since S H A D E S has provided differential counts for the first time, new possi-bilities for constraining luminosity evolution models have opened up. Only S M G integral counts have been available up unti l S H A D E S , and integral counts wi l l inherently tend to obscure any structure in the counts and to be strongly correlated wi th neighbouring bins by definition, giving them less power than differential counts wi th an accompanying covariance matrix in model fitting. Un t i l complete redshift information is available for S H A D E S , the only conclusion that can be drawn is that S M G s evolve strongly. 4.4. MODELS AND CUMULATIVE SOURCE COUNTS 139 4.4.7 Comparison of the Two Fields - Evidence for Sampling Variance? The expected sampling variance between the fields can be estimated in the following way. The variance of counts in cells is generally given by (Peebles 1980, eqn. 45.6) where J\f is the number per unit area on the sky, 17 is the solid angle of the cell, w(9) is the angular 2-point correlation function and the integrals are over al l separations 9n between 2 positions. If the size of the fields is much bigger than the correlation length, then one of the integrals can be done trivially, giving where 9 can now be considered as the angle from the centre, say. The term wi th the integral is the excess variance over Poisson. If one is in the power-law regime for w(9), then w{9) = (f l / f lo) - 7 , wi th 7 ~ 0.8 typically (e.g., Roche et al . 1993; Daddi et al . 2000). For simplicity it can be assumed that the area is a circle of radius 9 m a x . In that case the integral gives (27T00 8 /1.2)0^ (with any cut-off at some 9m\n being relatively unimpor-tant). Eventually this wi l l break down, since w(9) goes negative, but it is a reasonable approximation in the power-law regime. Put t ing in il ~ 400 arcmin 2 and AfQ, ~ 60 for S H A D E S , one obtains an R M S scatter in the counts of Measuring the value of the clustering angle, 90, is one of the key goals of S H A D E S , and a careful analysis wi l l be made once the forthcoming redshift distributions (Itziar et a l . and Clements et al . , i n preparation) are included. A s an example one can see that 9Q ~ 10 arcsec leads to an R M S which is twice that expected from Poisson fluctuations alone. (4.4) (4.5) c r ( A A ) ~ ( A ^ ^ 1 / 2 x ( l + 0 . 5 (V l (4.6) 4.5. SUMMARY AND FUTURE PROSPECTS 140 One might ask what constraints on 90 can be obtained from comparing the number of sources per square degree found in the two S H A D E S fields. In Section 4.4.1 189 ± 26 sources d e g - 2 m J y - 1 at S = 5 m J y were found in the L H and 136 ± 24 sources deg~ 2 m J y - 1 were found in the S X D F . The uncertainties are essentially Poisson, and are therefore underestimated by a factor ^ o ) = (l + 0 . 5 ( 0 0 / l T ) 1 / 2 if clustering is important. F i g . 4.15 is a plot of the likelihood to observe a difference, AN between the number counts in the two fields which is larger than the one observed here as a function of clustering angle, 9Q. van Kampen et al . (2005) estimate that for surveys like S H A D E S , 90 might range from 5 arcsec (for a hydrodynamic model 2 ) to perhaps 20 arcsec (for a high mass merger model 3 ) . Notice that the likelihoods in F i g . 4.15 remain wi th in the central 68 percent region even over a broader range of 90 than is anticipated, corresponding to values of T running from 1 to ~ 4. Thus, for this particular comparison one cannot provide even an interesting 1 a constraint on the clustering angle. 4.5 Summary and Future Prospects This is the first instance that a S C U B A data-set has been subjected to a detailed com-parison of differing independent reductions. A s a result, S H A D E S has produced the most robust and reliable submillimetre-selected source catalogue to date. In terms of S C U B A data reduction, it has been learned that using monthly average F C F s is just as good as using nightly calibration observations, but wi th the advantage of less time lost to cali-brat ion observations. Also, using larger pixels (3 arcsec as opposed to 1 arcsec pixels) to make maps of these data does not seem to increase the centroiding uncertainty in the positions of detected sources. 2 A hydrodynamic simulation includes collisionless non-interacting dark matter, gas, star formation and galaxy fragments that can heat or cool and evolve through gravitational interaction. 3Obscured star-forming S C U B A galaxies are produced by a violent rapid merger of two galaxy-sized haloes in this model. 4.5. SUMMARY AND FUTURE PROSPECTS 141 Figure 4.15: The likelihood that fluctuations would lead to a larger difference in the density of 5 m J y sources than has been observed between the L H and S X D F regions is plotted against clustering angle, 9Q. Even though the run of do which is plotted is broader than the range anticipated from physical models, the likelihood values al l lie in the central 68 per cent of the distribution. M i l d clustering is a slightly better fit to the data than no clustering (60 = 0), but these data do not provide an interesting constraint on clustering amplitude, even at the 1 a level. 4.5. SUMMARY AND FUTURE PROSPECTS 142 The S H A D E S survey is the final legacy of S C U B A , being the largest extragalactic survey undertaken to investigate the nature and redshift distribution of a complete and consistent sample of > 100 S M G s . Here, the 850 / im source catalogues and number counts (differential and integral) are presented using information from four independent reductions of the data, complete to about 720arcmin 2 , down to an R M S noise of ~ 2.2 mJy . 3 a upper limits to the 450 / i m flux densities of each S H A D E S source are also provided. W i t h approximately double the area of al l blank-field surveys combined, this work has produced the most robust submillimetre source catalogue for multi-wavelength studies, as well as the most accurate measurement of S M G number counts. In the near future, the remaining 7 per cent of the S H A D E S data that was not included in the preceding analysis wi l l be reduced and combined wi th the current maps and the source catalogue wi l l be updated. The maps and catalogues that have resulted from this work, in combination wi th multi-wavelength measurements from deep radio, far-, mid-, and near-infrared, optical and X- ray imaging, wi l l yield the photometric redshifts necessary to investigate the S M G contribution to the cosmic star-formation history of the Universe and to discover the true nature of the S M G population. It is found that the differential counts are better fit wi th a broken power-law or a Schechter function than a single power-law, the location of the break in the source counts being at several mJy. Using the ratio of the counts between the two S H A D E S fields, a useful constraint on S M G clustering cannot be made. Overall , the increased accuracy of the source counts due to the new measurement by S H A D E S wi l l allow us to study the evolutionary nature of S M G s in much more detail than has previously been possible. Further work on the S H A D E S data wi l l include a P(D) fluctuation analysis (which should be relatively straightforward because of the fairly uniform noise), and clustering estimates (again, significantly easier for S H A D E S than for previous surveys), as well as follow-up studies focussed on estimating redshifts and determining luminosities and other physical properties for the sample. Together these wi l l provide much tighter constraints on galaxy evolution models. Note that wider surveys, such as those planned for S C U B A -4.5. SUMMARY AND FUTURE PROSPECTS 143 2, the L M T , Planck or Herschel, w i l l be able to place better constraints on the bright end of the number counts, since these S H A D E S maps are insufficiently wide to detect rare bright S M G s . O n the other hand, deeper surveys, such as those also planned for S C U B A - 2 , are needed to push into the J C M T ' s confusion regime, and eventually A L M A wi l l provide the angular resolution which is required to study the morphologies of these S M G s at submillimetre wavelengths. 144 C H A P T E R 5 S H A R C - I I R E S U L T S 5.1 Introduction Now that a large robust sample of S M G s has been obtained through S H A D E S , S H A R C - I I photometry can be used to determine some of their important physical properties such as the dust temperatures, luminosities, dust masses and contribution to the star formation rate of the Universe. In the rest frame, the S E D of dusty galaxies peaks in the range 60-120 /xm due to the re-emission of absorbed o p t i c a l / U V radiation from intense regions of star formation at IR wavelengths (see e.g., Sanders k. Mirabe l 1996 and references therein). The shape of this S E D is generally well described by a modified thermal blackbody or 'greybody' spectrum, wi th an intrinsic dust temperature in the range 30-80 K (Dunne et al. , 2000). A modified blackbody's shape is determined by the dust temperature, Td, and dust emissivity, /3 (see Bla in et al. 2002). The simplest greybody is a blackbody function Bu oc v3 /[exp(hi>/kT) — 1] multiplied by an emissivity function e oc i/P, where /3 lies in a physically plausible range of 1-2 1 (Hildebrand, 1983). This yields a functional form for the S E D : Su = eBu oc u3+l3/[exp(hu/kT) - 1]. (5.1) Since S H A R C - I I samples close to the S E D dust emission peak at z ~ 2, the com-bination of 350 /mi , longer wavelength submillimetre and radio photometry are able to accurately constrain galaxy luminosities at these redshifts. The monochromatic intrinsic ^ l a i n et al. (2002) state that at low frequencies, scattering theory predicts that /? approaches 2 and that at high frequencies, a f3 near 1 is consistent with the absorption of opt ica l /UV radiation from the I S M and the trend seen in the interstellar extinction curve of Calzetti et al. (2000). 5.1. INTRODUCTION 145 luminosity, Lu> (at an emitted frequency u') as a function of the observed flux density, Sv (at an observed frequency of u), is given by equation 3.87 in Peacock (2003): ~ 7TT7T' ( 5 , 2 ) where D^ is the luminosity distance to the galaxy's redshift which is given by eqns. 3.91 and 3.76 in Peacock (2003): DL = (l + z)R0r, (5.3) where R$r = [<?-£- , d z , J 0 H ° v / ( i -n 0 ) (n-2 ) 2 +fiv ,o+n m ,o ( i+2 ) 3 +^r ,o ( i+z) 4 for a spatially flat Universe. RQ r is the comoving radius, H0 is the Hubble constant, c is the speed of light, Qo is the present-day total density of the Universe, f2m io is the present matter density of the Universe, f2v>o is the present vacuum density of the Universe, and n r ] 0 is the present radiation density of the Universe. The total far-IR luminosity for each S M G is calculated by integrating the fitted S E D (cf. equation 3.89 in Peacock 2003): Ltot = L F m = 4irDlStoU (5.4) where Stot = / Svdu is the total observed flux density. Using the results from Equa-t ion 5.4 directly, one can calculate the S F R using eqn. 12 from De Breuck et al . (2003), as-suming that the far-IR luminosity is predominantly powered by star-formation (i.e., neg-ligible contribution from an A G N ) : M S F = 5UF 6SB ( L F I R / 1 0 1 0 LQ) M 0 y r " 1 , (5.5) where <5MF depends on the mass function of the underlying stellar population (i.e., the mass composition of the stellar population) and C>SB is the efficiency of the starburst (i.e., the fraction of the stellar radiation that is absorbed and re-radiated by the heated dust). SUF is probably between 0.8 and 2 (see e.g., Omont et al . 2003; Kennicut t 1998). 5MF = 1 and 5$B = 1 are assumed here. Even though 5SB is likely to be less than 1 (as 5.1. INTRODUCTION 146 De Breuck et al . 2003 note) the S F R s implied by the data are st i l l extreme, indicating that these systems are undergoing a major phase of obscured star production at high redshifts. 850 / m i flux density measurements sample the Rayleigh-Jeans side of the S E D and can thus be used to estimate the dust mass, M j , in these obscured star-forming galaxies. The flux density of a galaxy at an observed frequency, u, is given by the following relation (see B la in et al . 2002): SV = BVI{T)KU, MD (1 + z)/Dl (5.6) where D L is the luminosity distance and BV> is the Planck function (cf. Equat ion 5.1) evaluated at the emitted frequency, v' = 1/(1 + 2 ) . The quantity KV is the frequency-dependent mass-absorption coefficient (or 'effective area' for blackbody emission by a certain mass of dust) and a value of rt850Mrn = 0.15 m 2 k g - 1 is adopted and was extrap-olated from an average rti25M m = 2.64 m 2 k g - 1 from Dunne, Eales & Edmunds (2003) assuming f3 = 1.5. Note that KV is uncertain by a factor of a few (see B l a i n et al . 2002 and references therein). More complex S E D modelling was not attempted (e.g., fitting 2-temperature dust components; Dunne & Eales 2001), since this requires too many parameters to be con-strained using the typically 2-3 photometric points which exist for each S M G . The Wein side of the spectrum (high frequencies; when kT/hv <C 1) is sometimes modified by a power-law of the form Sv oc u~a to make up for the increase in optical depth i n this regime of the spectrum and to agree wi th observed SEDs (see Bla in , Barnard & Chapman 2003). Kovacs et al . (2006) find that S E D models incorporating the full optical depth term (S„ = [1 — exp(—T„)] BU, where rv is a frequency-dependent optical depth of the cloud) or even a distribution of temperatures and power-law W i e n tails do not provide a better description of the data. Here, the Wein side of the spectrum is not very well sampled - only 24 / i m photometry is available for most of the S H A D E S sources and the addit ion of a mid-IR power-law to the S E D (mentioned at the beginning of this para-graph) would require 2 additional parameters (a slope and a normalisation) for only one 5.1. INTRODUCTION 147 additional data point. Thus only two parameters are needed to sufficiently describe the complete far-IR S E D : T and /3, which describe the global properties of the dust. T determines the location of the S E D peak and B determines the power-law index of the Rayleigh-Jeans port ion of the S E D . The overall normalisation of the S E D (i.e., luminos-ity) must also be fit. The predominant problem in fitting greybody SEDs to far-IR photometry is the de-generacy between T and /3, as seen in F i g . 5.1. The frequency of the S E D peak is roughly proportional to BT and therefore this product remains approximately constant, resulting in an inherent degeneracy in finding values that describe the underlying physical prop-erties of the dust grains responsible for the far-IR emission. The consequences for the derived far-IR luminosity are not dire - L F I R only varies by 5-10 per cent (Bla in et al . , 2002) across the expected T-B parameter space. A t high redshifts (z ~ 2-3) the peak of a typical S M G S E D (T d - 35-60 K ; B l a in et al . 2002) lies wi th in the 350/ im observing window. So observations at these short wave-lengths are crucial to determining the intrinsic dust temperatures, far-IR luminosities and star-formation rates in dust-obscured intense star-forming systems. Determining such physical parameters from S E D fitting is usually done once a redshift has been de-termined spectroscopically (since there is an inherent degeneracy between the redshift and dust temperature in S E D fitting). Many of the S H A D E S sources, however, do not yet have spectroscopic redshifts as these observations are time-consuming and st i l l ongoing. The assumed intrinsic simple thermal S E D shape of al l S M G s offers a hope for deter-mining redshifts photometrically using far-IR colour information. Determining the S E D peak has proven useful for photometric redshift estimation (when spectroscopic redshifts cannot be obtained), although Bla in , Barnard & Chapman (2003) warn that by assum-ing a narrow range of S E D s wi th little range in dust temperatures (e.g., Hughes et al . 2002), the error in the photometric redshifts might be underestimated, since the redshift and dust temperature parameters are very degenerate. The reason for the degeneracy is apparent in that the S E D peak comes from the vjT term in Equat ion 5.1. Redshifting the spectrum by (1 + z) is equivalent to altering the temperature by the same amount. 5.1. INTRODUCTION 148 3.0 2.5 CO. 2.0 1.5 1.0 " i — i — i — r i i i i j i i I i i i i I i i i i I i i i I 1 1—i—1_ 10 15 20 25 TJK] 30 35 40 Figure 5.1: Plot of dust temperature versus (3. The contour represents a fixed value of x2 for a greybody fit to the photometry of L O C K 8 5 0 . 4 for parameters j3 and T j . A l l points on the contour are an equally good fit to the data, demonstrating the degeneracy between the two parameters. 5.2. 350 /um FLUX DENSITIES OF THE SHADES GALAXIES 149 Therefore, as pointed out by Eales et al. (1999), it is difficult to determine if an S M G is hot and distant or cold and nearby without breaking the degeneracy wi th a spectro-scopic redshift. If the dust temperatures and redshifts cannot be adequately determined this has obvious serious consequences for relative contribution of S M G s to the global star-formation rate over the history of the Universe (Blain et al . , 2002). A follow-up observing campaign has been carried out to map several S H A D E S sources wi th S H A R C - I I in order to help wi th photometric redshift determinations (Aretxaga et al . in preparation), and in order to help constrain S E D shapes in order to probe the physics (i.e., dust temperature, far-IR luminosity, dust mass, and star-formation rates) of these intense star-forming galaxies at high redshifts. In Section 5.2 350 /ma counterparts to the S H A D E S galaxies are identified. For those sources for which no counterpart is detected, a flux measurement is provided (which can be used to derive an upper flux density l imi t ) . A comparison of complementary work by Laurent et al . (2006) and Kovacs et al . (2006) and photometry for additional S H A R C - I I observed S H A D E S sources is also provided. In Section 5.3, trends wi th other multi-wavelength data are explored and summarised. Finally, a simple modified blackbody is fit to the SHARC-II-detected S M G s in order to estimate dust temperatures, far-IR luminosities, star-formation rates and dust masses for the S H A D E S sources wi th S H A R C - I I photometry in Section 5.4. A summary and future prospects are given in Section 5.5. 5.2 350 rim Flux Densities of the SHADES Galaxies Since detections in the S H A D E S and S H A R C - I I maps are low S / N and the beam sizes are relatively large, there is an inherent positional uncertainty associated wi th every detection. In submillimetre astronomy, counterpart identification is usually performed by using Poisson statistics to find the probability of an object being associated wi th the S M G at random, given the surface density of the counterpart population and a search radius (e.g., Ivison et al . 2002). The probability that a counterpart wi th a population surface density £ is found within a search radius 9 of an S M G purely by chance is given 5.2. 350 fim FLUX DENSITIES OF THE SHADES GALAXIES 150 by: P r a w = l - e - ^ . (5.7) Ivison et al . (2002) and Ivison et al . (in preparation) adopt an 8 arcsec search radius around the 850yum position when searching for radio counterparts to S C U B A galaxies 2 , since this search radius is found to minimise the rate of false counterpart identifications empirically (see Pope et al . 