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A sub-millimetre survey of dust enshrouded galaxies in the Hubble Deep Field region Borys, Colin James Kelvin 2002

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A S U B - M I L L I M E T R E S U R V E Y O F D U S T E N S H R O U D E D G A L A X I E S I N T H E H U B B L E D E E P F I E L D R E G I O N Bv Col in James Kelvin Borys B. Sc. (Engineering Physics) University of Saskatchewan, 1993 M . Se. (Physics) University of Bri t ish Columbia., 1997 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 K 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 D E P A R T M E N T O K P H Y S I C S A N D A S T R O N O M Y We accept this t h e s i s j j c i f j c o t ^ n i m n g to the required standard University of British Columbia October 2002 (e) Colin .buries Kelvin Borys, 2002 In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of Br i t i sh Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my depart-ment or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Physics and Astronomy University of Br i t i sh Columbia Vancouver, Canada Abstract This thesis investigates the emission of sub-millimetre-wave radiation from galaxies in the Hubble Deep F ie ld Nor th region. The data were obtained from dedicated ob-serving runs from our group and others using the S C U B A camera on the James Clerk Maxwel l Telescope. The data were combined using techniques specifically developed here for low signal-to-noise source recovery. The sources found represent over 10% of all cosmological sources S C U B A has detected since it was commissioned. The number of sub-mm galaxies we detect account for a significant fraction of the sub-mm back-ground, and we show that mi ld extrapolations can reproduce it entirely. We comment on their clustering properties, both with themselves and other high-redshift galaxy types. A multi-wavelength analysis of these galaxies shows that S C U B A sources do not al l have similar properties, and are made of a collection including: star-forming radio galaxies; optically invisible objects; active galactic nuclei; and extremely red objects. Reasonable attempts to determine the redshift distribution of the sample show that S C U B A galaxies have a median redshift of around 2, and suggest that the global star formation rate may be dominated by such objects at redshifts beyond about 1. The thesis summarises the current state of extra-galactic sub-mm astron-omy, and comments on how new surveys and detectors w i l l allow us to place stronger constraints on the evolution properties of the high-redshift Universe. i i Table of Contents Abstract ii Table of Contents iii List of Tables vi i List of Figures viii List of Acronyms x Acknowledgments xii Preface: Astronomy primer for the non-expert xiii Chapter 1: Sub-millimetre Extra-galactic Astronomy 1 1.1 The Far-Infrared Background 2 1.2 Cont inuum sub-mm emission from galaxies 4 1.2.1 Mechanisms that can power the sub-mm emission 6 1.3 Parameterisation of the Dust Spectral Energy Distr ibut ion 7 1.3.1 Observed SEDs of local IR bright galaxies 8 1.3.2 Est imat ing dust mass from sub-mm flux 8 1.3.3 Est imat ing star formation rates from sub-mm flux 10 1.4 Multi-wavelength properties of sub-mm galaxies 10 1.4.1 G a m m a Ray 11 1.4.2 X - R a y 11 1.4.3 U V - O p t i c a l 12 1.4.4 N I R 12 1.4.5 M I R 13 1.4.6 Radio 13 1.5 The effects of redshift on sub-mm observations 13 1.5.1 Spectroscopic redshifts 14 1.5.2 Photometric redshifts from far-IR SEDs 16 1.5.3 Correlations between redshift and F I R / r a d i o flux ratios . . . . 16 1.6 Issues that sub-mm surveys hope to answer 16 1.7 A guide to this thesis 18 Chapter 2: S C U B A - Instrument and data properties 20 2.1 Opt ica l design 21 2.1.1 S C U B A Upgrades 22 2.2 S C U B A Observing Modes 22 i i i 2.2.1 Photometry Mode 23 2.2.2 Jiggle-map Mode 27 2.2.3 Raster-scan Mode 27 2.3 S C U B A data reduction process 27 2.3.1 Prel iminary Steps 28 2.3.2 Ext inct ion Correction 28 2.3.3 Removal of thermal sky and cosmic ray emission 28 2.3.3.1 Using the 850 pm data to remove atmospheric signals 29 2.3.3.2 Using the 450 pm array as an atmospheric monitor . 31 2.4 Mode Specific Cal ibrat ion 32 2.4.1 Photometry 35 2.4.2 Jiggle-map 35 2.4.3 Raster-scan calibrations 37 2.5 Correlation analysis of S C U B A time-stream data 38 2.5.1 Correlations between bolometers 38 2.5.2 Spectral analysis of individual bolometer time-streams . . . . 38 Chapter 3: Creating S C U B A maps and extracting point sources . 44 3.1 Maps 44 3.1.1 Raw maps 44 3.1.2 Small area surveys: Direct inversion of the mapping matr ix for jiggle-map observations 46 3.1.2.1 Direct inversion applied to simulated data 48 3.1.2.2 Direct inversion applied to real data 49 3.1.3 Large area surveys: Iterative matrix inversion for scan-maps . 50 3.1.3.1 Iterative inversion applied to simulated data 53 3.1.3.2 Iterative inversion applied to real data 54 3.2 Co-adding maps 59 3.3 Extrac t ing point sources from sub-mm maps 62 3.3.1 Is deconvolution required at all? 63 Chapter 4: The H D F Super-map I: Sub-mm properties 64 4.1 Da ta reduction and source extraction 65 4.1.1 F l u x and pointing calibration 65 4.1.2 Source detection 68 4.2 Monte-Carlo simulations 69 4.3 Sub-mm sources in the H D F 71 4.3.1 Comparing the source list against previous surveys 78 4.3.1.1 The central H D F region from Hughes/Serjeant et al . 78 4.3.1.2 H D F flanking field jiggle-maps from Barger et al . . . 78 4.3.1.3 Scan-map observations of Borys et al 80 4.3.2 Comparison wi th photometry observations 80 4.3.3 Comparison wi th the jiggle-map observation M 0 0 B C 0 1 . . . . 80 4.4 Number counts of sub-mm sources 82 4.4.1 The 850 pm number counts 83 iv 4.4.2 The 450 //m number counts 86 4.5 The 850 / im sub-millimetre background 86 4.5.1 Evolut ion of sub-mm sources 89 4.5.2 A connection with modern-day elliptical galaxies? 90 4.6 Clustering of sub-mm sources 90 Chapter 5: H D F Super-map II: Multi-wavelength analysis 96 5.1 Statistical criterion for finding counterparts 96 5.1.1 The P-s ta t is t ic 97 5.1.2 Statistical measures of sub-mm flux from known objects . . . 97 5.1.3 Comparison against local I R luminous SEDs 98 5.1.4 Our approach to counterpart identification 99 5.2 Overview of available multi-wavelength data 99 5.2.1 V L A and W S R T radio observations 101 5.2.2 Chandra X - R a y imaging 104 5.2.2.1 The clustering of sub-mm and X- ray sources 106 5.2.2.2 The nature of the X-ray emission 108 5.2.3 Opt ica l -NIR imaging 109 5.2.3.1 Opt ical L B G dropout surveys I l l 5.2.4 ISO mid-IR imaging 114 5.3 Breakdown of each S C U B A object 114 5.4 The pathological object HDF850.1 128 5.5 Radio jet induced star formation 129 5.6 Redshift distribution of S C U B A sources and star formation rates . . . 130 5.6.1 Star-Formation history of the Universe 131 5.7 Summarizing the S C U B A population 136 Chapter 6: Discussion 139 6.1 S C U B A / s u b - m m data collection and analysis 139 6.1.1 Sky correction 139 6.1.2 O n Scan-mapping versus Jiggle-map mosaics for large surveys 140 6.1.2.1 Efficiency for point sources 141 6.1.2.2 Source recovery rate 141 6.1.2.3 Scan/Jiggle-map Comparison 141 6.1.3 Observing strategies 142 6.2 Wha t we have learned about sub-mm sources 142 6.2.1 Resolving the F I R background into sources 143 6.2.2 How does the star formation rate change over time? 143 6.2.3 Are high redshift I R bright sources the progenitors of modern day ellipticals? 146 6.2.4 Do sub-mm sources cluster? 147 6.2.5 Wha t are the multi-wavelength properties of sub-mm sources? 147 6.3 Current or upcoming Sub-mm programmes 148 6.3.1 S C U B A multi-wavelength observations 149 6.3.2 The Half-Degree Fie ld B L A S T / S C U B A Survey 149 v 6.3.3 S H A R C I I 150 6.3.4 B O L O C A M and M A M B O 151 6.3.5 I R A M Interferometry 151 6.4 Future Sub-mm instruments 151 6.4.1 J C M T and S C U B A 2 151 6.4.2 The Large Mil l imetre Telescope 152 6.4.3 Interferometry wi th S M A / A L M A 152 6.4.4 S J H T F / S O P H I A 153 6.4.5 Herschel(FIRST)/Planck 153 6.5 The Future of the H D F - N 154 References 155 Appendix A : S C U B A Analysis Notes 164 A . l Converting raw data into a calibrated time-stream 164 A . 2 Est imat ion of sub-mm atmospheric opacity 165 v i List of Tables 2.1 Photometry calibration observations of C R L 6 1 8 36 2.2 Jiggle-map calibration observations of C R L 6 1 8 37 2.3 Scan-map calibration observations of C R L 6 1 8 38 4.1 Summary of S C U B A H D F Observations 66 4.2 Sub-mm detections in the H D F super-map 74 4.3 850 / im source counts from the H D F super-map 87 4.4 450 fim source counts from the H D F super-map 89 5.1 Counterpart search radii for various classes of objects. 98 5.2 Radio detected objects near S C U B A sources 103 5.3 X-ray detected objects near S C U B A sources 105 5.4 ISO 15/tm detected objects near S C U B A sources 115 5.5 Redshift Summary of H D F - N sub-mm sources 133 5.6 Multi-wavelength summary of S C U B A detections 137 v i i List of Figures 1.1 Opt ica l and F I R images of Centaurus A 2 1.2 The Extra-galactic background 3 1.3 General shape of a nearby U L I R G spectral energy distr ibution 5 1.4 SEDs of local I R luminous sources 9 1.5 The effect of redshift on sub-mm observations. 15 2.1 Sub-mm atmospheric transmission function 20 2.2 The S C U B A bolometer arrays 23 2.3 A schematic of the S C U B A chop/nod strategy 24 2.4 Chopping operation on an optical image 25 2.5 Chopping geometry 26 2.6 Raw time-streams from S C U B A observations of B1933 30 2.7 Using the 450 / i m signal to remove the atmosphere from the 850 / i m array 33 2.8 Comparing the sky monitors 34 2.9 Correlation coefficient between 850 / im bolometers 39 2.10 F F T of a scan-map 850 / im time-stream taken before the upgrade. . . 41 2.11 F F T of a scan-map time-stream taken after the upgrade 42 2.12 F F T of a jiggle-map time-stream 43 3.1 Inverting the mapping matrix 49 3.2 App ly ing matr ix inversion to an observation of MS0451 51 3.3 Residuals between input and output maps as a function of iteration. . 55 3.4 M a p of residuals as a function of iteration 56 3.5 Fourier transform of residual between input and maps made from an iterative solution 57 3.6 1 / / behaviour of residual power in iterated maps 58 3.7 Demonstrating baseline issues in scan-map data 59 3.8 Determining offsets between S C U B A maps 61 4.1 Layout of the S C U B A H D F observations 67 4.2 Number of sources in the 850 / i m map expected at random 70 4.3 450 / im source recovery Monte-Carlo results 72 4.4 850 /tm source recovery Monte-Carlo results 73 4.5 The 850 / im S N R map 75 4.6 The 450 / im S N R map 76 4.7 Finder chart for sub-mm sources detected in the H D F super-map. . . 77 4.8 Our new source list compared wi th previously reported detections. . . 79 4.9 Comparing super-map fluxes with photometry estimates 81 v i i i 4.10 Summary of the 850 /xm source-count calculation 84 4.11 The 850 / im cumulative source counts 88 4.12 Angular two-point correlation function estimate for the H D F super-map sources 93 4.13 Nearest Neighbour clustering analysis 94 5.1 Overlay of field coverage relative to the H D F - N super-map 100 5.2 Clustering between S C U B A and X-ray detected objects 107 5.3 Stacked sub-mm flux as a function of X - R a y hardness ratio 110 5.4 Stacked sub-mm flux as a function of E R O cut 112 5.5 Postage stamps of the > 4a 850 /mi S C U B A objects 117 5.6 Continued from previous page 118 5.7 Continued from previous page. 119 5.8 Postage stamps of the Aa < S N R < 3.5a 850 //m S C U B A objects. . . . 120 5.9 Continued from previous page 121 5.10 Continued from previous page 122 5.11 Postage stamps of the > Aa 450 / im S C U B A objects 123 5.12 A radio jet inducing star-formation? 130 5.13 Photometric redshift estimates of sub-mm sources 132 5.14 Star formation rate density over time 135 6.1 History of star production 145 ix List of Acronyms A C S Advanced Camera for Surveys A G N Active Galactic Nucleus A L M A Atacama Large Mil l imeter Array COBE Cosmic Background Explorer C M B Cosmic Microwave Background C S O CalTech Sub-millimeter Observatory C Y Ca r i l l i -Yun redshift indicator D A Q Data Acquisi t ion E R O Extremely red object F F T Fast Fourier Transform F I R Far-Infrared ( 1 5 - 1 7 0 pm) F W H M Fu l l W i d t h at Half M a x i m u m G R B G a m m a Ray Burst HETE High Energy Transient Explorer HST Hubble Space Telescope H W H M Hal f W i d t h at Half M a x i m u m I R Infrared I R A M Institut de RadioAstronomie Mill imetrique IRAS Infrared Astronomical Satellite I S M Interstellar Medium ISO Infrared Space Observatory J C M T James Clark Maxwel l Telescope L B G L y m a n Break Galaxy L I R G Luminous Infrared Galaxy ( L F I R ^ 10nLQ) M A M B O Max-Planck Mil l imeter Bolometer array M I R Mid-Infrared (2.5 - 15 pm) N E F D Noise Equivalent F l u x Density N I R Near-Infrared (0.5 — 2.5 pm) P A H polycyclic aromatic hydrocarbons P S F Point Spread Function R M S Root Mean Square R O I Region O f Interest X S C U B A Submillimetre Common User Bolometer Array S H A R C Sub-millimeter High Angular Resolution Camera SIRTF Space Infrared Telescope Facility S E D Spectral Energy Distr ibution S M A Smithsonian Mil l imeter Array S N R Signal-to-Noise Rat io S O P H I A Stratospheric Observatory for Infrared Astronomy S P U D Silicon Pop-Up Detector S U R F Scuba User Reduction Facil i ty SZ Sunyaev Zel 'Dovich T O D Time-Ordered Data U L I R G Ultra-luminous Infrared Galaxy ( L F I R 1 0 1 2 L Q ) U V ultra-violet V R O very red object x i Acknowledgments Trips to Hawaii to collect the data used in this dissertation were funded in large part by grants from the Canadian National Research Counci l . Addit ional ly , finan-cial support was provided for my research by Mark Halpern through N S E R C , and a generous scholarship from the University of Br i t i sh Columbia . Obviously this disser-tation would not have been possible without the help of Mark Halpern and Douglas Scott, my research supervisors. Their insightful questions have greatly enhanced the quality of this dissertation. Several colleagues have also contributed to this thesis in various ways. I thank Doug Johnstone for useful conversations regarding iterative map making algorithms. Wayne Holland, one of S C U B A ' s designers, was instrumen-tal in explaining some of the technical details, and T i m Jenness was very helpful in deciphering the data so that I could apply my own reduction algorithms. E d Chapin provided the parametric fits to the spectral energy distributions of local star-bursting galaxies that I used in Chapter 5. Scott Chapman was also a great resource in putt ing the results in the broader context of sub-mm astronomy, and played no small role in encouraging me to pursue a postdoctoral position at CalTech. Dur ing my tenure as a doctoral student I had opportunity to spend time working on this thesis at both C I T A and the Royal Observatory, Edinburgh. In addition a workshop at I N A O E or-ganized by Dav id Hughes was particularly informative. I would like to acknowledge their hospitality as well. Some of the S C U B A data used in this thesis were recovered from the archive at the Canadian Astronomy Data Center, which is operated by the Dominion Astrophysical Observatory for the National Research Counci l of Canada's Herzberg Institute of Astrophysics. In addition, A m y Barger offered the use of some her data before they became public, which is also appreciated. A portion of the S C U B A data used was collected under the Canadian C A N S E R V program, which allows t imely execution of interesting and/or urgent observations. x i i Preface: Astronomy primer for the non-expert Associated wi th this thesis are several ideas that someone outside astronomy may not be familiar wi th . To facilitate the understanding of the results, we present here a short overview of a few terms and concepts. Due to the expansion of the universe, the light from galaxies is redshifted. The redshift, z, is related to the distance and look-back time between us and the object of interest v ia a non-linear, but monotonic, mapping. A t z ~ 1, the light being detected was emitted when the Universe was approximately half of its current age. A t z ~ 5, the Universe was less than 10% of its current age, which observations estimate to be about 12 G y r . Astronomers typically refer to objects wi th z <> 1 as "local". These estimates depend on the value of various cosmological parameters which describe the geometry and expansion of the Universe. There is strong evidence that we live in a close to flat Universe, and we say that Q 0 — 1- The fraction of this which is attributed to matter is CIM, and it has a value of Q M ~ 0.3. The cosmological constant, Cl^ makes up the remaining 0.7. The rate of expansion of the Universe is referred to as the Hubble Constant, and its value to wi th in 10%, is HQ = 65 k m / s / M p c . The last unit, M p c , is a Megaparsec, and is appropriate for describing the length scales associated wi th the distribution of galaxies. 1 M p c ~ 3 x 10 2 2 m. We usually refer to the intensity of light being emitted from a galaxy in units of solar luminosity. 1 LQ = 3.8 x 10 2 6 W , and is the power output of our Sun. The objects that this thesis w i l l focus on have luminosities i n excess of 1 O 1 1 L 0 . For comparison, our M i l k y Way galaxy has a luminosity of ~ 1 O 1 O L 0 . We also use the mass of our Sun as a reference. Specifically, when we discuss the star formation rate of a galaxy, we use units of M 0 / y r . Our galaxy, a typical spiral, creates stars at rate of about 2-5 M 0 / y r . This thesis deals wi th star-bursts which can have rates of well over 100 M 0 / y r . To fully understand the galaxies we study, we need to observe them at different wavelengths. In general we wi l l use the unit / im, even though it is not the typical unit for al l wavelength regimes. The traditional optical wavelengths cover 0.4-0.8/ im. The infrared spectrum is approximately divided up into three different ranges: near infrared (NIR) refers to 0.8 — 2.5 /tm, mid infrared (MIR) refers to 2.5 — 15 /tm, and far infrared (FIR) refers to 15 — 250 /tm. The sub-millimeter regime spans 250-3000 /tm. The radio bands we use in this dissertation are at cm wavelengths, and of particular interest is the continuum band (corresponding to 21 cm) at 1.4 G H z . The conventional unit for X-ray energies is the keV, and observations are normally broken up into a soft X-ray band (0.5-2 keV) and hard X-ray band (> 2keV) . F I R fluxes are measured in units of Jansky, which is equal to 1 0 - 2 6 W / m 2 / H z . Sub-mm sources have fluxes measured in mJy, and for faint radio observations the appropriate unit is /tJy. Opt ica l observations use a different system, known as mag-nitudes, which is related to the flux by — 2.5 log 1 0 (flux) + constant. We often refer x i i i to the "colour" of an object as the difference between magnitudes measured in two different filter bands, wi th the shorter wavelength filter being the reference. Take for instance, the difference in flux from a source seen through an R - and K - b a n d filter. A value R — K that is lower than the "norm" for a given object means that the object has more emission across the R band than K, and we say that the object is blue. If it was more we would call it red. A change in flux due to observing a different rest-frame wavelength because of red-shifting is what astronomers call a K-correct ion. In the sub-mm, the K-correc t ion approximately compensates for the effect of dimming, so the flux from a galaxy is rel-atively independent of distance. This advantage is offset slightly by the low resolution of current sub-mm telescopes. W i t h the large beam-sizes, more than one source can be inadvertently imaged at once. We cannot resolve these objects separately, and we say that the image is confused. This does not affect the bright objects, which are rare enough that one does not find more than one per beam-size. As one looks at fainter (and more plentiful) objects, there reaches a point where confusion dominates, and we say we have reached the confusion limit. This sets a practical l imi t to the maximum observing time for a survey. This thesis uses a l l of these concepts and more to help understand a class of galaxies only recently discovered. The goal is to put these objects wi thin the context of galaxy and structure evolution in the Universe. Wha t are they? W h a t is the power source for their (implied) luminosity, which is greater than any galaxy in the local Universe? Into what do they evolve? x iv 1: Sub-millimetre Extra-galactic Astronomy Recent observations of the Cosmic Microwave Background ( C M B ) have offered strong support for the current paradigm explaining the formation of structure i n the Universe [1]. Quantum fluctuations i n the hot, dense plasma present after the B i g Bang give rise to regions of over-density. A s the Universe expands, the radia-t ion cools unti l eventually it lacks the energy to ionize neutral hydrogen. A t this point, the epoch of recombination, radiation and matter de-couple, and the radiation travels unimpeded from that point onward. Because this radiation does not interact very much unt i l i t strikes our detectors, an image of the microwave sky is essentially a snapshot of the structure at the recombination epoch. This is visible today as anisotropies at the 1 0 - 5 level in an otherwise uniform 3 K thermal background [2]. The behaviour of the matter component after recombination is much more compli-cated. The over-densities act as seeds which, over time, collapse due to gravity into galaxies and clusters of galaxies. This gravitational instabili ty process is highly non-linear and involves a wide range of different physical processes. Hence predicting the formation and evolution of galaxies has remained an elusive goal of astrophysics. One observational hurdle is that much of the distant Universe is obscured by the presence of dust which absorbs energy, particularly at ultra-violet ( U V ) and optical wavelengths, and re-radiates i t as thermal emission wi th a temperature of typically 2 0 - 6 0 K [3]. This emission peaks in the Far-Infrared (FIR) , and v ia redshifting due to the expansion of the universe, is detectable in the sub-millimeter. One spectacular example of how dust affects the optical picture of galaxies is evident in the galaxy Centaurus A (see Figure 1.1). To appreciate how significant this process is, it must be noted that the Far-Infrared Background (FIB) is slightly brighter than the entire integrated visible emission more commonly explored in astronomy [4] (see Figure 1.2). Another challenge is more practical in nature; the earth's atmosphere is completely opaque to F I R radiation except for narrow windows of ~ 75% transmission in the sub-mm regime, and only then at the best observing sights in the world. However, detectors unt i l recently were the l imi t ing factor in conducting extensive observations. It was not unt i l the introduction of the Sub-millimetre Common User Bolometer Ar ray ( S C U B A ) [7] in 1997, that we were able to begin to survey the high redshift universe 1 Figure 1.1: Opt ica l and F I R images of Centaurus A . The optical image on the left clearly shows that something is blocking the light from the core of the galaxy. The ISO 15 / im image on the right reveals strong IR flux coming from this very same absorbing region [5]. Also shown as contours are strong radio lobes apparently emanating from the core of the galaxy. The optical image was obtained wi th the U K Schmidt Telescope. and grapple wi th the role that dust plays. This dissertation describes observations taken wi th S C U B A and their implications for our understanding of galaxy formation. 1.1 The Far-Infrared Background In 1983, the Infrared Astronomical Satellite (IRAS) performed an all-sky survey at 12, 25, 60, and 100 /tm with sufficient sensitivity (~ 1 Jy) to detect thousands of galaxies which were too faint optically to have been previously catalogued [8]. In particular it discovered a class of object with an integrated luminosi ty 1 of > 1 O U L 0 which we now call L I R G s , for Luminous Infrared Galaxy. A class of less numerous U l t r a L I R G s ( U L I R G s ) exist that have Lm > 1 O 1 2 L 0 . Figure 1.3 shows a plot of power output across a wide spectral range. The emission from these sources provides strong evidence that the presence of dust can significantly influence theories of galaxy formation. IRAS was able to probe these sources out to a redshift of <i 0.3 [9]. Though not very numerous locally, it has been argued that many galaxies undergo a 1 This is integrated over the wavelength range at which the dust emission dominates the power output of the galaxy (roughly 8 - 1000 /mi). 2 1 0 0 0 1 0 0 h CO a 1 0 \ -c 1 0 0 0 A (/mi) 1 0 0 1 0 1 0 1 1 1 0 12 1 0 1 3 i/(Hz) 1 0 1 4 1 0 15 Figure 1.2: The Extra-galactic background. Plot ted are measurements and l imits for the background from cm-wavelengths through to the optical. The vertical axis is the energy output, and it is clear the C M B , which is a uniform, isotropic source, domi-mates. The energy output at other wavelengths is due to discrete sources (galaxies), and what is plotted is the integrated emission across the observable Universe. This figure has been taken wi th permission from Scott et al . (2001) [6]. 3 bright I R phase in their evolution, and therefore they are likely to have been much more common in the past [8]. More recently, observations of the IR background by the Cosmic Background Ex-plorer (COBE) have verified that the F I B is much brighter than what can be ac-counted for by adding up the flux from the local IRAS sources [10, 11, 12]. Thus a significant population of dust-enshrouded galaxies must exist past z ^ 0.3. Observations by the Infrared Space Observatory (ISO) satellite [13] near the F I R peak at 170 pm have resolved about 10% of this background into discrete sources [14]. Due to the ISO sensitivity, the detected sources lie within a redshift of ^ 1, therefore there is s t i l l a significant amount of activity at high redshift missing from such surveys. These satellite missions highlighted the importance of emission from dust. The only window to the F I R open to us from the ground is in the sub-mm, so the next round of observations geared toward understanding the high redshift universe are being conducted in that arena. 