2006). Ivison et al . (2002) and Ivison et al . (in preparation) also correct the raw Poisson probability of Equation 5.7 using the method of Downes et al . (1986) to factor in the effect of using catalogues wi th a finite depth. A value of corrected Poisson probability of P r a n < 0.05 is considered a secure or robust 'true' association and keeps the fraction of false associations low. In the spirit of Ivison et al . (in preparation), the relative probabilities that a given source is the actual counterpart or is a chance alignment are calculated. The radial positional uncertainty can be found by comparing the 850 / i m determined positions wi th precise radio positions. Ivison et al . (in preparation) quote a positional uncertainty of 3.2 arcsec in each of R A and D e c , for a combined radial uncertainty of \/2 x 3.2 arcsec ~ 4.5 arcsec. The positional uncertainty of S H A R C - I I observations is dominated by the telescope pointing uncertainty which is typically ~ 2-3 arcsec. The combination of these uncertainties and a S / N cut for S H A R C - I I detections come into play in choosing an appropriate search radius. The quadrature sum of the 2 a uncertainties of each of these two contributions yields a search radius of ~ 10 arcsec and should include 86 per cent of al l genuine S H A R C - I I identifications since the distribution of radial offsets is given by: r e x p [ - r 2 / 2 c r 2 ] , (5.8) where r is the radial positional offset and cr is a measure of the positional uncertainty. Equat ion 5.8 integrates to the following function: 2Ivison et al. (in preparation) identify counterparts to SMGs in the radio, whose positional uncertain-ties are negligible (i.e., subarcsec) compared with those of the SCUBA galaxies (typically ~ 4-5 arcsec). 5.2. 350 /im FLUX DENSITIES OF THE SHADES GALAXIES 151 1 - exp[-r 2/2], (5.9) which is the cumulative distribution of radial offsets. The basic calculation is to balance the odds that a source is as far as r from the nominal position against the odds that a circle of nr2 contains a background source (or for SHARC-II, a noise bump). A search radius of 10 arcsec is adopted in order to balance identifying the majority of the real 350 /um counterparts while keeping the probability of making a false identification to a minimum. The fraction of time a false identification will be made on average using this search radius and some adopted S/N threshold was checked using Monte Carlo techniques on the actual data, since the number density of sources at 350/xm is unknown. First, an area with radius 10 arcsec around each SHADES source is masked out so that any real counterpart will not contaminate the test3. Each S/N (from 1-4 a) and search radius (from 2-15 arcsec) combination is examined by selecting a random position on each map and searching for a detection in the map within the given search radius above the designated threshold. This is repeated 10,000 times over all the SHARC-II maps. Individual maps yield slightly different results, but on average it is found that using a search radius of ~ 10 arcsec and S/N > 2.5 finds a SHARC-II source at random less than 5 per cent of the time. This result is much more sensitive to the S/N of the counterpart than to the search radius, i.e., increasing the search radius more or less arbitrarily seldom leads to more counterparts at a given S/N since the maps are very small and there are typically only a few detections > 2.5 o in each map. The final composite 350 /um catalogue compiled from detections in the SHARC-II maps is comprised of 72 sources > 2 a, 32 sources > 2.5 a, 9 sources > 3 a, and 1 source > 4 a. Note that the LOCK44/45 field covered 2 SHADES source candidates from a preliminary list, although these sources were eliminated from the SHADES catalogue since they were deemed not to be robust, and thus this field is not used for counterpart searching or included in the estimate above. The total area of the maps (after omitting 3Recall that this survey has mapped regions of sky where there is expected to be a high probability of detecting a SHADES-associated SHARC-II source, i.e., it is not a blank-field survey. 5.2. 350 /ira FLUX DENSITIES OF THE SHADES GALAXIES 152 the field aforementioned) that are used for making S H A D E S / S H A R C - I I associations is 160,049 arcsec 2. Therefore, 0.14 > 2 a sources per search area have been detected using a radius of 10 arcsec. Calculating the Poisson probability P =1 — e~M, where ji = 0.14, tells us that any > 2 a detection is about 13 per cent likely to be a chance association (cf. Equat ion 5.7). If the minimum S / N threshold is pushed up to 2.5 a, then P decreases to only 6 per cent for these data (consistent wi th what was found from the Monte Carlo simulations described earlier). In principle, one should correct for the fact that special regions of sky that are known a priori to contain 850 /um-selected sources have been mapped at 350 lira. However, this effect is ignored since it was found to be negligible (tenths of a percent). A search radius of 10 arcsec and S H A R C - I I counterpart S / N cut of 2.5 cr is adopted. It is expected that 86 per cent of the time on average, a 350 lira counterpart w i l l lie wi th in 10 arcsec of the S H A D E S position, and the chance of making a false identification wi l l be less than 5 per cent on average. This set of criteria yields 7 S H A R C - I I detections of S H A D E S sources. See Table 5.1 and thumbnail images in F i g . 5.2. O n average, one genuine association might be missed if it lies outside of the search radius, and one counterpart might be mis-identified (i.e., a random association). The positional offsets of the claimed detections are consistent wi th a Gaussian error distribution (where 1 a corresponds to ~ 61 per cent here); 5/7 (71 per cent) of the detections lie wi th in the 1 a search radius of 5 arcsec. See F ig . 5.3. No trend is seen of decreasing positional offset wi th increasing S / N ratio of the 7 associations, though this might not be surprising given the low number statistics and the small dynamic range in S / N . One additional source (referred to hereafter as LOCK350 .1 ) is detected in the survey in map L O C K 2 6 / 3 2 (see F ig . 2.9) at 3.9 a and is not associated wi th a S H A D E S source since its location is well outside the adopted 10 arcsec search radius. Based on Gaussian noise statistics and the number of independent beam sizes in the survey area wi th noise less than 2 0 m J y (chosen arbitrarily, since higher S / N detections in noisier regions are more likely to be spurious), about 0.1 false positives are expected on average at a S / N of 3.9; L O C K 3 5 0 . 1 may therefore be real. The position and flux density of L O C K 3 5 0 . 1 5.2. 350 fj,m FLUX DENSITIES OF THE SHADES GALAXIES 153 are RA=10 h 52 m 43?2 , Dec .=57°23 '9" (J2000) and 32.8 ± 8 . 3 mJy, respectively. Addi t iona l sources unassociated wi th S H A D E S sources at lower S / N (> 3 a) were uncovered, though the number density of detections at such a low threshold is consistent wi th the expected number of false positives and are therefore likely to be spurious. A s a reality check, the maps were turned upside-down and sources were extracted in the same way as for the positive map (see Section 2.3.4; L O C K 4 4 / 4 5 is again omitted from the exercise for consistency). The corresponding composite negative catalogue can be used to test if real associations are being found or just noisy peaks in the SHARC-II maps. There is a slight excess of positive detections in the maps at S / N > 2 compared wi th negative detections: 66 sources > 2 a, 28 sources > 2.5 a, 7 sources > 3 a, and 0 sources > 4 a are found in the negative maps (cf. numbers in the positive composite catalogue). Using this list, counterparts to S H A D E S sources are searched for i n the same way using a S / N threshold of 2.5 and search radius of 10 arcsec and no 'negative' counterparts are identified. 5.2. 350 / m i FLUX DENSITIES OF THE SHADES GALAXIES 154 LOCK850.1 LOCK850.3 LOCK850.4 -5 0 5 Offset [arcsec] -10 -5 0 Offset [arcsec] 5 0 5 Offset [arcsec] Figure 5.2: 30" x 30" S H A R C - I I postage stamp images of S H A D E S sources observed at 350 /mr centred on the 850 /mr positions. Each thumbnail is extracted from a map that has been convolved wi th the beam yielding a final resolution of 12.4 arcsec F W H M . The images are displayed on the same flux density scale for comparison and the colour bar is given on the last page of the figure. L O C K 8 5 0 . 6 , 63 and 77 lie on the map edges, as indicated by a jagged white region in each of those plots. See Table 5.1 for the corresponding flux densities, noise estimates and S / N values. 5.2. 350/im FLUX DENSITIES OF THE SHADES GALAXIES 155 Figure 5.2: (continued) 5.2. 350yum FLUX DENSITIES OF THE SHADES GALAXIES 156 SXDF850.1 SXDF850.3 SXDF850.8 [mJy beam' 1 ] Figure 5.2: (continued) pi Table 5.1: S H A R C - I I measured 350 yum flux densities of S H A D E S sources. F lux densities quoted represent the highest S / N detection wi th in a 10 arcsec search radius of the S H A D E S catalogue position. Coordinates are only given for detections. Non-detections (which are biased high) are given in parentheses; measurements were also made on the S H A R C - I I maps at the S H A D E S 850/ im and radio positions (which are biased low). The best possible flux measurements for each S H A D E S source are provided, however sources marked 'Obs. inc.' indicate that the maps are left out of the general analysis since they are insufficiently deep (see text). SHADES ID SHARC-II position offset 5350 Comments R A Dec. brightest pixel (< 10") at 850 jum position at robust radio position (J2000) (J2000) (arcsec) (mJy) (mJy) (mJy) LOCK850.01 - - (~ 4.3) (23.0 ±21.2) 12.7 ±22.2 22.6 ±21 .4 see Laurent et al. (2006) LOCK850.03 10 h52m38f70 57°24'37?36 ~ 4 67.1 ±18 .5 (3.6 a) 59.7 ± 18.0 65.0 ± 18.2, 58.2 ± 18.0 Obs. inc.; Kovacs et al. (2006) LOCK850.04 10 h52m04?42 57°26'54^'34 5:0 37.3 ± 9 . 1 (4.1 a) 21.0 ± 9 . 2 18.9 ± 9 . 3 , 33.2 ± 9 . 1 LOCK850.06 - - (~ 10) (57.0 ± 37.6) 1.8 ±43 .1 23.6 ± 3 9 . 1 edge of SHARC-II map LOCK850.10 - - (~ 10) (36.2 ± 12.0) 14.9 ± 11.9 19.4 ± 12.2 LOCK850.15 - - (~ 4.2) (9.8 ±55.7) -32.7 ±53 .7 -8.3 ±52 .5 , 6.9 ±54 .9 Obs. inc. LOCK850.16 - - (~ 4.9) (38.6 ± 15.8) (2.4 a) 26.6 ± 15.5 33.3 ± 15.6 LOCK850.21 - - (~ 6.5) (25.1 ± 13.2) 14.3 ± 12.9 -LOCK850.22 - - (~ 10) (13.1 ±15.6) -1.3 ±15.6 -LOCK850.26 - - (~ 4.5) (18.3 ±8 .8) (2.1 a) 6.9 ± 8 . 5 13.4 ± 8 . 6 LOCK850.28 10 h52m57?86 57°30'59'.'67 10.2 34.9 ± 11.7 (3.0<r) 8.3 ±11.8 (29.6 ± 11.6) LOCK850.33 10h51m55?82 57° 23'11" 25 1.4 24.7 ± 8 . 4 (2.9 CT) 21.5 ± 8 . 4 20.4 ± 8.4 LOCK850.41 - - (~ 7.5) (42.5 ± 25.4) 15.9 ± 24.4 12.4 ±24 .2 , 34.8 ±24 .8 see Laurent et al. (2006) LOCK850.47 - - (~ 9.4) (24.4 ± 20.9) -8.3 ±21.2 - Obs. inc. LOCK850.48 - - (~ 6.5) (24.3 ± 13.5) 9.9 ± 12.3 -LOCK850.63 - - (~ 10) (52.3 ±29.1) 9.9 ±31.4 15.6 ± 2 9 . 1 LOCK850.64 - - (~ 10) (17.4 ± 12.4) -5.1 ±12.8 -LOCK850.77 10h51m56?22 57° 22'09'.'76 6.3 62.1 ±24.6 (2.5 a) 9.9 ±18 .7 -0.2 ± 17.9 edge of SHARC-II map SXDF850.1 - - (~ 6.2) (24.5 ± 13.9) 15.9 ± 14.5 15.9 ± 14.6 SXDF850.3 02 h17m41?95 -05°56'26"26 3.4 39.3 ±14 .3 (2.7 a) 23.1 ± 14.1 23.1 ± 14.1 SXDF850.8 - - (~ 6.3) (24.5 ± 14.1) 10.5 ± 14.1 18.1 ± 14.5 SXDF850 . i l 02 h17m24?81 -05°59'37'.'19 4.6 46.6 ± 15.0 (3.1a) 26.6 ± 14.2 22.2 ± 14.1 SXDF850.17 - - (~ 10) (18.6 ±21.0) -13.0 ± 17.3 -SXDF850.119 - - (~ 7.6) (23.8 ± 14.9) 13.0 ±15.3 0.8 ± 15.4 co Cn o 3 to to CO O to I to 5 to to CO to CO 5.2. 350 /im FLUX DENSITIES OF THE SHADES GALAXIES 158 For the S H A D E S sources for which a S H A R C - I I counterpart is not found, a useful measurement of its flux can sti l l be made in order to place an upper l imit on its flux at 350 /mi , to be used as an additional constraint in the determination of photometric redshifts or physical S E D properties. In general, the non-detection of a S H A D E S source at 350 / m i could be due any of the following reasons: (1) The S H A D E S source could be spurious, which seems unlikely since the S H A D E S catalogue has been carefully con-structed to be the most robust submillimetre catalogue ever compiled; (2) the S H A D E S source could lie at a redshift in excess of about 3, this being more likely if there is also no radio counterpart, since these radio data are sufficiently deep to obtain a large frac-t ion of counterparts for S M G s at redshifts less than about 3 (see Ivison et al . 2005); (3) the S H A D E S source could be intrinsically less luminous and/or have a different S E D shape, making the peak of the S E D escape detection at 350 /mi . Deep multi-wavelength photometry (especially from Spitzer) w i l l be able to help constrain S E D shapes where S H A R C - I I cannot. To understand the selection biases at 350 /mi , one needs to investigate precisely how flux densities are extracted from the S H A R C - I I maps. A s was discussed in Section 4.2.8, one can perform several different flux measurements, each of which is biased in some way: (1) measure the flux density of the brightest pixel wi th in 10 arcsec of the 850 / im SHADES-de te rmined position, a measurement which wi l l be biased high on average since one is likely to find nearby brighter noise (and sometimes unassociated) peaks (Kovacs et al . 2006 and Laurent et al . 2006 adopt this approach for non-detections) ; (2) measure the 350 / m i flux density of each object at the 850 / i m position, a measurement which wi l l be biased low on average because of the uncertainty in the true location of each object due to the large beam sizes and low S / N in the maps; (3) measure the 350 / m i flux density of each object at the radio position. This last approach is complicated if there is more than a single radio counterpart identified for a given S H A D E S source. This mea-surement is less biased on average than choice 2, since there is less combined uncertainty in the true source position when using the radio positions to measure the 350 /um flux densities. However, not al l of the S H A D E S sources examined wi th S H A R C - I I have radio 5.2. 350 / i m FLUX DENSITIES OF THE SHADES GALAXIES 159 Figure 5.3: The cumulative distribution of radial positional offsets between the S H A R C -II positions and corresponding 850//m S H A D E S positions of the 7 statis-tically secure 350 / /m counterpart associations. The curved line shows the predicted distribution (cf. Equation 5.9), assuming that the positional un-certainty is given by the a = 5 arcsec (cf. the adopted 2 a search radius is 10arcsec). The two distributions do not appear to be inconsistent wi th each other. 5.2. 350 nm FLUX DENSITIES OF THE SHADES GALAXIES 160 counterparts, so any sample comparison using these flux densities wi l l be incomplete. Therefore, flux densities for the non-detections are measured here using method 1, since this measurement can be performed for al l SHARC-II-non-detected S H A D E S sources in a uniform way. Nevertheless, each of measurements 1, 2, and 3 are given in Table 5.1 for completeness and inter-comparison. One can also see if a significant positive 350 / m i flux density is detected on average for the S H A D E S sources which are individually undetected. 350 / i m flux densities and errors of the 17 non-detected S H A D E S sources are measured on the S H A R C - I I maps at the S H A D E S catalogue positions and averaged together. The choice was made to use the flux density measurement that is biased low on average (method 2) in order to not artificially boost the stacked signal; this is concordant wi th what was done wi th the 450 / i m data earlier in Section 4.2.8. A Gaussian is constructed for each source using the measured 350 / i m flux and error and the product of these Gaussians is taken to produce a new flux density probability distribution for the sample (see F i g . 5.4). The stacked signal for the group of 17 non-detected S H A R C - I I sources is 8.8 (±3 .8 ) m J y (a ~ 2.3 a detection). 10,000 Monte Carlo simulations were run on the S H A R C - I I maps (with the S H A D E S / S H A R C - I I associations masked out) in order to determine that a stacked flux equal or greater in magnitude than the result above would occur less than about 4 per cent of the time on average for sets of 17 randomly selected positions distributed pro-portionately among the maps. The resulting S / N image of the stacked maps centred on the 850 / i m positions of the non-detections also yields a hint of positive flux nearby (see F i g . 5.5), although offset slightly (~ 5 arcsec from the stacking centre. For compar-ison, the stacked image for the 7 S H A R C - I I detected sources gives a stacked signal of 23.7 (±4 .1 ) m J y (a ~ 5.8 a detection) and is offset only by about 1 pixel. The stacked measurement of the non-detections provides a significant statistical detection at the ~ 2 a level, even though none of these sources are individually detected at 350 / im. 5.2. 350yum FLUX DENSITIES OF THE SHADES GALAXIES 161 0.0010 0.0008 •8 2 0.0006 PH • 13 jg 0.0004 0.0002 0.0000 T 1 r Flux [mJy] Figure 5.4: Stacked signal at the 850//m positions of the 17 non-detected S H A D E S sources at 350 / im. Each source's flux and error is represented by a solid Gaussian. The product of these Gaussians is the maximum-likelihood esti-mate of the stacked flux probability distribution of the non-detections and is indicated by the dot-dashed distribution. The vertical dot-dashed line indi-cates the location of the maximum value of the new distribution, indicating a positive stacked signal of 8.8 mJy. The dashed line x = 0 is plotted to guide the eye. The inverse-variance weighted stacked signal of the non-detected sources is 8.8 (±3 .8) mJy (i.e., S/N=2.3). 5.2. 350nm FLUX DENSITIES OF THE SHADES GALAXIES 162 Figure 5.5: Composite stacked beam-convolved S / N map of 17 individual non-detections centred on the 850 pm S H A D E S positions. A clear excess of signal is seen to the lower left hand quadrant, near the centre of the composite map. The S / N of the brightest pixel here is about 3.0, and the S / N of the centre of the map is 2.3. The crosshairs indicate the centre of the 60 x 60 pixelised area (pixels are 1.62 x 1.62 arcsec). The region of the composite map wi th noise < 5 m J y is inside the solid curve and regions outside of this are higher in noise and so any peaks in the map are more likely to be spurious. There is another more significant peak inside the region that is ~ 2.7cr and it is further from the stacking centre (~ 11 arcsec). Note that the negative regions inside the curved region are all > — 2.9 a. Table 5.2: Multi-wavelength photometry of S H A R C - I I observed S H A D E S sources (this work). 850 and 450yum photometry are from this thesis, 1 .4GHz and 24 mn data are from Ivison et al. (in preparation) ('tent.' refers to tentative identifications), 1.1mm and 1.2mm photometry are from Laurent et al. (2005) and Dunlop (private communica-tion; an improved reduction of the Greve et al . 2004 M A M B O data), respectively. In cases where 2 robust radio and/or 24 m n IDs exist for a single S H A D E S source, both are listed. Photometric redshifts are from Tables 3 (sources which have spectroscopic redshifts), 4 and 5 (for those sources without) in Aretxaga et al . (in prepa-ration) and optical spectroscopic redshifts (and are a l l currently under debate) are from: 1. Chapman et al . (2005); 2. Ivison et al . (2005); 3. Greve et al . (2004); 4. Chapman et al . (2003); 5. Swinbank et al . (2005); 6. Chapman et al . (2002). 'no C O ' refers to optical redshifts that have not been re-confirmed wi th C O ob-S H A D E S ID 5 8 6 0 5 4 5 0 Si A G H z S24 S1.1 m m Si.2 m m phot 2 spec 2 (mJy) (mJy) (/Jy) (MJy) (mJy) (mJy) LOCK850.01 8.85 ( ± l ; g ) < 47 78.9 ± 4.7 217 ± 16 4.4 ± 1.3 3.6 ± 0 . 5 2-4 (±J;J) (2.1481-2)2 LOCK850.03 10.95 ( ± } ; | ) < 34 35.0 ± 5 . 2 , 2 5 . 8 ± 4 . 9 183 ± 33,175 ± 2 3 4.8 ± 1.3 4.6 ± 0 . 4 2-6 (±8:?) (3.0361)2, no C O 3 LOCK850.04 10.65 ( ± i ; | ) < 134 32.0 ± 5 . 1 , 7 3 . 0 ± 5 . 0 261 ± 73,179 ± 6 8 - 3.7 ± 0 . 4 1.6 (±8;?) (0.526 or 1.482)2 LOCK850.06 6.85 (±1;1) < 77 15.0 ± 4 . 8 (tent.) 75.1 ± 12.7 - - 3.6 ( ± 0 ; ? ) -LOCK850.10 9.15 (±11) < 365 25.5 ± 6.3 candidate IDs only - - 3.1 (±8:1) -LOCK850.15 13.25 (±H) < 149 43.9 ± 7 . 8 , 61.5 ± 7 . 6 353 ± 20 4.1 ± 0 . 7 2.4 (±8:2) -LOCK850.16 5.85 (±\i) < 67 106.0 ± 6.0 314 ± 24 - 1.8 ± 0 . 5 1.9 (±8;f) (1.1471)2 LOCK850.21 4-15 ( ± l ; g ) < 70 5cr < 30 97.9 ± 14.1 - 1.6 ± 0 . 4 > 1.0 -LOCK850.22 7.55 (±|-1) < 76 5cr < 30 402 ± 21 - - > 2.0 -LOCK850.26 5.85 (±H) < 48 31.4 ± 5 . 2 195 ± 16 - - 3.6 (±8; 8) -LOCK850.28 6.45 (±\l) < 56 candidate ID only candidate ID only - - > 2.0 -LOCK850.33 3.85 (±\i) < 49 51.0 ± 4 . 3 candidate ID only - 2.8 ± 0 . 6 3.6 (±%%) (3.6991-4,2.6862) LOCK850.41 3.85 (±?;§) < 16 43.6 ± 4 . 7 , 22.1 ± 4 . 8 651 ± 46,475 ± 37 4.0 ± 1.3 2.4 ± 0 . 5 3-4 (±8:5) (0.6891)2-6 LOCK850.47 3.55 (±l:D < 21 - candidate ID only - - > 1.5 -LOCK850.48 5.45 ( ± | ; i ) < 79 candidate ID only 203 ± 17 - 1.6 ± 0 . 4 2.4 (±8;f) -LOCK850.63 3.65 (±\i) < 50 22.6 ± 4 . 8 ' 236 ± 1 7 - - 2-6 (±81) -LOCK850.64 5.85 ( ± § ; 5 ) < 95 candidate IDs only candidate IDs only - 1.7 ± 0 . 4 > 1.5 -LOCK850.77 3.25 ( ± } ; | ) < 39 15.5 ± 4 . 4 (tent.) 51.7 ± 13.1 - - 2-6 (±8;?) -SXDF850.1 10.45 (±\i) < 65 54.3 ± 9 . 7 candidate ID only - - 2-6 (±83) SXDF850.3 8-75 (±U) < 81 77.2 ± 9 . 3 no ID - - 2.1 (±8;?) -SXDF850.8 6.05 ( ± } ; | ) < 45 52.0 ± 9 . 5 candidate ID only - - 2.6 (±J;f) -SXDF850. i l 4.55 ( ± i ; § ) < 79 56.8 ± 10.0 195 ± 47 - - 2.4 (±81) -SXDF850.17 7.65 ( ± \ - 7 7 ) < 71 - candidate ID only - - > 2.0 -SXDF850.119 4.55 (±l-\) < 70 38.0 ± 9 . 7 (tent.) 784 ± 47,275 ± 47 - - 2-1 (±8:1) -to co Cn O •5 3 3 % to ft Co to CO I to CO to co 5.2. 350 /ira FLUX DENSITIES OF THE SHADES GALAXIES 164 5 .2 .1 C o n s t r a i n t s o n 350 /jm S o u r c e C o u n t s Even though the S H A R C - I I data acquired here are not blank-field observations (i.e., only places where S H A R C - I I sources were expected to lie were observed), at the very least crude estimates of the limits of the 350 /ira source counts can be made. A n upper l imit can be placed using the number of detections acquired in the observed area; one would expect to do worse than this in a blank-field survey since here known S M G s were observed. Given a total observed area of 48.3 arcmin 2 and 7 350 / i m detections above a flux density of S350 — 25mJy , an upper l imit can be placed on the source counts of N(> S) < 500 d e g - 2 . A lower l imit on the source counts can be estimated by applying the S H A R C -II detection rate of S H A D E S sources to the whole S H A D E S area; one would expect to do at least as well in a blank-field search. Given a S H A R C - I I detection success rate of 7/24 ~ 0.25 and a total of 120 S H A D E S sources found in ~ 720 arcmin 2 , a lower l imit can be placed on the source counts of N(> S) > 2 0 0 d e g - 2 . These results are plotted in F i g . 5.6, along wi th a prediction of the 350 jira source counts derived by Lagache et al . (2004) using a phenomenological model that constrains the IR luminosity function evolution wi th redshift (and which fits al l existing source count data from the mid-IR to the submillimetre). The limits derived here are consistent wi th the prediction from Lagache et al . (2004). Large surveys planned wi th Herschel, S C U B A - 2 and Planck wi l l be able to provide further constraints to the source counts at shorter submillimetre wavelengths of 350 and 450 /ira. 5 .2 .2 S u m m a r y o f O t h e r S H A R C - I I D a t a o f S H A D E S Complementary S H A R C - I I observations of S M G s (including several S H A D E S sources) have been performed by Laurent et al . (2006) and Kovacs et al . (2006) and are now sum-marised and put into context wi th this thesis. Kovacs et al . (2006) conducted follow-up observations of S C U B A sources wi th radio identifications and optical spectroscopic red-shifts. 7/15 sources were picked based on predicted bright 350 fim flux densities. The sample is therefore biased to single radio-identified, bright (> 5 m J y ) , 850/xm-selected 5.2. 350 /mi FLUX DENSITIES OF THE SHADES GALAXIES 165 10 I i i i i i i i i I i i i i i i i i I i i i i—i i i i I 0.1 1.0 10.0 100.0 Observed 350 urn Flux Density S [mJy] Figure 5.6: Cumulative 350 /mi source counts. The solid line is a prediction of the source counts from Lagache et al . (2004) using a phenomenological model that con-strains the IR luminosity function evolution wi th redshift. The arrows are upper and lower l imits on the source counts based on this work (see text) and are consistent wi th the source count prediction. 5.2. 350/im FLUX DENSITIES OF THE SHADES GALAXIES 166 S M G s . O f the 15 objects, 12 are detected; 4/15 are S C U B A - 8 m J y Survey sources (Scott et al . , 2002), and hence also L H S H A D E S sources: L O C K 8 5 0 . 3 ; L O C K 8 5 0 . 1 4 ; L O C K 8 5 0 . 1 8 ; and L O C K 8 5 0 . 3 0 . 3 of these are detected: L O C K 8 5 0 . 3 ; L O C K 8 4 0 . 1 4 ; and L O C K 8 5 0 . 3 0 . Laurent et al . (2006) performed follow-up observations of 17 Bolo-cam 1.1 mm-selected L H galaxy candidates wi th S H A R C - I I . Of the 17, only 10 are de-tected. 8/17 of these Bolocam sources are associated wi th S H A D E S sources: L O C K 8 5 0 . 1 ; L O C K 8 5 0 . 2 ; L O C K 8 5 0 . 3 ; LOCK850 .12 ; LOCK850 .14 ; L O C K 8 5 0 . 2 7 ; L O C K 8 5 0 . 4 1 ; and L O C K 8 5 0 . 7 6 4 (see Laurent et al . 2005 for counterpart identifications 5. 6 of these are claimed detections: L O C K 8 5 0 . 1 ; L O C K 8 5 0 . 2 ; L O C K 8 5 0 . 3 ; LOCK850 .12 ; L O C K 8 5 0 . 1 4 ; and L O C K 8 5 0 . 4 1 . 7 new S H A R C - I I detections of S H A D E S sources are claimed by Laurent et al . (2006) and Kovacs et al . (2006) combined. In total, including the 6 new detections from this work, there are now 13 claimed 350 / m i detections for the S H A D E S catalogue. In total there are flux measurements (detections and upper limits) for 25 per cent of the S H A D E S sources, of which this thesis has provided 21 of the 31 sources wi th 350 / m i flux density constraints. The S H A R C - I I sources observed for this thesis have been selected differently from the other groups in a few important ways. First , due to weather and time constraints, only a sub-set of the S H A D E S sources could be observed wi th S H A R C - I I . The only bias in our sample is that they must have been detected at 850 / m i and lie near to another S H A D E S source in order that they fit wi thin a single S H A R C - I I F O V . A mix of S M G s which preliminarily showed single or more complex radio morphologies or no radio counterpart at al l were deliberately chosen for observations. This sets apart our sample from Kovacs et al . (2006) who inherently miss d im S M G s and S M G s wi th low or no radio flux. Our selection also differs from that of Laurent et al . (2006) who use a 1.1 m m candidate source list (see Table 5.2). Here, the starting point is a large robust S M G 4Strictly speaking, LOCK850.3 and LOCK850.14 are detected by Kovacs et al. (2006). 5LOCK850.27 and LOCK850.76 were not previously associated with Bolocam sources since they are new SHADES detections. LOCK850.27 and LOCK850.76 lie 4.8 and 10.6 arcsec away from two Bolocam sources and so two new SCUBA/Bolocam associations are claimed here. 5.2. 350 nm FLUX DENSITIES OF THE SHADES GALAXIES 167 catalogue that was deliberately constructed to contain a very low fraction of spurious sources. This is important because a non-detection wi th S H A R C - I I either means that the observations were not sufficiently deep, that the S M G is much less luminous than is typically found, or that the S M G lies at high-redshift (if there is also no radio or Spitzer counterpart), and not because the S M G is spurious. This is therefore the first instance of an unbiased S H A R C - I I follow-up programme that is based on a robust list of submillimetre-selected galaxies. For the S H A D E S sources that were looked at, the detection rate is less than half that of either Kovacs et al . (2006) or Laurent et al. (2006). However, note that a large port ion of our data were taken in less than ideal conditions (contributing to noisier maps and therefore fewer detections than Laurent et al . 2006), and that the observations have not been deliberately biased to radio-detected submillimetre-bright S M G s at z < 3-4 like Kovacs et al . (2006). Even if the maps that were omitted from the counterpart searches (i.e., excessively noisy, shallow maps) are excluded in the quoted detection rate here, the detection rate only rises to 40 per cent (compared to 75 per cent for the other groups). Note that the overall detection rate of Laurent et al . (2006) for Bolocam 1.1 mm-selected sources is also only about 40 per cent, whereas for the S H A D E S / B o l o c a m subset of sources, the detection rate is much higher (65-75per cent). This could mean that either the S H A D E S / B o l o c a m subset is a more robust list of sources than the Bolocam candidate list alone, or that 1.1 mm-selected galaxies are simply not the most efficient way to select 350/^m-bright objects since they are likely a colder and/or higher redshift sub-set of submillimetre galaxies. Here, there is one shallow field which overlaps wi th the observations of Kovacs et al . (2006) including source L O C K 8 5 0 . 3 , and another overlapping field wi th the Laurent et al . (2006) coverage of L O C K 8 5 0 . 1 and L O C K 8 5 0 . 4 1 . The flux densities (albeit wi th large er-ror bars) are compared as a consistency check of the data and the calibration (known to be more uncertain at these short submillimetre wavelengths). L O C K 8 5 0 . 1 and L O C K 8 5 0 . 4 1 are not re-detected in our S H A R C - I I maps, since the maps are somewhat noisier than those of Laurent et al . (2006), although the 350 fjm flux densities measured either at 5.2. 350/ im FLUX DENSITIES OF THE SHADES GALAXIES 168 the 850 / i m position or at the brightest pixel within the 10 arcsec search radius (see Ta-ble 5.1) are consistent wi th the detections claimed by Laurent et al . (2006) wi th in 1 a (see Table 5.3). L O C K 8 5 0 . 3 is re-detected here (albeit in a noisier map than Kovacs et al . 2006), but this source is not included in the count of 6 new detections since it was de-tected previously by Kovacs et al . (2006). The 350//m flux density measured either at the 850 /xm position or at the brightest pixel within the 10 arcsec search radius (see Ta-ble 5.1) is consistent wi th the detection claimed by Kovacs et al . (2006) wi th in 1.5 a (see Table 5.3). Ox to Table 5.3: Multi-wavelength photometry and redshifts of S H A R C - I I observed S H A D E S sources from other work (Kovacs et al . 2006 and Laurent et al . 2006). 850 and 450 /mi photometry are from this thesis, 1.4 G H z and 24/ /m data are from Ivison et al . (in preparation), 1.1 m m and 1.2 mm photometry are from Laurent et al . (2005) and Dunlop (private communication; an improved reduction of the Greve et al . 2004 M A M B O data), respectively. Photometric redshifts are from Table 3 in Aretxaga et al . (in preparation) and spectroscopic redshifts (and are all currently under debate; see references in Table 5.2). Note that some of the sources overlap wi th sources in SHADES ID 5 3 5 0 5 8 5 0 5 4 5 0 5 l . 4 G H z 5 2 4 Sl.l m m 5 l . 2 m m phot z spec z (mJy) (mJy) (mJy) (^Jy) (*»Jy) (mJy) (mJy) LOCK850.01 24.1 ±5 .5 8.85 ( ± } ; 8 ) < 47 78.9 ± 4 . 7 217 ± 16 4.4 ± 1.3 3.6 ± 0 . 5 2-4 (±kl) (2.1481'2)2 LOCK850.02 38.0 ± 10.3 13.45 (±2:i) < 123 40.7 ± 5 . 6 , 52.4 ± 5 . 6 545 ± 31 6.8 ± 1.4 5.7 ± 1.0 2.9 ( ± 8 ; « ) , 3.6 ( ± g ; J ) -LOCK850.03 40.5 ± 6.5 10.95 (± l ; | ) < 34 35.0 ± 5 . 2 , 25.8 ± 4 . 9 183 ± 33, 175 ± 23 4.8 ± 1.3 4.6 ± 0 . 4 2-6 ( ± 8 ; ? ) (3.0361)2,no C O 3 LOCK850.12 44.0 ± 16.0 6.15 (±\1) < 35 44.3 ± 5 . 1 263 ± 1 9 4.1 ± 1.3 2.6 ± 0 . 4 2.6 ( ± g : ? ) (2.1421)2 LOCK850.14 41.0 ± 6 . 8 7-25 ( ± i ; l ) < 96 candidate IDs only candidate IDs only 5.1 ± 1.3 3.4 ± 0 . 6 2-6 ( ± 8 : ! ) 2.6112'4,no C O 3 LOCK850.18 (11.3 ±6.7) 6.05 ( ± 1 ; ? ) < 84 29.4 ± 4 . 4 candidate ID only 5.1 ± 1.3 3.4 ± 0 . 6 3.1 ( ± g : ? ) (1.9561)4 LOCK850.27 (< 15.4) 5.05 (± l ; | ) < 32 candidate ID only candidate ID only 5.2 ± 1.4 3.2 ± 0 . 7 4-6 (±hi) -LOCK850.30 38.0 ±7 .2 4.75 (±}; | ) < 86 245 ± 13 233 ± 19 - (0.4 ± 0.8) i . i ( ± 8 : 1 ) 2.6891 LOCK850.41 15.5 ±5 .5 3.85 ( ± ° : g ) < 16 43.6 ± 4 . 7 , 22.1 ± 4 . 8 651 ± 46, 475 ± 37 4.0 ± 1.3 2.4 ± 0 . 5 3-4 ( ± 8 3 ) (0.6891)2-6 LOCK850.76 (< 20.0) 4.75 (±11) < 90 48.0 ± 6 . 0 592 ± 26 4.4 ± 1.4 - 4-6 (±\i) -c o O l o S CO CO O ft I ft CO 5 ft CO ft CO co 5.3. TRENDS WITH FLUX DENSITIES AT OTHER WAVELENGTHS 170 5.3 Trends with Flux Densities at Other Wavelengths The 350 yum flux densities of the detections and non-detections alike are plotted against photometric data at other wavelengths if they have either appeared in a circulated S H A D E S paper draft (850, 450, 24 / im, or 1.4 G H z ) or in the literature (1.1 or 1.2 mm) in order to look for any trends in the S H A D E S data. The 24 /um and radio photometry are from Ivison et al . (in preparation). 6/31 sources wi th S H A R C - I I coverage have double robust radio and/or 24 yum counterparts (Ivison et al. , in preparation). B o t h radio sources are likely associated wi th each other and wi th the S M G so the sum of the robust radio components and the sum of the 24 / i m flux components are used in those cases. Also, the 1.1mm Bolocam photometry in the L H region from Laurent et al . (2005) are used where available. A n unpublished catalogue of a re-reduction of the 1.2 m m M A M B O data of the L H , originally reduced by Greve et al . (2004), is also employed (Dunlop private communication). These multi-wavelength photometries are also used in S E D fitting in Section 5.4. Scatter plots of 350 / /m flux density versus other photometry data, spanning 24 yum to the radio were examined in order to look for correlations. Relationships between observed flux densities in different bands could reveal hints as to the intrinsic properties of the galaxies, including dust temperature or S E D shapes. The scatter plot which demonstrates the only hint of a positive correlation between the 350 yum detections and flux density at other wavebands is shown in F i g . 5.7. In this plot, 24 yum flux density is plotted against radio flux density for a l l S H A D E S sources that have robust counterparts in both wavebands. Note that there is one point in the plot (a filled star; detected S H A R C - I I source LOCK850 .41) which appears to lie at a much higher 24 / i m than the others; it has a high 24 yum flux density since it is the sum of two bright M I P S counterparts. Given its spectroscopic redshift of 0.689 (cf. Table 5.2), this source is consistent wi th being an Arp220-like IR-luminous galaxy when compared wi th fig. 3 of Pope et al . (2006) for S M G s i n G O O D S - N (so there is nothing striking about this source in particular compared to the rest of the points on the plot). Linear Pearson correlation coefficients of the radio and 5.4. INTRINSIC PROPERTIES OF SMGS 171 24 / i m flux densities are calculated for the sub-sets of detected and non-detected S H A R C -II sources and are found to be 0.19 and 0.05, respectively (the correlation coefficient for al l S H A D E S sources in the plot is 0), indicating a hint that bright (i.e., detected) S H A R C - I I sources might also be more often detected simultaneously in deep radio data and at 24 / m i (probably owing to a combination of warmer S E D s and lower redshifts). The S H A R C - I I detections seem to occupy a phase space distinct from that of the non-detections. This indicates that 24 /im-bright and radio-bright (> 50 pJy) sources seem to be preferentially detected wi th S H A R C - I I relative to fainter sources in these bands. Histograms are plotted in Figs. 5.8, 5.9, and 5.10 comparing the number of objects ob-served to the number of objects detected (ignoring al l sources wi th noise > 20 mJy, since they did not have a 'fair' chance at detection) to see if there is a preference for detecting objects at 350/mi that are bright in other wavebands (850/im, radio and 24/mi) . Since the Kovacs et al . (2006) detections are biased (i.e., they were selected to be 350/im-, 850/im-, and radio-bright), two separate sets of each plot are presented: one including 350 / i m from al l groups and one including just the photometry in this thesis. In each plot, a preference or bias is seen for detecting radio- or 24 /im-bright objects at 350 / im, even when they are not selected for observations based on their brightness in these bands (cf. lower panel in each plot). Detectable radio and 24pm sources typically lie at low redshifts (z < 3), and at these low redshifts the 350 /mi window probes the peak of the S E D . It also appears that a larger fraction of the 850 /mi-bright objects are detected at 350 / i m on average, though the trend is not so clear, since the only object in the faintest b in is also detected wi th S H A R C - I I . 5.4 Intrinsic Properties of SMGs The 350 / m i photometric data in combination wi th far-IR/submill imetre/radio photome-try provide powerful constraints on the S E D shape and the nature of the source powering the emission when values of ft and z are assumed or known. Dust temperatures, far-IR luminosities, star formation rates and dust mass estimates are al l physical properties of 5.4. INTRINSIC PROPERTIES OF SMGS 172 1400 1200 1000 S 800 s C N 00 600 400 200 i 1 1 r i m 1 r—fl—I I—ffl—I a—I r - I U 1 T H§H i i t 1 i ffl 1 i—ft J , j ,, * J I J I I L_ 50 100 1.4GHz 150 [nJy] 200 250 Figure 5.7: 24 / m i flux density versus radio flux density. Fi l led and open symbols indi-cate detections and non-detections, respectively, from this work (circles) and -Kovacs et al . (2006) and Laurent et al . (2006) (stars). S H A D E S sources that were not observed are indicated by the smaller open squares and S H A D E S sources without a radio or 24 / m i counterpart are omitted from the plot. Ob-servations were made in al l regions of the scatter plot (i.e., faint and bright ra-dio and/or 24 / m i sources were observed), but the S H A R C - I I detections seem to occupy a phase space distinct (top right-most section of the plot) from that of the non-detections, indicating that 24 yum-bright and radio-bright sources are preferentially detected at 350 /mi . 5.4. INTRINSIC PROPERTIES OF SMGS 173 • i-H a , A L L PHOTOMETRY 10 8 6 4 2 0 A l l SHADES sources Observed sources Detected sources 0 50 100 '1.4GHz 150 [nJy] 200 250 THIS WORK ONLY 10 8 6 4 -2 0 A l l SHADES sources Observed sources Detected sources 0 50 100 M.4GHz 150 Qtfy] 200 250 Figure 5.8: Histograms of S H A D E S source radio flux densities of al l S H A D E S sources (dotted line), sources observed with S H A R C - I I (solid line), and of al l sources detected wi th S H A R C - I I (dashed line). Only sources lying in a region of the S H A R C - I I maps wi th a noise less than 20mJy are included in the last two distributions. The upper panel displays histograms of al l photometry done on the fields, including this work and that of Laurent et al . (2006) and Kovacs et al . (2006). The lower panel displays histograms of S H A R C - I I photometry from this work of all observed sources since the upper panel is more biased towards detecting bright radio, 850 / m i and 350 / /m sources. 