1.2 Continuum sub-mm emission from galaxies The material that sub-mm astronomy is concerned with is small particles of carbons and silicates which are collectively called "dust". The topic is vast and the interested reader is encouraged to read the colourful review found by Aigen & Greenberg [3]. Al though the presence of some type of diffuse matter that absorbs starlight has been known for over a hundred years, details on the composition, formation, and behaviour of dust remain sketchy. However, based on observations taken of the interstellar medium (ISM) of our own Galaxy, we can make some general statements about its properties. The continuum absorption of light is stronger at shorter wavelengths. This explains what astronomers refer to as "reddening"; blue light is more strongly absorbed and/or scattered than red. It also places constraints on the size of the scattering medium to be ~ l O O A - sub-micron [15]. In many observations, the light that does make it through the dust layer is observed to be polarised, implying the presence of magnetic fields and that the dust has a finite magnetic dipole moment. There are many absorption features noted in the spectra of stars obscured by dust. Some of these s t i l l remain unexplained (the so-called diffuse interstellar bands for example), but others are thought to be caused by very small grains of silicon that are boosted into an energetic, non-equilibrium state when struck by a U V photon. The 4 Frequency/GHz 106 105 104 1000 100 10 1 p i |i 1111 i—i—i 111111 i—i—i | u 111 i— i — i 111111 i—i—i 111111 i ^ 10"1 3 10- 2 b" i o -T T T UV/OPT NIR MIR FIR S U B - M M RAD 1111 i I i i I i il i i 1 1 1 1 1 0.1 10 100 Wavelength//xm 1000 104 Figure 1.3: General shape of a nearby U L I R G spectral energy distribution. The featureless blackbody dominates the energy output of a U L I R G . The features in the M i d - I R are due to emission from P A H molecules. The data for this modelled spectrum was provided by G . Lagache. 5 type of dust susceptible to this are called polycyclic aromatic hydrocarbons (PAHs) . Similar non-equilibrium absorption is speculated to cause some dust grains to spin rapidly and contribute microwave radiation, complicating studies of the C M B [16]. The dust is infrared (IR) bright, and emits as a modified blackbody at temperatures typically between 20-60K, though lower and higher temperatures are possible depend-ing on the environment. The energy must come from the absorbed light. Al though generally featureless, there are emission lines in the mid-IR that are attributed to the P A H absorption features in the optical. The F I R emission is particularly important for the star formation process; clouds of gas and dust contract as they radiate I R energy and eventually condense into star forming cores. Thus the amount of dust present is intimately tied to the level of star formation. A natural way to describe galaxy evolution is in terms of the star formation rate as a function of time, and therefore it is immediately clear that an understanding of dust relates to the broader issue of galaxy formation. Model ing dust behaviour has benefitted from the advancement of computer tech-nology that allows more complicated numerical codes to be executed. Al though there is s t i l l much work to be done to understand al l the features, it is generally necessary to invoke a collection of dust molecules that vary in size, configuration, and compo-sition in order to reproduce observations [17]. Luckily, in the F I R and sub-mm, the observed emission properties of the dust are largely independent of these details. 1.2.1 Mechanisms that can power the sub-mm emission The dust re-radiates energy it absorbs from the local radiation field, but unt i l now we have not discussed by what means this radiation is created. The presence of stars is an obvious candidate, and it is not difficult to conjecture that the higher the star-formation rate in a galaxy, the higher the F I R luminosity w i l l be. Another mechanism involves energy being released during the process of matter accretion onto a super-massive black hole (> 1 O 6 M 0 ) at the centre of a class of galaxy known as an A G N (Active Galactic Nucleus). A t "soft" energies (0.5 - 2 keV), about 75% of the X - R a y background ( X R B ) has been resolved into discrete sources that have later been identified optically as unobscured A G N . The emission observed from an A G N depends crit ically on its orientation; face-on systems make up the soft X R B . Edge on systems are heavily obscured by a dusty torus, and therefore hard X-rays and thermal emission are dominant. Observations of the merging galaxy pair known as the "Antennae" [18] clearly show that sub-mm emission is coincident not with the nucleus of either galaxy, but rather 6 in the extremities where the galaxies are beginning to merge. This case suggests that the dominant source of sub-mm flux arises from star formation i n at least some galaxies. Using arguments based on efficiency of energy conversion in accretion and stellar nucleosynthesis, only 15% of the total sub-mm luminosity is expected from acretion onto A G N [19]. 1.3 Parameterisation of the Dust Spectral Energy Distribution In describing other galaxies, we start wi th a single temperature model and modify the blackbody spectrum wi th an emissivity factor that changes as a function of frequency, KV oc . Observationally, /3 falls i n the range 1-2. Th i s approach bundles up our ignorance of the distribution of temperatures, sizes, and radiation efficiencies of dust grains. Therefore the simplest form of the emission spectrum from dusty galaxies is fvocB(u,T)uP, (1.1) where B(v, T) is the Planck function. Since the dust temperatures involved place the sub-mm band deep in the Raleigh-Jeans part of the spectrum, this can be further simplified to / „ oc T&v 2^  for al l but the highest redshift galaxies. O n the Wein side of the thermal peak, one can use another simple power law (fv oc uaiR). This is motivated by observations (which we show in the next section) that the M i d - I R portion of many SEDs do not fall off as as fast as a Planckian function. This suggests a second, warmer, population of dust grains. Indeed it is better to think of Td not as a physical quantity, but rather as a shape parameter. Later we wi l l describe in more detail how radio fluxes are tightly matched to F I R luminosity in star-bursting galaxies. The radio S E D is best described by a negative power law with an index aT. More complicated forms are available, but currently we lack the information to constrain many parameters for high redshift sources. The F I R emission becomes too faint to measure for sources at high-2, and at best sub-mm observations are available at only a few different wavelengths, but much more commonly only at one! Certainly as the resolution and sensitivity of sub-mm detectors improves the data w i l l warrant a more sophisticated treatment. However, observations of 14 nearby L I R G s across F I R and sub-mm bands verifies this parameterisation is reasonable [20]. 7 1.3.1 Observed SEDs of local IR bright galaxies The most extensive series of local observations has been the S C U B A Loca l Universe Galaxy Survey ( S L U G S ) [21, 22]. This survey observed 104 galaxies selected from the low-redshift IRAS bright galaxy sample [23] at 850 / im, and found that the F I R component of the sample as a whole was well fit using a modified blackbody param-eterisation wi th T d = 38 ± 3 K and 8 = 1.3 ± 0.2. Unfortunately, these fits are only based on fluxes from three different wavelengths (60, 100, and 850/tm), and hence there is a significant correlation between estimates of Td and 3. A high-/3, low Td model is as good a fit to the sample as a low-/5, high T d one. 19 of these objects also had a detection available at 450 /tm. From this subset, there is weak evidence that the population can be broken up into two categories. The first has the ~ 38 K temperature already mentioned and are the more luminous members of the sample, but the other is lower luminosity and cooler. Attempts to fit the sources with a 2-temperature model do not provide significantly better results. The estimated luminosity of these sources identifies them as L I R G s . To make progress, more flux estimates from different wavelengths, and the abil i ty to resolve different regions, are required from a sample both L I R G s and U L I R G s . It is worth plott ing the SEDs of three of the brightest local sources that have been studied in more detail. We stress that high redshift sources may have S E D s systematically different from local ones, but plots such as the one in Figure 1.4 are useful as a rough guide. We use the parametric fits to measured fluxes of Arp200, M82, and Mkn231 calculated by Chapin [24]. Arp220 is the "typical" S E D used as a template for star-bursting high redshift S C U B A galaxies. M82 is another local star-burst, as is Mkn231 but wi th the added contribution from A G N activity; this is clear from the shallow slope in the M I R caused by the presence of warm dust. These three objects bracket the range of L I R G SEDs seen in the local Universe. 1.3.2 Estimating dust mass from sub-mm flux In the literature, one often sees estimates of the dust mass, M d from sub-mm detected galaxies: Lv = 4.irK„B(v,T)Md. (1.2) Here, Lu is the luminosity of the source at the frequency being observed, and the formula is based on the assumption that the dust emission is an optically th in process. KU is the frequency dependent mass absorption coefficient, which is estimated to be ~ 0 . 1 4 ( A / 8 5 0 / i m ) ~ ^ m 2 k g - 1 [25]. However, observations of different I R bright 8 1000 p I i i i i i i i i I 1 1 rp— i i MI | 1 1 1—i—i i i I_J 10 100 1000 10 4 X/fj,m Figure 1.4: S E D s of local IR luminous sources. These are fits to the measured S E D s of three local galaxies thought to be representative of the S C U B A population. The plots are restricted to the M I R - r a d i o range, which are affected most strongly by star-burst activity and dust emission. For each of the three local galaxies, we have normalised the flux to unity at 850 /mi . Note that since the bandwidth of receivers across this range are similar (all use similar bolometer technology), the fluxes at different wavelengths can be compared directly. Measured fluxes for Arp220 are shown, wi th error bars omitted for clarity. 9 objects lead to estimates of K„ that vary by factors of 3. Piecing together equations 1.1 and 1.2 shows that Lv oc u2+^ TdMd. Therefore an uncertainty in the dust temperature influences estimates of the dust mass. In addition, the above prescription misses any optically thick dust, and it only describes the portion of dust that is being energized. U n t i l the data improve, dust masses are in general not the best quantity to use in describing galaxies. Despite these caveats, it is st i l l useful as a crude guide to the amount of dust involved with star-formation. 1.3.3 Estimating star formation rates from sub-mm flux There are many star-formation rate estimators available (see, for example Rosa-Gonzalez, Terlevich, and Terlevich [26]). Most of them are based on spectral lines that are sensitive to the ionizing photons produced by young stars, but at high red-shift these lines are shifted out of band and other methods must be relied on. Using the usual form of the F I R S E D , one can calculate the total I R luminosity of an object. Observations of local star-forming galaxies suggest that S F R = 2.1 x K T 1 0 (L60lim/LQ) M 0 y r - \ (1.3) where Le0ytm = vSv(y = 60/im) is the 60 / im luminosi ty 2 [27, 28]. This is accurate to wi thin a factor of ~ 3. Note when observing rest-frame wavelengths other than 60/tm, we must first extrapolate to 60 /mi by using some model for the source S E D . Since the luminosity of a blackbody is oc Td, small errors in the dust temperature can yield quite different results. 1.4 Multi-wavelength properties of sub-mm galaxies To fully understand the population of sub-mm bright galaxies, we need to study them over a wide range of wavelengths. This is the subject of Chapter 5, but here we present a general overview of what multi-wavelength data is needed. The order starts wi th high energy gamma rays at the shortest wavelengths, and from there spans fifteen orders of magnitude in frequency. 2 There is nothing particularly special about 60 fim except it was the main IRAS channel for which these types of calculations were originally done. 10 1.4-1 Gamma Ray The origin of G a m m a Ray Bursts ( G R B ) remains unknown despite two decades of research. Their distribution on the sky is uniform, suggesting an extra-galactic origin (stars in our Galaxy are more concentrated in the disk, therefore i f G R B s are local in origin one would expect the distribution of bursts to be concentrated along there). A popular model for G R B progenitors is that the intense radiation is released when a massive, young star dies [29]. One might then expect more G R B activity in systems actively producing stars, and hence sub-mm bright galaxies, which trace star formation, are plausible candidates. This has the additional benefit of explaining why G R B s are often faint or undetectable in optical images of the region: the dust is absorbing the optical light. The observational evidence is s t i l l unclear however: observations of six G R B s with S C U B A [30] fail to detect significant sub-mm flux, while there is at least one observation [31] that convincingly detects a sub-mm galaxy at the position of the burst, though at a faint flux level. W i t h the launch of new G R B detecting satellites such as HETE-II, and ongoing S C U B A observations of burst positions, stronger constraints can be placed on the relationship between S C U B A galaxies and G R B s . Note that since the Universe is transparent to gamma-rays, G R B s could be used to trace global star-formation i n a manner similar to that done wi th observations of sub-mm emission. To date, there has been no recorded burst from the region of space that this thesis deals wi th , so we wi l l not consider this issue further. 1.4.2 X-Ray The Chandra telescope [32] has revolutionized the study of the X- ray Universe in much the same way that S C U B A has for sub-mm astronomy. In particular it has allowed researchers to also resolve the hard X-ray ( 2 - 8 keV) background into sources. Since the presence of the dusty torus determines the observed X- ray emission from an A G N , one would then expect that selecting X-ray sources with low soft-to-hard X- ray flux ratios would pick out sub-mm bright A G N . A n active galactic nucleus is not the only mechanism from which X-rays are pro-duced; X- ray binary stars, supernova remnants, and diffuse hot gas are also contrib-utors [33]. Since these are related to stellar processes, a galaxy undergoing active star-formation would be expected to exhibit these signatures. We w i l l later show that the overlap between X-ray and S C U B A detected sources is at about the 20-25% level, but the fraction of S C U B A detected A G N is only ~ 10% 11 [34]. This lack of a significant detection might be due to selection effects however. For instance, it might be that the dust is at high enough temperatures as to render their sub-mm flux too weak to detect. Also, X-ray observations tend to select lower redshift sources (z ^, 3) because they become too faint to measure. We w i l l return to this issue later, since determining the nature of the F I R population is a key goal of sub-mm surveys. 1.4.3 UV-Optical Emission shortward of the L y m a n - a line is suppressed in galaxies because photons this energetic ionize the neutral hydrogen in the I S M (and are hence absorbed). A t a z ~ 3, the spectrum is shifted such that emission in the U band is absent due to the L y m a n - a line passing out of the band. This "drop-out" technique has has been exploited to photometrically find thousands of these "Lyman Break Galaxies" ( L B G ) [35]. The slope of the rest-frame U V continuum and strength of the H/3 emission line suggest the presence of interstellar dust obscuring the star formation. Al though a prescription for converting this into a estimate of the S F R is not well determined, rates as high as a few hundred M 0 y r _ 1 are expected. Therefore they fall wi th in the interest of sub-mm observers, since this implies fluxes measurable wi th S C U B A . 1.4.4 NIR W i t h i n the past few years, advances in detector technology have made possible deep near-IR surveys. From these a new class of galaxy was discovered. K n o w n as E x -tremely Red Objects (EROs) , they are relatively faint (K ~ 20) and have a colour difference3 of R — K > 5. To produce such red colours, the galaxy must either be an ell iptical at z > 1 containing old, cool stars from which the light is redshifted into the K band, or a heavily dust-enshrouded galaxy that reddens the underlying S E D . Only the latter is detectable by sub-mm instruments. Bo th types of objects have been observed; spectroscopic studies and analyses of the surface brightness profiles have confirmed that at least a few E R O s are these quiescent ellipticals [36, 37]. S C U B A observations by several groups have also detected sub-mm flux at the position of a few E R O s [38, 39]. It is necessary to point out that unlike in the sub-mm, the near-IR K-correction is not strong enough to keep the sources wi thin detection l imits as they increase in redshift. Detected E R O s are l imited to a redshift of at most z ~ 2.5. 3 Different authors use slightly different definitions, but R - K > 5 is the criterion used in many studies. 12 Clustering is another argument that connects E R O s wi th the possibility that they may be bright when seen by S C U B A . It has been shown that the brighter (K ~ 19) E R O s are very strongly clustered [40], suggesting that they trace out the regions of over-density in the Universe. S C U B A galaxies are thought to be massive ellipticals in the process of formation [41], and therefore form in these same deep potential wells. Thus even i f the E R O s do not exhibit strong sub-mm emission, the two populations may trace out the same large scale structure. 1.4.5 MIR Observations at wavelengths blueward of the thermal peak allow tighter constraints to be placed on the dust temperature. To date, only ISO has been able to provide 15 /mi fluxes, and then only wi th the sensitivity to measure the brighter, local sources. M I R observations are important however, especially when coupled wi th X-ray observations. It is expected that A G N heats dust to temperatures higher than that from star-formation, and therefore a warmer thermal component w i l l flatten out S E D toward the M I R . This has been confirmed for ISO detected X-ray sources in the field of A b e l l 2390 [42]. 1.4-6 Radio There exists a tight correlation between the 60 and 100//m fluxes determined by IRAS and 1.4 G H z radio observations. This correlation spans over four magnitudes in luminosity, and holds for a very diverse range of galaxy types [43, 44]. The nature of this relationship is not certain, but it is thought to be associated wi th regions of star-formation: the sub-mm flux is due to the re-radiated optical light and the radio flux arises from synchrotron radiation caused by relativistic electrons that are produced in supernova activity. A s we wi l l show later, this fact has been exploited to measure redshifts of sub-m m objects wi th radio-detected counterparts. Its importance to the field of sub-mm astronomy cannot be under-stressed: Roughly two-thirds of a l l S C U B A galaxies have detected radio emission. 1.5 The effects of redshift on sub-mm observations Despite the technical difficulties of observing in the sub-mm regime, there is one aspect of I R bright sources that makes things easier. The rest frame wavelength that we observe is closer to the peak of the S E D the further the galaxy is from us, due to 13 the redshifting of galaxies. This negative K-correct ion offsets the effect of the inverse square law that describes the dimming of sources over distance. A s Figure 1.5 shows, the result is that the observed flux density of sub-mm sources at wavelengths between ~ 250 — 2100 / im is essentially constant for redshifts between roughly 1 and 10. This result approximately holds for al l reasonable cosmological models [45]. The abil i ty to probe galaxies out this far is one of the driving forces behind sub-mm cosmology. Unfortunately this advantage means that once a galaxy is detected in the sub-mm, there is no way of knowing its redshift, even if the luminosity and S E D slope are known. Determining the redshift distribution of sub-mm galaxies is crucial to our understanding of the population however, so other methods have to be turned to. Here we give a very general outline of the procedures used to measure redshifts. A more detailed treatment wi l l be presented in Chapter 5, where we discuss S C U B A sources we detect in an large area survey. 1.5.1 Spectroscopic redshifts In tradit ional optical surveys, the redshift of a source is determined by measuring its spectrum and identifying known spectral lines. The same idea can be applied in the sub-mm. Observations of star forming regions wi thin our own Galaxy show that molecules, such as carbon monoxide, trace the presence of dust. C O does exhibit strong line features spaced roughly 115 G H z apart, but unfortunately the bandwidth of line receivers in use today is only a few G H z , making observing more than one line at a time impossible. This also assumes that one knows where to tune the receiver in the first place, which is rarely the case. In addition, the equivalent width of the galactic spectral lines is not much less than the currently attainable bandwidths, meaning there is no baseline from which to detect a well offset emission line. Therefore dedicated searches for C O and other low ionization cooling lines in high redshift galaxies w i l l have to wait for improvements in the detectors. If we were able to determine with certainty a counterpart to the sub-mm source from optical images, we could obtain the redshift from its optical spectrum. However, even in the cases where such a counterpart is found, the optical emission is usually extremely faint. Because it does not benefit from the strong K-correction, the optical flux of high redshift sources wi l l become quite low and wi l l remain faint even in the N I R . Thus obtaining redshifts this way is usually not feasible, except for a small fraction of S C U B A detected galaxies. 14 Figure 1.5: The effect of redshift on sub-mm observations. Plot ted are the expected flux densities at 3 different wavelengths for a U L I R G wi th the dust parameters shown. Note that past a redshift of ~ 1, the long wavelength fluxes are essentially constant. The sudden drop occurs when the rest-frame wavelength being observed moves over the thermal peak. 15 1.5.2 Photometric redshifts from far-IR SEDs Although less accurate, optical astronomers have had great success in determining redshifts based on broad-band continuum measurements. The technique requires one to assume a form of the S E D , so that the expected flux in each band can be calculated and then compared against the observations. It should be pointed out that because the S E D of dusty galaxies is thermal, redshifting an object has the same effect as modifying its dust temperature. Therefore it is important to have multi-wavelength observations across the whole S E D to constrain the temperature, and hence redshift. Recently, it has been shown that crude redshifts accurate to ± 0 . 5 can be achieved based on observations at 500 and 850 /xm by using a library of known S E D templates [46]. Whether or not templates based on local sources apply to the high redshift universe remains to be seen. It may be that in the future, correlations between luminosity and temperature (for example) w i l l narrow down the range of templates and improve the redshift estimates. 1.5.3 Correlations between redshift and FIR/radio flux ratios C a r i l l i & Y u n [47, 48] have shown that i f the radio-FIR relationship is val id at high redshift, the ratio of the sub-mm to radio flux can be used to determine the redshift. Essentially this tracks the decrease in radio flux due to cosmological dimming, because the sub-mm flux, as already shown, remains relatively constant. The method does not work for sources past a redshift of ~ 3, where the radio flux drops below the detection threshold of the world's best telescopes. This procedure also suffers from a degeneracy between temperature and redshift, and also assumes that one can extrapolate relations at low redshift to high. A n y radio emission not associated with star-formation (for instance from A G N activity) w i l l result in larger radio fluxes and hence lower estimated redshifts. Nevertheless it is at present the best way to get at least some idea of the redshift of a source. 1.6 Issues that sub-mm surveys hope to answer In general the promise of sub-mm astronomy is to help us understand the history of galaxy evolution back to the first epoch of star formation. In practice this breaks down into a series of individually more modest issues. We reserve a more detailed description unti l the later chapters of this thesis that deal wi th results from our surveys, but it is useful to present an overview here and give the reader an idea of 16 what questions sub-mm surveys address. i) Resolving the F I R background into sources. The COBE satellite measured the intensity of the F I R background with the F I R A S instrument [10, 11, 12]. Because of the large beam-sizes, no individual galaxy was resolved, but rather a uniform glow of radiation was detected from the sum of al l galaxies in the field of view. Are the numbers and luminosities of sources detected wi th S C U B A (which has the abil i ty to discriminate individual galaxies) sufficient to account for this F I R background? Ear ly S C U B A surveys have shown that this seems to be the case, wi th well-detected sources contributing > 50% of the sub-mm background and mi ld extrapolations to fainter fluxes consistent with 100% [49, 50]. Subsequent work has concentrated on measuring the form of the number counts (the number of sources wi th a flux between S and dS as a function of S). These number counts can be used to constrain the evolution of the sub-mm flux over time. ii) How does the star formation rate change over time? Hot young stars generate an abundance of U V radiation, and this is used to estimate the star formation rate as a function of time. Such plots (sometimes called the "Madau plot" [51]) suggest that star formation was much higher in the past, peaking at a redshift of about 2 and then declining afterward. However, the correction for attenuation by dust is not well determined. If dust plays a more important role in the past as we suspect, then the star formation wi l l be obscured and undetected in the U V . Sub-mm observations can potentially offer an independent means of measuring the S F R over time, particularly at the higher redshifts. iii) A r e high redshift I R bright sources the progenitors of modern day ellipticals? IRAS detected no local elliptical galaxies, implying that they have ex-hausted their supply of dust. Optical studies of the stars in ellipticals show that these systems are old by z ~ 1, meaning that their star-burst phase must have hap-pened long ago [52]. Also, their stellar populations are very homogeneous, suggesting they formed very quickly [53]. The inferred star formation rates from the brightest sub-mm sources, coupled wi th their number density, suggest that these sources can produce the population of massive ellipticals that we observe today [54]. Whether they are star-bursts collapsing monolithically or forming gradually v i a mergers of smaller galaxies remains to be determined. To address this requires a good con-straint on the number density of the brighter (higher star formation rate) sub-mm sources, a handle on their redshift distribution, and crucially an estimate of their masses. iv) D o sub-mm sources cluster? Observations of two classes of high redshift 17 sources, L y m a n Break Galaxies ( L B G ) and Extremely Red Objects (EROs) , have revealed that they are strongly clustered [40]. These sources lie at the peaks of the density field in the early Universe, and since the sub-mm sources have inferred masses that are greater than these two populations, they are expected to show strong spatial clustering as well. Detailed measurements of their clustering properties w i l l offer complimentary information obtained from counts and redshifts, enabling us to understand the bias of S C U B A - b r i g h t galaxies. v) W h a t are the multi-wavelength properties of sub-mm sources? Because the blackbody emission from sub-mm sources is featureless, the underlying physical processes are hidden to us. Though detections at other wavelengths are often difficult because of the dust attenuation, they do allow us to constrain the power source of the sub-mm emission. Multi-wavelength coverage is also required to separate sub-m m sources into different populations. Overlap between S C U B A - b r i g h t galaxies and samples obtained at other wavelengths is also crucial. It helps us understand the nature of sub-mm galaxies and determines whether or not inferred star-formation rates should simply be added together. 