5.4. INTRINSIC PROPERTIES OF SMGS 174 A L L PHOTOMETRY A l l SHADES sources Observed sources Detected sources 0 200 400 600 800 1000 1200 '24um D*Jy] THIS WORK ONLY 6F A l l SHADES sources Observed sources . Detected sources 2 Oil 0 200 400 600 800 1000 1200 '241X111 [MJy] Figure 5.9: Histograms of S H A D E S source 24/im flux densities of al l S H A D E S sources (dotted line), sources observed wi th SHARC - I I (solid line), and of al l sources detected wi th S H A R C - I I (dashed line). See the caption of F i g . 5.8 for details. 5.4. INTRINSIC PROPERTIES OF SMGS 175 g OH .s t-c OH IO F £ 4 2 0 10 8 £ 4 0 A L L P H O T O M E T R Y A l l SHADES sources; Observed sources Detected sources 8 10 12 14 Sssoum [mJy] THIS W O R K O N L Y A l l SHADES sources; Observed sources Detected sources 10 12 14 5850nm [mJy] Figure 5.10: Histograms of S H A D E S source 850 / m i flux densities of al l S H A D E S sources (dotted line), sources observed wi th S H A R C - I I (solid line), and of a l l sources detected wi th S H A R C - I I (dashed line). See the caption of F i g . 5.8 for de-tails. 5.4. INTRINSIC PROPERTIES OF SMGS 176 S M G s that one might wish to estimate in order to characterise and place these objects in context wi th other populations of star-forming galaxies. A s a first approach to this simple analysis, the greybody function of Equation 5.1 was fit to available relevant submillimetre photometry of the S H A R C - I I sources in the observed frame. Because there are usually more parameters (3 here) to fit compared wi th data points (2-4), (5 is fixed to a value of 1.5. This value is in line wi th the findings of Dunne & Eales (2001) for local galax-ies and consistent wi th values obtained for carbonite and silicate grains from laboratory measurements (Agladze et al. , 1994). Since the S E D is being fit to observed photometry and (3 is now fixed, the parameters that need to be solved for are the normalisation of the S E D and the observed temperature, i.e., Td/(1 + z). Two data points are therefore sufficient to constrain the 2-parameter SEDs , though we should proceed wi th caution as we run the risk of overfitting the data (3 data points of more would be better). The intrinsic (i.e., rest frame) dust temperature, T j , is derived by mult iplying the 'observed' temperature by (l + z). The multi-colour submillimetre and millimetre flux densities and spectroscopic or photometric redshifts used are summarised in Tables 5.1, 5.2, and 5.3. For the non-detected S H A R C - I I sources, the 350 / m i flux density used i n the fitting is the peak flux wi thin the 10 arcsec search radius of the S H A D E S position (column 5 in Table 5.1). The best estimate of each submillimetre/millimetre photometric point available has been utilised. Note that only the 850 points have been individually corrected for flux boosting effects, since the other flux densities are derived from pointed observations at S H A D E S source positions, and hence suffer minimal effects from thresholding a map. A n d in any case, because the source counts are not as well determined at 350 /um, one cannot correct the flux densities in the same manner as for the 850 / i m data 6 . Published values for the 1.1 and 1.2 m m photometry are used, where flux boosting effects have been determined through simulations to affect extracted sources by about 10-20 per cent on average (see Greve et al . 2004 and Laurent et al . 2005). This w i l l not greatly change 6 There is the added complication in that the other data were taken in different observing modes (e.g., no chopping at 350 /mi), which would alter the form of the prior distribution of pixel flux densities. 5.4. INTRINSIC PROPERTIES OF SMGS 177 the resulting fits, since the error bars of individual submillimetre photometry points are relatively large. The best available photometric or spectroscopic redshift is also used (see Section 5.3). Spectroscopic redshifts are listed if available from the literature (see Tables 5.2 and 5.3 for references), although some of them may be less secure, because they failed to be confirmed wi th C O observations or because of problems wi th counterpart ambiguity. Photometric redshift estimates from Aretxaga et al . (in preparation) are used when spectroscopic redshifts are unavailable. The photometric redshifts quoted have been determined using all available far-IR and radio photometry except the 350 data from this thesis (since it is hoped to be able to characterise the shape of S E D s using these new data independently of the redshifts). Aretxaga et al . (in preparation) derive photometric redshifts for each S H A D E S source by performing a series of Monte Carlo simulations using a l ibrary of 20 local starburst galaxies, U L I R G s and A G N (spanning a wide range of temperatures and luminosities) that take into account prior information of S M G number counts and the favoured luminosity and density evolution up to z ~ 2 (see Hughes et al . 2002, Aretxaga et al . 2003, and Aretxaga, Hughes & Dunlop 2005 for details). For sources wi th only a redshift 90 per cent confidence lower l imit , the redshift is taken to be at this l imit . Al though the results for any individual S M G obtained using a photometric redshift estimate should be used wi th caution, the results should be reasonably accurate for a large ensemble of S M G s . The photometric redshifts are inherently less precise, although they should just contribute to a larger scatter in the derived physical properties unless they are biased in some way. The mean redshift of the 10 spectroscopically-identified objects is z — 2.2 ± 0.3 7 , and the mean redshift for the 21 S M G s wi th photometric redshifts is slightly higher, wi th z = 2.6 ± 0.2. The slightly lower mean for the spectroscopically-identified sub-sample is not surprising given that the spectroscopic redshifts require radio identifications, which l imits one to lower redshifts. B o t h means are consistent wi th the Chapman et al . 7 T h e quoted error is the error on the mean, i.e., the standard deviation of the sample redshifts divided by the square root of the number of samples. 5.4. INTRINSIC PROPERTIES OF SMGS 178 (2005) median redshift of 2.2 (with an interquartile range z = 1.7-2.8) for spectroscopic redshifts of 73 radio-detected S M G s wi th a median flux density of 5.7mJy. A two-sided Kolmogorov-Smirnov (KS) test reveals that the two redshift distributions are 65 per cent likely to have been drawn from the same distribution and thus the ensemble of photometric redshifts is not obviously biased; the 2 sub-sets can therefore be combined and the resulting mean is z = 2.5 ± 0.2. A n y differences in the derived properties between the group of S M G s wi th spectroscopic redshifts and those wi th photometric redshifts is therefore probably not attributable to the two subsets lying at significantly different redshifts, and meaningful trends of physical parameters (e.g., dust temperature) evolving wi th redshift can be probed. For each 350 /fm-observed S H A D E S S M G , the set of far-IR photometry is fit wi th a modified blackbody by minimising x2 to solve for the dust temperature and the S E D normalisation. Note that for sources wi th only two far-IR photometric points available (namely 350 and 850yum), the best-fitting S E D s are not formally well-constrained and the min imum reduced x2 values are significantly less than 1; the parameters derived from such best-fitting S E D s should therefore be used wi th caution. Al though upon visual inspection of the best-fitting S E D s in F i g . 5.11 wi th poor x2 values, one can see that the S E D s appear to be constrained i n a l l but a few cases (LOCK850 .77 and L O C K 8 5 0 . 6 3 , as noted later). Note that L O C K 8 5 0 . 7 7 is omitted from further discussion since the derived dust temperature is unphysical. L O C K 8 5 0 . 7 7 is possibly a S C U B A / S H A R C -II mis-identification (which is reasonable, given that the S H A R C - I I counterpart was found on the edge of the map and 1 mis-identification out of 7 is expected on average). L O C K 8 5 0 . 6 3 is also omitted from further discussion since the far-IR luminosity (derived directly from the fitted S E D normalisation) and resulting S F R are unphysically high. For the sample of 10 S H A R C - I I detected S M G s fit using spectroscopic redshifts a mean = 36.2 K wi th a standard deviation of 17.5 K is derived. Similar results are ex-pected for the S M G s wi th only photometric redshifts, but wi th a larger scatter due to the imprecise photometric redshifts being used and the larger uncertainty in the S H A R C - I I non-detection flux densities. For the sample of 19 S H A R C - I I detected S M G s fit us-5.4. INTRINSIC PROPERTIES OF SMGS 179 ing photometric redshifts in the fits, a mean T = 35.6 K wi th a standard deviation of 13.2 K is derived. The scatter here is much less than that of the spectroscopically-identified subset, hinting that a narrow range of S E D s may have been used by Aretxaga et al . (in preparation) for determining the photometric redshifts in the first place. A two-sided K S test reveals that the temperature distributions of the photometric redshift and spectroscopic redshift sub-sets are 92 per cent likely to have been drawn from the same distribution. Since the two distributions are consistent wi th each other, a mean T = 35.8 ± 14.5 K is quoted for the entire sample of S H A R C - I I observed S M G s here. The results are summarised in Table 5.4 and the best-fitting observed S E D s are shown i n F i g . 5.11. These results are consistent wi th previous estimates of the intrinsic dust temperature of S M G s of about 35 K using a subset of these data wi th radio IDs and spectroscopic redshifts (Kovacs et al . 2006: T ~ 35 K ) , for local IRAS-hfight S C U B A galaxies (Dunne & Eales 2001: T ~ 3 5 K ) , for S M G s (Pope et al . 2006: T ~ 3 0 K ; and Chapman et al . 2004: T = 36 K ) , and for a sample of local U L I R G s (Farrah et al . 2003; median T = 32 K ) . For comparison, the dust temperature of the M i l k y Way estimated by the all-sky COBE-FIRAS survey is 17 K (Reach et a l , 1995), and Beelen et al . (2006) and Priddey & M c M a h o n (2001) find dust temperatures of Td ~ 47 and 41 K , respec-tively, for high redshift quasars. One should also note several caveats that have not been included in the uncertainty estimates above. First of al l a constant /3 = 1.5 is assumed in the fits. B y doing this it is assumed that the slope of the Rayleigh-Jeans tai l is constant and that the dust has similar properties in al l galaxies, which is probably a reasonable assumption on the average although not individually. A s additional precise photometric data become available from BLAST and Spitzer, (3 w i l l be able to be constrained by direct fitting. Note however that changing the value of j3 by ± 0 . 5 (between physically plausible values) has the effect of changing the derived dust temperature by about ± 5 - 1 0 K , which in turn affects the derived luminosity of the S M G by only 5-10 per cent. Errors in the photometric redshifts have been ignored and so the temperatures for those sources are uncertain by approximately an additional ± 1 0 K (depending on the redshift). 5.4. INTRINSIC PROPERTIES OF SMGS 180 Observed X [ timl 1000 100 100 1000 Observed v [GHz] Observed X [ um] 1000 100 100 1000 Observed v [GHz] 6 100 10 O Observed A. [ um] 1000 100 L 0 C O 5 0 . 2 8 z= 2.00 T.= 35 100 1000 Observed v [GHz] 100 1000 100 1000 100 1000 Observed v [GHz] Observed v [GHz] Observed v [GHz] £ 100 Observed X [ urn] 100 1000 Observed v [GHz] JL ioo O Observed X [ um] 1000 100 LOCK850.1 • ^ 2.15 z T = 27 d 100 1000 Observed v [GHz] B 100 O Observed X [ um] 1000 100 100 1000 Observed v [GHz] Figure 5.11: Best-fitting observed S E D s for S H A D E S S M G s wi th S H A R C - I I photometry wi th B fixed to 1.5. The solid circles indicate photometry used to fit the S E D , while the open circles indicate the 450 yum upper limits and are not used explicitly in the fits (though they are never violated). Also, the 24yum flux densities for each S M G have not been used explicitly in the fits (see Section 5.1), although in each case (save LOCK850 .77 , which is deemed a possible mis-identification in Section 5.4) the best fit S E D lies above the 24 y«m photometry. The spectroscopic or photometric redshifts used in the fitting and determination of T<j are indicated in each panel. Notice how important the 350 /xm point is in determining the location of the S E D peak. .4. INTRINSIC PROPERTIES OF SMGS 181 Observed X [ um] 1000 100 100 1000 Observed v [GHz] £ 100 "8 6 Observed X [ um] 1000 100 100 1000 Observed v [GHz] JL 100 10 Observed X [ um] 1000 100 1.96 20 , 100 1000 Observed v [GHz] Observed X I 1000 LOCK850.30 um 00 100 1000 Observed v [GHz] Observed X [ urn] 1000 100 100 1000 Observed v [GHz] O Observed X [ um] 1000 100 E, 100 10 LOCO'50.06 z = 3.60 T.= 73 100 1000 Observed v [GHz] Observed 1000 LOCK850j>10 z= 3.10^ • T = 41 a M ^ o 100 1000 Observed v [GHz] >> E J O o 100 10 Observed A, [ um] 1000 100 LOCK850.15 z = 2.40 0 T = 33 X /I tv 100 1000 Observed v [GHz] Observed X [ um] 100 1000 100 1000 Observed v [GHz] Figure 5.11: (continued) .4. INTRINSIC PROPERTIES OF SMGS 182 Observed X I ami 1000 100 LOCK850.22 z= 2.00 T = 22 I A 100 1000 Observed v [GHz] Observed X \ uml 1000 100 100 1000 Observed v [GHz] J 3 o £ 100 Observed X [ um] 1000 100 LOCO'50.27 z= 4.60 T,= 25 100 1000 Observed v [GHz] Observed X [ um] 1000 100 >> £ 100 LOCK850.47 z= 1.50 • T = 34 a > in 1 10 / Jo ° 1 \ 100 1000 Observed v [GHz] > "8 J 2 o 100 Observed X [ um] 1000 100 100 1000 Observed v [GHz] Observed X [ um] 1000 100 100 1000 Observed v [GHz] £ 100 O 10 Observed X [ um] 1000 100 LOCK850.64 z= 1.50 T = 26 9 I ^ 100 1000 Observed v [GHz] 100 Observed X [ um] 1000 100 100 1000 Observed v [GHz] Observed X [ um] 1000 100 100 1000 Observed v [GHz] Figure 5.11: (continued) 5.4. INTRINSIC PROPERTIES OF SMGS 183 3bserved X [ um] 1000 100 100 LOCO'50.2 z = 3.60 > "8 10 / \ 6 1 / , \ 100 1000 Observed v [GHz] Figure 5.11: (continued) Table 5.4: Derived dust temperatures (T<j), far-IR luminosities (Z-FIR), illuminated dust masses (Ma) and S F R s for the S H A R C - I I observed S H A D E S sources. The error in each parameter is the average error estimated using the photometric errors. Emissivi ty 8 is fixed at 1.5 and the best spectroscopic (s) or photometric (p) redshifts were used i n fitting to the 350 and 850/xm photometry, plus 1.1 and 1.2 mm data if available. The second section presents new fits using the data from Kovacs et al. (2006) and Laurent et al. (2006), wi th deboosted S H A D E S photometry and new M A M B O constraints. The last sub-set is based on S H A R C - I I non-detections (using the nearest peak flux from Table 5.1 as an estimate of the 350 yum flux density). SHADES ID z Td log Z/FIR log M d SFR Notes (K) (L©) (M©) ( M o y i -1 ) LOCK850.04 1.482 (s) 25 ± 1 12.2 ± 0 . 2 9.3 ± 0 . 1 170 ± 50 LOCK850.28 > 2.0 (p) > 35 ± 2 > 12.6 ± 0 . 2 > 8.8 ± 0 . 1 > 400 ± 170 x 2 « i LOCK850.33 3.699 (s), 2.686 (s) 50 ± 4, 39 ± 3 13.0 ± 0 . 2 , 12.7 ± 0 . 3 8.2 ± 0 . 1 , 8.5 ± 0 . 1 960 ± 450, 440 ± 2 1 0 LOCK850.77 2.6 (p) 300 ± 51 16.1 ± 0 . 5 7.2 ± 0 . 1 1200000 ± 1300000 X 2 <3C 1, unphysical, misID? SXDF850.3 2.1 (p) 33 ± 3 12.6 ± 0 . 3 9.0 ± 0 . 1 430 ± 220 x 2 « i SXDF850 . i l 2.4 (p) 66 ± 9 13.5 ± 0 . 1 8.2 ± 0 . 3 3000 ± 450 X 2 « 1 LOCK850.01 2.148 (s) 27 ± 1 12.4 ± 0 . 1 9.2 ± 0 . 1 230 ± 50 see Kovacs et al. (2006) LOCK850.02 2.9, 3.6 (p) 34 ± 1, 40 ± 1 9.1 ± 0 . 1 , 9.0 ± 0 . 1 10.3 ± 0 . 1 , 10.3 ± 0 . 1 740 ± 210, 1240 ± 350 LOCK850.03 3.036 (s) 39 ± 1 13.0 ± 0 . 1 8.9 ± 0 . 1 960 ± 180 see Kovacs et al. (2006) LOCK850.12 2.142 (s) 40 ± 5 12.8 ± 0 . 6 8.7 ± 0 . 1 690 ± 430 see Kovacs et al. (2006) LOCK850.14 2.611 (s) 40 ± 1 12.9 ± 0 . 1 8.7 ± 0 . 1 800 ± 110 see Kovacs et al. (2006) LOCK850.30 2.689 (s) 76 ± 5 5 13.6 ± 0 . 7 8.1 ± 0 . 4 4000 ± 30000 see Kovacs et al. (2006) LOCK850.41 0.689 (s) 15 ± 1 10.9 ± 0 . 2 9.1 ± 0 . 1 8 ± 3 see Kovacs et al. (2006) LOCK850.16 1.147 (s) 31 ± 3 12.3 ± 0 . 3 8.7 ± 0 . 1 190 ± 110 LOCK850.18 1.956 (s) 20 ± 3 11.9 ± 0 . 3 9.3 ± 0 . 1 70 ± 5 0 see Kovacs et al. (2006) LOCK850.06 3.6 (p) 73 ± 3 0 13.7 ± 0 . 8 8.2 ± 0 . 2 5500 ±13000 x 2 « i LOCK850.10 3.1 (p) 41 ± 1 13.0 ± 0 . 2 8.8 ± 0 . 1 940 ± 600 x 2 « i LOCK850.15 2.4 (p) 33 ± 14 12.6 ± 0 . 7 9.1 ± 0 . 3 430 ±1100 LOCK850.21 > 1-0 (p) 25 ± 4 8.8 ± 0 . 4 9.5 ± 0 . 1 60 ± 5 0 LOCK850.22 > 2.0 (p) 22 ± 10 9.3 ± 0 . 3 10.3 ± 1.6 100 ± 83 x 2 « i LOCK850.26 3.6 (p) 41 ± 1 12.8 ± 0 . 3 8.6 ±0 .2 610 ± 3 1 0 x 2 « i LOCK850.27 4.6 (p) 25 ± 3 12.2 ± 0 . 2 9.2 ± 0 . 1 160 ± 90 LOCK850.47 > 1-5 (p) 34 ± 11 8.5 ± 0 . 8 9.4 ± 0 . 2 190 ± 270 x 2 « i LOCK850.48 2.4 (p) 41 ± 7 12.7 ± 0 . 4 8.6 ± 0 . 1 490 ± 400 LOCK850.63 2.6 (p) 110 ± 5 0 14.3 ± 1.0 7.7 ±0 .2 22000 ± 80000 X 2 C l , unphysical LOCK850.64 > 1-5 (p) 26 ± 5 11.9 ± 0 . 5 9.0 ± 0 . 1 80 ± 8 0 LOCK850.76 4.6 (p) 20 ± 8 12.1 ± 0 . 5 9.6 ± 0 . 5 110 ± 180 SXDF850.1 2.6 (p) 29 ± 5 12.5 ± 0 . 3 9.2 ± 0 . 1 350 ± 210 x 2 « i SXDF850.8 2.6 (p) 36 ± 5 12.6 ± 0 . 4 8.7 ± 0 . 1 420 ± 3 1 0 x 2 « i SXDF850.17 > 2.0 (p) 24 ± 12 12.1 ± 0 . 5 9.2 ± 1 . 5 140 ± 160 x 2 « i SXDF850.119 2-1 (p) 36 ± 5 12.5 ± 0 . 5 8.6 ± 0 . 1 300 ± 250 x 2 « i O l I o o S3 Pa £ CO O ft Q CO OO 5.4. INTRINSIC PROPERTIES OF SMGS 185 . t The specific intrinsic luminosity, L„, is plotted as a function of rest frequency for the each SHARC-II-observed S H A D E S source in F ig . 5.12. Effects of instrumental filters have been neglected here, since any corrections are negligible at this level of precision. This figure provides a useful characterisation of S M G S E D s which can be used as a template for other S M G s when only l imited far-IR/submillimetre photometry are available. A significant scatter in the photometric points and SEDs exists. Note that the scatter i n this plot is neither decreased nor increased if just sub-sets of S M G s wi th spectroscopic or photometric redshifts are considered, indicating that there is a real spread in S E D properties here in terms of luminosity and temperature. The spread in the photometry could be reduced if the effects of luminosity could be removed; since 850 / m i is a proxy for luminosity (cf. negative k-correction), the luminosity effect on the spread could essentially be taken out of the plot by normalising the S E D s by the 850 / m i flux densities. This was attempted, but the spread in the photometry was not significantly reduced, suggesting that indeed other factors (such as the temperature or uncertainties i n the photometric redshifts) are probably responsible. Corresponding values for Z/FIR are calculated using Equation 5.4 and are given in Table 5.4. For our sample, the mean far-IR luminosity is ~ 7 x 10 1 2 L 0 , which is consistent wi th what has been found previously for S M G s . The average S F R for our sub-sample of SHARC-II-detected S H A D E S sources is ~ 8 0 0 M Q y r ~ 1 , as calculated from Equation 5.5. This is consistent wi th previous work, indicating that S M G s are significant players in the global star-formation of the high-redshift Universe (see e.g., L i l l y et al . 