1.7 A guide to this thesis This dissertation describes an extensive series of observations taken of the Hubble Deep F ie ld ( H D F ) using the S C U B A instrument. The first half of the thesis (Chap-ters 2 and 3) w i l l concentrate on the data reduction. The treatment of S C U B A data requires a series of steps that standard available packages for the analysis of astro-physical data do not have. Therefore we develop our own software and algorithms. We pay particular care to the treatment and understanding of systematic effects, since the sources found in this and other surveys are typically only a few times brighter than the background noise level. The techniques developed borrow heavily from analysis of C M B data-sets which deal wi th similar data and detector technology. However, most of what is described here has not previously been applied to sub-mm data. Chapter 4 presents the sub-mm properties of the H D F survey. We report a list of detected objects, and from it measure the surface density of sub-mm objects. Because these sources are expected to be clustered on the sky, we attempt to measure the clustering strength of the sources. This chapter relies on careful Monte-Carlo simulations that assess systematic errors and allow us to account for the fact that the sub-mm map created has strongly varying noise properties. The next chapter confronts correlations of the sub-mm flux wi th objects detected 18 at other wavelengths. We compare other data-sets wi th our S C U B A map i n an effort to understand the nature of the sub-mm bright population. Final ly , we collate the results and speculate on the implications this survey has on galaxy formation. We also discuss what future observations need to be carried out wi th new instruments (sub-mm and other) in order to make further progress. 19 2: SCUBA - Instrument and data properties Observing in the sub-mm regime presents some particular difficulties. Only a l im-ited number of atmospheric "windows" exist, but even for the most accessible one at 850 /xm the transmission is only ~ 75% on average from the worlds' best sites. In Figure 2.1 we plot the observed transmission at Mauna K e a across the S C U B A relevant wavelengths. The atmosphere further complicates observations by emitt ing sub-mm radiation, thus adding noise to the data. U n t i l recenly however, bolometers were the dominant source of noise. For example, the sub-mm instrument previously used on the 15 metre James Clerk Maxwel l Telescope ( J C M T ) was U K T 1 4 [55], a single bolometer photometer which could observe the brightest extragalactic sources only after lengthy integration times. 400 600 800 1000 Wavelength / yum Figure 2.1: Sub-mm atmospheric transmission function. The solid black line shows the transmission function assuming a precipitable water vapour content of 1 m m . The grey lines near 450 /xm and 850 fj,m are the measured S C U B A post-upgrade filter responses. This figure is a modified version of the one found in Archiba ld et al . [56]. The Sub-millimetre Common User Bolometer Array ( S C U B A ) [7] was buil t by the Royal Observatory Edinburgh and was made available to astronomers at the J C M T in M a y 1997. Due to improvements in detector technology, S C U B A was one of the 20 first sub-mm instruments to be sky-noise l imited. B y placing dozens of bolometers in the focal plane, common mode noise from the sky emission can be removed, further enhancing the sensitivity of the observations. Bolometer arrays are so powerful that several others have been developed by other facilities. O f particular note are the M A M B O array [57] on the I R A M telescope in Spain, and S H A R C [58] and Bolocam [59] on the Caltech Sub-millimeter Observatory (CSO) . However none of these have yet matched the impact S C U B A has in the field of sub-mm cosmology. Al though new detectors are being developed even at the time of writ ing, S C U B A is s t i l l the pre-eminent sub-mm facility in the world. This chapter is broken up into five major sections. First it w i l l describe the optical arrangement of the telescope and detector. This is necessary to help understand the implications on observing modes, which is described in the second section. A section discussing the general approach to sub-mm data reduction is then presented, followed by specific notes for each of S C U B A ' s observing modes. Final ly, a section is devoted to studying systematic effects that can be manifest in the final data. 2.1 Optical design S C U B A is mounted to the Nasmyth focus 1 of the J C M T , but unlike some instruments on other telescopes, it does not turn to account for sky rotation. Since the bolometers are read out quite rapidly (< Is), this is not a problem, although there are impl i -cations for observing strategies as wi l l be demonstrated later. The camera has two primary sets of bolometers organized into hexagonal arrays that have a field of view on the sky of 2(3. Light is reflected off a series of optics to convert the focal ratio to f/4, then separated v ia a dichroic beamsplitter and routed to 37 and 91 element arrays sensitive to radiation at 850 and 450 /mi respectively. The F W H M of the A i r y disk at these wavelengths is 11'! 7 and 6'! 7 respectively, which corresponds to linear scales on the focal plane of / A =3.4 and 1.8 mm. The requirement for Nyquist sampling of the focal plane means spacing the bolometers / A / 2 apart, but the conical feedhorns to the bolometers cannot be mounted closer than 2 / A [60, 58], meaning that the array has to be moved around to fully sample the image plane. This "jiggling" of the telescope wi l l be described in detail later. Figure 2.2 shows the arrangement of the bolometers. A t the edge of the 850 /xm array lie 3 single photometric channels for use at 1.1, 1.3, and 2.0 mm. Unfortunately, these have not typically been in operation for 1 Instruments can be attached to different places on (or near) a telescope. Since the J C M T is an alt-az telescope, a natural position to place a detector is at the "Nasmyth" focus. 21 much of the lifetime of S C U B A . Addit ionally, they can not be used simultaneously wi th the imaging arrays. 2.1.1 SCUBA Upgrades After two years of operation on the telescope, it was determined that S C U B A ' s sen-sit ivity could be dramatically improved by upgrading ribbon cables attached to the bolometer leads, and the atmospheric filters directly in front of the arrays. Before reaching the bolometric detectors, the light passes through wire-mesh filters which are matched to to the atmospheric transmission windows. Pr ior to the up-grades in December 1999, the filters suffered too narrow a passband (hence useful signal was rejected), and they had significant response outside the transmission win-dows (meaning more atmospheric noise was introduced to the signal). The wideband filters in use now have improved overall sensitivity, especially at 450 pm. Filters are also available that match the windows at 750 and 350 pm but these are not used very often since the feedhorns to the bolometers are specifically matched to the 450 and 850 pm channels, and operation at other wavelengths is penalised by a loss of efficiency. Also, since the upgrades the filter wheel has failed therefore making any-thing but 450/850 pm work impossible. However the sensitivity of these two channels did increase significantly, especially at 450 pm where the noise equivalent flux density ( N E F D ) dropped by over a factor of two. 2.2 SCUBA Observing Modes S C U B A was designed to be sky noise l imited. The power spectrum of atmospheric emission above the Mauna K e a site is well studied, and has a dominant 1 / / compo-nent below 4 Hz [62, 63, 64]. To remove atmospheric emission, the secondary mirror "chops" the telescope beam between a source and reference position on the sky. The angular separation between the positions is called the "chop throw". Provided sky emission is the same in both chop positions, the difference between the signal at the two positions should cancel out the common-mode noise. This differential measure-ment is often dubbed a "single-difference". Addit ionally, the main telescope "nods" periodically such that the chopper's reference position lies on the other side of the astronomical target. The differences from each of the two nod positions are combined to yield a "double-difference", and is able to remove signals caused by linear gradients in the atmospheric emission along the chop direction. A schematic diagram describing these concepts is given in Figure 2.3. The two 22 SW A r r a y LW A r r a y Figure 2.2: The S C U B A bolometer arrays. The left half shows the 450 pm (short) array, and the long wavelength array and single pixels are shown in the right. Bolome-ters are referenced by numbers and by letter/number combinations. Each letter cor-responds to a specific analogue-to-digital card. This figure is taken from the S U R F manual [61]. reference positions that do not lie on the target are often called "off" beams. In Figure 2.4 we show what an optical image would look like if it were subject to such a chopping operation. The user is allowed to change the chop throw and direction at their discretion, but the chop frequency is fixed at 7.1825 Hz. This is well above the 1 / / knee in the sky-noise power spectrum. It also ensures that an integer number of chops are taken wi th in the integration time of 0.128n seconds, where n is 1 or 8 depending on which observing mode is in use. Chopping is mandatory for S C U B A observations. Wi thout it, the data w i l l be noisier (by several factors) and wi l l have stronger non-Gaussian features. 2.2.1 Photometry Mode For isolated point sources, the quickest way to get to the desired sensitivity is by pointing the central bolometer directly at the target. In practice the array is jiggled over a 3 x 3 square pattern with 2" spacing. This helps account for the 1.5" offset between the centre of the 850 jum and 450 / /m arrays, plus the quoted 2" pointing uncertainty of the J C M T . A t each jiggle point, the telescope integrates for 8 full chop cycles, or roughly 1 second. Upon completion of the 9 point pattern, the tele-scope nods and repeats the operation. Thus each double difference is made from two 23 Figure 2.3: A schematic of the S C U B A chop/nod strategy. A , B, and C represent three different regions on the sky. In the first nod position, S C U B A measures the signal SB — SA by chopping between them at a rate of ~ 8 Hz. After integrating for 1 second, the telescope moves over and measures the difference S c — SB- These signals are combined and then normalized to yield the final signal, —0.5SU + SB — 0 . 5 S c -The chop is spatially symmetric. 24 Figure 2.4: Chopping operation on an optical image. O n the left is the original "unchopped" image, wi th darker pixels representing real flux from sources. O n the right, we show the same map but with chopping artifacts (bright pixels) included. Isolated point sources are reasonably simple to find, but recovering structure wi th length scales on the order of the chop throw (the face on spiral galaxy for example) is problematic. 1 second integrations taken 9 seconds apart. B y carefully selecting the chop orientation and throw, the off-position of another bolometer on the array can be made to chop directly onto the source. The signal from these off-beams can be used to improve the estimate of the flux density from the source. For a source with flux density S, measured wi th an efficiency e and measurement error a, the probability that the measured value is x is given by: P(x) oc exp x-eS' (2.1) B y minimizing the joint probability of N measurements, the maximum likelihood estimator of the source flux density is £ > 7 2 (2.2) where x' = x/t and a' = a/e. A s the sky rotates during an observation, the effective efficiency, e, for the off beams varies. F i g 2.5 shows an illustration of this effect during observations of a L y m a n Break galaxy, W - M M D 1 1 . For our double-difference observations there are 25 instantaneously N — 3 beams, wi th the central beam having an efficiency of unity and the two off beams having e = —0.5 exp d 2 (2-3) where d is the angular distance of the off-beam centre from the source, and is the Gaussian width of the beam. In the case of W - M M D 1 1 , our detection level increases from ~ 3 . 0 a to 3.9a, after folding in the negative flux density from the outer pixels. Chop configuration for mmdll 1 2 0 6 0 o w S o CO < - 6 0 - 1 2 0 T O O o - 1 2 0 - 6 0 0 Aa[arcsec] 6 0 1 2 0 Figure 2.5: Chopping geometry. The S C U B A 850 fim bolometer configuration on the sky is depicted. The solid filled circles give the position of the central bolometer in al l three chop positions (the chop throw for these observations was 45 arcsec). The open circles wi th solid lines show the array in the central chop position, while the dashed circles give the off-beams. Clearly there wi l l be some off-beams that chop onto the source, wi th an efficiency which varies as the array rotates relative to the sky. 26 2.2.2 Jiggle-map Mode The Nyquist criterion for fully sampling the image plane at 850 pm requires that the spacing between points is 6". To do this, the secondary mirror walks around a 16 point pattern of telescope offsets. Since less time is spent at any given spot, longer integration times are required to reach the same noise level as in photometry mode. A t 450 pm, 3" spacing is required, which necessitates a 64 point jiggle pattern. Because the atmosphere is likely to change on timescales of 128 seconds, the jiggle pattern is broken up into four sets of 16, with a nod in between each set. 2.2.3 Raster-scan Mode To sample areas on the sky larger than the S C U B A array, one can either piece together several smaller jiggle maps, or raster scan the array across the region. Due to how the bolometers are arranged on the hexagon, the array must be scanned at angles of 15.5 + 60n degrees in the camera's coordinate frame to ensure that the final strip has no gaps, wi th n an integer (giving 3 t r ivial ly different angles). The array is then scanned along several strips, pausing at the end-points to write the data out to disk. B y slightly offsetting these strips,and repeating the scan, the region is filled in . Al though the scan direction has to be fixed due to the orientation of the bolometers, the chop parameters are free to vary. The integration time per sample is only 0.128 seconds, and the scan rate is 3" per sample. Unlike the other two modes, there is no nodding operation in scan mapping, and therefore each scan-map is made up of single difference data only. Each chopped signal has an instrumental D C level associated wi th i t . This is not a problem for photometry of jiggle-map mode, since the nod wi l l remove this. However for scan maps it is necessary to estimate and then remove this baseline. For blank field surveys wi th few sources contributing flux, it is sufficient to simply average a bolometer's signal across the whole scan. For observations of bright, extended objects however, baseline removal is a more involved process [65, 66]. 2.3 SCUBA data reduction process The S C U B A User Reduction Facil i ty ( S U R F ) [61] is normally used to analyze S C U B A data. However for the low S N R data which is the focus of this thesis, S U R F is not the ideal tool since a very detailed analysis of the noise properties is required. Therefore the data analysis was done using custom software developed in the.C language. In order to facilitate the description of the steps required, and to gauge the "flavour" 27 of S C U B A observations, the following discussion wi l l centre on the analysis of actual data. Photometry observations of the lensed A G N B1933+503 are used [67, 68]. In order to discuss the analysis procedure, the following notation is adopted: The indices b and j denote bolometer and jiggle number respectively, each starting at 1. The variable N subscripted with one of these indices represents the total number of the quantity. For example, Nb = 37 or 91 (for the 450 pm and 850 /zm channels respectively). S w i l l be flux density in units of mJy, and V is the bolometer signal measured in Volts. 2.3.1 Preliminary Steps For photometry and jiggle data, the individual nods are combined to produce the triple beam pattern. The relative gains of each bolometer compared to the central bolometer of the long array is then corrected for, using the measured response to a known load. 2.3.2 Extinction Correction Light from astronomical sources is attenuated due to absorption by the atmosphere. Th i s extinction can be corrected for using the known air-mass of the observation and the zenith sky opacity, r . The S C U B A method of determining r is to measure the sky brightness temperature as a function of elevation angle, using references at ambient temperature (hot-load) and a cold-load at 45 K . A fit is then performed to determine the zenith sky opacity. This operation is called a "skydip". Using archived data, Archibald [69] was able to determine a tight relationship be-tween the S C U B A determined opacities and those measured by the CalTech Sub-millimeter Observatory 225 G H z radiometer (dubbed the C S O tau-meter). This is a instrument dedicated to performing a skydip every 10 minutes at a fixed azimuth. The fit between C S O and S C U B A r estimates are so good that most observers no longer perform extensive skydips wi th S C U B A . The C S O r is automatically read by the J C M T computers and stored in the file header of data collected by S C U B A . For completeness, the C S O - S C U B A tau relationships taken from Archiba ld [69] are given in the appendix. 2.3.3 Removal of thermal sky and cosmic ray emission The signal time-stream for two representative bolometers from each of the short and long-wavelength arrays is shown in F i g . 2.6. It is clear that the output is highly 28 correlated in time between bolometers, even at different wavelengths. Furthermore, a detailed inspection of all the time-streams shows that the correlation is strong even for bolometers at opposite ends of the array, indicating that a common atmospheric signal subtends an angle greater than 2 arcminutes. Rough calculations based on nominal windspeeds and scale lengths suggest that the relevant patch is of order 1000" [63]. Much of this signal is removed in the process of chopping and nodding, but some atmospheric noise inevitably remains [62]. It is reasonable to use the correlation across the array to calculate a common atmospheric signal that can be removed from the data. We wi l l now consider two separate methods of removing the atmospheric signal from the long wavelength data, namely use of the average across the long wavelength array, or of the independent average from the short wavelength array. 2.3.3.1 Using the 850pm data to remove atmospheric signals The raw data contain the 2 second double difference signal, vbj, which we use to compute a mean sky signal on a jiggle by jiggle basis: Here, qb takes the value 0 for bolometers that are excluded from this sky calculation and 1 otherwise. Excluded bolometers include the central pixel (which is 'contami-nated' by B1933+503 in this example) and any bolometers that exhibit noise more than twice as high as the average of the others. Nb q is simply the sum of qb, and is the number of "good" bolometers used in the calculation. The sky-corrected signal is then simply Vbj = vbj - Mj. (2.5) If we assume that the residual noise is uncorrelated from integration to integration, we can compute the mean and variance of the sky-corrected signal using: 1 N j bj j = i 1 N i -and (aft2 = w ]T (Vbj - Vbjf qbj. (2.7) bj j = i In Figure 2.6, samples j = 1-360 and j = 900-1260 were taken while clouds were 29 16 8 0 -8 -16 16 8 0 > " 8 6-16 (0 C A &p 4 0 -2 -4 4 2 0 -2 -4 a) Bolo 75 - 450 f i m 1 1 1 1 i i i i 1 1 i i i i i i i 1 i i -- 1 1 1 1 1 1 1 I I 1 ,1 i i i 1 1 1 1 1 1 ~ 0 500 1000 1500 2000 b) Bolo 46 - 450 yum - i i i i 1 i i i i l, 1 i i , 1 1 1 I Z V^^ y^ - ^ ^ 4 ^ — ^ = ^ / W N — ^ ^ ^ - ^ J -M — i • • • 1 • • • : 1 I , , , , • = 0 500 1000 1500 2000 c) Bolo 33 - 850 jum - i i i i i i i i i 1 1 1 , 1 , E 4 1 - i i i i 1 i i i fi , 1 i i i i i i i i i i i -0 500 1000 1500 2000 d) Bolo 19 - 850 /xm _ I I i i i i i i i I 1 i i i i i i i i i i i _ M - i i i i 1 i i i fi , 1 i i i 1 i i i i 1 i i -0 500 1000 1500 Jiggle Number 2000 Figure 2.6: The raw time-streams from 2 bolometers on each of the 450 / im and 850 fxm arrays. The central pixels at 450 / im and 850 /tm are shown in panels b) and d). The pixels plotted in panels a) and c) were chosen to be far from the central pixel to help illustrate the correlated signal caused by the atmosphere. 30 obscuring the target region, rendering them unusable because the rapidly changing opacity cannot be easily characterised. To account for these data, we introduce the quantity qbj, which takes the values 1 and 0 for good and bad data respectively. AT'-is the sum for qbj for each bolometer, and is the number of good samples in a given bolometers' time-stream. Anomalous signals (e.g. cosmic ray hits) in the sky-corrected data are removed on a bolometer by bolometer basis. A n y sample that deviated by more than Zo^ was removed and the variance recalculated. This procedure is repeated to ensure that any statistically significant anomalies shadowed by even larger ones were removed. Typica l ly only 2 or 3 passes are required to remove al l of these spikes. This operation is commonly referred to as "despiking". The method of removing atmospheric signal described above is very successful, as evident from decrease in noise seen in the cleaned data. This technique is used for almost a l l earth-based C M B and sub-mm instruments, and some variant of it is the usual method adopted by S U R F . One disadvantage however, is that its use requires knowing in advance which pixels contain signal, or using some iterative process to remove the sky when low-level signals are present. Another disadvantage is that this method correlates al l of the pixels, since the mean has been subtracted from each one. In other words we lose one degree of freedom. 2.3.3.2 Using the 450pm array as an atmospheric monitor We can avoid these problems altogether by using an independent estimate for re-moving the atmospheric signal from the data. The mean sky signals calculated from Equat ion 2.4 are strongly correlated for the 450 pm and 850 pm data, and therefore it is feasible to attempt to subtract the sky using the independent data from the other channel. This may be particularly useful for future S C U B A cosmology or Sunyaev-Zel 'dovich (SZ) studies, since for 'blank' fields the 450 pm data w i l l generally contain no signal (while the 850 pm data may contain a contribution from extra-galactic sources). Hence this method may have general ut i l i ty for helping to look for low levels of fluctuations in long integrations at 850 pm, where it becomes important not to remove any of the signal along wi th the sky. Certainly the C M B has a negligible contribution to the signal at 450 pm, due to the sharp drop in the W i e n part of its spectrum, and the SZ signal at 450 pm is negligible. Therefore it is safe to treat the 450 pm band as an independent monitor of the sky signal. The 450 pm channel is more susceptible to changes in opacity, so we divide the data 31 into roughly 10 minute sections, and perform a least-squares fit of the form X2 = E [ M f ° - ( c M f ° + 0)] 2 ' (2-8) 3 where j runs over the appropriate section (excluding, of course those dominated by noisy atmospheric signal). The value of c is typically near 0.2, as also seen by [70], and does not vary by more than 10 per cent). The offset o is on the order of a few pV, and we found it necessary to include it; i f we redo the fit and fix o = 0.0, the integrated signal tends to be biased lower by approximately 4 pV. In F i g . 2.7 we plot the 450 jum and 850 pm mean sky for a section of the data. Also in the figure we plot the residual between the 850 pm mean sky and the scaled 450 pm mean sky. To appreciate how small this residual is, note that its R M S is 100 pV, whereas the R M S of the sky-corrected signal for a typical bolometer using either the 850 pm or 450 pm mean is about 380 pV. After forming the new mean signal, we subtract it from the 850 pm data and cal-culate the integrated signal. A s evident in F i g . 2.8, the signal level changes by at most 4 pV compared to the results obtained by using the 850 pm data to subtract a sky signal (top panel). There does not appear to be any bias introduced due to this method, although the variance is systematically higher by about 0.5 pV (or 0.12 m J y when applying the standard gains) (bottom panel). The increased variance is consis-tent wi th a signal wi th an additional independent noise term about one-third the size of the main noise term, as we can predict from the residual of the 850 and 450 pm mean signal level. Therefore this method invariably introduces more uncertainty in the integrated signal, but may be the best option when there is, for example, extended structure in the 850 pm map, and nothing but noise in the 450 pm. In this case, however, care must be taken to avoid removing a D C level in the 850 pm data v ia the parameter o, which is a systematic effect that could be calibrated by analyzing other data sets that are largely free of sources in both channels. 