1999). Using Equat ion 5.6, the dust masses implied by the 850 / m i observations are ~ 1 0 8 -10 9 MQ. Uncertainties in the dust masses are dominated by the uncertainty in and the flux at 850 (im. in the Rayleigh-Jeans regime as well as the uncertainty in the value of K V . Note that KV is uncertain to a factor of a few, but the relative dust masses i n our sample wi l l be correct assuming the same value holds for al l S M G s (see B la in et al . 2002 for a discussion). Also note that increasing the redshift wi l l increase the gas mass, holding al l other parameters fixed. Assuming that the maximum possible interstellar dust mass for 5.4. INTRINSIC PROPERTIES OF SMGS 186 10 27 26 o C •5 c 10 25 10 24 1000 Rest Frame X [ \im] 100 100 ^ S H A R C - I I (this work) * SHARC-II (others) O SCUBA 450 • SCUBA 850 Bolocam • M A M B O 1000 Rest Frame v [GHz] Figure 5.12: Emit ted monochromatic luminosity versus rest frame frequency and wave-length for S H A R C - I I observed S H A D E S sources. The best fitting S E D s for each set of photometry are plotted, along wi th photometric points indi-cated by different symbols. Open symbols indicate non-detections or upper limits and filled symbols indicate formal detections. The scatter is neither decreased nor increased if just sub-sets of S M G s wi th spectroscopic or pho-tometric redshifts are considered. 5.4. INTRINSIC PROPERTIES OF SMGS 187 a galaxy is about 1/500 of its total baryonic mass (see Edmunds & Eales 1998), the total mass of in each S M G is ~ 1 0 1 0 - 1 0 n M 0 . The S M G population is therefore confirmed to be dominated by very massive (~ 5 x 1 O 1 O M 0 ) , luminous (~ 1 O 1 2 L 0 ) star-forming ( S F R ~ 1 0 0 0 M Q y r _ 1 ) galaxies wi th intrinsic dust temperatures of ~ 35 K . In contrast, Arp220, a well-studied nearby U L I R G has a dust temperature of ~ 37 K but is about 7 times less luminous than the average S M G studied here! The relationship between dust temperature and redshift is examined in F i g . 5.13 s . The first thing to note on this plot is that the spectroscopic and photometric redshift samples have about the same scatter, and similarly for the S H A R C - I I detected and non-detected samples. S M G s seem to span a range of intrinsic dust temperatures; however hotter S M G s seem to inhabit the high redshift Universe more often on average, while colder S M G s seem to dominate at low redshifts. Is this due to selection effects or is this evidence for evolution of S M G s / U L I R G s wi th redshift? This idea can be further investigated when the relationships between Z/FIR , redshift (since there is an intrinsic correlation between temperature and Z-FIR) and observed 850 /ira are examined, in Figs. 5.14 and 5.15, respectively. In F ig . 5.14, a solid line is plotted to indicate possible selection effects: this line represents an S M G wi th ft = 1.5, = 20 K , and average observed 850 and 350 nm flux densities of 7 and 35 mJy, respectively. Rougly, S H A D E S is insensitive to the region under this curve. Even taking into account the selection effects, there appears to be a hint of a dearth of lower luminosity S M G s at higher redshifts compared to lower 8 A few peculiar points on this plot are discussed. The 2 points in the lower right hand region of the plot are LOCK850.27 and LOCK850.76 and there is nothing notable about either of these sources, except that the photometric redshifts seem unusually high for SMGs. The points at the top of the plot are (L-R) S X D F 8 5 0 . i l , LOCK850.30, and LOCK850.6 . There is nothing notable about any of these points: they are all fairly bright 24 /un sources, though nothing can be said about A G N activity (which could help explain the hotter temperatures) in these particular sources since the slope of the mid-IR part of the spectrum (an A G N diagnostic) is unknown and there are no 60 or 170/jm detections for these sources. LOCK850.30 has been spectroscopically identified by Chapman et al. (2005) and has starburst features (Lya and Ha) in its optical spectrum. 5.4. INTRINSIC PROPERTIES OF SMGS 188 Redshift Figure 5.13: Dust temperature versus redshift for S M G s wi th more precise spectroscopic redshifts (filled circles) and for S M G s wi th photometric redshift estimates only (open circles). Boxes are drawn around sources that are 'detected' wi th S H A R C - I I . Arrow indicate redshift lower limits. The horizontal line Ta = 36 K represents the mean dust temperature of the sample. The data deviate about this line by about ± 5 K between redshifts of about 1 and 4 (except for a few outliers). The diagonal solid line indicates an observed dust temperature of 10 K , i.e., T d = 10(1 + z)K, and appears to fit the data better; a similar conclusion was also noted by Kovacs et al . (2006). The dearth of sources in the lower right hand corner of the plot is due to selection effects (see text). The dearth of sources in the upper left hand corner of the plot is a real effect and shows that only cooler S M G s seem to inhabit the low redshift Universe. See F ig . 5.14. Figure 5.14: Far-IR luminosity versus redshift for S M G s wi th spectroscopic redshifts (filled circles) and for S M G s wi th photometric redshift estimates only (open circles). Boxes are drawn around sources that are 'detected' wi th S H A R C - I I . Arrow indicate redshift lower limits. The solid line is drawn to demonstrate the selection effects that result from S M G s wi th (3 = 1.5, T d = 20 K , and av-erage observed 850 and 350 /mr flux densities of 7 and 35 mJy, respectively. Even taking into account the selection effects, there appears to be a hint of a dearth of lower luminosity S M G s at higher redshifts compared to lower redshifts. The dearth of high luminosity objects at low redshift is a real effect (i.e., not due to selection effects), indicating possible evolution. 5.4. INTRINSIC PROPERTIES OF SMGS 190 Figure 5.15: Far-IR luminosity versus 850//m flux density for S M G s wi th spectroscopic redshifts (filled circles) and for S M G s wi th photometric redshift estimates only (open circles). Boxes are drawn around sources that are 'detected' wi th S H A R C - I I . Arrow indicate redshift lower limits. There appears to be a hint of a lack of lower luminosity S M G s wi th bright 850 /mi-selected flux densities (see text), though formally L F I R = constant is a better fit to the data than a L F I R OC S$5Q. 5.4. INTRINSIC PROPERTIES OF SMGS 191 redshifts. 850 /mi-selected galaxies appear to be biased against lower luminosity sources. M A M B O , Bolocam and A z T E C are sensitive to cooler S E D s and could perhaps select S M G s to fill in this dearth. There does seem to be a real lack of S M G s at low redshifts and high luminosity, indicating that S M G s are intrinsically more luminous at high redshift. F i g . 5.15 examines the relation between L F I R , and Ssso9- There appears to be a hint in this plot of a lack of lower luminosity S M G s wi th bright 850 /xm-selected flux densities, though formally L F I R = constant is a better fit to the data than a L F I R OC S ^ O - This hint suggests a strong evolution of U L I R G s with redshift, as noted by Pope et al . (2005). Larger samples of S M G s wi th robust redshifts and a wider dynamic range i n 850 /xm flux density and luminosity are needed to test this idea further and to fully describe the luminosity function of S M G s . 5.4.1 Star Formation Rate History Using the S F R values calculated for the S H A R C - I I observed S H A D E S galaxies, an esti-mate can be made of their contribution to the total star-formation density of the U n i -verse. In order to make a rough estimate, the S F R s of the 29 physically plausible values (i.e., L O C K 8 5 0 . 7 7 and L O C K 8 5 0 . 6 3 are omitted; cf. Table 5.4) from the previous sec-t ion are summed and this number is corrected for the S H A D E S survey incompleteness at 2mJy, assuming that the other S H A D E S galaxies wi l l have similar S F R s . It is also assumed that al l of the S H A D E S galaxies lie in the redshift range 1.7-2.8 (the interquar-tile range quoted for S M G s by Chapman et al . 2005) in order to calculate the comoving volume of the survey (cf. equation 3.85 from Peacock 2003). Div id ing the complete total 9Peculiar points on this plot are explained here. The dark solid point in the lower left hand corner is LOCK850.41 and is found to be a cool, less luminous, low redshift SMG and is probably representative of a separate population of cold low luminosity SMGs as it lies significantly away from the other points. The 3 points at Sg5o > 12mJy are LOCK850.2 (there are 2 points for this source since there are 2 photometric redshift values, z=2.4 and 3.6, given the 2 robust radio counterparts for this source) and LOCK850.15 at z = 2.4. They are bright new SHADES sources and have not been targetted yet for spectroscopic follow-up. 5.5. SUMMARY AND FUTURE PROSPECTS 192 S H A D E S S F R above 2 m j y by the comoving volume between redshifts of 1.7 and 2.8 gives an S F R density of p* ~ 0.03 M Q y r - 1 M p c - 3 . See F i g . 5.4.1 where this number has been plotted as a lower l imit (since the contribution from fainter S M G s than those seen by S H A D E S are not included here), placing the S H A D E S contribution to the total S F R density in context wi th other data and models. S H A D E S is able to produce an unbiased l imit on the epoch of the peak of dust-enshrouded star formation. Al though this estimate makes it clear that there is substantial dust-enshrouded star formation going on at z ~ 2, it is s t i l l not clear how important the S M G contribution might be, and whether it con-tinues to higher redshift. Multi-wavelength follow-up of the S H A D E S catalogue should help by providing redshift estimates for a uniform sample of ~ 100 S M G s . However, thousands of S M G s wi th robust redshift estimates are needed to properly constrain the peak star-forming epoch, which wi l l be possible wi th upcoming S C U B A - 2 surveys. 5.5 Summary and Future Prospects Extracted S H A R C - I I 3 5 0 / m i sources are claimed to be associated wi th the S H A D E S 8 5 0 / m i sources if they are the highest S / N peak within 1 0 arcsec and have S / N > 2.5 a. For S H A D E S sources which do not appear to have 3 5 0 /mi-detected counterparts, the brightest pixel wi thin 1 0 arcsec is used to estimate an upper l imit of the flux density. The results are summarised in Table 2 . 3 . For completeness, flux measurements from Kovacs et al . ( 2 0 0 6 ) and Laurent et al . ( 2 0 0 6 ) for S H A D E S sources are also included. In total, including the 6 new detections from this work, there are 1 3 claimed 3 5 0 / i m detections for the S H A D E S catalogue. This thesis has thus doubled the number of 3 5 0 / u m detections. In total there are flux measurements (detections and upper limits) for 3 1 / 1 2 0 S H A D E S sources (roughly 2 5 per cent), of which this thesis has provided 2 1 new flux constraints. The combination of 8 5 0 /mi , 1.1, and/or 1.2 m m photometry, spectroscopic or good photometric redshifts, and the 3 5 0 / m i flux densities can provide an estimate of L F I R and T d . This alllows us to begin searching for trends wi thin the S M G s in order to understand 5.5. SUMMARY AND FUTURE PROSPECTS 193 1 + z Figure 5.16: Contr ibut ion to the star-formation rate per comoving volume of the Universe from S H A D E S sources (large upward arrow). This figure is adapted from Bla in et al . (2002), wi th permission from Elsevier, and shows the S H A D E S data in context wi th data from various optical and near-IR surveys (see full references in B la in et al . 1999 and Smail et al . 2002). The most im-portant points here are from L i l l y et al . 1996 (filled stars) and Steidel et al . 1999 (crosses, wi th and without an extinction correction). The other up-ward arrow (and open circle) is the S C U B A limit from the H D F survey of Hughes et al . (1998). The thick solid lines are best fits to the far-IR and submillimetre data in a simple luminosity evolution model (with 68 per cent confidence limits), while the thick dashed lines are predictions using a hi-erarchical model of merging galaxies by B la in et al . (2002). The th in and thick dotted lines are from Bla in et al . (1999). 5.5. SUMMARY AND FUTURE PROSPECTS 194 how they are linked wi th other galaxy populations. Evidence of S M G evolution wi th redshift is found, indicating that hotter more luminous S M G s inhabit the high redshift Universe more often compared to low redshifts. The S H A R C - I I observational campaign is an on-going programme. Future observa-tions wi l l target A z T E C / S H A D E S cross-identified sources. The A z T E C data reduction is s t i l l a work in progress, however already several bright 1.1mm counterparts to S H A D E S S M G s have been identified. Together, the two S H A D E S S C U B A / A z T E C fields represent the largest survey area wi th overlapping data at 850 / i m and 1.1 mm, yielding the largest sample to date of bright, confirmed S M G detections. The combination of 350 /mi , 850 / i m and 1.1mm photometry can be used to constrain the S E D s of the S H A D E S sources in order to quantify their dust content, temperatures, and star-formation rates to help un-derstand the underlying physics responsible for powering S M G s . These constraints w i l l also aid in refining photometric redshift techniques. Wha t is the nature of the galaxies which dominate the background at 350 or 450 /mi? The far-IR extragalactic background peaks at a wavelength of approximately 200 / i m (Fixsen et al . , 1998); large blank-field surveys at 350 and/or 450 / m i wi l l allow us to study a statistically significant population of lower redshift and/or hotter dust temperature galaxies, responsible for emission nearer to the peak of the extragalactic background than those selected at 850 / im. These studies should provide a link between galaxies detected at ~ 1 m m and the even shorter wavelength data from Spitzer. Such comparisons should allow us to investigate the evolution of far-IR emitting galaxies and how they contribute to the background at different wavelengths. Such wavebands are challenging from the ground, but ambitious 450 /xm surveys are planned wi th S C U B A - 2 , while the Herschel Space Observatory w i l l carry out surveys over the 60-700 / i m range. 195 C H A P T E R 6 E P I L O G U E 6.1 Future Far-IR/Submillimetre/Radio Instruments Due in part to the success of submillimetre astronomy in identifying and establishing the cosmological importance of a large population of optically-obscured galaxies, billions of dollars worth of facilities and instruments are being constructed using state-of-the-art technology to make further progress on probing the nature of this significant and unique population of galaxies. Many of the upcoming instruments such as S C U B A - 2 and A L M A wi l l help bring submillimetre astronomy into the realm that optical surveys have enjoyed for several decades: high S / N detections and fine spatial resolution. Here is a summary of far-IR/submillimetre telescopes coming on-line within the next decade, listed in order of expected availability. 6.1.1 SCUBA-2 S C U B A - 2 1 (Holland et a l , 2006) is the first large-format ~ 10 4 detector element ' C C D -like' camera for the J C M T and should begin collecting data in 2007. A r m e d wi th background-limited sensitivity and a large F O V , S C U B A - 2 wi l l map large areas of sky up to 1000 times faster to the same S / N than its predecessor, S C U B A . Like S C U B A , S C U B A - 2 wi l l have a 450 / i m channel as well as an 850 / m i channel but much faster data-rates should allow for much more efficient removal of variable atmospheric emission. Thus S C U B A - 2 wi l l be able to deeply map a significant region of sky at both wavelengths to high S / N , and wi l l therefore be able to act as a 'pathfinder' for new and upcoming submil-limetre interferometers to study individual objects in detail at high resolution (e.g., S M A and A L M A ) . :www.roe.ac.uk/ukatc/proj ects/scubatwo 6.1. FUTURE FAR-IR/SUBMILLIMETRE/RADIO INSTRUMENTS 196 6.1.2 LABOCA on APEX The Large Apex BOlometer C A m e r a ( L A B O C A 2 ; Kreysa 2003) is a 295-channel bolome-ter array that wi l l be operating in 2007/08 at 870 m n on the 12-m Atacama Pathfinder Experiment ( A P E X ) in Chile at 5000-m. The A P E X beam size at the operating wave-length is 18 arcsec and the total F O V for L A B O C A is 11.4arcmin in diameter. Like S C U B A - 2 , L A B O C A wi l l not employ a chopping strategy for observations, and instead use well-tested scan patterns in order to facilitate efficient removal of dominant atmo-spheric contributions at the data reduction stage. Whi le L A B O C A wi l l not be able to compete wi th S C U B A - 2 in terms of mapping speed and depths, given the l imited number of detectors, it w i l l be useful as it wi l l be the only submillimetre imager operating in the southern hemisphere before the advent of A L M A . 6.1.3 AzTEC on the LMT The 50-m Large Mil l imeter Telescope ( L M T ) is situated in Mexico at 4600-m and wi l l be the largest and most sensitive single-aperture telescope operating at wavelengths of 850 /zm-4 mm, beginning in 2008. O n the L M T , the A z T E C 3 (Wilson et al. , 2004) 1.1 m m camera (essentially Bolocam II) wi l l have mapping speeds about 1000 times that of S C U B A and wi th a factor of 3 improvement in resolution. A z T E C wi l l be able to produce millimetre-wave sky maps tens of square degrees in size in only a few hundred hours of observation. 6.1.4 Herschel The European Space Agency's Herschel Space Observatory4 (Pilbratt , 2003) 3.5-m space telescope is scheduled for launch in 2008 to orbit at the Earth-Sun ' L 2 ' point. It wi l l be the first space observatory covering the full 60 — 670 / m i regime and wi l l study the 2www. mpif r-bonn .mpg. de/staf f /gsiringo/laboca/laboca j L t_the_mpif r_bolometer_group. html 3www.astro.umass.edu/ wilson/CDL/BCII.html 4sci.esa.irit/science-e/www/area/index.cfm?fareaid=16 6.1. FUTURE FAR-IR/SUBMILLIMETRE/RADIO INSTRUMENTS 197 formation of galaxies i n the early Universe and their subsequent evolution using 3 main instruments: the Heterodyne Instrument for the Far Infrared (HIFI); the Photodetector Ar ray Camera and Spectrometer (PACS) ; and the Spectral and Photometric Imaging Receiver ( S P I R E ) . H I F I is a very high-resolution heterodyne spectrometer and observes in 7 bands covering 480 to 1910 G H z (625 to 160 pm). P A C S is an imaging photometer and an integral field spectrometer operating at wavelengths between 60 and 210 fim, wi th a F O V of a few square arcminutes. S P I R E is a 3-band imaging photometer (images at 250, 350, and 500 pm simultaneously) as well as an imaging Fourier transform spectrometer (recall that BLAST is using its prototype array!) and has a F O V of 4 x 8 arcmin. 6.1.5 Planck Planck5 (Tauber, 2004) was designed primarily as an 18-month (minimum) European Space Agency (ESA) C M B anisotropy and polarisation experiment using a 1.5-m off-axis telescope, though the primary product of the mission wi l l be 9 publicly available calibrated all-sky maps, ranging in frequency from 30-900 G H z and wi th a resolution from 30-4.5 arcmin. These maps wi l l be long wavelength versions of the IRAS and COBE-D I R B E maps, which have been i n use for over 10 years by the astronomy community. These maps are expected to contain several thousand extragalactic sources at millimetre and submillimetre wavelengths and allow a thorough investigation of the spectra of the brightest starburst galaxies, A G N , radio galaxies and quasars. Al though the sensitivity (1 a ~ 20 A i m ) and beam size (5 arcmin) wi l l not be optimal for detailed studies of S M G s , Planck w i l l see every bright S M G at 850 /im. Planck w i l l be launched wi th Herschel in 2008. 