2.4 Mode Specific Calibration Each bolometer is corrected for a relative gain with respect to the central bolometer in the appropriate array, but overall calibration is done by observing astronomical targets wi th known flux densities. Planets are the most favoured targets. They are not ideal choices however, because they are not true point sources (not only are they 32 1350 1395 1440 1485 1530 1575 Jiggle number (first half of scan 4) > 6 6 4 2 S3 0 2 -2 OT ^ PH -4 1 1 1 1 i i i i I ji M i i i | i i i i | i i i i - : I jwlj - i \ i i i i , , , , i i i i i i i i i i i i i i i 0 450 900 1350 Jiggle number 1800 2250 Figure 2.7: Using the 450 pm array to remove the atmosphere from the 850 pm array. The top panel shows the mean sky signals for both arrays over a subset of the time-stream, wi th the 850 pm data solid and the 450 pm data dashed. The signals are clearly correlated. The bottom panel demonstrates the small residual between the 850 pm mean and scaled 450 pm mean. 33 > 2 a 0 Of) - 4 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 I I I I I ' ' I I I I I I I I I I I J 1_ 0 5 10 15 20 25 30 35 B o l o m e t e r i i r n | i i n |— i—n — i — i— i — r ~ \ — i — i — i — i — i — i — i — r n— i — i— i — i — i— i — i— i — r ~ r > A 2 0 CD o c < - 4 • • • i i i i i i i i i i i .i i i I i ' i i 1 i i i i i i i i i I 0 5 10 15 20 25 30 35 B o l o m e t e r Figure 2.8: The difference in the integrated signals between 850/ im data sky-subtracted using the 850 and 450 / im array averages. 34 so close, they have moons and rings that are sources of appreciable amounts of sub-m m flux). In addition, the planets are so bright that the electronics must be switched to a different gain setting to avoid saturating the bolometers. Final ly , the planets are moving, and for even mi ld integration times can span a distance on the sky of the order of 5". For these reasons, calibrations for the data used in this thesis are performed on a list of fixed sources on the sky [71], except for those cases when a calibration source was not reasonably accessible. Unless one requires precise flux density estimates, it is sufficient to use the "standard gains", which are averages determined from archived data. The values determined by the J C M T staff are based only on three months of data, so we re-analysed al l the calibrations performed on the standard source C R L 6 1 8 from September 1997 unti l October 2000. Sandel [71] estimates the flux density of this calibrator to be 5 8 5 0 = 4.57 ± 0.21 Jy, S450 = 11.9 ± 1.9 Jy. 2.4-1 Photometry For photometry observations the estimate of flux from the source is taken simply from the integrated time-stream of the bolometer pointed at it. The error in the flux conversion factor is based on the scatter of observations and the uncertainty in the flux from C R L 6 1 8 itself. The shape of the telescope surface is sensitive to temperature changes and elevation angle of an observation. In addition, the 450 /mi beam-shape is very sensitive to the surface accuracy, and therefore it is no surprise that the calibrations at 450/tm are strong functions of time of day and elevation angle [72]. It has often been stated that larger chop throws make the measurements noisier due to chopping onto a region of sky different in emission properties than toward the target area. Archibald et al . [56] have recently conducted an extensive investigation of this issue using the archived photometry data. They find that after sky subtraction using the array average, no trend between chop throw and noise remains. We performed a similar analysis using the C R L 6 1 8 data, and also fail to uncover a significant correlation between chop throw and noise level. 2.4-2 Jiggle-map Optica l astronomers use aperture photometry and/or a fit to the point spread func-tion (PSF) to estimate the flux of sources in a fully sampled map. For "aperture photometry", the flux is measured by summing the signal in the pixels wi th in a cer-tain radius of the source. From that, an estimate of the mean sky level is subtracted 35 Table 2.1: Photometry calibration observations of C R L 6 1 8 . The number in brackets after each number is the number of observations used in the calculation. Only obser-vations taken wi th TQSO < 0.08, and with a chop throw of 60", were used. The units are J y / V . Fi l ter Pre-Upgrade Post-Upgrade 450 / im 850 /mi 836 ± 180(122) 238 ± 2 1 ( 1 2 2 ) 393 ± 105(29) 199 ± 25(29) using an annulus centred on the source. The size of the annulus and aperture radius are usually varied to find the maximum S N R . Another method, " P S F photometry", uses a least-squares fit on sources in the field to estimate their flux. In either case, it is usually assumed that the position of the source is known in advance. Much of this thesis w i l l concentrate on large area sub-mm surveys where the typical S N R of a source is very low, and the position is not known a priori . This makes aperture photometry not very useful, since we wi l l not know where to lay down the apertures. The added complication of chopping means one has to carefully choose apertures that do not overlap the negative flux region. Since the sources we are looking for have an angular extent much less than the S C U B A beam, fitting the beam profile to every pixel in the final map is the best way to find sources. The next chapter w i l l describe this procedure in detail. Here we concentrate instead on the effect various observing parameters and conditions have on the signal. The time-stream of the bolometer pointed at the target is strongly variable not due to the atmospheric emission, but rather because the jiggle pattern takes the bolometer on and off the source as it moves around. Thus the variance in the signal cannot be used as estimate of the true underlying noise for bright sources. For a 2 second jiggle integration the N E F D at 850 / im is about 70 mJy. Using the 64 point jiggle pattern as the worst case scenario, it is found that the R M S of the signal that results from jiggling is ~ 0.2 times the intensity of the source. Since extra-galactic sub-mm sources are < 20 mJy, the added variance due to jiggling is negligible compared to the atmospheric noise contribution. However, since S C U B A calibration sources are al l > 2 Jy, an alternate way of estimating the noise should be used. However in practice the calibrators are so strong that we can fit them without weighting by the noise. For C R L 6 1 8 , the S N R is greater than 10 even ~ 3a away from the peak. Table 2.2 presents the calibration results based on the archived data. It is interesting to note that the 850 / im values are almost identical to their photometry counterparts, 36 Table 2.2: Jiggle-map calibration observations of C R L 6 1 8 . The number in brackets after each number is the number of observations used in the calculation. The units are J y / V . Fi l ter Pre-Upgrade Post-Upgrade 450 / im 707 ± 214(106) 306 ± 88(52) 8 5 0 / i m . 235 ± 2 5 ( 1 1 4 ) 199 ± 20(53) but jiggle-map observations at 450 / im are slightly more efficient by a factor of around 20%. The average of 9 samples at 450 / im taken using the 3 x 3 jiggle pattern used in photometry mode is about' 0.8 of the flux from a single measurement pointed directly at the source. Thus this drop in effiency can be explained completely by the requirement to jiggle the photometry observations. 2.4-3 Raster-scan calibrations Scan mapping is substantially different than the other two observing modes. Da ta are collected 8 times as quickly (integration time is only 1 full chop cycle as opposed to 8). The lack of nodding also means that the baseline zero-point of each bolometer must be subtracted. In the method used in this thesis, for each strip a line is fit and removed from the time-streams of each bolometer. For calibration measurements, observations that fall on the source are not included, as they substantially alter the fit. Despiking and sky subtraction are then done in the usual way, and the map created. Sources are then extracted using the same prescription as in jiggle mapping. The calibrations listed in Table 2.3 differ considerably from the other two modes, especially pre-upgrade. The reason remains elusive; fits to the beam profiles from scan-map calibrations are comparable to those from jiggle-map observations, and are consistent wi th the ex-pected P S F of the telescope. There also seems to be no obvious reason why the act of j iggling would result in an inefficiency in measuring signal either. It has been sug-gested that there is simply a multiplicative factor within either S U R F or the S C U B A transputer firmware that is responsible, which is possible because of the different ways that the system treats scan-map data. Nevertheless there is a significant difference in scan-map and jiggle-map calibrations, which have to be taken into account when comparing or co-adding data. 37 Table 2.3: Scan-map calibration observations of C R L 6 1 8 . The number in brackets after each number is the number of observations used in the calculation. The units are J y / V . Fi l ter Pre-Upgrade Post-Upgrade 450 / im 370 ± 138(4) 225 ± 80(17) 850 / im 175 ± 1 9 ( 4 ) 174 ± 2 1 ( 1 8 ) 2.5 Correlation analysis of SCUBA time-stream data When dealing wi th very low signal to noise observations, care must be taken to ensure that signals are uncorrelated. In practice it can be hard to remove such correlations completely, so the next best thing is to characterise them and develop techniques to deal wi th their effects in the data reduction. 2.5.1 Correlations between bolometers Bolometers are grouped into banks of 16, each bank having a r ibbon cable that con-nects the group to a 16 channel A / D card. It is reasonable to assume that correlations might exist between bolometers in the same group, especially neighboring bolometers. For the archived photometry data, the following statistic was calculated: J _ sr~Ni q q p(bub2) = — . (2.9) Here, p is the correlation coefficient between bolometers b\ and 6 2, and Sjh is the time-stream signal (modified so that each bolometer has zero-mean). Because the number of bolometer pairs is large, the statistic was calculated only between 1) the first and second bolometer on the same A / D card, and 2) the first bolometers on different A / D cards. In Figure 2.9 the results of a correlation analysis of 100 pho-tometry observations at 850 /mi is shown. The procedure was repeated for different combination of bolometers for both filters, but in al l trials the results show no obvious trends between the bolometers. 2.5.2 Spectral analysis of individual bolometer time-streams A Fourier analysis of S C U B A data was performed in an effort to characterise the statistical properties of the noise. Instead of the calibration data described earlier, the data which are the focus of Chapter 4 and 5 is used. Cal ibrat ion data contains 38 0.4 h 0.2 -0.2 -0.4 ~i 1 r -i 1 r n 1 r • A J I I I I I I I I I L -L 20 40 60 80 Observation Number 100 Figure 2.9: Correlation coefficient between 850/xm bolometers. There are 3 A / D cards on the 8 5 0 p m array, and the correlations are denoted by black circles (1-1), red triangles (1-2), and blue squares (1-3). The results show no trends between bolometers. 39 too much signal and too few temporal samples to accurately gauge the frequency behaviour of the data. The observations of Chapter 4 and 5 however are ideal, because they employ al l 3 modes of S C U B A operation, consist of lengthy integrations, and are very low signal-to-noise. Eventually we wi l l show how to co-add these data and extract signal from them, but for any given single observation it is safe to assume that the time-stream is dominated by noise. Figure 2.10 shows the power spectrum from a typical scan-map observation taken before the upgrades program. The 1/f nature of the sky emission is evident, but more alarming is the strong feature at ~ 2.5 Hz. It is clearly common to a l l bolometers, since it disappears after removing the array average. This feature is not present in the post-upgrade data (see Figure 2.11), suggesting that there was a resonance of some sort either in the ribbon cables or the filter drum assembly. Because we always use sky subtraction throughout this thesis, we can safely ignore this effect. The sky-corrected power spectrum st i l l shows a non-white frequency response, however, it is strongly suppressed compared to the raw data. O f particular interest is the apparent diminishing rol l off in noise beyond about 2 Hz . There is an undocumented filter applied by the S C U B A D A Q hardware that effectively smooths the time-stream. It is unclear why it is required, but it is present nevertheless. The effect' of such a filter spatially is to smooth the beam along the direction of the scan. From maps made of the calibration sources, we verify that this is indeed observed. The beam is widened from 14" 7 to 15'!0. This filter suggests that it is important to scan in as many directions as possible in order to keep the final P S F circularly symmetric. The situation at 450 pm is more pronounced: the 7"5 beam increases to ~9"0 along a scan direction. A similar analysis is performed on a typical jiggle-map observation. Figure 2.12 was made from data taken pre-upgrade, but they are comparable to the post-upgrade data. Due to the 2 second effective integration time, the data are insensitive to the feature evident in the scan-map data. Again , the sky corrected signal suppresses the 1/f component of the sky emission. In the next chapter we address issues associated wi th converting time-stream data into a fully sampled map of a region of sky. The effectiveness at which that can be done without artifacts depends on the correlations in the data. The auto-correlation analysis shown in these last 3 figures demonstrates how effective sky-subtraction is at removing these correlations. 40 Sample Number Sample Number Sample Number Figure 2.10: F F T of a scan-map 850 / /m time-stream taken before the upgrade. From left to right, the plots show the raw data from the central bolometer, the estimate of sky taken from the array average, and finally the sky corrected signal for the central bolometer. The top panels are the power spectra, while the bot tom show the associated auto-correlation plots. 41 3 o CL-IO €7 CD 3 O CL " ' I ' ' I ' " I' 1 Sky corrected bolometer 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 Frequency [Hz] Frequency [Hz] Frequency [Hz] i 1 1 1 i 1 1 1 i Raw bolometer •O.Pl . . . i . , , i 1.01 ' 1 1 l 0.8 0.6 Sky signal 1.01 1 1 1 I 1 1 1 I 1 1 1 I Q g L Sky corrected bolometer 0.6 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Sample Number Sample Number Sample Number Figure 2.11: F F T of a scan-map time-stream taken after the upgrade. Layout is before. 42 10 a> 5 4 I 1 1 1 ' I 1 1 1 1 I 1 1 1 1 I 1 Raw bolometer 0.00 0.05 0.10 0.15 0.20 0.25 0.00 0.05 0.10 0.15 0.20 0.25 0.00 0.05 0.10 0.15 0.20 0.25 Frequency [Hz] Frequency [Hz] Frequency [Hz] 1.0 0.8 0.6 t 0-4 Raw bolometer 1.0 0.8 0.6 £ 0.4 i 1 1 1 i 1 1 1 i 1 1 1 i Sky signal 1.01 ' 1 1 l 0.8 0.6 t 0.4 l 1 1 1 l 1 1 1 l 1 1 1 Sky corrected bolometer 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Sample Number Sample Number Sample Number Figure 2.12: F F T of a jiggle-map time-stream. Layout is as before. Note that information between 0.25 Hz and 4 Hz is not available because the sample rate is lower than in scan-mapping by a factor of 8. 43 3: Creating SCUBA maps and extracting point sources Photometry is the preferred mode of observation when given a list of objects from which one requires sub-mm fluxes estimates. However, as already explained, such lists are biased by selection effects, and indeed there are sub-mm sources that have no counterparts in other catalogs at al l . In addition, there are catalogues in which the source positions are not well determined. Thus it is necessary to make fully sampled maps of regions of the sky. This allows one to detect multiple sources in the field and any extended emission as well. A s we have seen in the previous chapter, obtaining a map of the sky with S C U B A is not as straightforward as wi th optical cameras; the necessity to chop and jiggle the secondary mirror complicates the process. This chapter w i l l focus on the various ways of inverting S C U B A data to make the best map. "Best" is a relative term, and the exact approach to map-making depends on the science that is to be extracted from the data, and the level at which systematic effects can be tolerated. Several techniques wi l l be outlined, and for each their effectiveness wi l l be demonstrated by an application to simulated and real data. Ul t imate ly the purpose of this chapter is to develop a set of tools that can be used to measure fluxes of distant sub-mm galaxies with the maximum signal-to-noise ratio. Hence the last part of this chapter details methods of finding and characterising the flux of objects wi thin these maps. 3.1 Maps Given that current S C U B A surveys are < 1 square degree on the sky, a simple tangent plane projection can be used to map the celestial sphere wi th negligible distortions. For the same reason, the pixels wi thin the map can be made square. Future large scale sub-mm surveys may need to apply pixelization schemes such as H E A L P I X [73], which is employed by current all-sky C M B experiments. 3.1.1 Raw maps The most straightforward way to construct a map using S C U B A data is by looping through each bolometer at each time-step and adding the measured flux to the pixel being pointed at. One would like the number of samples per pixel to be large enough 44 that Gaussian statistics can be assumed. Also, it is desirable, though not strictly-necessary, to have every pixel within the map sampled. In general, a pixel size of 3" x 3" w i l l result i n a fully sampled map 1 ; the 64-point jiggle pattern has a 3" spacing, and in scan mode the telescope moves 3" per sample. It is also important to keep track of the noise estimate for each pixel. Maps of the estimates of signal and noise within each pixel can be created using two different prescriptions. The first employs the variance of the data collected from each bolometer (which wi l l typically be calculated for different sections of the data) to weight each sample as it is added into a pixel. The map and noise are found from: The index, i, refers to individual pixels in a map, m. Aga in , b,j index bolometer and jiggle number respectively. The delta function, is used to isolate only those samples where the positive beam points toward the pixel i. One can also ignore the variance estimates for the individual bolometers and estimate the flux and noise in each pixel by using the scatter among the measurements themselves: Here, iVj is the total number of samples contributing to pixel i. In the case where measurements are al l derived from bolometers wi th the same variance, these two methods are identical. However, this is never the case wi th S C U B A data, since several bolometers of varying sensitivity usually sample a pixel, and the sensitivity of a given bolometer changes during the course of even a single night of observations. Also, many extra-galactic mapping projects span several nights (even years!), and the sensitivity of a measurement is based almost entirely on the weather. Weighting by the inverse of the bolometer time-stream variance assumes the noise is normally 1 This is fully sampled in the Nyquist sense, where we have at least 2 samples per beam size. S W J ( + ) W (3.1) (3.2) 45 distributed. This is reasonably true for sky-corrected data, but as seen in Chapter 2, the noise s t i l l demonstrates non-Gaussian features. Also, the atmospheric opacity changes over the course of an observation, and therefore the R M S of the time-stream is not a perfect estimator for the noise of each sample. Bo th approaches have been used in the literature, but in this thesis we adopt the weighted case since we wi l l develop algorithms that require knowing the error of individual samples and not just the error estimate for a particular map pixel . For the data dealt wi th in this thesis, the unweighted noise maps typically have ~ 15% higher noise than those made by weighting the data. Neither method provides an opt imal estimator of the noise i n each pixel when dealing wi th real data. Therefore it is important to simulate the data to carefully assess the statistics of the final map, and in particular whether any biases are introduced. This is a point we wi l l return to in the next chapter. It is worth noting, nevertheless, that tests show that the noise does integrate down at close to the expected y/i [56]. 3.1.2 Small area surveys: Direct inversion of the mapping matrix for jiggle-map observations The most obvious problem with the simple picture so far is that S C U B A takes dif-ferential measurements, and thus each pixel is connected to flux estimates in other pixels v i a the chop pattern. Ignoring this wi l l result in a map that exhibits the chop configuration; for each positive source there wi l l be negative echoes. Due to this com-plication, observers often choose to chop well off their source. Thus, no bolometer i n the "off" position sees signal in the target region. It is usually assumed that there are no bright sources being chopped onto, but even if there were, the fact that the sky rotates means that only a small number of samples wi l l be contaminated. Also , the number of times a pixel outside the central region is sampled is much lower due to sky rotation, and therefore the noise wi l l dominate al l but the brightest of sources. How true this is depends on the form of the sub-mm number counts as well as the sensitivity of the observations. For deep pointings, it becomes increasingly more likely that a source of significant flux is being chopped onto. However, when relatively sparse and compact sources are being searched for, it is desirable to chop in-field so that the flux from the reference positions can be added back into the source flux to improve the S N R . The procedure to fully deconvolve such a map can be posed as a linear algebra problem. Following the notation given in [74], the M measurements that make up the time ordered data vector ( T O D ) , d t are related to a pixelized region of sky, rrij that has N elements v ia a pointing matrix, 46 dt = Atimi + nt (3-3) Here, the vector n t is the noise in each measurement. The best estimate of the flux in the pixelized map, m,, in a least squares sense, has a well known solution [74, 75, 76]. Dropping the indices for compactness, the solution is: provided that Aftt =< ntnf >, the time-stream noise correlation matrix, is known in advance. n, the pixel noise correlation matrix, measures how much correlated noise exists between pixels, wi th the diagonal element being the variance estimate for each pixel. One expects that in ideal circumstances, pixels are only correlated wi th their neigh-bors v ia the beam, plus the pixels connected by the chop pattern. A is very sparse, wi th each row having only 2 or 3 non-zero entries depending on whether or not the S C U B A observation was in raster (2 beams) or jiggle mode (3 beams). For example, in jiggle-mapping observations, each row of A w i l l contain a —0.5, +1.0, and —0.5, representing the beam weighting factors. Given that S C U B A observations are dif-ferential in nature, the matr ix ( A J V - 1 A T ) is formally singular, since there exists a non-zero vector m where A m = 0. Specifically, and unsurprisingly, the degeneracy is in the overall mean of the map, which S C U B A is insensitive to (i.e., setting m to a constant). AT measures how correlated the noise is i n the t ime domain. For anything but uncorrelated noise this matrix is difficult to manage without special techniques, since M can easily reach 10 6 samples. This is a topic we wi l l return to later. One advantage of the above formalism is that m need not be restricted to pixel fluxes in the real map. Any term that the data are affected by can be fit in this manner. For example, in the analysis of COBE data, the magnetic susceptibility of the fer-rite switches on the satellite was included in addition to flux estimates wi th in each pixel [77]. In the M A X I M A C M B analysis[74], offsets, synchrotron noise terms, and dummy pixels to allow for gaps in the time-stream data were added. Assuming uncorrelated noise, M is diagonal and therefore the matr ix ( A J V - 1 A T ) and vector A j V _ 1 d t can be populated in time order, requiring O (M) operations. Thus we are faced only wi th the task of inverting an N x N matrix. Given the 2.3' field of view of a jiggle-map observation, and the typical pixel size of 3" the number of pixels is O (2000), which is small enough that any modern workstation can invert m n = (AA/* _ 1 A T ) ATAf~1d (3.4) (3-5) 47 the required matr ix in an acceptably short time. 3.1.2.1 Direct inversion applied to simulated data To verify that this algorithm works for jiggle-map data, we create a simulated dataset and compare the output against the original input image. We start by modelling a single point source in the centre of the array. For the pointing matrix, the attitude information from an observation of the cluster MS0451 2 was used. The cluster was observed wi th three different in-field chops with 30" throws. The flux of the input source is 100 Jy, and noise was added to the system to make the noise per pixel have an R M S of 1 Jy. A region of interest (ROI) is defined, inside of which we pixelize the map. For these studies we use a circle centred at the middle of the map, and control the radius to l imi t the solution area. The next problem to address is what to do wi th those data points that have bolometers pointing outside the RGT. For the moment we wi l l assume that there are no sources present beyond the R O I and therefore assign a l l pointings outside the solution area to a single "dummy" pixel. There is no reason to avoid solving for all the pixels outside the circle, but most of these wi l l only be sampled a small number of times, and thus wi l l be dominated by noise. The algorithm used to invert the matrix was based on a singular value decomposition routine taken from LAPACK [78] . This allows one to isolate the singular mode and set it to zero so that the inversion can be performed. Since the matr ix to be inverted is symmetric and positive semi-definite, its properties can be exploited to perform an eigenmode decomposition. Not only is this faster but also many eigenmode codes allow the user to choose the first basis vector. B y forcing this to be c r f 2 ^ 2 . . . ^ 2 , we isolate the eigenvalue associated with the map mean and can set it to a known value to ensure that the inversion is stable. The output, shown in Figure 3.1 demonstrates the effectiveness of the procedure. B y design, the mean of the final map is zero, therefore when used in practice a mean level must be added back into the map. To do this, we take the mean of pixels away from the source and correct the map accordingly. O f course for real data-sets this may be rather subjective since it might be that there are faint sources in this region that we do not quite detect. However, without obtaining a map of a larger field surrounding the target, there is no way of avoiding this ambiguity. 2 In fact all that was done was that the signal measured by SCUBA in these observations was replaced by a simulated one derived from a point source smoothed by a Gaussian beam. 48 a) b) c) d) Figure 3.1: Inverting the mapping matrix. The maps are binned into 6" pixels and each panel is ~ 3' x 3'. a) is the input point source, smoothed wi th a 14.7" Gaussian beam, b) shows the "raw" map, and c) the one obtained from inverting the mapping matrix. The residuals between the input map and inverted one are shown in d) and exhibits noise only. The top panel shows the case for single source, and below it are two sources of different amplitudes positioned such that the chopping configuration cancels out some of the flux. Note how the algorithm is able to recover the lost signal. In the simple case of a single source, the procedure works well, as is evident from the residuals between the input and output maps in the upper panel. Also of interest is the abili ty to disentangle the chop pattern for sources that overlap each other. The lower panel of Figure 3.1 show the results from a source configuration where the chops from two sources interfere with each other; without the deconvolution, the sources are roughly 20% fainter. Again , after deconvolution the residuals are consistent wi th the noise. In this case, the deconvolution worked only because the chop configurations were such that each pixel was connected to 6 others. One can see how this procedure would fail to recover information if only a single chop was used and sources happened to lie along that same orientation. Since this approach is close to the optimal solution,its lessons are important ones: It is crucial to observe fields wi th as many different orientations as possible in order to interconnect pixels. 3.1.2.2 Direct inversion applied to real data This algorithm has been applied with some success to several data sets. Results from Chapman et a l . [79] revealed that the cluster MS0451 is rich i n sub-mm flux. Part icular ly str iking is an extended region of emission coincident wi th a strong gravi-49 tationally lensed arc seen in optical images. However the chop pattern was such that flux along this ridge, in addition to a point source off to the east of the field, was part ial ly canceled out. In separate observations taken a year later, a wide chop throw of 180" was used, ensuring no flux within the field was removed. The intent of this second program was to detect the Sunyaev Zel'dovich increment, which has a profile extending over a few arcminutes. If we use this second map as a "standard" and compare it against the raw and deconvolved map from the full set of observations, we find that the x2 is lower for the latter map. In other words, applying the deconvo-lut ion described here resulted in a more consistent pair of maps, not subject to flux cancellation due to the chop. A n image of this cluster is shown in Figure 3.2 and a full description of this object is given in Borys et al . [80]. This exercise began as an attempt to find a method of recovering point sources when the chop confused the map. A s this object demonstrates, provided there are enough modulations of the data this formalism can be used to recover arbitrari ly complex source configurations. This technique has never before been applied to S C U B A data, and the map of MS0451 could not have been made otherwise. Wi thout the assumption that the noise is uncorrelated, the inversion is much more difficult. Recently, van Engelen [81] has demonstrated that issues related to correlated and changing noise levels in S C U B A data can be dealt wi th by iterating on the noise and signal correlation matrices simultaneously, improving estimates on both at each step. This is a method adapted from Stompor et al . [74], used in the reduction of C M B maps. The data probably does not warrant such an intense treatment (it is particularly time intensive), but the next generation of C M B and sub-mm cameras may require a more sophisticated treatment. 3.1.3 Large area surveys: Iterative matrix inversion for scan-maps Direct map inversion becomes impractical with more than ~ 5 x 10 3 pixels, which is the case for typical scan-maps which span at least 10 x 10 arcminutes. In these cases it is necessary to find alternative ways to construct the map. The standard S U R F approach to deconvolving scan-maps makes use of the fact that the raw map is the convolution of the true underlying signal wi th the chopping pattern and beam function: m' = m eg) C, (3.6) 50 Figure 3.2: A p p l y i n g matr ix inversion to an observation of MS0451. Sub-mm contours are overlaid on the HST R-band image. Contour levels are 4, 6, 8, and 9a. a) shows the S C U B A measurement taken wi th multiple in-field chops. A 2a contour is shown in grey for comparison wi th the other images. The important point is that the ridge of emission near the centre is decreased and shifted due to the chop cancelling out signal, b) S C U B A measurement taken using large out-of-field chops, c) a l l the data co-added using the direct map inversion algorithm described in the text. The contours apparently co-incide wi th a strong gravitationally lensed arc i n the cluster. 51 where m' is the raw map and C is the effective point-spread function (beam + chop pattern). To recover the map, m, one inverse transforms the quotient of the Fourier transform of the observed map with that of the chop pattern. This technique, known as Emerson reconstruction [82, 83], has several shortcomings, as has been recently described by Johnstone et al . [66]. First , a l l information on the scale of the chop throw is lost (essentially the chop forces zero power at those scales and their harmonics in the Fourier domain). This is not unexpected, as we have already warned about the importance of using multiple chop configurations in order to better connect the map. Use of this approach also enforces a very specific chopping strategy: two chop directions orthogonal to each other and fixed in orientation on the sky. This is required in order to achieve reasonable sampling in the Fourier plane, however it is not always desirable. Where the technique is particularly weak is in its treatment of noise, for which great care must be taken in the detection and understanding of the weak sources that compose most extra-galactic surveys. Note that even in the absence of signal, the Fourier plane of m' w i l l be fully populated due to the presence of white noise. The chop function however wi l l have a transform that wi l l drop to zero for modes longer than the chop throw. Therefore the quotient of the two wi l l amplify the noise at large wavelengths. In addition, the technique does not provide a means to deal with non-uniform noise levels. Using simulated data sets, [66] found that the Emerson reconstruction effectively causes high noise regions of a map to diffuse into lower noise ones. It should be noted that the technique provides reasonable estimates in the high S N R regieme. It also has the advantage of being very fast to apply, since computers are able to perform Fourier transforms very quickly. To summarize, the three shortcomings of Fourier methods are: 1) Some frequencies are not sampled by the chop and therefore must be interpolated. 2) Scales that are the same (or harmonics of) the chop are lost. 3) noise affects the frequency domain division, and amplifies noise on small scales unless the map is heavily smoothed. Each of these affects the spectral division leading to large variance in the determination of the map. Methods now exist that allow us to solve equation 3.4 using relatively fast numerical tricks. Al though not as fast as the Emerson reconstruction, the codes s t i l l provide output in a reasonable amount of time and therefore, since they are more accurate, matr ix inversion methods should be preferred over Fourier methods for this appli-cation. If one does not require the pixel noise correlation matrix, n, there exists a simple iterative scheme for solving for m [77]. Developed for use in analysis of differential data from current and next generation of C M B anisotropy experiments 52 ( B O O M E R A N G , MAP, Planck, etc.), the procedure works by averaging the signal measured toward each pixel after first correcting for the flux in the reference beams determined from the previous iteration, i.e. n+l _ E f e /( + ) K _ ) + gfeJX + ^-)(m^ •(+) ~ Sbj)crbj' (3.7) Here, m n + is the flux in map pixel, i in iteration number n + l . The subscript on m" refers to the flux in the pixel being pointed to by the positive (+) or negative (—) beam for the sample corresponding to b, j. The only difference between this equation and that presented in Wright et al . [77] is the inclusion of noise weighting. A strength of this approach is that the algorithm can be performed in time-order, and the computer needs only enough memory to store the current map and that from the previous iteration. 3.1.3.1 Iterative inversion applied to simulated data Again , we tested the algorithm on a simulated dataset, but this time used two different observing philosophies. The first employs the Emerson chop configuration, which is a set of 3 different chop throws (30, 44, and 68 arcseconds) taken in two fixed directions on the sky (typically R A and D E C ) . The second is a set of 2 chops (40 and 68 arcseconds in this case) in each of 3 directions which correspond to the scan direction. There are two major advantages of the second approach. Firs t , sky rotation means that pixels w i l l be connected to more than six others, which is the case for the Emerson observing strategy. Also, because the differencing is occurring along the scan direction, the baseline is guaranteed to be zero. This is a topic we shall return to later. A s in wi th the simulations pertaining to the direct inversion method described in the last section, we used the real astrometry information from actual S C U B A observations and replaced the signal wi th a group of bright sources designed to give structure at a variety of scales. Specifically, 5 point-sources were added and 2 much broader ones which represent an extended region of emission (say from a star-forming cloud within our Galaxy) . Noise was added to the data such that the R M S of the pixel distribution in a signal-free region of the map is 1.0 mJy. The faintest simulated source was 40 mJy, and therefore this exercise is exploring the high S N R case. We used the standard map size for the scanning mode: 10' x 10'. O n a 400 M H z Pentium class computer, 100 iterations take just over 5 minutes to perform. Figure 3.3 plots the mean and R M S of the residuals between the input map and output map as a function of iteration. The procedure recovers the map very well 53 after only ~ 100 iterations using either chopping configuration. In general it appears that the regions wi th longer wavelength modes converge more slowly. Intuitively we expect this; for each iteration, information can only move at the rate of the longest chop through used. The maps of the residuals are shown in Figure 3.4, i l lustrating how information propagates across the image. A Fourier analysis is instructive: in Figure 3.5, the 2-dimensional Fourier transforms of the residuals between the input and output map are shown. The cross in the centre is orthogonal to the map edges, and a plot of the intensity along it, (see Figure 3.6) shows that it has a l / / - t y p e behaviour. In other words, there is residual power on large scales. In retrospect this is not. surprising considering that it takes several iterations to move information from one edge of the map to another, given the short chop throws. The long wavelengths modes tend to zero as more and more iterations are performed. Also evident in the 2D Fourier maps is substructure induced by the observing strategy. It appears that the Emerson strategy is more prone to this than the more interconnected approach. 3.1.3.2 Iterative inversion applied to real data This procedure has been used effectively in studies of bright molecular clouds wi th in our Galaxy [66, 65]. Since the signal-to-noise ratio was so high in those observations, the iterative approach was only marginally better than the Emerson reconstruction. It was noted however that the biggest problem in the analysis of that data was the ambiguity i n baseline removal. Because the chopping was not along the direction of the scan, the integrated signal across each strip was not guaranteed to be zero. These authors found that iterating on estimates of the baseline yielded acceptable results. However, this added complication is only required because the Emerson scan strategy necessitates chops which are not parallel to the scan. To verify that the iterative map making approach could yield excellent maps and bypass this chopping requirement, time was obtained on the J C M T to conduct a pilot study of different scanning strategies. Da ta were collected using both observing philosophies, and maps were created using the iterative technique. The target was a region of the sub-mm bright molecular cloud O M C 1 , which is a region of active star formation wi th in our Galaxy. The results, shown in Figure 3.7 indicate that the Emerson configuration results in a map replete wi th artifacts. Note that this is a result of observing a field wi th extended, bright emission. In extra-galactic surveys, any single strip across the sky is dominated by noise and therefore forcing a zero baseline is acceptable regardless 54 Figure 3.3: Residuals between input and output maps as a function of iteration. The abscissa is in units of mJy. The dotted lines show the expected asymptotes based on the simulated signal and noise level. 55 Figure 3.4: M a p of residuals as a function of iteration. The top left panel simply shows the input source distribution, scaled between 0 and 25 mJy. The next four rows show the difference between the input map and the solution for each of the Emerson and chop-along-scan scan configurations as a function of iteration. The solution converges near iteration 100, where the residual is s imply noise. For these, white and black correspond to ± 0 . 0 1 mJy, wi th grey being zero. 56 Chop-along Emerson scan Figure 3.5: Fourier transform of residual between input and maps made from an iterative solution. The scale at each iteration is the same for both the Emerson configuration (left) and the chop-along-scan approach (right). The Emerson maps seem to have residual power on scales of the chop throw (and their harmonics), which this effect is smaller i n the chop-along-scan configuration (where the chop direction is constantly changing). 57 Figure 3.6: l/f behaviour of residual power in iterated maps. Only the F F T s from the Emerson maps are plotted here; The other approach yields very similar results. The knee of the power spectrum moves toward lower frequency as the number of iterations increases. This indicates that the long wavelength modes take longer to converge. 58 Figure 3.7: Demonstrating baseline issues in scan-map data. After 200 iterations, the left map, taken using the Emerson configuration, suffers from baseline issues. This is evident by the dark streaks along the scan directions. The alternative approach on the right is free of these artifacts. The map on the left can be improved by an iterative method of baseline estimation, but there is no such ambiguity in the chop-along-scan approach shown on the right. of chop configuration. Nevertheless it appears that chopping along the scan direction offers a mi ld advantage. In addition multiple scan directions are useful for distinguish-ing genuine large scale features from systematic noise effects i n the scan direction. 3.2 Co-adding maps Extra-galactic surveys require extensive observation time to reach the areas and sensi-tivities needed to detect significant numbers of objects. Opt ica l surveys can shift and scale separate images before co-adding them because each image has sufficient signal to identify common sources. This is not the case wi th S C U B A surveys, and there-fore it is important to investigate alternative methods of registering images before co-adding them. This is even more important in practice considering that the J C M T has suffered from various types of tracking problems during S C U B A ' s lifetime. The first known issue was in a clock drift that affected the conversion from horizontal coordinates (the J C M T is an alt-az mounted telescope) into equatorial coordinates. This issue can be resolved in software when creating S C U B A maps, as it s imply involves correcting the recorded time. A more serious issue became apparent for data collected near the 59 local meridian [84]. The "transit-error" as it is now called, occurs when the telescope tracks an object across transit 3 . Later it was revealed that any change in elevation direction could result in a pointing offset in elevation of variable amplitude. Therefore combining data-sets spanning several years first requires some estimate of pointing offsets. Later in this thesis we w i l l demonstrate correlations between objects detected at other wavelengths and S C U B A flux. We can attempt to use such objects to register the images in the following manner: for each night of data, create a map and measure the average S C U B A flux at a list of coordinates given in the reference catalogue. We can then shift the S C U B A map by reasonable amounts i n an attempt to find the maximum average flux. For an average flux, 5 , in a map'with a noise per pixel of am, the S N R of this average is S\/~N jam. Later we wi l l show that the strongest correlation comes wi th radio catalogues, where we wi l l find an average S C U B A flux of about S = 2 mJy. Radio catalogues have positions accurate to less than an arcsecond, and therefore are good references to register the S C U B A images against. Typ ica l jiggle-maps reach a noise level of am = 2 m J y in single night. If we require a 3a detection of the mean radio flux, then we need N ~ 9 radio sources wi thin the field. This is about a factor of 2 higher than the surface density of radio sources in the deepest radio surveys. Wha t this rough calcuation shows is that the S C U B A noise is too high to definitively detect the average radio flux on a night by night basis. Another option is to attempt to cross-correlate the S C U B A maps themselves. How-ever, this w i l l only work for maps that overlap, which is not common for surveys that are composed of adjoining jiggle maps. There is also the question of how much S N R is required in each sub-map in order to perform the registration. In the next chapter, we w i l l present a survey in which every data set can at least be anchored to a wide area scan-map. We can solve for the best fit offset in a least-squares sense by taking two maps and shifting them wi th respect to each other. However, this is prone to the same difficulty as before; on any given night the noise per pixel is too high to discriminate a variance induced by the residual of offset Gaussians from the noise. A Monte-Carlo simulation was performed to test the l imits of this approach. Maps of a single point source were made and noise added. It was then shifted and compared against the input model. The residual follows a x2 distribution, and therefore we can use the statistic v = (x2 — N)/y/2N where N is the number of pixels (see, for example, the paper by Tegmark [85]). This measures how inconsistent the residuals 3 By "transit" we mean the point at which an object passes through its highest elevation (which always occurs due North for observers at positive latitudes) 60 are from zero in units of "sigmas". As Figure 3.8 shows, when the R M S noise of the map is ~ 0.15 times the amplitude of the input point source, we can detect the presence of an offset wi th better than 3cr certainty. In practice the noise level must be smaller, since this plot is comparing a noisy map wi th a noiseless model map. Offset (arcseconds) Figure 3.8: Determining offsets between S C U B A maps. Each curve represents the constraining power at different fractional noise levels ( R M S noise/peak flux of point source). The dashed lines show the 850/mi H W H M and 3a l imi t . Given that the objects in the survey about to be described are < 20 mJy, we require a noise level of <i 2mJy. This is much lower than is possible in a single shift of observing time, and hence this approach is impractical for current S C U B A data. In efforts to combine C M B data sets, it was found that a stronger test can be used when one knows the form of the residuals [85, 86]. However, in C M B maps, every pixel contains information; in maps that are largely free of sources this is not true. 61 Subsets of the data in which the R M S is sufficiently low are probably worth regis-tering relative to each other. However, sub-mm extra-galactic surveys at the moment rarely have the luxury of spare signal-to-noise. U n t i l they increase in sensitivity, the only approach to registering sub-mm images is to pay extra attention while at the telescope taking the data and by performing regular pointing checks. 3.3 Extracting point sources from sub-mm maps The rest of this thesis wi l l concentrate on probing properties of distant sub-mm galaxies wi th S C U B A . Given the large beam size in both the 450 and 850 pm channels, and the small angular scale of the sources themselves (< 3"), the profile of the emission in the maps wi l l be simply the P S F of the beam itself. Therefore to estimate the fluxes of objects we need only fit the P S F to sources in the map. Unfortunately, these objects are often so faint that we cannot see them in the map to begin with . However, we can use our knowledge of the shape of the P S F to simultaneously find and fit sources. A common trick is to convolve the map wi th the P S F . A t those locations where the P S F pattern matches a source in the map, the output w i l l be larger. B y picking off the bright peaks in the convolved map, one creates a list of "detections". This procedure is not l imited to sub-mm astronomers; smoothing an image like this effectively reduces the noise because more data is added together (albeit at the expense of lower resolution). Thus image smoothing is per-formed on optical images, data obtained from remote sensing of the earth, and any other image processing instrument. Th i s operation is numerically equivalent to least squares fitting of the map wi th the P S F function, assuming the noise in each pixel is the same. However, since we have been careful to construct a noise map alongside our estimate of the signal, we can use this to better estimate the fluxes of sources in the map. We set up the fit like any other linear, least squares problem: ^ ^ ^ ( a x P S F ^ - ^ ) 2 ^ 2 . (3.8) v Again , % is the pixel we are fitting an amplitude, a for. P S F ^ is the response of the P S F at pixel i' when centred on i. A n advantage to this approach is that one can tolerate missing pixels in the map. Indeed missing pixels can be filled in by the best estimate determined from its neighbours. To get the P S F , we can either just assume a Gaussian beam of the appropriate 62 width, or take calibration observations of bright targets at the telescope to get a more accurate picture of the true beam-shape. In fact, the beam at 850 /zm is very well fit by a Gaussian wi th a F W H M of 14.7" and is stable over time. The 450 zzm beam however, is particularly sensitive to surface inaccuracies and therefore can have considerable power in the side-lobes. Also, for scan-map observations the beam is slightly extended in the direction of the scan. Thus it is necessary to take calibration images at the time of observation i f 450 fim fluxes are required. This discussion has assumed that sources are not overlapping, because we have been using the P S F of a only single source in our fit. In the event that some sources do blend together, fluxes can be determined v ia a C L E A N approach, where the P S F of the brighter source is removed from the map and a second pass is made over the residual map to pick out the fainter object. Alternatively, one can simply fit that portion of the map to a model that has blended sources of variable amplitude. A n example of the first method applied to S C U B A data can be seen in the survey of the 14h field [87]. The fitting approach was used in the U K 8-mJy survey [54], although they used fixed source positions from the maxima in the beam-convolved images. In general the fit could include source positions in addition to the flux estimates, however the S N R is rarely strong enough to make this additional effort worthwhile. 3.3.1 Is deconvolution required at all? The above prescription does not require the fitting function (or convolution kernel) to be a single Gaussian. The approach used by other groups [88, 54, 87] has been to use the raw maps and fit the multi-lobed P S F directly to i t . To simplify this, the observations are taken wi th a chop fixed in orientation on the celestial sphere. This approach has often been preferred over a scheme that interconnects pixels enough to enable a deconvolution to be performed. The reasoning here has been that there is some sense of re-assurance i f one can detect the triple beam pattern (dual in the case of scan-mapping) in the map. Since al l wide area extra-galactic surveys to date do not detect many objects per unit area, this approach is perfectly reasonable. However, as the sensitivity of sur-veys increases, the case for deconvolution becomes much stronger. In addition, full statistical analysis of S C U B A images, such as w i l l be done in the following chapters, would be much easier wi th a carefully deconvolved image. 