5www.rssd.esa.int/index.php?proj ect=Planck 6.1. FUTURE FAR-IR/SUBMILLIMETRE/RADIO INSTRUMENTS 198 6.1.6 A L M A The Atacama Large Mill imeter A r r a y 6 ( A L M A ; Wootten 2003), an international astron-omy facility, w i l l be the largest and most sensitive instrument in the world at millimetre and submillimetre wavelengths by 2009. A L M A wi l l be comprised of about 50 12-m antennae located in Chile at 16,400 feet above sea level, and wi l l operate wi th baselines of 150 m to 10 km. A L M A is designed to image the sky in select windows from 350 Atm-10 mm, wi th a spatial resolution down to an unprecedented lOmilliarcsec. A L M A wi l l be able to reach to fainter flux densities more efficiently and thus be able to probe the very faint end of the submillimetre number counts. It is anticipated that A L M A wi l l be able to detect ~ 50 galaxies per square arcmin, advancing submillimetre astronomy into the realm of what opt ical /near-IR studies have been able to do for decades. The advent of A L M A wi l l lead us into a new era where we can spatially resolve S M G s over a wide dynamic range in brightness and redshift to understand the link between stars, dust and A G N in galaxies as a function of redshift. 6.1.7 E V L A Identifying S M G s at radio wavelengths has been the key to l inking S M G s to other pop-ulations of galaxies in order to try and disentangle their nature. The Extended Very Large Ar ray ( E V L A ) project 7 is a major upgrade to the existing V L A and wi l l provide a radio telescope wi th a high sensitivity (improvements of factors of 5-20 over the V L A for a point source sensitivity of about 1 / /Jy at 2-40 G H z ) , high resolution (200-4 milliarcsec between 1-50 G H z ) and superb imaging capability. The improved sensitivity and reso-lut ion of the E V L A wi l l improve the efficiency of identifying S M G radio counterparts in deep submillimetre-imaged regions. • 6www.alma.nrao.edu 7 www.ao c.nrao.edu/evla 6.2. FUTURE IMAGING OF THE SHADES FIELDS 199 6.1.8 J W S T The James Webb Space Telescope8 (JWST; Sabelhaus & Decker 2004) is a 6.5-m IR-optimised NASA-funded orbital observatory and is scheduled for launch in 2013. The main scientific workhorses of the mission are the Mid-Infrared Instrument (MIRI ) , the Near-Infrared Camera (NIRCam) , and the Near-Infrared Spectrograph (NIRSpec). K e y objectives of the mission include finding the first luminous objects i n the Universe and studying in detail the assembly and evolution of galaxies, dark matter, gas, stars, metals, and A G N from the epoch of reionization to the present day. 6.2 Future Imaging of the SHADES Fields The S H A D E S fields were chosen mainly because of the wealth of existing or planned multi-frequency data. Even now that the ini t ial follow-up phase of S H A D E S is coming to a close, many other programmes have since added the S H A D E S fields to their target lists because of the wealth and quality of multi-frequency data available in these regions of sky. The full S H A D E S 0.5 deg 2 area was targetted in late 2005 by A z T E C (Wilson et al . , 2004) at 1.1 m m to a 1 a depth of ~ 1.2 mJy. The data are currently being reduced and analysed by groups at the University of Massachussetts (PI Grant Wilson) and at the University of Br i t i sh Columbia. Upon an ini t ial examination of the S H A D E S / A z T E C overlap, it seems promising that a larger more robust catalogue can be constructed by using a combination of sources detected by both instruments in a manner similar to Ivison et al . (2005) wi th a combination of S C U B A and M A M B O data. A proposal to map additional S H A D E S sources also detected wi th A z T E C using S H A R C - I I has been granted time and observations wi l l be underway this semester. Addi t iona l deep near-IR imaging of the S H A D E S fields in the 7, H, and -bands (down to K ~ 23 i n the S X D F and K ~ 21 in the L H ) is underway as part of the on-going 7 year United K ingdom Infrared Deep Sky Survey ( U K I D S S ; Lawrence et al . 2006) using the new U K Infrared Telescope 8www.j wst.nasa.gov 6.2. FUTURE IMAGING OF THE SHADES FIELDS 200 Wide Fie ld Camera ( U K I R T W F C A M ; Henry et al . 2003). The S X D F is an equatorial field and wi l l be accessible to A L M A and wi l l most definitely become a target for deep studies. In fact, several sources are currently being targetted by the SubMill imetre Ar ray in Hawaii ( S M A ; the world's first submillimetre interferometer; Chen et al . 1998), after Iono et al . (2006) showed that is is feasible to detect brighter S M G s wi th S M A . The goals of S H A D E S are important, but necessarily l imited. For example, the originally planned S H A D E S area was only just wide enough to measure the clustering of these galaxies. Even wi th the complete area of S H A D E S , the question Are these submillimetre galaxies the progenitors of today's massive elliptical galaxies? was going to be difficult to answer at best. Since S C U B A did not map the full S H A D E S area, the survey is not sensitive to adequately addressing this question, and so it remains to be anwered by future instruments. In addition, S H A D E S is deep enough to help clarify their redshift distribution, but only for the extremely luminous sub-population. Spectroscopic and photometric redshift work is underway now and is helping to determine the redshift distribution for this population in order to answer the question What is the star-formation history of the Universe?, which this thesis has been able to crudely estimate using the mean redshift distribution of S M G s and the S F R s estimated from fitted S E D s constrained by 350 fim data. The last question What fraction of SMGs harbour dust-obscured AGN? is being addressed by the S H A D E S consortium using X-ray and Spitzer data in hopes of determining the nature of the power source of S M G s . The S H A D E S source catalogue presented in this thesis is central to answering all of these questions and is being used to characterise the largest, most robust, and uniform sample of S M G s ever compiled. It is clear that a larger, more sensitive instrument is required to take the next leap i n this young field. Perhaps S H A D E S ' most important contribution is as a bridge to the next generation of surveys that have been planned wi th S C U B A ' s successor, S C U B A - 2 (see Hol land et al . 2006). The revolutionary design and scale of this instrument means that its observational programmes wi l l be unique for a decade to come. The U K , Canada, and the Netherlands are leading the S C U B A - 2 Cosmology Legacy Surveys to study important regions including the S H A D E S , C O S M O S and G O O D S fields, 6.2. FUTURE IMAGING OF THE SHADES FIELDS 201 wi th existing or upcoming complementary multi-wavelength data, ensuring the high im-pact of the results. This survey is a key part of a comprehensive extragalactic programme and wi l l be ~ 100 times wider and 2 times deeper than S H A D E S at 850 mn, while simul-taneously providing the first significant deep 450 (xm survey. Not only wi l l this survey uncover rare bright submillimetre galaxies, but it wi l l deliver a large number of fainter sources, facilitating for the first time a statistical study of the faint S C U B A source popu-lation that has evaded less sensitive preceding surveys. The objective of the survey is to answer some of the most fundamental questions: 1. Are these submillimetre galaxies the progenitors of today's massive elliptical galaxies?; 2. Does the bright submillimetre phase represent an early or final stage of galaxy formation, or is it more complex?; 3. What is the relationship between submillimetre galaxies and other high-redshift populations such as Lyman-break galaxies or Extremely Red Objects (EROs)?; 4- What is the nature of the galaxies that dominate the 450 fim sky? 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E . , 1980, The Large-Scale Structure of the Universe. Princeton Univ . Press, Princeton, N J Percival W . J . , Scott D . , Peacock J . A . , Dunlop J.S., 2003, M N R A S , 338; L31 BIBLIOGRAPHY 210 Pi lbra t t G . L . , 2003, S P I E Conf. Proc. V o l . 4850, IR Space Telescopes and Instruments, ed. J . C . Mather, 586 Pope A . , Borys C , Scott D . , Conselice C , Dickinson M . , Mobasher B . , 2005, M N R A S , 358, 149 Pope A . et al . , 2006, M N R A S , 370, 1185 Priddey R .S . , M c M a h o n R . G . , 2001, M N R A S , 324, L17 Puget J . L . , Abergel A . , Bernard J.P., Boulanger F . , Bur ton W . B . , Desert F . X . , Hat-mann D . , 1996, A & A , 308, L5 Ratnatunga K . U . , Griffiths R . E . , Ostrander E . J . , 1999, A J , 118, 86 Reach W . T . et al . , 1995, A p J , 451, 188 Roche N . , Shanks T. , Metcalfe N . , Fong R., 1993, M N R A S , 262, 456 Sabelhaus P . A . , Decker J .E . , 2004, S P I E Conf. Proc. V o l . 5487, Microwave and Terahertz Photonics, eds. A . Stohr, D . Jager, S. Iezekiel, 550 Sajina A . , Scott D . , Dennefeld M . , Dole H . , Lacy M . , Lagache G . , 2006, M N R A S , 369, 939 Salpeter E . E . , 1955, A p J , 121, 161 Sanders D . B . , 1999, A p & S S , 266, 331 Sanders D . B . , Mirabe l F . , 1996, A R A & A , 34, 749 Sanders D . B . , Soifer B . T . , Elias J . H . , Madore B . F . , Matthews K . , Neugebauer G . , Scoville N . Z . , 1988, A p J , 325, 74 Sawicki M . , Webb T . M . , 2005, A p J , 618, L67 Schechter P., 1976, A p J , 203, 297 BIBLIOGRAPHY 211 Scheuer P . A . G . , 1974, M N R A S , 166, 329 Schmidt J . H . M . M . , Maccacaro T. , 1986, A p J , 310, 334 Schmitt H .R . , Calzet t i D . , Armus L . , Giavalisco M . , Heckman T . M . , Kennicut t Jr., R . C . , Leitherer C . , Meurer G . R . , 2006, A p J S , 164, 52 Scott D . et al . , The Promise of the Herschel Space Observatory. Eds. Phi lbrat t G . L . , Cernicharo J . , Heras A . M . , Prust i T. , Harris R. , 2001, E S A - S P , 460, 305 Scott S.E., Dunlop J.S., Serjeant S., 2005, M N R A S , 370, 1057 Scott S .E. et al . , 2002, M N R A S , 331, 817 Searle L . , Z inn R. , 1978, A p J , 225, 357 Serjeant S. et a l , 2003, M N R A S , 344, 887 Simard L . et al . , 2002, A p J S , 142, 1 Smail I., Ivison R . J . , B l a in A . W . , 1997, A p J L , 490, L5 Smai l I., Ivison R . J . , Kneib J . - R , Cowie L . L . , B la in A . W . , Barger A . J . , Owen F . N . , Morr ison G . , 1999, M N R A S , 308, 1061 Smail I., Ivison R . J . , B l a in A . W . , Kneib J . - R , 2002, M N R A S , 331, 495 Smail I., Chapman S . C , B la in A . W . , Ivison R . J . , 2004, A p J , 616, 71 Somerville R .S . , in: Multiwavelength mapping of galaxy formation and evolution, Ben-der R. , Renzini A . , eds., E S O Astroph. Symp., Springer, Heidelberg, pre-print (astro-ph/0401570) Spergel D . N . et al. , 2003, A p J S , 148, 175 Steidel C . C . , 1999, Proc. Na t l . Acad . Sci. U S A , 96, 4232 BIBLIOGRAPHY 212 Steidel C C , Adelberger K . L . , Giavalisco M . , Dickinson M . , Pet t ini M . , 1999, A p J , 519, 1 Stevens J . A . , Page M . J . , Ivison R . J . , Carrera F . J . , Mi t t az J .P .D. , Smail I., M c H a r d y I . M . , 2005, M N R A S , 360, 610 Swinbank A . M . , Smail I., Chapman S . C , B la in A . W . , Ivison R . J . , Keel W . C , 2004, A p J , 617, 64 Swinbank A . M . et a l , 2005, M N R A S , 359, 401 Tacconi L . et al . , 2006, A p J , 640, 228 Takeuchi T . T . , Ishii T . T . , 2004, A p J , 604, 40 Tauber J . A . , 2004, A d S p R , 34, 491 Tilanus R . P . J . , 2004, J C M T Technical Report TR/001 /106 , http:/ /www.jach.hawaii-. e d u / J A C d o c s / J C M T / t r / 0 0 1 / 1 0 6 Teerikorpi P., 2004, A & A , 424, 73 Toomre A . , Toomre J . , 1972, A p J , 178, 623 van Kampen E . et al., 2005, M N R A S , 359, 469 von Hoerner S., 1967, A p J , 147, 467 W a l l J . V . , Jenkins C . R . , 2003, Practical Statistics for Astronomers. Cambridge Univ . Press, Cambridge Wang W . - H . , Cowie L . L . , Barger A . J . , 2004, A p J , 613, 655 Webb T . M . et a l , 2003, A p J , 582, 6 Webb T . M . et a l , 2003, A p J , 587, 41 BIBLIOGRAPHY 213 Webb T . M . A . , Yee H . K . C . , Ivison R . J . , Hoekstra H . , Gladders M . D . , Barrientos L . F . , Hsieh B . C . , 2005, A p J , 631, 187 Whi te S . D . M . , Frenk C.S. , 1991, A p J , 379, 52 Wiedner M . , 1998, P h D thesis, Cambridge Wi l son G . W . , Austermann J . , Logan D . W . , Y u n M . , 2004, S P I E Conf. Proc. V o l . 5498, Mil l imeter and Submillimeter Detectors for Astronomy, eds. J . Zmuidzinas, W . S . Ho l -land & S. Withington, 246 Wootten A . , 2003, S P I E Conf. Proc. V o l . 4837, Large Ground-based Telescopes, eds. J . M . Oschmann & L . M . Stepp, 110 Wright E . L . , Hinshaw G . , Bennett C . L . , 1996, A p J , 458, L53 Zemcov M . , Halpern M . , Pierpaoli E . , 2005, M N R A S , 359, 447 Zheng Z. , W u H . , Mao S., X i a X . - Y . , Deng Z . - G . , Zou Z . - L . , 1999, A & A , 349, 737 214 APPENDIX A NOISE SPIKE REMOVAL TESTS In June 2003, Co l in Borys, a former U B C P h D . student, discovered a large power spike at ~ 1/16 Hz coincident wi th the frequency of the secondary chopper in de-nodded, flatfielded, and extinction corrected 64-point jiggle map data. The telescope perfoms 1.024 second integrations on each of the 16-point jiggle pattern positions and nods to one side before repeating this procedure and nodding to the opposite side. This pattern is repeated two more times to complete a 64-point jiggle pat tern 1 . Thus, the telescope is moving by a large amount every 16 seconds (1 nod every 16 points x 1.024 s/point ~ 16nods/s). There may be some microphonic noise pickup when the telescope moves during the nod, corresponding to the noise appearing stronger in the bolometers at a frequency of « 1/16 Hz (see Zemcov et al . 2004, Coppin 2003) 300 jiggle map observations between 1998 and 2003 were analyzed by Co l in Borys and Remo Tilanus of the Joint Astronomy Centre ( J A C ) , and only observations taken between December 2002 and March 2003 seem to be affected by this anomaly (see F i g . A . l ) . The S C U B A fridge cycle at the end of March is likely responsible for fixing the problem (Borys 2003, private communication). Upon analysis of the Fourier spectrum of a sample of 2003 data, we discovered that this power spike occurs on the long-wave array in about two-thirds of the bolometers, while the remaining third had nominal signals, similar to what Borys found. The effect is also present in the short-wave array, but to a lesser extent. On ly about 10 per cent of the bolometers show this noise spike. This effect would be automatically removed after subtracting off the sky signal, if al l of the bolometers had this same spurious signal present in their frequency spectra. But since only a fraction of the bolometers have this signal, the effect of removing the mean 1When S U R F de-nods the data, each data point it reports is actually the sum of two 1.024 second measurements taken 16 seconds apart. 215 2 . 0 x i o - 4 r 0.00 0.05 0.10 0.15 Frequency (Hz) 0.20 0.25 > 1.2x10" 4 1.0x1 0" 4 8.0x1 0 - 5 o 6.0x10~ 5 c cn 4.0x10-5 2.0x10-5 0 0.00 0.05 0.10 0.15 Frequency (Hz) 0.20 0.25 Figure A . l : The top plot is the F F T of the timestream for bolometer G15 (or number 12) of the long-wave array, from 64-point jiggle map data taken of the S D F in M a y 2002. The bottom plot shows the F F T of the timestream for the same bolometer from 64-point jiggle map data taken of the same field i n March 2003. Note the power contained in the large noise spike at about 1/16 Hz in the lower plot. 216 sky background actually introduces this signal in the non-affected bolometers, corrupting them as well. The concern is that the presence of a periodic noise fluctuation on a similar timescale to the jiggle pattern may be affecting the data, thereby imposing unwanted structure on the map data to some degree. (Borys 2003, private communication). The effect of the noise spike was investigated specifically for the S H A D E S data by A l e x Pope, a member of the S H A D E S team. A summary is provided below. In order to assess its effect on the data, an aggressive attempt was made to remove the noise spike (see Section 2.2.5) as follows. First , the array average was removed as a function of time, using only the least-affected bolometers to estimate the sky at each time, so as not to introduce the spike into bolometers which do not already exhibit the excess power. Next, another function of time (essentially a template of the spike effect in the timestreams) was subtracted, for which each bolometer sees a different fraction. This fraction was found by minimising the spread i n each bolometer over time (i.e., using a minimum variance estimator) and is expected to be close to 0 for the bolometers which exhibit little evidence of any excess power and close to 1 (after being appropriately normalised) for the bolometers exhibiting the highest degree of excess power. This approach was applied to Reduction D , but the results should be applicable to al l reductions. Approximately 20 per cent of the S X D F data files appear to be contaminated by the noise spike. Whi le a l l 37 bolometers may contain the effect to some extent, about 30 per cent of them exhibit a significant excess of power in the power spectrum at a period of 16 samples. So overall, about 8 per cent of the data going into the S X D F map is significantly affected by the noise spike. A s a result of the spike removal, the R M S of Reduction D 's (my reduction) S X D F map was decreased by a mere 1 per cent, as compared to the reduction in which the spike's presence was ignored. It is found that the L H map is slightly more affected than the S X D F map: 30 per cent of the Lockman data files are affected and once the spike is removed the map R M S is improved by 3 per cent. For the 10/14 Reduction D-detected L H S H A D E S catalogue sources lying in regions wi th more than 50 per cent of their data affected by the spike, 217 no positional offsets are detected from the corresponding spike-removed map sources. Posit ional offsets of up to the 3 arcsec pixel size occur in the spike-removed Reduction D map for only 4 of the L H S H A D E S catalogue sources. In general the contaminated files are distributed fairly uniformly around the maps, although the worst examples are localised to specific regions. Hence even although the overall map R M S changed very little, it may sti l l be that the flux densities or positions of particular sources could be affected significantly. Signal, noise and S / N variations were checked and it was found that small differences do occur for sources detected in the noise-spike removed maps versus the regular maps, as expected. The flux densities and S / N values differ from the regular map values by about 5 per cent on average, and never by more than 10 per cent. Overall 28 per cent of the S H A D E S sources have been affected to any discernible extent by the presence of the noise spike, in terms of flux density, S / N or position. Approximately 25 per cent of these sources show positional offsets of < 3-4 arcsec from their original positions in the map, while the rest show no discernable positional differences. Therefore, it is found that the noise spike mainly contributes additional random noise to the source flux densities and centroids of the data, and thus can be safely ignored in our data reduction treatment. However, for a few of the most-severely affected sources a discussion of the effects is included in the individual source notes in Appendix B . 