63 4: The HDF Super-map I: Sub-mm properties The Hubble Deep Fie ld Nor th ( H D F - N ) [89], a small region of the sky targeted by the Hubble Space Telescope (HST), has stimulated the study of the high redshift Universe ever since the data were released in 1995. This optical image ( U B V R filter bands) of the H D F is one of the deepest ever obtained, and resolves thousands of galaxies out to distant redshifts. However, since optical images capture only a narrow part of the spectrum, and since the rest-frame wavelength range detected depends on the redshift, it is necessary to supplement the HST image wi th data at other wavelengths to obtain a more complete understanding of galaxy evolution. In the years since the H D F image became public, deep pointings using radio, X - R a y , N I R , and M I R telescopes have been conducted. Addit ionally, optical spectroscopy has been carried out on a l l suitable objects in the field, thereby obtaining redshifts for most of the brighter HST-detected objects. The original H D F field is the size of a single HST field of v iew 1 , 2' x 2'. HST also obtained shallower observations in fields adjacent to this, extending the region of study to roughly 6' x 6'. These "flanking fields" have also been covered by other telescopes, and in fact over time the region associated wi th the H D F has been extended to about 10' x 10' in most wave-bands. For an excellent review of the H D F - N region and its impact on the optical view of astronomy, refer to the article by Ferguson, Dickinson, and Wi l l i ams [90]. Our group was awarded several nights of telescope time to scan-map the region wi th S C U B A . Given its high profile however, groups from the U K and Hawaii also targeted the H D F to exploit the rich multi-wavelength observations available. The ~ 3' x 3' area centred on the H D F itself, studied originally by Hughes et al . [91] was recently re-analysed by Serjeant et al . [92] and we use their published results here . Results from observations taken by the Hawaii group can be found in Barger et al . [93]. We have obtained these data from the J C M T archive or from the observers directly. The extra data increase the sensitivity of the final map in the overlap regions considerably, but at the expense of much more inhomogeneous noise and a correspondingly more complicated data analysis. Co-adding data taken in different observing modes has 1 The relevant field of view here is that of the W F P C 2 camera aboard the Hubble Space Telescope 64 not previously been performed for extra-galactic sub-mm surveys. This chapter w i l l bui ld on the tools developed in the previous chapters in order to create a sub-mm image of the H D F based on all the available data and extract sources from it . The resulting map is compared against extensive Monte-Carlo simulations which are required to determine the number density of S C U B A sources as well as any clustering properties. A detailed description of the individually detected sources is reserved for the next chapter, which concentrates on the correlations of this combined map wi th data from other wavelengths. To distinguish our map from the individual sub-maps wi thin this region, we wi l l hereafter refer to it as the "super-map". 4.1 Data reduction and source extraction The full list of projects allocated time to study the H D F is extensive. Observing details for each project are given in Table 4.1. Almost a l l work done in the region has used the jiggle-map mode in deep, yet small surveys. Three projects involved targeted photometry observations taken in "2-bolometer chopping" mode. Due to S U R F software constraints, these data could not be co-added directly to the map. We shall return to these observations later. M 0 0 B C 0 1 is a single jiggle map observation taken in such a way that co-adding it to the map is difficult. This shall be described later as well. We start by making a raw map, ignoring for a moment the effect of a strongly varying effective P S F (i.e. the effect of the different chops) across the field. Figure 4.1 demonstrates just how different the observations are. Shown is the P S F at various locations in the field, alongside the 850/ im noise map.with contours overlaid. 4-1.1 Flux and pointing calibration Registering the individual images with respect to each other is difficult due to the lack of bright sources in the field. The pointing log for each night of data was inspected, and in a l l but a few cases there is no reason to distrust the pointing; pointing checks were always performed on the same side of the meridian as the H D F , and observations were not conducted through transit. Al though night-to-night pointing comparisons between data sets is not feasible, it is st i l l possible to check for a systematic pointing offset between scan and jiggle maps. One might be concerned about errors on the order of 3", due to the speed at which the telescope moves while scanning. In a map made solely from the scan-map observations, a group of sources is detected that correspond to the same objects, seen in the deep jiggle map of Barger et al.[93] 65 Table 4.1: Summary of S C U B A H D F Observations. Type refers to either photometry (P), jiggle-map (J), or scan-map (S). Approximate la noise estimates in m J y are provided, though they do vary somewhat across the individual images. The area surveyed in square arcminutes is also listed. Projects denoted by a * were photometry observations that could not be added directly to the map due to the inabil i ty of S U R F to extract the bolometer positions for two-bolometer chopping observations. In addition, M 0 0 B C 0 1 was taken using an unfortunate chopping configuration, and is not folded directly into the map. In total, there have been 50 8 hour shifts in which the telescope was observing this region. Project ID Type Shifts a 4 5o (mJy) (7 8 5 0 (mJy) Area (arcmin 2 ) M 9 7 B U 6 5 P , J 17 4 0.4 9 M 9 8 A C 3 7 P 2 65 2 3 M 9 8 A H 0 6 P 4 11 1 3 M 9 8 B C 3 0 S 2 75 6 160 M 9 8 B U 6 1 P 1 33 3 2 M 9 9 A C 2 9 S 2 95 6 160 M 9 9 A H 0 5 J 11 20 2 39 M99BC41* p 1 N / A N / A N / A M 9 9 B C 4 2 P,J,S 3 120 6 160 M00AC16* p 1 N / A N / A N / A M 0 0 A C 2 1 * p 1 N / A N / A N / A M 0 0 A H 0 7 J 4 40 2 12 M 0 0 B C 0 1 J 1 N / A 3 5 66 Figure 4.1: Layout of the S C U B A H D F observations. These images cover approxi-mately 12' x 18'. The majority of the data is contained wi th in a 12' x 12' square, but a single jiggle map was also taken to the left of the main map. The left panel is a map of the H D F using simulated sources and the real pointing information. This allows the P S F to be easily seen. Black corresponds to sources, and white to the negative echos caused by the necessity to chop. Various parts of the field were observed in different ways, as is evident from the different PSFs . O n the right is the actual noise map at 850 pm wi th contours at 1, 3, 5, 7, and 9 m J y overlaid. The deepest pointing of Hughes et al.[91] is in the centre of the image, while other jiggle-maps and pho-tometry observations can be seen superimposed on our scan-map. The corresponding images for the 450 pm map are very similar in appearance, though wi th higher noise levels. 67 (project M99AH05) . A least squares comparison between a 4' x 4' square in the scan-map against the same area in the jiggle-map indicates a 4 ± 4 arcsecond offset. The source of this offset is not entirely understood, though we note that i t is along the direction of the chop. The pointing was also checked against V L A and W S R T radio sources for each of the combined scan-map and two largest jiggle-map projects. In each case the best offset was at most one pixel (3"). The final combined sub-mm map does not require any significant shifting to maximize the average sub-mm flux at the radio positions. For each night of jiggle-map and photometry observations, flux calibrations were performed on suitable targets in the area. In each case the calibrations were consistent wi th the averages determined in Chapter 2, and since individual calibrations may have larger statistical variation, the average flux conversion factors were used instead. F l u x calibration of the scan-maps is more problematic. Since this mode is currently not so well characterised, it is important to compare the map against those taken from the better understood jiggle-maps. Al though pointing seems well constrained, the fluxes in the H D F scan-map are generally larger than their jiggle-map counter-parts when using the "standard" gains derived in Chapter 2. This was an issue first discovered in Borys et al . [88]. Unfortunately no usable calibration measurements were taken during the scan-map observations. Therefore we proceed by adjusting the overall calibration of the scan-map and finding, in a chi-squared sense, the value that minimizes the difference between the two maps: X2(0 = E ( ^ - r 5 s c a „ ) 2 . (4.1) Here the sum is over al l the pixels. Because the beam patterns (two- versus three-beam) are different, we use only those pixels wi thin a beam-width of the sources detected in the jiggle-maps. Based on these results we reduce the standard scan-map calibration factor by 20%. 4-1.2 Source detection No effort was made to deconvolve this combined map; the observing strategies em-ployed by both our group and others do not interconnect pixels very well, and there-fore a robust deconvolution cannot be performed. In order to gain back the extra sensitivity from the off-beams, we would like to fit each pixel in the map to the multi-beam P S F . This procedure has been adopted by other groups as well, but the complication in this case is the variable P S F across the field. 68 Instead of fitting to the P S F , we can fold in the flux from the off-beams in a time-wise manner. For each sample, we add the measured flux to the pixel being pointed to in addition to its negative flux (appropriately weighted) at the position of the off-beam. This is equivalent to performing one iteration of the map-making procedure described in section 3.1.3. A single Gaussian is then used to fit for sources in the final map. It requires an image relatively free of sources that might lie in the location of the off-beam of another source, but produces the same output as one would obtain from fitting wi th the beam pattern. The resulting image should be considered not so much as a map but rather the answer to the question: what is the best estimate of the flux of an isolated point source for each pixel? 4.2 Monte-Carlo simulations There are several simulations that must be performed to assess the reliability of the maps. To determine how many detections might be false positives, we created a map by replacing the 850 pm data wi th Gaussian random noise wi th a variance equivalent to the noise estimated for each bolometer. The map was then run through the same source-finder algorithm as the real data. This was repeated 100 times. The average number of positive and negative detections as a function of signal-to-noise threshold is plotted in Figure 4.2, along with the number one would expect based simply on Gaussian statistics and the number of independent beam-sizes in the map (which is an underestimate because we are assuming well-behaved noise). A 3.5a cut is commonly used, but these results suggests about four detections wi l l be spurious in our map (two positive and two negative detections). Given that the slope of this plot is s t i l l rather steep at 3.5a, small errors in the noise estimate can lead to more false positives. Therefore we adopt a 4.0 a cut to determine sources in the H D F super-map. Note that the number of false positives for the 450 pm map w i l l be four times larger because the beam is half as big. O f course i f the noise is not well behaved this can be even larger! Therefore, one wants to set a high detection threshold for 450 pm objects. To further estimate the reliability of our detections, we added 500 sources (one at a time) of known flux for a range of flux levels into the map and attempted to extract them using the same pipeline as for the real data. A source was considered "recovered" i f it was detected wi th a S N R greater than 4.0 and its position was wi th in half the F W H M of the input position. Several interesting points can be made based on the results, which are shown in Figures 4.3 and 4.4, for the 450 pm and 850 pm 6 9 12 11 10 A ~i 1 i r n i i r 8 h 7 h A 1 0 A J I I L A • A —1 I 1 l_ 3.0 3.5 4.0 a t h r e s h o l d 4.5 Figure 4.2: Number of sources in the 850 / im map expected at random. The filled circles show how many spurious sources were detected in simulated maps made from noise alone. Error bars are omitted for clarity, but are small because of the large num-ber of sources generated in the many simulations. The number of positive and nega-tives sources one would expect by chance given Gaussian statistics and a Gaussian-shaped beams wi th a F W H M of 14".7 in an 11' x 11' region is plotted wi th open triangles. 70 maps, respectively. The panel showing completeness is self explanatory; it plots the percentage of sources recovered in the Monte-Carlos as a function of input flux. A s one expects, it is difficult to recover faint sources around the noise l imit , but very bright sources are always recovered. We wi l l discuss this issue more when deriving source-counts. The ratio of output and input flux in the adjacent panel verifies the presence of E d -dington bias [94]; sources fainter than the threshold have been scattered up due to the presence of confusion noise and are "detected" wi th higher than their true flux. The R M S of the difference between input and output positions allows us to estimate a positional error for real detections as a function of flux level. A s one would expect, the uncertainty is smaller as the input flux goes up. The final plot in the sequence shows the average noise level associated with the recovered sources as a function of input flux. A t the faint end, the noise is lower because they are only detected in the deepest parts of the map. A s the flux of the source increases above the noise level of the least sensitive region in this case the underlying scan-map), the average noise of the detections levels off to the average noise level of the field. A basic conclusion is that at a flux l imi t of 8 mJy the source counts are about 80% complete, fluxes are biased by only a few percent, and positions are accurate to about 3.5". The brighter objects are constrained much better than this, but there are fewer of them. A t the faintest levels confusion has a significant affect on fluxes, positions, and completeness. 4.3 Sub-mm sources in the HDF Most of the 850 /mi sources exhibit off-beam signatures that are distinguishable by eye (the negative echos to the left and right of the sources). F ind ing sources at 450 /mi , however is difficult. The single beam pattern is not well described by a Gaussian, plus the sensitivity at 450/ im is too poor to detect any but the brightest sources. In addition, being more weather-dependent, the noise is more inhomogeneous st i l l . Nevertheless, we w i l l report the 3a upper l imi t to the 450 / i m flux for each 850 / i m detection. To avoid reporting spurious detections, we have set a threshold of 4.0a on the 850 / i m catalogue derived from the super-map. However, a supplementary list of sources at 850/ im detected above 3.5a is also provided for comparison against other data sets. The full list of 850 / im and 450 / im sources is presented in Table 4.2. A simple test of source reality is to search for negative flux objects. A l l but two negative sources found were associated wi th the off-beam of one of our detections. Based on the Monte-Carlos, this is not unreasonable. There are 19 sources at 850 / im 71 100 80 60 40 20 0 w 1 2.0 o o w o t* t0 as m w c -l-> s O 1.5 K o I 1.0 (D GO 0.5 o OH 1 I . I | 1 ^ L ^ * | g W " « 1 | • • * -• • • • • • 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 • • • • -• • • • • -• • • i i i 1 i i i i i i i T '» 1 1 1 1 | 1 1 1 1 1 1 1 1 1 1 • • . • • • • • •• •• 1 1 1 1 1 1 1 1 1 I T •*! 1 1 1 1 1 I I 1 1 1 I I 1 1 1 1 «w» • „ . • -• * i • • • • -• " • . • \ \ V • • _ •• • _ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 + 1.10 1.08 1.06 * 1.04 5" in o 1.02 V in a 1.00 9.0 8.0 7.0 6.0 5.0 > < CD -j S» 0Q CD 2. W° CD C - i 100 200 300 100 200 300 Input F lux [mJy] Input F lux [mJy] Figure 4.3: 450 pm source recovery Monte-Carlo results. From left to right and top to bot tom the plots are: a) completeness; b) flux bias ratio; c) pointing error; and d) noise level. Error bars, which are based on the number of objects simulated, are small and not plotted for clarity. The scatter in the plots is due to the non-uniform noise property of the map. 72 GO co C a a o 100 80 60 4 0 20 0 W X ) § 5.0 o OQ 2 4 .0 co o 3.0 s-. CD g> 2.0 C o 1.0 O H L _ s : i i i 1 i i i 1 i i i 1 i i i 1 i i i ^ \ i • i i | i i i i | i i i i | • • * • _ • • -• • • • • • « _ • • • • v v.v//.v • i i i i i i i i i i i i i 1 1 | 1 1 1 1 | 1 1 1 1 | 1 1 ! I | 1 1 1 |l 1 1 1. •A i         i• • • • • --v - * .• .-• • -• i i i i i i i i i i i i i i i 1.10 1.08 1.06 * 1.04 o 1.02 1.00 H l .o > 0.8 » o> CD 0.6 3 m 0-4 ^ 3 0.2 ^ 10 20 30 0 10 20 30 Input F lux [mJy] Input F lux [mJy] Figure 4.4: 850 jum source recovery Monte-Carlo results. The order is the same as in the last figure. 73 -6 B CD O ~ x CD 3 CO 0> CP S 4* oo a; o S H O CO 43 CJ a3 CD .a I SbL CD (-1 o3 CD el el 03 43 o S H CD 43 o CD 43 -4J CO f-c CD b CO CD S-i CD 43 TP CO lei co -H-H + + CO 00 o o to co CO CO 22 2 |co to h b p a s x " 2 =? -H S. 2 4<S 3 ^ S » F g " 2 « ^ § CO 3 2 ^ fH © « 5 » u * 3 &H 3 3 « cn E cn cn D CD w CN Cn 6<3 CD I D _ T P • . 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C O C O O O C O C O O '—* CO CO *—' CO CO CO —' CO *— —' *— *<P ~~—' —' CO TP ' QO '—' CO CO CO r-< CO ^ o o + i ^ i r t i n ^ i + l ^ 1 c D + i c o ^ O ) t - O i ( O H ' f f M C N H H C N l O C N t - H C N ' - C N I N « © CO Tp CN CO ( O) S * O H co CO C N C N C N C N N N M C N N M M C S C S C N C N C N N co m CN CO •—< O TP CN CN CN CN CO CO CO + + + r- oo - H O O H | CD CD CO CN CN CN 00 Ol O CN f M O Tf io O CN t - 00 CO ^ ^ O r-l r-4 CN (N CN CN CN CO CO CO CO CD + + + + + oo m co co CN CN co eo p^ m CD CD CO CO CO CO CO CO CO CO CN CN CN CN CN CN CN CN CO CO CD + + + co cn co m m o CO CD t -CN CN CN I a N N o i o m in co ) T~\ o oo TP CN CN CN CN CO CO CD CD + + + + Ol O •—' CO t- b- t-CO CO CO CO CN CN CN CN b- Tp CN CN CN CO CN CN CD CD + + i-l CO TP TP co co CN CN ,*-}>-)>-i>->>-i*-ii-^i-i>-^>-)r tS 2222222222222222 2 2222222222222222 ; m m r / i c n r / j « c n c n w c n c n c n c n c n c n c n c n o »o o o o O CN CN O H CN « CO Ol CO Tf 00 CN CN CN CN CN t- CN Cl CN Ol CN TP O TP O CN CN CN CN CN CD CD CD CD CO + + + + +I Ol CN CN t- CO iH CO O CN Tp CD CD N c- N CO CO co co co CN CN CN CN CN 22222 22222 cn cn cn cn cn 74 detected over 4<r, 5 of which have not been reported before in the individual surveys. Apar t from a few exceptional cases, described below, a l l sources previously reported in the region are recovered at comparable flux levels. A n addit ional 17 sources are detected between 3.5<r and 4<j, but we note that many are near the edges of the map, and hence might be spurious. A n image of the 850 pm super-map is given in Figure 4.5. There are only 5 sources recovered from the 450 pm image, which is shown in Figure 4.6. There have been no 450 pm detections previously reported in the H D F . The finder chart in Figure 4.7 can be used to identify the sources extracted in each of the maps by our algorithm BbOum SNR -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2,5 3.0 3.5 4.0 Figure 4.5: The 850 pm S N R map. The greyscale is stretched exponentially to high-light sources. This image can be used in conjuction wi th the finder chart in Figure 4.7 to identify the objects reported in the source list. 75 Figure 4.6: The 450 fim S N R map. The greyscale is stretched exponentially to high-light sources. This image can be used in conjuction with the finder chart in Figure 4.7 to identify the objects reported in the source list. 76 62:20 — 18 O in Q 16 14 12 10 08 06 h _ L i i i i i _ 12:38:00 Figure 4.7: Finder chart for sub-mm sources detected in the H D F super-map. The outlines are 850 pm noise contour levels from 1 to 11 m J y (darkest) in steps of 2 mJy. On ly the main square region of the survey is shown (no sources were detected in the isolated jiggle map to the left of the main survey). Triangles are 850 pm source positions from Barger et al . [93], diamonds from Serjeant et al . [92], squares wi th an embedded plus are the 4a sources from Borys et al . [88], and the plus symbols are the lower S N R sources from that survey. Circles are sources recovered above 4a from the super-map, and crosses show those additional sources detected at lower significance. The 5 450 pm sources detected in the super-map are shown as the 5 circled asterisks. 77 4-3.1 Comparing the source list against previous surveys A plot comparing the recovered fluxes against those previously published is given in Figure 4.8. We show the difference between the published fluxes and super-map estimates. The anticipated flux difference is then zero, and based on the size of the error bars it is clear that no significant variations exist between the estimates. The objects that appear discrepant are discussed at length below, and al l sources are described in detail in the next chapter. Something to note is that the error bars on the sources recovered from the super-map are generally smaller than those obtained from the individual sub-maps. 4-3.1.1 The central HDF region from Hughes/Serjeant et al. Eight sources, labeled HDF850.1 through HDF850.8 are associated wi th the data collected by Hughes et al . [91]. The more thorough analysis by Serjeant et al . [92] found that one of them (HDF850.3), detected in the original map of Hughes et al . fails to meet detection criteria. It is also the only source undetected in the super-map presented here. HDF850.4 and HDF850.5 appeared to be a blend of two sources in their original map, and therefore both Hughes et al . and Serjeant et al . took the extra step of attempting to fit the amplitude and position of them. W i t h the super-map however, this pair of sources is better fit by a single source wi th flux comparable to the sum of fluxes from the two extracted by Serjeant et a l . This may be because we use larger pixels (3" compared to 1" from Serjeant et al.) and therefore lose some resolution required to separate adjacent objects. Sources HDF850.6 and HDF850 .7 are detected at a fainter level than that reported in Serjeant et al . These discrepancies might be partly due to their positions; both are in a noisier region of the individual sub-map, and near its edge. The super-map contains additional data (especially photometry) in the central H D F region, and so one would expect our flux estimates to be mi ld ly improved over those of Serjeant et al . 4-3.1.2 HDF flanking field jiggle-maps from Barger et al. The seven sources detected individually by Barger et al . [93] are confirmed in the super-map at comparable flux levels except for one object, "Uncatalogued 1". This is most likely due to differences in analysis methods; Barger et al . used aperture photometry wi th annuli centred on radio positions believed to be associated wi th the sub-mm detection. The source in question had no counterpart, and therefore determining flux wi th aperture photometry is not as straightforward. Even when 78 Figure 4.8: Our new source list compared with previously reported detections. We show the difference between previously reported flux and that derived here for each source in common. The outline denotes the size of the error-bars from the previously reported estimates. We subtract the reported fluxes from our own, and plot the difference and error-bar as the filled triangles. See the text for a more complete description on those few points that seem discordant. 79 the sub-map alone is considered individually, the measured flux does not match that originally reported. 4-3.1.3 Scan-map observations of Borys et al. A l l six sources from the 4a list of Borys et al . [88] are recovered, although two of them are detected at lower significance in the super-map. Four of the six sources from the supplementary list of 3.5cr sources are not recovered i n the super-map. Three of these exist in regions of overlap between surveys. This supports the claim made in Borys et al . [88] that 4a detections are more secure than lower S N R ones. 4-3.2 Comparison with photometry observations A s we have mentioned, a number of photometry observations taken in the two-bolometer chopping mode were conducted. Al though these data sets cannot be co-added into the map, we can compare flux estimates for the photometry bolometer wi th the position in the super-map. Whi le the scan-map observations were being taken, several photometry observations were conducted at positions of tentative detections in order to verify them. None of these positions correspond to detections i n the final map, but a l l have fluxes consistent wi th the corresponding position in the super-map. This illustrates that the practice of picking out low S N R sources "by eye" in S C U B A surveys is not very effective. Our group has also conducted two observing programs designed to understand the sub-mm properties of Lyman break galaxies (LBGs) and optically faint radio sources ( O F R S ) [95]. These types of source wi l l be discussed more in the next chapter. Three measured L B G s that fall within the region of the H D F are not detected in either the photometry measurements or the super-map. O f the seven O F R S photometry measurements, a l l have comparable fluxes at their corresponding position in the super-map. A summary plot similar to the one shown previously when comparing known detections is given in Figure 4.9. Again , no significant discrepancies exist between the estimates. 4-3.3 Comparison with the jiggle-map observation M00BC01 A trio of sources toward the western edge of the original scan-map was reported in Borys et al . [88]. F ind ing bright sources spaced so closely together is unusual, and might be indicative of clustering. Therefore we obtained time under the C A N S E R V observing program to make a follow-up jiggle-map of the region. Inadvertently, the 80 S c a n - m a p m CM 00 CO W H a Ed U O o CJ OS K os K D D D D O O o O CO CO CO CO EL. Ex, DL, EL, Q Q Q Q x X X X >^ 2 0 !-3 - 2 0 L B G CO CJ 2 2 a> •* Q O O 03 2 2 o 9 3 9 a x EL. Q X EL, a x i 0 F R S OS CO o CO .—1 O o o o .—1 CM « N CO CM CM CM CO CO CO CO CO CO CO + + + + + + + CO m •* CM o in m o CM o in T-1 in m CO CO CO CO i> CO CO CO CO CO CO CO C\J CM (M CM CM CM CM H .—< .—< r H X X X X X X X Figure 4.9: Comparing super-map fluxes wi th photometry estimates. We plot the difference between reported photometry fluxes from observations not added into the map and those derived from the super-map. A s before, the outline shows the error-bar from the reported values, and our points (after subtracting off the reported fluxes) are plotted as solid triangles. Since some of the photometry goes much deeper than our map, their error estimates are in those cases much lower. A l l sources agree wi th each other wi thin the combined error-bar of each estimate. 