218 APPENDIX B NOTES ON INDIVIDUAL SOURCES Here are notes for some of the individual S H A D E S sources. LOCK850.1: This source has a relatively poor spatial x2 (3.13, where the +2 a range of the distribution extends to 2.16), which could perhaps be explained by its proximity to L O C K 8 5 0 . 4 1 (22arcsec away). LOCK850.2: More than 50 per cent of data in this region of the map were affected by the noise spike. Treating the noise spike as discussed i n Appendix A resulted i n a 2 per cent decrease in the flux and S / N and no discernible positional offset. LOCK850.5: Treating the noise spike as discussed in Appendix A resulted in an apparent offset in R A of 3 arcsec, an offset of 3 arcsec in D e c , and approximate differences in flux, noise and S / N of 2, 4, and 2 per cent, respectively. LOCK850.8: This source has a relatively poor temporal x 2 (—1-72, where the —2a range of the distribution extends to —1.60). LOCK850.10: This source was detected in the noisier edge region of the map (a > 3 mJy) . LOCK850.il: Treating the noise spike as discussed in Appendix A resulted in an apparent offset of —3 arcsec in Dec. and approximate differences in flux, noise and S / N of 1, 2, and 0 per cent, respectively. LOCK850.12: This source has a relatively poor temporal x2 (~ 1-70, where the —2a range of the distribution extends to —1.60). LOCK850.144- L O C K 8 5 0 . 1 8 is a nearby neighbour, 20arcsec away. LOCK850.15: This source has a relatively poor temporal x2 (—2.12, where the 2 a of the distribution extends to —1.60). This source also has a relatively poor spatial x2 (7.82, where the +2<7 range of distribution extends to 2.16). This source was detected in the noisier edge region of the map (a > 4 m J y ) . 219 LOCK850.18: L O C K 8 5 0 . 1 4 is a near neighbour, 20arcsec away. LOCK850.21: Treating the noise spike as discussed in Appendix A resulted in an apparent offset of 2.9 arcsec in R A and —3 arcsec in D e c , and approximate differences in flux, noise and S / N of 1, 1, and 2 per cent, respectively. LOCK850.22: Treating the noise spike as discussed in Appendix A resulted in an apparent offset of —3 arcsec in R A and approximate differences in flux, noise and S / N of 5, 2, and 2 per cent, respectively. LOCK850.33: Treating the noise spike as discussed in Appendix A resulted in an apparent offset of 3 arcsec in R A and —3 arcsec in D e c , and approximate differences in flux, noise and S / N of 3, 2, and 0 per cent, respectively. LOCK850.34' This source was detected in the noisier edge region of the map (a > 3 m J y ) . LOCK850.35: More than 50 per cent of data in this region of the map were affected by the noise spike. Treating the noise spike as discussed in Appendix A resulted i n a 4 per cent decrease in the flux, 2 per cent decrease in S / N and no noticeable positional offset. This source has a relatively poor temporal x2 (—1-94, where the —2a range of the distribution extends to —1.60). LOCK850.39: More than 50 per cent of data in this region of the map were affected by the noise spike. Treating the noise spike as discussed in Appendix A resulted in a 7 per cent decrease in the flux, 5 per cent decrease in S / N and no noticeable positional offset. LOCK850.40: This source has a relatively poor temporal x2 (—2.05, where the —2a range of the distribution extends to —1.60). LOCK850.41 '• This source has a relatively poor spatial x2 (5.98, where the +2 a range of the distribution extends to 2.16), which could be explained by its proximity to L O C K 8 5 0 . 1 (22arcsec away). LOCK850.43: Treating the noise spike as discussed in Appendix A resulted in an apparent offset of —3 arcsec in Dec. and approximate differences in flux, noise and S / N of 12, 0, and 12 per cent, respectively. 220 LOCK850.47: Treating the noise spike as discussed in Appendix A resulted in an apparent offset of —3 arcsec in R A and approximate differences in flux, noise and S / N of 6, 2, and 3 per cent, respectively. LOCK850.48: Treating the noise spike as discussed in Appendix A resulted in an apparent offset of —3 arcsec in D e c . and approximate differences in flux, noise and S / N of 4, 3, and 3 per cent, respectively. LOCK850.60: Treating the noise spike as discussed in Appendix A resulted in an apparent offset of 3 arcsec in Dec. and approximate differences in flux, noise and S / N of 6, 2, and 3 per cent, respectively. LOCK850.66: Treating the noise spike as discussed in Appendix A resulted in an apparent offset of 3 arcsec in Dec. and approximate differences in flux, noise and S / N of 2, 1, and 5 per cent, respectively. LOCK850.67: Treating the noise spike as discussed in Appendix A resulted in an apparent offset of 3 arcsec in Dec. and approximate differences in flux, noise and S / N of 3, 1, and 3 per cent, respectively. LOCK850.76: More than 50 per cent of data in this region of the map were affected by the noise spike. Treating the noise spike as discussed in Appendix A resulted in a 13 per cent decrease in the flux, a 9 per cent decrease in the S / N and no discernible positional offset. LOCK850.il: Treating the noise spike as discussed in Appendix A resulted in an apparent offset of —3 arcsec in R A and approximate differences in flux, noise and S / N of 1, 0, and 3 per cent, respectively. LOCK850.19: Treating the noise spike as discussed in Appendix A resulted in an apparent offset of —3 arcsec in R A , 3 arcsec in D e c , and approximate differences in flux, noise and S / N of 4, 4, and 9 per cent, respectively. LOCK850.100: This source was detected in the noisier edge region of the map (a > 3 mJy) . SXDF850.1: This source appears to be extended in the map in the NS direction. SXDF850.5: More than 50 per cent of data in this region of the map were affected 221 by the noise spike. Treating the noise spike as discussed in Appendix A resulted in a 6 per cent decrease in the flux, a 2 per cent decrease in S / N and no discernible positional offset. SXDF850.6: This source has a relatively poor spatial x2 (—2.28, where the —2a range of the distribution extends to —2.05). SXDF850.7: This source has a relatively poor spatial x2 (2.03, where the +2 a range of the distribution extends to 2.05). The poor fit could be a result of it being separated by less than 22arcsec from a lower significance rejected source (SXDF850.110). SXDF850.9: More than 50 per cent of data in this region of the map were affected by the noise spike. Treating the noise spike as discussed in Appendix A resulted i n a 1 per cent decrease in the flux, and no discernible change in S / N or position. SXDF850.10: This source has a relatively poor temporal x2 (2.27, where the +2a range of the distribution extends to 1.60). SXDF850.18: More than 50 per cent of data in this region of the map were affected by the noise spike. Treating the noise spike as discussed i n Appendix A resulted in a 6 per cent decrease in the flux, a 0 per cent change in S / N and a positional offset of —3 arcsec in Dec. SXDF850.19: Treating the noise spike as discussed in Appendix A resulted in an apparent offset of 3 arcsec in R A and approximate differences in flux, noise and S / N of 1, 2, and 0 per cent, respectively. This source has a relatively poor spatial x2 (2.75, where the + 2 a range of the distribution extends to 2.05). SXDF850.21: This source has a relatively poor spatial x2 (2.23, where the +2 a range of the distribution extends to 2.05). This source also has a relatively poor temporal x2 (1.84, where the +2 a range of the distribution extends to 1.60). SXDF"850.22: Treating the noise spike as discussed in Appendix A resulted in an apparent offset of 3 arcsec in R A , —3 arcsec in D e c , and approximate differences in flux, noise and S / N of 11, 2, and 7 per cent, respectively. SXDF850.27: More than 50 per cent of data in this region of the map were affected by the noise spike. Treating the noise spike as discussed in Appendix A resulted i n a 5 222 per cent decrease in the flux, a 3 per cent decrease in S / N and no noticeable positional offset. This source has a relatively poor spatial x2 (2.15, where the +2 a range of the distribution extends to 2.05). SXDF850.28: More than 50 per cent of data in this region of the map were affected by the noise spike. Treating the noise spike as discussed in Appendix A resulted in a 10 per cent increase in the flux, a 13 per cent increase in S / N and a positional offset of 3arcsec in R A . This source has a relatively poor temporal x2 (~ 1-75, where the —2a range of the distribution extends to —1.60). This source was detected in the noisier edge region of the map (cr > 3 m J y ) . SXDF850.37: Treating the noise spike as discussed in Appendix A resulted in an apparent offset of —3 arcsec in R A , and approximate differences in flux, noise and S / N of 1, 1, and 0 per cent, respectively. SXDF850.45: This source has a relatively poor temporal x2 (—1-85, where the —2a range of the distribution extends to —1.60). This source was detected in the noisier edge region of the map (a > 4 mJy) . SXDF850.41- This source has a relatively poor temporal x2 (1-80, where the +2 a range of the distribution extends to 1.60). SXDF850.50: More than 50 per cent of data in this region of the map were affected by the noise spike. Treating the noise spike as discussed in Appendix A resulted in a 10 per cent decrease in the flux, a 10 per cent decrease in S / N and no discernible positional offset. SXDF850.56: Treating the noise spike as discussed in Appendix A resulted i n an apparent offset of 3 arcsec in D e c , and approximate differences in flux, noise and S / N of 4, 1, and 3 per cent, respectively. SXDF850.63: More than 50 per cent of data in this region of the map were affected by the noise spike. Treating the noise spike as discussed i n Appendix A resulted in a 5 per cent decrease i n the flux, no discernible change in S / N and a positional offset of —3 arcsec in R A . SXDF850.69: More than 50 per cent of data in this region of the map were affected 223 by the noise spike. Treating the noise spike as discussed in Appendix A resulted i n a 15 per cent increase in the flux, a 15 per cent increase in S / N and a positional offset of —3 arcsec in R A . SXDF850.76: Treating the noise spike as discussed in Appendix A resulted i n an apparent offset of —3 arcsec in R A , —3 arcsec in D e c , and approximate differences in flux, noise and S / N of 1, 3, and 3 per cent, respectively. SXDF850.86: This source has a relatively poor temporal x2 (2.21, where the +2 a range of the distribution extends to 1.60). SXDF850.93: Treating the noise spike as discussed in Appendix A resulted in an apparent offset of 3 arcsec in Dec. and approximate differences in flux, noise and S / N of 3, 1, and 0 per cent, respectively. SXDF850.95: More than 50 per cent of data in this region of the map were affected by the noise spike. Treating the noise spike as discussed in Appendix A resulted in a 8 per cent decrease in the flux, a 6 per cent decrease in S / N and positional offsets of —3 arcsec in R A and —3 arcsec in D e c SXDF850.96: More than 50 per cent of data in this region of the map were affected by the noise spike. Treating the noise spike as discussed in Appendix A resulted in a 4 per cent decrease in the flux and a 3 per cent decrease in S / N , wi th no noticeable positional offset. 224 APPENDIX C E F F E C T I V E EXPOSURE TIMES It is common and straightforward to give total observation times, or perhaps in chopped systems the total time on source. These times give an indication of the amount of effort expended to collect the data. However, because the atmosphere is far from transparent at submillimetre wavelengths (even in the atmospheric windows) and the transmission is so weather dependent, the total exposure time does not give a good indication of data quality or expected noise level in the final output. It is more useful to refer to the effective total exposure which is the noise-squared weighted sum of exposure times referred to a completely transparent atmosphere. The optical depth of the atmosphere in a given direction is determined from the wavelength dependent optical depth at zenith, r \ , and the cosecant of the zenith angle, 9, of observation, called the airmass, A. Thus, the strength of an observed astronomical flux, S0 is: So = Se-T*®A<-0\ ( C . l ) A t 850/xm, the zenith optical depth, r 8 5 o, ranges from 0.16 in very good weather to 0.7 i n bad weather, and the optical depth at 350 or 450/xm is typically 7 times higher. The first step in combining data collected at different times of night wi th different values of T\ and A is to correct S0 for atmospheric absorption by mult iplying by eTxA (see Archiba ld et al . 2002). After correcting for atmospheric transients, etc., but not opacity, the output noise at the detector is fairly independent of atmospheric opacity, at least for S C U B A operating on the J C M T on Mauna K e a at 450 and 850 /mi , and for S H A R C - I I operating at 350 / m i at the C S O also on Mauna Kea . Therefore, the effective noise of an observation is inflated exponentially in T\ and A. The sum 225 Teff = ^ A T 0 e 2 T ^ t ) A (C.2) is the integration time that would be required wi th a completely transparent atmosphere to get the same noise level as a given noise-squared weighted sum of observations. We call this the effective exposure time and find that tracking this quantity during observations is an effective way to monitor experimental progress. This idea was conceived by M a r k Halpern during an observing run at the C S O . In practice, the optical depth as a function of time is obtained from automated mea-surements made at the C S O at 225 G H z every 10 minutes. The optical depths at sub-millimetre wavelengths are very well correlated wi th these values and one multiplies r225 by 4 and by 24 to get optical depths for S C U B A at 850 and 450 pm, and by 26 to get r for S H A R C - I I at 350pm (Archibald et al., 2002). A s a numerical example, observation of a source which rises through transit wi th an average airmass of 1.3 and T225 = 0.05 for 4 hours results in effective exposure times of 2.4 hours at 850 pm, 20.7 minutes at 450 pm wi th S C U B A , and 9.5 minutes wi th S H A R C - I I . The shorter effective times at shorter wavelengths is a consequence of the fact that the atmosphere is not very transparent at those wavelengths. This is why space experiments like S P I R E and BLAST are useful even wi th comparatively small apertures, and why neither of those experiments carries an 850 pm channel. Experience has shown that effective exposures of between 500 and 600 seconds wi th S H A R C - I I are often sufficient to detect faint extragalactic high-redshift sources (Col in Borys and A t t i l a Kovacs, private communication). 226 APPENDIX D OTHER ESTIMATES OF THE N U M B E R COUNTS This appendix provides an account of complementary approaches undertaken by Reduc-tions B (another version of the 'direct estimate', an approach also used by the author and described i n Section 4.3) and C (a 'parametric fitting' approach which self-consistently estimates the prior source density spectrum, the F D R and the source deboosting). A p -pendices D . l and D.2 describe work not done by the author; the work is presented for completeness (Coppin et al. , 2006) since the results of the other reductions are used as a consistency check in Section 4.3. In addition, a summary and comparison of a l l three methods is provided by the author at the end of this Appendix (D.3). D . l Another Direct Estimate of the Differential Source Counts Direct estimation of the source count density was carried out independently working from a catalogue derived from Reduction B . The main differences in the approach are listed below. Instead of calculating an effective area, an explicit coverage area, A, corresponding to the port ion of a given map wi th observed noise below aQ = l O m J y is used. Source candidates are rejected outside of this region. Deboosted source posterior flux probability density functions are obtained using the normalised histogram of S / N in the coverage area of a given map, H(S0/a0) to estimate P(Si\S0,a0) in Equation 3.2 instead of the Gaussian distribution used i n Coppin et al . (2005). This is a small difference, since the noise is very well described by a Gaussian distribution. However, the posterior probability density functions D.J. ANOTHER DIRECT ESTIMATE OF THE DIFFERENTIAL SOURCE COUNTS 227 are truncated outside the region (S0/2 < S\ < 2SQ). Examples of these deboosted flux density distributions are plotted in Fig. 4.2. Source completeness is estimated by Monte Carlo techniques. This is defined to be C(S[), the detection probability for a source of actual flux density S\ which is located within the coverage area. Sources are inserted into a given map and are counted as detected if they are found by the source detection algorithm, if their recovered location is within 7 arcsec of the insertion position, and if the recovered flux density is within a factor of two of the input flux density. Simulated sources recovered within 7 arcsec of a genuine catalogue source in this process are discarded. C(S{) is the ratio of recovered sources to simulated sources, calculated in half mJy bins. Source reliability, R(S0/a0), is calculated as a function of recovered S/N. For each of the six chop-maps, an artificial sky is generated consistent with the source count models of Scott et al. (2002) and random noise is added, consistent with the actual noise maps. Source extraction is performed just as it is on the actual survey data. Recovered sources are identified with input sources if they lie within 7 arcsec in position and their recovered flux densities are within a factor of two of each other. R is calculated as the ratio of the number of identified sources at a given S/N to the total number of recovered sources at that S/N. A selection catalogue is formed from Reduction B containing all sources with S/N > 3.5 and with a0 < 10 mJy. The mode of the posterior flux density probability distribution is found for each source, S — mode[Pd(S'i|S'o, er0)], and the contribution of each source in this catalogue to the number of sources per square degree is calculated as ^ = R(S/a0) A x C(S) The total source number density in a given flux density bin is the sum of AN(S) over all members of the catalogue whose mode, S, lies in the flux bin. The uncertainty is D.2. PARAMETRIC MODEL FITS TO ESTIMATE THE DIFFERENTIAL SOURCE COUNTS 228 calculated as the quadrature sum of uncertainties estimated for R, A, and C, added to the Poisson uncertainties calculated for the number of members of the catalogue wi th S in the flux bin. D.2 Parametric Model Fits to Estimate the Differential Source Number counts are calculated from Reduction C by fitting models to observed source catalogues. This technique is similar to the methods used by Borys et al . (2003) and Laurent et al . (2005) for the analyses of S C U B A and Bolocam data, respectively. Source catalogues were first generated for each field by identifying al l 2.5 a peaks in the maps. The area of the maps analysed are defined as the regions having a