81 observations were taken wi th an azimuthal chop wi th a 40" throw. Given the ori-entation of the sky at the time, this meant that two of the three sources effectively cancelled each other out. It is for this reason that the observations were not folded directly into the map. Even a direct inversion of the mapping matr ix does not place strong l imits on these detections; the pixels are not strongly enough tied together, and the noise level is only about 4 mJy. Nevertheless the observations are not inconsistent, and the flux of the one unchopped source that corresponds to SMMJ123607-I-621145 is only la lower than the super-map flux. Al though these data end up being not very useful, we mention them here in the interest of completeness. 4.4 Number counts of sub-mm sources In order to estimate the density of sources brighter than some flux threshold S, N ( > S ) from our list of detected sources in Table 4.2, we must account for several anticipated statistical effects: 1. The threshold for source detection, ST = ma is not uniform because the noise varies dramatically across the map. 2. Due to confusion and detector noise, sources dimmer than ST might be scattered above the detection threshold and claimed as detected. 3. Similarly, sources brighter than ST might be missed because of edge effects, possible source overlaps, and confusion. Item (3) is simply the completeness of our list of sources. For a source density N ( S ) d S which falls wi th increasing flux, the effect of item (2) can exceed that from item (3), resulting in an Eddington bias in the estimated source counts. One can calculate the ratio of the integrated source count to the number of sources detected using the "detectability" 1 _ f ~ N ( S ) d S 7 (5' ) f 0 ° ° t t S , S > ) N ( S ) d S > l ' J where N ( S ) d S is the number of sources wi th a flux between S and S + d S . We have introduced the quantity 4>(S, S 1 ) which is the fraction of sources between a flux, S and S + d S , that are detected above a threshold, S'. Note that <j>(S, S ' ) ranges between zero and unity, but 1 / 7 (5 ' ) can be larger than one, depending on the form of N ( S ) 82 and choice of 5'. For bright sources where the completeness is 1.0, and the S N R is high, 0(5, 5') should approach unity. The numerator is the quantity we are t rying to determine, and the denominator is the output from the survey. To determine N ( > S) we simply take the raw counts from our survey and mult iply them by 7(5'). The calculation of 7(5') from the Monte-Carlo estimates of 0(5,5') requires a model of the source counts, of which there are many different forms in the literature. A l l share the property that they are steep at the bright end and shallow at the faint end. They are also constrained such that the total amount of energy does not exceed the measured value of the sub-mm extra-galactic background. We employ the two-power form described in Scott et al . [54], for each value of 5'. This was chosen empirically to match the shape of 0(5,5'). A n alternative approach would be to perform more Monte-Carlos wi th a finer spacing in A S and then spline the result to allow for interpolation between the sample points. Using this and the source-count model, 7(5') can be computed numerically using Equat ion 4.2. 7 relates the quantity we want to determine, N ( > 5), wi th the number of sources our survey detects. Obviously 7 is influenced by what model is used in the calculation described above, and other forms of the source spectrum are found in the literature. We find 7 at the bright end (> 6mJy) varies by no more than 15% across a wide range of reasonable parameter values. This is smaller than the Poissonian error caused by having so few sources detected. 4.4-1 The 850pm number counts In Figure 4.10 we plot the 7 determined using the source count parameters described above as well as 0(5, 5') determined from the Monte-Carlos. The detectability passes through unity at around 7mJy ; sources fainter than this are not detected very effi-ciently, and therefore we must boost the raw count to account for the incompleteness. Past this, brighter source counts get a slight boost from fainter sources that have been (4.3) and use 5 0 = 4.0 mJy, a = 1.0, B = 2.6, and N0 = 0.2 x 10 4 deg~ 2 Our Monte-Carlos give us 0(5,5'), which we fit using the form 0(5,5') = 1 - exp (A(S - B)c). (4.4) 83 3.0 2.0 1.0 1.0 0.8 0.6 CO co ^ 0.4 0.0 1 1 1 1 I T. 1 1 1 1 1 1 1 ' 1 1 1 1 | i 1 t i i i i 9 1 9 1 1 i I I I 1 1 1 1 1 1 ft ™ • • ' H 0 1 — - — / 4 / 8 1 1 - r - ( / 1 1 J 12 16 -A J i 10 S / m J y Figure 4.10: Summary of the 850 ^ m source-count calculation. In the top panel we plot the detectability determined using the source-count parameters described in the text. A s expected, it is higher at low flux levels (indicating that the survey has missed sources) and approaches unity at the bright end. Between 7—12 m J y the detectability is slightly lower than one, demonstrating that some sources below the threshold are contributing. The error bars are represent the scatter obtained when using a range of source-count models that roughly fit the measured counts and sub-mm background. In the lower panel, we plot (p(S,S') for 5" ranging from 0-16 m J y in steps of 4mJy . The S' = 0 case is simply the completeness of the survey. 84 scattered above the threshold due to noise. Given 7(5) , we can now calculate the counts based on the number of sources detected in the entire 0.046 square degree super-map. Th i s is given i n tabular form (Table 4.3) and as a plot alongside other estimates of the 850 pm source counts (Figure 4.11). A n alternative way to plot the counts, and the one most often seen in the literature, is to perform the following routine: Start by using the flux bias estimates to correct the fluxes of each of the sources. Sort them by decreasing fluxes, and then divide by the effective area of the survey. To first order, the effective area is simply the total area multiplied by the completeness at that particular flux level. We plot the the results as a jagged line on Figure 4.11. The estimates derived by this method and that using the description from the previous section agree quite well, except at the faint end. This is due to the stronger biases and uncertainty in the completeness correction. In general the derived counts are in excellent agreement wi th estimates from other surveys. They also agree wi th the input model used to estimate 7 (5) . It should be noted that while other surveys use 68% confidence bounds, we prefer to quote 95% l imits . It is interesting to note that the bright counts from this survey and the U K 8-mJy project are slightly lower than those found from surveys of smaller areas [96, 39]. Comparing the ratio of counts derived from our survey relative to the 8-mJy project yields a factor of ~ 0.85 from the 6-12 m J y range. If we fit to the average of the cluster counts and interpolate across this same range, this ratio between our counts and theirs is roughly 0.4. This might indicate that those surveys had been sensitive to clustering, which would naturally lead to an overestimate of the number counts. It could also be that the cluster lens surveys were contaminated by sources intrinsic to the clusters, or that there was some systematic bias in the lens models. Al though the current survey is l imited by the lack of bright sources in the H D F , it is clear that the counts fall off quite steeply wi th increasing flux. Different surveys are often compared v ia the slope of a power-law form of the number counts (N(S)dS = NoS~a). We take our counts in 2 mJy bins between 2 and 16mJy and obtain a normalisation of 0.7 ± 0.3 x 1 0 4 d e g - 2 and a slope of a = 2.4 ± 0.2 (95% confidence l imits) , which agrees wi th estimates obtained by other groups: a — 2.8 ± 0.7 from Bla in et al . [49], ?>.1^\ from Barger et al . [50], and 3.2 ± 0.7 from Eales et al . [87]. A t the faint end, it seems that the counts turn over and flatten out wi th decreasing flux. Indeed i f they do not then the sub-mm background w i l l be overproduced. Note that our extrapolation to the counts fainter than 2 mJy is much lower than the points measured from cluster surveys. We have already noted the apparent discrepancy 85 between "blank" and "cluster" field counts. Deeper surveys that reach these lower flux levels may be able to determine this unambiguously. 4.4.2 The 450pm number counts Since we have only detected 5 objects at 450 pm, we choose to quote only a single value for JV(> 100 mJy) . Because the number counts are not well contrained at a l l at 450 pm it is difficult to know what functional form of the number counts should be used. We chose a simple power law form wi th N(S)dS oc S~a. Our estimates of the detectability were largely insensitive to the choice of a, and turned out to be simply the inverse of the completeness at 100 mJy (80%). The result, along wi th two previous estimates at lower fluxes, is given i n Table 4.4. A fit to a power law with these counts gives a = 2.2 ± 0.4. This is not too disimilar from the 850 pm slope, though it is slightly shallower. This is an interesting result: i f the S C U B A sources are concentrated past z ~ 1, then one would expect the 450 pm fluxes to drop off more steeply than the 850 pm counts because the K-correct ion becomes positive for 450 at these redshifts. W i t h only three estimates for the 450 pm number counts however, it is premature to draw strong conclusions. Nev-ertheless, this hows that constraints on the number counts at different wavelenghts serve as a good probe of the evolution and redshift distribution of sub-mm galaxies. 4.5 The 850pm sub-millimetre background Because we have detected so few sources, it is difficult to contrain the parameters in our parametric model of the source counts (See equation 4.3). If we adopt in -stead the single power-law, and use the crude fit to a and N0 derived in the last section, we can estimate the total 850 pm flux density by calculating the integral of SN(S)dS. For sources brighter than 2mJy, we calculate an integrated background of 1.3 ± 0 . 2 x 1 0 4 m J y d e g - 2 . Taken on their own, this results places a lower l imit on the C I B at 850 pm. However, in the literature one often sees the ratio of the recovered flux density to the F I R 850 pm background measured by F I R A S (3.1 - 4.1 x 1 0 4 m J y d e g - 2 ) [10, 11, 12]. Doing this, we find that roughly 30-40% of the F I R A S determined background is recovered. This is consistent wi th estimates from several groups, and demonstrates that a significant fraction of the sub-mm universe is st i l l below the flux threshold attainable from current S C U B A surveys. However, given the freedom which s t i l l exists in the faint end counts, the entire F I R background can easily be made up of sources wi th 86 CD CU (H CO o3 cp s-i SH o S-I S-I cp cp -J3 T3 o3 C J SH o3 CO a o CO • f—I SH o3 a B o o SH «s co CP > ! - i CO SH CP H ^ o SH CP o el - a o o cn SH co 9? CO CP "3 co w 2 I . S 3 o & ^ 0) CP -73 a ^ 'X ^ 8 CP ^ CO o3 SH a. CP co 2 s J3 3 +3 o CP •§2 03 cp q 3 % 1 SH J5 CO Pi Q EC o  "a; q=l C! 03 ^ B ^ CO > > CP H CP o o b p o3 IS SH >i =3 HO 03 cp -a 4J (=! o3 CP o ^4-1 CO S3 O CP o 03 . —H o 03 C! O CP CP S-i 03 3 ~° 03 ^ a i o s o o CP . . c o «C ^ O C P . o £ 3 o3 o3 SH + J co el o M CP cp SI O CP co SH CP CP 1 o - a =3 CP - a el X 03 fc>0 cn D O 3 O D O O O O O o O O O 0 ) o O O O O O lO MtO Olio <NO O) + I C N . - I r H ^ H 0 > <D O + 1 + 1 + I o o o o O O O 00 m 00 i-l to CO . - I o o o m + I o o +1 o o o o o © O o o o o o O o o o o * — ' - ^ T T ^ r o o 4- I eo H o + 1+ I o o o o o o t— LO CT: M ft (N o o o O O O O o O O O O o o o o CO COtN O o O O O tO H H OITJ" O l O O o o + I + I o o o o o o o o to oo o ic M H 05 M o o o o 00 00 +1 o o 00 co LO lO +1 o o o o oo CO + 1 o o i-H CN +1 CO O OJ Tj" CN + I o o o o o t - o o o o i-i woo wc£> ( O O O + 1 + 1 + l « « O O O + I LO CM 00 O l O CO T-1 TP o IHCO o t - CN »•. . CO CNCN t-Hi-l Olio T"T WtN i—11 O l I O 00 + 1 + 1 + I OO 00 74 EC IQ CO * M H O l ID n o <D l>- 00 00 o I—1 CO C J cn o CO d CD d d CO l O o d d rH O i ^ CO CN T-H O M Tji CD H W M T f l O W O O H H 8 7 S/mJy Figure 4.11: The 850/xm cumulative source counts. The solid diamonds denote the results from the current work. The jagged yellow line shows counts derived fron the same data, but using a different recipe (see text). Counts derived from cluster studies by Chapman et al . [79] and Smail et al.[39] are shown by the open squares and circles respectively. The U K 8 mJy survey counts (Scott et al.[54]) are shown as open triangles. Stars represent the counts from Hughes et al . [91] , and the open diamond is from Borys et al . [88]. Some points are slightly offset along the flux axis for clarity. Overlaid is the two power-law model used in the calculation of 7 (solid line), and two predictions based on representative galaxy evolution models from Rowan-Robinson [97]. The dashed line represents a universe wi th QM = 1.0 and Q\ = 0.0 while the dotted line is VtM = 0.3 and = 0.7. The dot-dashed line below the curves is the count prediction obtained from extrapolating the IRAS 60 pm counts and invoking no evolution. 88 Table 4.4: 450 pm source counts from the H D F super-map. We present here our estimate and those compiled from the literature. The other estimates are based on an approach different than that present here. They also use a Monte-Carlo approach, but choose the estimate such that the error bars are symmetrical. F l u x (mJy) JV(> S) Comment S&50nm > 0-1 m J y - This result is important, and can be used to constrain models that predict the evolution of IR luminous galaxies. Future surveys that detect more sources wi l l constrain the source counts further, and extend the l imi t ing flux down to fainter levels. 4-5.1 Evolution of sub-mm sources The counts are much greater than what one would get by estimating the 850 pm flux from the IRAS 60 pm counts. As pointed out by B la in et al . [19], a S C U B A galaxy wi th a flux J> 5 mJy has an inferred luminosity in excess of 1 0 1 2 L Q i f they are distributed at redshifts greater than 0.5 (and in the next chapter we w i l l provide very strong evidence that they are). This means the number of such objects per co-moving volume is several hundred times greater than it is today. Therefore there must be significant evolution past z J> 0.3 (the IRAS l imi t ing redshift). Model l ing this evolution has been difficult due to the lack of observational data on the redshift distribution of S C U B A sources. Attempts to model the luminosity evolution of the S C U B A sources have been carried out using semi-analytic methods [98] and parametric ones [99, 97]. In many cases, the starting point is the well determined IRAS luminosity function. This gives us the number of sources of a given luminosity per co-moving volume. These luminosities are then modified as a function of redshift, and then 850 pm fluxes are extrapolated and source counts determined. We expect the number of galaxies to increase in the past due to merger activity, so number evolution must play some role, but it is noted that strong number evolution overproduces the F I R background. There are a number of models (and a range of parameters wi th in them) that fit the current data. Therefore, unti l we can better constrain the counts and determine redshifts, the only firm conclusion one can make is that S C U B A sources do evolve strongly. 10 25 100 89 4-5.2 A connection with modern-day elliptical galaxies? We can estimate the the total luminosity for a given T d u s t and B as per Equat ion 1.3. Integrating this simple dusty S E D and fixing the observed 850 yum flux at 5 m J y suggests a S F R in excess of 1000 M 0 y r - 1 for redshifts past about 1. O f course the conversion between detected flux and inferred star formation rate is highly dependent on the dust S E D , and can change by factors of 10 for changes in temperature and B of only 2. Also, the simple relation between F I R luminosity and S F R may be different for these more luminous sources [27, 28]. Despite these uncertainties, it has been recently suggested [54] that S C U B A sources can be associated wi th the elliptical galaxies we see today v ia the following argument: Producing the local massive elliptical population with a homogeneous stellar distribu-tion requires a sustained period of star formation on the order of 1000 MQyr~ l lasting about 1 G y r . The number of bright S C U B A galaxies per unit co-moving volume, i f one assumes a redshift distribution that places them all past z — 1, is comparable to the volume density of the local elliptical population. Currently this is just specula-tion unt i l the S E D s and redshifts of a significant number of sub-mm galaxies can be determined. Nevertheless it is an interesting hypothesis, and one wi th some testable predictions. We w i l l revisit this issue i n the next chapter when we provide contraints on the redshifts of al l of our sources. 4.6 Clustering of sub-mm sources If S C U B A sources really are associated wi th ellipticals, they should exhibit spa-t ia l clustering like their local counterparts. There are other reasons one might sus-pect clustering; E R O s , which are discussed in the next chapter, are very strongly clustered[40], and seem to have a correlation with S C U B A sources. A s we have already mentioned, the presence of clustering may also affect estimates for the source counts. Peacock et al . [100] have found weak evidence of clustering in the ~ 2 x 2 arcminute map of Hughes et al . [91] in the sense of statistical correlations wi th L B G s . The U K 8 mJy survey [54] which covers over 250 square arcminutes, and the smaller yet deeper C F R S 3-hour field [101] also show some sign of clustering. There appears to be clustering in the super-map; in particular the concentration of sources near the centre of the map, the trio of sources to the west of the map, and the group of 4 north of it might suggest a clustering scale on the order of 30" or so. Al though one would expect more sources here because of the increased sensitivity i n some of these regions, it is s t i l l useful to attempt a clustering analysis. 90 Clustering is usually described as the probability, p, of finding a source in a solid angle Q, and another object in another solid angle separated by an angle 9. This probability is described by [102]: p{6) = N2[l + w(9)]rt2. (4.5) where N is the mean surface density of objects on the sky and w(9) is the angular two-point correlation function. If w(9) is zero, then the distribution of sources is completely random, while otherwise i t describes the probability i n excess of random. There are several estimators for w(9) in the literature, and the one we employ is that proposed by Landy & Szalay [103]: This particular estimator has been shown to have no bias and a lower variance than alternatives. In this equation, D represents sources in the S C U B A catalogue, and R are sources recovered from Monte-Carlos. D D is the number of pairs of real sources that fall wi th in a bin of width 59. D R are data-random pairs, and RR are random-random. Each pair is normalised to have the same number. To obtain the random catalogues, we created 1000 mock fields based on the source count model used in the previous section. These sources were placed randomly throughout the field, and the resulting mock data were placed into the same pipeline as our real data. This approach is slightly different from that of Webb et al . [101], and Scott et al . [54], the only other two surveys to attempt a clustering analysis of S C U B A sources. In those analyses, the mock images were modified only by adding noise to each pixel. The amount of noise added was taken from the noise map created along wi th the real signal map. Therefore their final mock images do not exhibit the chop pattern that one would expect to see. Recognizing this l imitat ion, Webb et al . [101] took the added step of masking out regions i n the mock images that correspond to the positions of the off-beams in the real map. Our simulations involve a full sampling of the mock images using the astrometry information from the real data. Therefore the simulated and real maps have the same beam features. We used 30" bins, and estimated w(9) using both the 3.5 and 4a catalogues. We added a restriction that sources must fall within the central 11' x 11' of the map. A l l of the 4cr sources fall wi thin this, but the lower significance sources at the edges w{9) DD - 2DR + RR RR (4.6) (4.7) 91 are excluded. This prevents sources due only to edge effects from contributing to the estimate. Though some of 3.5<r source may be spurious, the increased number of objects helps bring down the error bars. A s Figure 4.12 shows however, there is no evidence for clustering in the H D F super-map, since there is no angular bin that has a w(9) significanly different from zero. This is not the only clustering estimator one can use. We also performed a "nearest-neighbour" analysis [104] to test i f sources were closer together than expected at random. This statistic simply determines the distance to the nearest source for each source and then bins the result as a function of angle. Here we use the same 30" bin sizes as in the two-point w(9) statistic. The histogram of nearest-neighbors is then compared against our set of Monte-Carloed catalogues to determine i f a clustering signal is present. The results are shown in Figure 4.13. There is some suggestion from this analysis that there is an excess of neighbors at ~ 90". However the error-bars, given the low number statistics, are large. A formal Kolmogorov-Smirnov [105] analysis of these data indicates a 40% chance of having a difference as large as 0.2 between these two distributions. Note that in each of these clustering analyses, it is difficult to estimate the clustering strength on scales near to the beam size. Our source extraction algorithm is insensitive to a fainter source closer than 12" to a brighter one. One can do better by using a more sophisticated source extractor, but in the H D F super-map the low surface density of sources does not justify the additional complication. W i t h the exception of the blended HDF850 .4 /HDF850 .5 , there is only one other source (SMMJ123703+621303) that appears to be a blend wi th another. We wi l l discuss this more in the next chapter. If S C U B A galaxies truly are the progenitors of modern day ell iptical galaxies, then they must exhibit clustering stronger than that of the E R O and (perhaps) L B G populations, which are (presumably) forming in the same overdense regions in the universe. Al though this plot shows no sign of clustering, the data are not powerful enough to rule it out. First we need more detected sources in order to bring down the error-bars, which are purely Poissonian in nature. Also, the E R O and L B G clustering observations are taken from samples that exist at a common redshift (~ 1 i n the case of E R O s and ~ 3 for L B G s ) . Because of the strong negative K-correct ion, detected S C U B A sources are spread across a much wider redshift range, therefore di lut ing the clustering signal. To make progress requires a larger survey that also has the abil i ty to discriminate, even i f only crudely, a redshift distribution. Note that i f S C U B A sources are clustered in a similar manner as E R O s or L B G s , then the signal in w(9) would be expected to be strongest at ^, 30". This is only a 92 l M CD 0 . 5 h--0.5 h l M <t5 0.5 -0.5 i 1 i 1 r >3.5CT sources i — 1 — r V - r 1 J ( ) J H h H h >4.0a sources j i J I I 1 I I L J i L 0 60 120 180 240 300 360 420 0/arcsecond Figure 4 .12: Angular two-point correlation function estimate for the H D F super-map sources. Our estimates of w(6) are shown as the open circles (for the > 3.5a catalogue) and closed circles (for the > 4.OCT catalogue). The measured clustering signal of E R O s is shown as a dashed line, and that of L B G s as a dotted line. There is no evidence of sub-mm clustering, though the errors are st i l l quite large. 93 0 6 0 1 2 0 1 8 0 Nearest Neighbor/arcsecond Figure 4.13: Nearest Neighbour clustering analysis. In the top panel we plot the nearest neighbor distribution of the data compared both against itself and a set of Monte-Carlo generated catalogues. A t ~ 90" there are 3 more sources than expected. This is also reflected in the bottom panel, where we plot the cumulative distribution of nearest neighbors. 94 factor of 2 larger than the S C U B A beam, and therefore one expects that a clustering detection wi th S C U B A wi l l be rather difficult due to blending of the sources. Also , the L B G s and E R O s are confined to thin redshift shells. S C U B A sources can be detected across a wide range of redshifts and hence the angular clustering signal may be largely washed out. Aga in we conclude that having more accurate redshift information on the S C U B A sources is required to make significant progress. Despite the hints of a clustering signal offered by Scott et al . [54] and Webb et al . [101], the results are s t i l l tentative, and what is needed is a very large (~ 1 square degree) survey in order to decrease the error bars on the clustering estimate. 95 5: HDF Super-map II: Multi-wavelength analysis Find ing sources such as those described in the previous chapter is now a routine occurrence for S C U B A , with roughly 300 detections since the commissioning of the instrument 1 . Much more challenging is t rying to find out what the galaxies are. To get a more complete picture it is necessary to compare the sub-mm map against data obtained at other wavelengths. There are two approaches; first, we take the source list obtained i n the previous chapter and find objects detected at other wavelengths that are spatially coincident with them on the sky. This is easier in the case of radio sources, in which the number per unit area on the sky is low, but very hard for objects detected optically, where there are several sources wi thin a reasonable distance from the S C U B A source. The second method involves calculating the average sub-mm flux at the positions from another catalogues. Al though individual sub-mm sources are not resolved, "stacking" the objects like this allows us to say something statistical about the sample as a whole. 5.1 Statistical criterion for finding counterparts To identify the most likely counterparts to our S C U B A detections, we need to first choose a search radius outside of which we reject any object. We are confident that our super-map has astrometry reliable to within 3", since pointing corrections were rarely much larger, and i n addition because the stacked radio/sub-mm flux begins to drop i f the map is shifted more than this (see section 3.2). From the Monte-Carlo simulations (see Figure 4.4), there is an additional uncertainty of at most 5" for the fake sources recovered at 850 pm. Since some parts of the map are dominated by single observations, we need to consider the overall 2" pointing uncertainty of the J C M T as well. Weighing al l these things, we adopt a very conservative search radius of 12". This w i l l produce more candidate objects, but it is unlikely that we wi l l miss anything. 