photometric error a0 < 5 m j y b e a m _ 1 . The model is developed by first expressing the probability distr ibution of the source catalogue p(S0,a0), where S0 and aQ are the observed flux densities and photometric uncertainties respectively, as the sum of the probabilities of the source being a real detection of an object wi th intrinsic flux density S„ Pd(S\, S0, aQ), and being a false detection, Pf(S0,a0), The subscript d (f) is shorthand for the conditional probability that the source is a true (false) detection. Also, note that p(S0,a0) integrates to 1. The joint probabili ty distribution for al l of the true detections can be further factored: The scattering function P d ^ o l S i j ^o) is the probability distribution of observed flux densi-ties given an intrinsic flux density and measurement error, and hence contains information about the flux bias due to source blending. The function Pd(o~0\S[) is the differential com-pleteness, since integrating over aa is C(S\), the probability of detecting a source wi th Counts (D.2) pd(Si, S0, e r 0 ) = Pd(S0\Si, cr0)pd(a0\Si)p{Si). (D.3) D.2. PARAMETRIC MODEL FITS TO ESTIMATE THE DIFFERENTIAL SOURCE COUNTS 229 intrinsic flux density Si (see Figs. D . l and D.2). The final factor p(<Si) is the underlying probabili ty distribution of sources wi th intrinsic flux densities S\. The total number of sources detected in the catalogue is the number density of sources per square degree N multiplied by the survey area A. Mul t ip ly ing each side of Equa-t ion D.2 by AN, and applying the factorisation in Equation D.3, gives the observed number density of sources in the catalogue Af as a function of SQ and a0: M(So,a0) = Afpd(S0\Si,a0)pi(*0\Si)N(Si)dSi (D.4) +ANt(S0,a0). Here J\f(S0,a0) = ANp(S0,a0), N(S[) = Np(S{) is the underlying differential source counts per square degree, and JVf = Np((S0, a0) is the spurious detection rate per square degree. The left hand side of this equation and the area A are measured directly from the survey. B o t h the scattering and differential completeness functions are calculated using Monte Carlo simulations, leaving the differential source counts N(S\) as the only free parameter to be solved for. It is t r ivial to extend this model to a combined source catalogue J\fcom(S0, aQ) from M independent surveys i taken wi th the same instrument, provided the different pd(a0\Si), Nf(S0,a0), and A1 are known: Afcom(SQ, a0) = / pd(S0\Si, <T0)N(Si) [ ^VdKISi ) ] dS{ (D.5) ^ i i To calculate Pd(S0\Si, cr0) and Pd{o~0\Si) mock bolometer data were generated using realisations of Gaussian noise wi th the same variance as the real data. To these data were added the effect of a population of spatially uniformly distributed point sources wi th a flux density distribution following the number counts measured by Borys et al . (2003). Source catalogues of al l 2.5 a peaks were created in the same way as the catalogue for the real data. A n attempt was then made to identify each observed point source wi th objects D.2. PARAMETRIC MODEL FITS TO ESTIMATE THE DIFFERENTIAL SOURCE COUNTS 230 in the input catalogue within a 6 arcsec radius. If there were intrinsic sources associated wi th the peak, the brightest was considered the match, S{. In this way the observed flux density in an aperture was related to the flux density for the single brightest source that fell wi th in the measurement aperture; other fainter sources simply contribute to the upward flux bias of this one source through blending. To avoid sensitivity to extremely faint counts that were not sampled by the survey (whose effect is highly model-dependent) only sources wi th Si > 2 m J y were allowed to be matched (the survey was found to be approximately 10 per cent complete at this level). The survey is therefore defined to have a completeness of 0 for Si < 2 mJy wi th this model. The rate of detection of sources Si, and the distribution of Si, SQ and a0 using 500 sim-ulated maps was used to estimate ^ ( S o l - S i , ao) ( s e e F i g . D.2) and Pd(o-0\S{) (see F i g . D . l ) in bins of width l m J y for 5; and 0.125 mJy for .So and aQ. The b in sizes for SQ and aQ were chosen so that the probability of having more than one source in a b in is small, so that one can use simple Poisson statistics. The coarser b in size for Si was adopted so that the Monte Carlo simulations would converge more quickly, and since Si does not require high resolution because of the width of the posterior flux density distribution (see F i g . 4.2)., A t flux densities > l O m J y Pd{S0\Si,a0) did not fully converge after the 500 simulations since the number density of sources is so low (<C 1 source per bin). A t fainter flux densities it was compared wi th a Gaussian model truncated appropriately for the 2.5 a source selection criteria (see F i g . D.2) and was found to be indistinguishable. Rather than run a much larger number of Monte Carlo simulations, the scattering function was instead replaced by the smooth theoretical model. Peaks in the map wi th no intrinsic counterparts were considered spurious detections (either pure noise or in extremely rare cases blended sources wi th flux densities < 2 mJy) and were used to estimate the false detection rate Nf(S0, a0) per square degree using the same bins. To solve for N(S{) in Equation D.5, a discrete non-parametric binned model was first adopted, N(j). Each flux density b in j was chosen to be 2 m J y wide (comparable to the photometric uncertainty). Rather than assuming a constant density of sources across the bin, the counts were modelled by the product of a free scale parameter, a,j, w i th D.2. PARAMETRIC MODEL FITS TO ESTIMATE THE DIFFERENTIAL SOURCE COUNTS 231 an exponential template function similar to the counts spectrum measured in previous surveys: N(j) = ajTj (D.6) T / S-38dS, (D.7) where S{ovr and 5 ^ i g h are the flux density limits for the jth bin. A downhill simplex optimiser was used to solve for the a, by maximizing the joint Poisson likelihood, £ , of observing the true number of detected objects in each b in J\f(j, k) given the expected distribution k) produced by the model in Equation D.4, where j and k denote bins of S0 and aQ respectively: In order to prevent non-physical answers the ctj were constrained to be positive. In addi-tion, it was discovered that the solutions were highly unstable and adjacent bins would frequently oscillate between 0 and very large values. To remedy this type of problem the fits were further constrained such that the N(j) were monotonically decreasing wi th 5\. To calculate the uncertainty in the model, maximum likelihood solutions were re-calculated for 500 realisations of mock data. These data were generated by drawing the same number of sources as i n the real list from the maximum likelihood distribution JV(S0, <T0) for the real data. In Figs. 4.10 and 4.11, the error bars represent the frequentist 68 per cent confidence intervals for the distribution in each bin. The integral source count spectrum (and uncertainty) was obtained by directly integrating each model N(j). Finally, the 500 fits of N(j) allowed us to directly calculate the sample covariance matr ix (N(j),N(k)). Despite the non-negative and monotonically decreasing constraints placed on the binned source counts model, the binned differential number counts have a significantly larger scatter than was observed in the other groups' estimates. This behaviour in the D.3. SUMMARY OF DIFFERENCES BETWEEN THE THREE METHODS 232 model fitting process is probably due to the bin size being inappropriately small given the uncertainty i n the posterior flux density distributions for individual sources, and also the fact that less prior information was used as a constraint (see discussion in Section D.3). This problem is analagous to the increased noise one obtains in an astronomical image when trying to deconvolve the point spread function wi th small pixels compared wi th the F W H M . Finally, the model fitting procedure was constrained by replacing the binned represen-tat ion of N(Si) in Equat ion D.5 wi th a smooth parametric model following Equat ion 3.1 (for consistent notation replace dN/dS wi th N(S{)). A s wi th the binned model, max-imum likelihood solutions were found for the model parameters N',S',a and B. The parameter covariance matrix was also obtained using 500 sets of data generated from Monte Carlo simulations. The 68 per cent confidence envelope for these models is clearly smaller than the uncertainties of the individual count bins (see Figs. 4.10 and 4.11). A l l of the analysis undertaken for each field separately was repeated using Equa-t ion D.4 to calculate joint fits of the differential source counts to both fields simultane-ously. Reduction C tested for bias in the recovered number counts by simulating 10 data-sets wi th a range of reasonable source count models. Source catalogues were produced from these data in the same manner as for the real data. Using the methods of Section D.2 (with the same fixed estimates of Pd(<S'o|>S'i, o~0) and Pd{o-0\Si)) the recovered binned counts were in each case consistent wi th the input counts wi th insignificant systematic bias. The correction factor in the lowest bin is consistent wi th what was found by Reduction D's direct estimate of the source counts (cf. 4.3.1). D.3 Summary of Differences Between the Three Methods Having described each group's techniques for calculating posterior flux density distribu-tions and number counts, it is now appropriate to discuss several key differences: the amount of information used; the interpretation of posterior flux densities; and the prob-D.3. SUMMARY OF DIFFERENCES BETWEEN THE THREE METHODS 233 Figure D . l : The completeness for L H as calculated by Reduction C . The left panel shows the differential completeness Pd(&0\Si), the probabili ty of a source being de-tected at a noise level a0 given an intrinsic flux density S[. The variations in the vertical direction in this plot reflect the relative areas of the map that reached a given noise level. The L H map had a small deep port ion wi th a mean noise ~ 1.2 mJy, and a large shallower region wi th a mean noise ~ 2mJy, corresponding to the lower and upper horizontal bands, respec-tively. Marginalizat ion over aQ (right panel) gives the more typical definition of completeness, the probability that a source is detected as a function of instrinsic flux density, Pd(Si). D.3. SUMMARY OF DIFFERENCES BETWEEN THE THREE METHODS 234 J O . O 10 15 Input Flux Density [mJy] Figure D.2: The scattering function Pd(S0\Si,a0) at a fixed noise level aQ = 1.94mJy for Reduction C . Vertical bands in this plot are the distr ibution of observed flux densities that could be measured for a fixed intrinsic flux density and photometric error. In the absence of bias and wi th Gaussian photometric uncertainties this distribution is simply a Gaussian wi th standard deviation a0 and a mean S0 equal to S[ (the dashed line). However, at flux densities S\ < l O m J y the scattering function changes shape. The decision to impose a 2.5 a cut in the source list makes it impossible to detect a source at lower S / N and is shown by the dotted line. In addition, confusion wi l l tend to cause the faintest sources to appear brighter than they really are. Since the 850 /xm extra-galactic confusion limit is at ~ 1 mJy, however, this effect is negligible. D.3. SUMMARY OF DIFFERENCES BETWEEN THE THREE METHODS 235 Observed Flux Density [mJy] Figure D .3: Reduction C s observed source distribution (red stars) compared wi th the expected distribution N(S0,a0) (shaded region) in L H for the maximum likelihood differential counts distribution N(S{). The diagonal black line shows the detection threshold of 2.5 <r0 that was used to construct the source list for determining the counts. The dashed contour indicates where the real and spurious parts of Equation D.5 are equal. Therefore sources detected along this contour have equal chances of being true detections of objects wi th intrinsic flux densities greater than 2mJy, or spurious detections (i.e., fainter than 2 m J y ) . Similar to the detection threshold line i n F i g . 4.4 this contour is not parallel to the line of constant S / N . Sources are more likely to be true detections in the bot tom right region of this plot. D.3. SUMMARY OF DIFFERENCES BETWEEN THE THREE METHODS 236 lems inherent i n calculating the F D R and completeness. The philosophies adopted by each group to calculate posterior flux density distribu-tions vary in a number of subtle ways. First , what flux density was calculated? In the case of Reduction C the method is attempting to estimate the flux density of the bright-est source in the beam, while Reductions B and D calculate the posterior distribution for the beam-smoothed flux density map. The former may be more desirable for determining source counts, since it directly ties measurements to individual objects. In practice, cor-recting for the confusion is a difficult procedure, which depends not only on knowledge of the source counts, but also their spatial clustering (Takeuchi & Ishii, 2004). However, since the bulk of the sources detected in S H A D E S have flux densities well above the extra-galactic confusion l imit , simply taking the total posterior flux density in a beam as in the case of Reductions B and D is acceptable for the purpose of calculating source counts. Furthermore, this deboosting technique avoids the possibility of introducing fur-ther model-dependent errors into the posterior flux densities in the S H A D E S catalogue; for this reason the selection procedure for the S H A D E S catalogue uses the Coppin et al . (2005) algorithm. How much information is derived completely from the data, and how much informa-tion is assumed? Each of the reductions uses prior knowledge of the 850 / m i extra-galactic source counts measured in previous blank-field and lensing cluster surveys to create sim-ulated source catalogues, and to simulate maps exhibiting the chop pattern. Reductions B and C use such maps (including noise) to Monte Carlo the source detection procedure, and to cross-correlate detected sources wi th the input catalogue in order to determine completeness. Sources in the output catalogue wi th no corresponding sources in the in-put catalogue are used to measure the F D R based on the selection criteria for the source list. Reduction D uses the simulated maps (with no instrumental noise added) strictly as a prior for the posterior flux density distributions. Spurious sources are handled by constructing the catalogue in such a way that it is nearly free of spurious sources. C o m -pleteness is determined by introducing fake sources into the real map and attempting to recover them over a range of input flux densities. A n additional completeness correction D.3. SUMMARY OF DIFFERENCES BETWEEN THE THREE METHODS 237 is calculated in a manner similar to Reductions B and C by ensuring that the recovered source density matches the input source density in a separate simulation that includes both sources and noise. Reductions B and D both choose to calculate the differential source counts i n bins directly from the posterior flux density distributions of sources in their catalogues. There is clearly a possiblity for the prior used in the posterior flux density calculation to bias the estimate of the source counts. Reduction B handles this problem by using the pixel distribution in the observed map itself as a prior for individual sources. Reduction D tests the procedure on maps wi th sources drawn from several different source count models, while keeping the prior for de-boosting fixed to test for bias (see Section 4.3.1). Rather than assuming a prior, Reduction C leaves the prior as a free parameter and attempts to fit it to the observed catalogue. The simulations undertaken, by al l reductions indicate that the uncertainty i n the completeness introduced by different source count models is dominated by other un-certainties in the counting procedure (map noise and Poisson counting uncertainties). In the case that sources are completely isolated, the probability that they are detected (i.e., completeness) is only a function of the noise. O n the other hand, source blending near the detection threshold may affect completeness as a function of the underlying source density. Sources that blend together and are detected as a single bright source increase the completeness if individually they would not have been detected, but decrease the completeness if individually they could have been detected. The faintest sources that are counted are > 2 mJy. The full range of integral source counts at this flux density measured here, and in previous work, is conservatively between 1000 and 10000 sources per deg 2 . Therefore, for spatially uniformly distributed objects there are on average ~ 0.02-0.2 sources that land wi thin a beam (the solid angle of the S C U B A beam is ~ 2 x 10~ 5 deg 2 ; the F W H M 2 ) . Given the Monte Carlo simulations undertaken i n Sec-tions 4.3.1 and D.2, using a plausible range of different input source counts models, it is therefore not surprising that the variations in the completeness corrections down to 2 m J y are dominated by uncertainties other than the variations in the counts model. D.3. SUMMARY OF DIFFERENCES BETWEEN THE THREE METHODS 238 W h i c h method is best? Since the 850/mi source counts are known well enough to construct a useful prior, it makes sense to use this information in the analysis of S H A D E S data. It is not surprising that Reductions B and D quote smaller uncertainties than Reduction C in the binned differential counts, since more information is being used. O n the other hand, for surveys at a wavelength for which little information is known, the technique for binned counts described in Section D.2 is more conservative. The technique adopted by Reduction C is more useful once a smooth parametric model is assumed to describe the source counts. Constraining the counts i n this way produces a range of models, wi th a spread generally consistent wi th the smaller error bars quoted by the other groups for the flux density bins. Furthermore it offers the cleanest way for constraining the model; the model parameters are varied directly to calculate the likelihood of observing the source catalogue. W i t h Reduction D , on the other hand, parametric models are fit to. the binned counts calculated previously. However, the binned differential counts from Reduction D can more easily be combined wi th counts from other surveys to constrain models over wider ranges in flux density, because the data products that come out of the procedure are binned counts and a bin-to-bin covariance matrix. For this last reason, the number counts and bin-to-bin covariance matr ix of Reduction D are used. It is reasonable to select one group's reduction, since the three sets of counts cannot be easily combined like what was done for flux densities or positions, and moreover al l of the counts across reductions appear to be consistent wi th each other wi th in the error bar estimation, for al l but the lowest b in (where Reduction B appears to be low). In model tests the best fit parameters using the counts of Reduction D (my reduction) are quoted, since that reduction provides the smallest error bars (cf. Section 4.1.1), while using the 68 per cent confidence intervals of Reduction C as a consistency check. The differential counts for L H and S X D F are shown in Figs. 4.10 and 4.11, respectively. 

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