1 i.e. ~ 300 detections between the years 1997 and 2002 96 5.1.1 The P-statistic W h i c h of the objects corresponds to the S C U B A source however? A statistic to help answer that is presented in Downes et al . [106]. Given a surface density of some class of object of N per unit area, the probability that one or more lies wi th in a distance, d, of our source just at random is: P = l-exp(-ird2N). (5.1) The lower the number, the less likely it is that the object is associated wi th our source by chance. This statistic gives greater weights to rarer objects further away. This statistic fails when objects are clustered because this effectively increases the odds that a source can be spatially co-incident with our S C U B A source. One can obviously do better by adding a priori assumptions about the correlation between objects. For instance Sutherland & Sanders [107] modified the statistic to include terms related to the colour distribution of the sources under study. In the present case we might expect S C U B A sources to have red optical colours, so we could assign a higher weight to red objects than blue. Clearly this can lead to bias if we do not have a good handle on the properties of our objects. The consensus among groups involved wi th sub-mm multi-wavelength follow-up is that the counterparts have diverse properties, so we choose to use the P-s ta t is t ic in its original form. Table 5.1 lists the search radii required for each of the classes of objects we describe in this chapter. In each case, we list a radius wi thin which there is only a 5% chance of finding an object there accidentally. Many of the object classes require search radii smaller than what our astrometric errors are, but in some cases (radio and E R O s ) , i t is unlikely to have a counterpart wi thin a reasonable distance just by chance. 5.1.2 Statistical measures of sub-mm flux from known objects That being said, we wi l l later show that S C U B A objects do in fact have correlations with , for example, the colours of optically detected galaxies. It has become popular to compare a catalogue of objects against a sub-mm image v i a a "stacking" analysis. The procedure is to take a list of detected objects from a survey, make cuts of some sort (isolate a subset of galaxies with a similar property), and then sum up the flux from the sub-mm map at the positions of a l l the objects. In this way one can get a sense of the average sub-mm properties of the sample. This technique is not restricted to sub-mm maps; recently [108] have compared a sample of L B G s against Chandra 97 Table 5.1: Counterpart search radii for various classes of objects. Calculations are based on allowing only a 5% chance that the counterpart is associated wi th a S C U B A position by chance. Class Number wi thin Surface Density 9 Comment survey area / square arcmin /" 1.4 G H z 140 0.97 7.8 8.5 G H z 41 0.28 14.5 15 pm 99 4.95 3.4 K < 22 1849 22.83 1.6 K < 20 638 7.88 2.7 K < 18 104 1.28 6.8 I - K > 3 318 3.92 3.9 V R O I - K > 4 17 0.21 16.7 E R O L B G 149 1.83 5.6 X r a y 249 1.73 5.8 Hard and Soft band X - R a y maps, for example. It is extremely important to check for systematic effects in these analyses. We take the list of 51 stars in the H D F region from the work of [109] and correlate them against the H D F super-map. One would expect no signal from these stars as they are not sub-mm emitters. The stacked average, —0.14 ± 0 . 1 6 mJy, is compatible wi th both the average value of the map (0.04mJy), and the flux derived from 51 random positions in the map (0 .09±0 .16 mJy) . Therefore we can proceed wi th some assurance that any significant signal measured in a stacked analysis is real. Another effect to consider is the variation in the number of stacked objects being compared. For large N, the stacked flux wi l l approach the average value of the map i f the objects are distributed randomly on the sky(this is another aspect of confusion). Therefore the stacked flux from N\ objects cannot be directly compared to that from N2 objects i f Ni is very different from N2. Hence in our stacking analyses we only compare samples wi th comparable number of objects. 5.1.3 Comparison against local IR luminous SEDs In general it is difficult to use optical fluxes to constrain the shape of the F I R S E D . We wi l l tend to give more weight to F I R and radio fluxes, and use the optical detections only to gain additional insight into the morphology of the S C U B A sources. It is therefore useful to compare fluxes of possible counterparts against templates drawn from local I R luminous galaxies. Again we stress that high redshift sources may have 98 S E D s systematically different from local ones, but plots such as the one in shown in Chapter 1 (Figure 1.4) are useful as a rough guide. We use the parametric fits to determine fluxes of Arp200, M82, and Mkn231, which bracket the range of S E D s found in the local Universe. Again , Arp220 is the "typical" S E D used as a template for star-bursting high redshift S C U B A galaxies. M82 is another local star-burst, and Mkn231 has a contribution from A G N activity, which is clear from the shallow slope i n the M I R caused by the presence of warm dust. Note that redshift effects w i l l only serve to decrease fluxes at other wavelengths relative to 850 pm. Later in this chapter we w i l l use these curves to predict the ratio of fluxes as a function of redshift. 5.1.4 Our approach to counterpart identification We wi l l use a hybrid approach to finding counterparts. First we w i l l identify galaxies wi th in 12" of our sources and assign them a probability using the P-s ta t i s t ic . This w i l l be repeated for most of the catalogues we have available. However, based on Table 5.1 we wi l l need to be cautious about assigning identifications when P is only modest. For a l l of the catalogues, we wi l l also perform a stacking analysis to see i f there is some trend that we can use to help interpret our decision. Final ly , we wi l l compare the candidates across al l wavelengths and assess which is the most likely counterpart (if any) for each S C U B A source. 5.2 Overview of available multi-wavelength data We have obtained catalogues, and in most cases the full maps, of observations taken in the H D F - N for a wide range of wavelengths that are relevant to understanding the nature of the sources detected in the sub-mm maps. Some of the objects have been targeted separately by other telescopes in order to gain better constraints than provided by the wider area catalogues. Not a l l of the supplementary data completely cover our H D F - N sub-mm super-map. A n illustration of the coverage for those that do not is shown i n Figure 5.1. Before discussing the objects, we present an overview of each catalogue and explain their relation to the sub-mm population. For each section, we wi l l highlight objects that may be the S C U B A counterpart, and then tie al l the information together at the end to make a coherent picture for each source. Instead of moving from one end of the spectrum to the other, we wi l l start wi th the radio associations, which represents arguably the most important link to the S C U B A population 99 o u to 0 "T 1 r "i 1 1 r V L A 8 . 5 G H z X - 5 0 ARA/arcmin Figure 5.1: Overlay of field coverage relative to the H D F - N super-map. The 1.4 G H z , / band, and Chandra X- ray observations completely cover the field. The plot is centered on the original H D F position. Crosses represent our > 3.5cr detections at 850 fim, and circles are from the > 4tr list. 100 5.2.1 VLA and WSRT radio observations The entire H D F region has been imaged to roughly 8/xJy R M S by the V L A and the W S R T [110] radio telescopes at 1.4 G H z [111]. The V L A and W S R T catalogues generally agree except for a few objects. It has been suggested by Garrett et al . [110] that these are variable radio sources, though their fluxes are near the sensitivity l imi t of the field and may be spurious. Also, the W S R T used a different set of baselines when taking the data, and they claim that they are able to detect objects that have been "resolved out" wi th the V L A . In general we wi l l use the V L A catalogue, since its resolution is superior (1"8 as opposed to 15" for the W S R T ) . Obviously, discrete sources detected by the V L A are blended together in the W S R T map if they are close enough. A smaller area survey covering a 12' x 12' area surrounding the central H D F region was conducted wi th the V L A at 8.5 G H z [112] to an R M S of 1.6/iJy. The resolution of this map is 6". We have obtained the catalogues from each survey and the V L A maps at both frequencies in order to perform comparisons wi th our sub-mm map. W i t h i n the H D F - N super-map there are 140 1.4 G H z V L A sources detected at > 5cr. The presence of correlated noise across the V L A image means that a lower detection threshold wi l l produce many spurious sources, but we w i l l tend to consider 4 — 5CT sources as real that have a counterpart in another band. High resolution images (25 mas) were taken at 1.6 G H z wi th the European V L B I Network on selected targets wi thin the central 3' of the H D F [113]. Al though the R M S noise is higher (5<J = 210 /uJy), they can better resolve the structure of the detected sources. Since the wider area V L A and W S R T observations go deeper, we w i l l use them exclusively. The other relevant radio observation of the region was an 18 hour M E R L I N exposure. The noise level in the combined V L A / M E R L I N map is 3 times lower than the V L A map alone. Neither the full map, or revised source list have been released, but some indication of the strength of the observation was mentioned in [114] in the context of identifying a single faint S C U B A source wi thin the H D F . The results of our radio/sub-mm counterpart search are summarized in Table 5.2. It is str iking that so many of our S C U B A sources have plausible radio counterparts. W i t h i n 12", 13/19 objects from the 4cr list have a radio counterpart. This drops to only 9/19 when we restrict this search to 6", but the percentage is st i l l quite high. To estimate how unlikely it is to have 50% of the sources have a radio counterpart wi thin a given search radius, we performed some simulations. In each of 1000 realisations, we laid down 140 "radio sources" at random positions wi thin the sub-mm super-101 map and calculated the number of matches within the search radius. W i t h i n 6" the simulations found only a 30% chance that 1 out of the 19 S C U B A sources would be matched to a radio counterpart. The highest number of false detections found was three, which occurred once out of the 100 trials. We considered the entire published 5a catalogues for the 1.4 G H z and 8.5 G H z maps. The only radio object we disregarded was an 8.5 G H z detection (3646+1447 in the catalogue found in Richards et al . [112]). There are two 1 .4GHz detected objects in the vicinity, one of which is securely detected at 8.5 G H z . However, the object we threw out cannot be reasonably associated wi th the second 1.4 G H z source (posi-tional offset of ~ 4"). This object is also extremely faint, just passing the detection threshold. From inspection of the 8.5 G H z map, it appears to be a blend wi th the other 8.5 G H z source in the area. Radio galaxies are often characterised by the slope of their spectrum (/„ oc z/* r), so we estimate this based on the 1.4 G H z and 8.5 G H z fluxes (or upper limits) and also list this in column 5 of the table. Roughly speaking, an inverted spectrum (aT > 0) indicates the presence of self-absorbed synchrotron radiation from an A G N . F la t spectrum (0 > ar > —0.5) also indicate self-absorption and A G N , but can also be due to increased high frequency radio emission from star-formation. Steeper values of the index are associated wi th diffuse synchrotron radiation from star-forming galaxies [43], wi th the "canonical" index being -0.8. The radio spectral indices in Table 5.2 represent each of these types of objects. A l l but two of the S C U B A sources near detected 8.5 G H z radio sources are also detected at 1.4 G H z . SMMJ123652+621354 and SMMJ123659+621454 exhibit steep radio indices due to this lack of 1.4 G H z flux. The later of these objects we rule out as a counterpart, but SMMJ123652+621354 seems like a secure match, and we shall describe it in more detail in the next section. When we stack a l l the radio positions on the super-map, we calculate an average 850 /mi flux of iS85oMm = 1-7 ± 0.1 mJy, which is a very significant detection, and comparable to results from Barger et al . [93] and Chapman et al . [95]. To see i f there are correlations between radio objects and the sources we do not detect, we have applied a C L E A N [115] algorithm to the sub-mm map. For each source, we subtract the measured flux from the position of the primary and off beams, resulting in a map free of our detected sources. The stacked radio flux from this map is 5850/im = 0.6 ± 0 . 1 mJy, suggesting that radio sources are indeed associated wi th sub-m m producing galaxies. The bulk of the radio-stacked flux comes from the sub-mm detected sources, although the additional flux associated wi th radio galaxies which 102 T J -43 CD CX 43 o CO o {if 5? 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The results from this section demonstrate that radio/sub-mm overlap is real. In retrospect this is not surprising, since we know that radio emission and F I R luminosity are strongly correlated (presumably) by star-formation. Using this correlation, we wi l l later exploit the radio fluxes to estimate redshifts to each of of sources, as outlined i n Chapter 1. 5.2.2 Chandra X-Ray imaging We wi l l now address the issue of what powers the sub-mm emission using X- ray observations of the H D F . The Advanced C C D Imaging Spectrometer (ACIS) [116] on board Chandra performed a 1 Msec integration on a 10' x 16' region surrounding the H D F - N , making it the deepest X-ray observation ever obtained. The survey reaches 0.5 - 2.0 keV (soft) and 2 - 8 keV (hard) flux l imits of ~ 3 x 1 0 - 2 0 and 2 x 10~ 2 0 W / m 2 respectively. To examine the relation between S C U B A sources and X-ray flux, we use the H D F - N catalog [117] that covers the entire sub-mm map. The catalogue lists 370 objects: 325 in the soft band, 265 in the hard band, and 145 more in the 4 — 8 keV (ultra-hard) band, with many sources detected in several bands. The positions are accurate to wi th in 0.6" near the centre of the field, but the uncertainty increases to 1.7" near the edge. O f these detections, 249 fall wi th in our sub-mm map. A table similar to the one presented for the radio observations from the last section is given i n Table 5.3. For each possible counterpart, we compute the X- ray / sub-mm spectral index[118], asx (fu o c V * s x ) , which can be used to help distinguish galaxy types. To compute this index, one must convert the wide band X-ray flux into a flux density (power per unit frequency). To do this we assume the spectral shape is flat across the X-ray band, and after some manipulation obtain: l o g ( ^ ) + 6 . 3 8 a s x = - 5 . 8 4 - log F  (5-2) is in units of mJy, Px is the measured X-ray power in units of 1 0 _ 1 8 W m - 2 , B and F are the band-pass and centre wavelength in units of keV. Unfortunately the spectral slope across an X-ray band is not typically flat, so this parameter is useful mostly as a rough indicator. We choose to calculate the index based on the soft-band fluxes only, since the spectrum cannot change very much over the relatively narrow 0.5-2.0 keV range. The raw numbers indicate that 11 of the 19 sources have an X- ray source wi th in 12", 104 CO cu + J o cu CP -a cn s c o ' 3 3 CD > • i-H bO CD t—i a co CD X s? f - l CJ CD 3 O cc «< PQ CJ co (-1 cc3 o o 13 o • i-H CM O c o a CD CC3 S ^  CO R •s o CD o R CD CJ CD CD T3 O |Q I JS-H > o CN TP q io liH lO CO i r i id A ^ o o d < > © © o o o o o O) O O O ID M N I H CN lO IO CN i CN (D H lO N T)1 (O lO CO I lO CO* IC I Q CO lO U5 N CO 15 H n CN N <o io oi tN 00 O tN O O o o 00 O O C N O H 1 i V V d I d V C N W H V V ID a w w M d CN V V CN d d « o o o o o H ^ O O CN O O CO CN O »0 CN "3 CN N CO 00 I CO CO lO lO oi <N 6 A I CD CTt TP TP ? 6 6 2oS d V d Ol CN fH 00 n o d 00 t-CO CO C -H-H* >o to e CN CN CN to to to + + + ,t- oo to O O rH to (0 o CN CN CN CO CO CO • 00 cO TP co TP i d n d d d CO CN t td ^ -O O i O ' O i O O O l N C O O O H N C O N i f t M CI TP TP O ifi iO O iO CN CM CN CN to CO to + + + CO CC H •—i i—l CN to to to CN CN CN CN CO O) N H N (D 1" H f CN CM CN CN CN to to to to to + + + + + H CN TT N ( O CN CN CO CO TP to to to to to CO CO CO CO CO CN CN CN CN CN 00 b- CO H CN O CO CN CN CN CN CN to to to + + + O CN CO )A lO iO tO to tO CO CO CO CN tN CN wcocococococococncoco H CO CO IO CN d d CN H •H-H-H-H-H <o o T)- a H 00 "d" CO Ol CD CN CO CO CN tO 1h TP © i-H O O ) H « T CN O rH rH rH W CN CN CN CN CN CO (0 CO to to + + + + + O H M N « O O O O rH I- t- t- C- b-CO CO CO CO CO CN CN CN CN CN cn cn to co co s OH OH PH CN CO iO r-co CO CO CN 6 lO IO CO to CO to ? co t~- TP to" b-"-H-H-H-H-H « H a N OJ rH CO CN CO O N- 00 o o to to CO CO CN CN lO 00 TH TP CN © to to CO CO CN CN cn o CN -CO O TP 1 CN K CO C rH © rH , CN CN CN to CO to + + + iO to CO to to to CN CN CN CN CN CN tO CO to + + + CN CO Ol i-o in o to to to CN CN CN 1 C J N > i s o to 1 00 H O CN CN CN to to to + + + to 01 o O H CO b- N- r-CN CN CN N O N f lO CO CN CN CO TP CN CO CN CN CN CN to to to to + + + + H CO H CO CO CO TP TP t-- b- b-eo co co co CN CN CN CN h^hjI-jl-jl-jl-j^hll-jhjnTI-J^r)!-) s s s s s s s s s s s s s s s s s •SSSSSS22SSSSSSSSS CN CN CN CN TP t--H -H -H-H lO o o CN o o CN © CN CO N CN c3) CN 0) CN TP O TP O rH lO © O tO CN CN CN CN CN to to to to to •+ + + + + Ol CN CN b- CO i—' CO O CN TP CD CD N N S CO CO CO CO CO CN CN CN CN CN CO CO CO CO CO 105 but wi th twice as many X-ray detected objects than radio objects, the probabili ty of a chance occurrence is much higher. Repeating the simulation as in the last section suggests a 10% probability that as many as 7 sources w i l l fall wi thin 12" by chance. This is reflected in the P-s ta t is t ic which shows that only 6 of the detected objects have a 10% or lower probability of being associated with the S C U B A source by chance. However, in the case of X-ray sources, the P-s ta t is t ic may not be entirely appropriate due to the possible presence of clustering, as we discuss next. 5.2.2.1 The clustering of sub-mm and X-ray sources There is an observed clustering signal between X-ray and S C U B A objects in the U K 8-mJy survey[119]. This means that the number of true associations may be less than discussed above. Indeed, in that paper, the authors have performed an angular correlation analysis, like that described in the last chapter, to quantify the level of clustering. They used both the published positions from the 8-mJy survey[54] and those from our original H D F scan-map publication [88] finding a 4.3a and 2Aa detection respectively. Given our new, more complete list of sources in the H D F - N , i t is only fitting to repeat this exercise. Using the statistic (see Hami l ton 1993 [120]), SX x RxRs -. /j, Q\ W { 6 ) = SRX x XRS ~  1 ( 5 - 3 ) where SX are S C U B A / X - r a y pairs and Rx and Rs are random X-ray sources, we fail to find a clustering result comparable to that previously reported (see Figure 5.2). In these simulations, we assume that the sensitivity to X-ray sources is the same across the entire field. This is not precisely true, but the sources we are using are quite significantly detected, and therefore we can safely assume that we are not biasing our results. A s in A l m a i n i et al . [119], we also attempted the analysis using only those X -ray sources brighter than 5 x 1 0 _ 1 8 W / m 2 . A t this level a l l there is no incompleteness across the field. S t i l l no detection was found. Certainly the sensitivity to S C U B A sources is not constant across the field, and therefore we ran 500 Monte-Carlos using the source count model described in the last chapter. In each iteration, a fake map was made and sources above 4a extracted using the same pipeline as the real data. If a clustering signal is real, what would it mean? The clustering signal at small angular separations can be due to objects which are the same galaxy identified at both wavelengths. However, a positive correlation out to ~ 1' cannot be due to objects in common between S C U B A and Chandra, but must be due to the two populations tracing out the same large scale structure. So, the 8-mJy results imply a spatial 106 Figure 5.2: Clustering between S C U B A and X-ray detected objects. Solid circles show the cross-clustering estimate based on our > 4a sources and the published X -ray coordinates from Chandra. No detection is seen. The open squares are estimates from [119], who claim a 2.4a detection of clustering in the H D F based on the shallower, though uniform scan-map data in Borys et al.[88]. 107 l ink between X-ray bright and sub-mm bright populations. It has been speculated that these two catalogues trace the same population, but at different stages in their evolution. Th i s would explain why there is no enhanced overlap between S C U B A and X-ray sources yet a clustering signal between the two objects can s t i l l be detected. High redshift clusters cover angles typically ~ 1', which is consistent wi th this picture. Note that the poor beam size of S C U B A (much larger than the 1" size of typical high redshift galaxies) means that we cannot distinguish how much of the small scale clustering comes from spatially coincident objects. In other words, the stacked sub-m m flux at Chandra positions is partly due to S C U B A flux which is clustered wi th Chandra sources, but not necessarily from the same galaxies. However, the estimate of w(9) from A l m a i n i et al . [119] is weak, and the probability of finding an X-ray galaxy wi th in 5" just by chance is only 5%. That we have not detected a clustering signal here is interesting, since it makes this hypothesis suspect. One idea is that the measured clustering signal is due to gravitational lensing of S C U B A sources behind the foreground large scale structures that host the X-ray objects [119]. If this were true, one might expect a stronger signal when using only the brightest (and presumably more strongly lensed ) S C U B A sources, since the steepness of the source-counts here leads to a stronger bias in the number of objects detected. Indeed, this may explain the moderate detection in the scan-map only data, which detects only the brightest objects. We re-did the clustering analysis using only the > 7 mJy sources but st i l l found no detection. Even including the > 3.5a detections to increase the sample size did not help. We conclude there is no evidence of an X - r a y / S C U B A clustering correlation in the H D F , but this does not mean the effect in other surveys is not real. The 8-mJy survey shows a fairly convincing detection. It is worth noting that the clustering estimator we have used is designed to be unbiased, but that which was used in the 8-mJy survey was not. It is entirely possible that using a biased estimator could produce results that mimic a real clustering signal. However, the uniform noise levels in that survey suggest that the bias should be small. Larger uniform surveys wi l l be useful in investigating this in more detail. 5.2.2.2 The nature of the X-ray emission We can characterise the relative strength of the X-ray flux v ia the hardness ratio, (H — S ) / ( H + S). It is conventional to use the counts in hard (H) and soft (S) band instead of the fluxes. Figure 5.3 reveals a strong correlation between those sources wi th strong hard X-ray emission and stacked sub-mm flux. We obtain an overall 108 average 850 / /m flux of Ssso^m = 1-0 ± 0.1 mJy and Ssso/wn = 0.4 ± 0 . 1 mJy, for the full and cleaned map respectively. Most of this signal comes from the hardest th i rd of the sources, although even the softer ones are statistically detected. There are no trends obvious between sub-mm flux from the undetected sources and hardness ratio. This may be a slightly misleading statistic, since at high redshift hard counts w i l l appear softer in our frame. Following the work of Fabian et al . [118], we can compare the X- ray / sub-mm spectral index against expected (and known) values for different types of galaxies: observations of the quasar 3C273 suggest that G J S X — 0.9 would be expected at al l redshifts; the heavily obscured A G N NGC6240 has an index that increases from ~ 1.0 at z — 0 to 1.25 at z = 5 (though this depends on the fraction of scattered energy, and can go up to ~ 1.4); and finally the "standard" star-burst Arp220 predicts high values for the index (asx > 1-2) at a l l redshifts. Even without knowing which (if any) of the sources in Table 5.3 are the correct S C U B A counterpart, al l of the objects, except for SMMJ123637+621157 and SMMJ123736+621430 have X- ray flux consistent wi th a star-burst only. It is difficult to draw detailed conclusions, but it is seems clear that A G N s do not dominate our S C U B A sources and that the bulk of the X- ray emission we see originates in processes related to star-formation rather than black hole accretion. Note that i f these were A G N , they would have to be very Compton-thick in order to produce the F I R luminosity we observe. The radio spectral indices for these source do not show evidence for self-absorption, and therefore we st i l l conclude that star-formation is the dominant source of energy. 5.2.3 Optical-NIR imaging There are two near-IR wide-area surveys of the H D F available. The first[121] was conducted as a prelude to a campaign to obtain spectroscopic redshifts for al l sources in the field wi th R < 23 [122]. The 8.6' x 8.7' images were taken using the 200-inch Hale Telescope at Palomar. A source list was made from detections in each of the separate images. Their R- and K- selected catalogues contain 3607/488 sources and reach l imits ofR = 25.5 and K = 20 magnitudes respectively. A s wi th a l l flux-limited surveys, completeness near the faint end is not very good, and therefore we also use the sources detected in a second survey [123]. It employed the C F H T to obtain deep wide-area I band images (roughly 24' x 24') to supplement a 9' x 9' H K image 2 of 2 HK is essentially a wider K band filter. To convert this to an equivalent K magnitude the authors suggest using K = HK — 0.3 109 3.0 2.0 o tO a in XI cu o CO -(-> CO 1.0 h 0.0 A A 111 1 111 111 1111 111 1.0 -0.5 0.0 0.5 H - S / H + S 1.0 -1.0 -0.5 0.0 0.5 U H - S / U H + S 1.0 Figure 5.3: Stacked sub-mm flux as a function of X - R a y hardness ratio. We have split the Chandra sources into 3 equal sized bins. Black circles show binned averages, wi th horizontal bars denoting the size of the bins. The triangles are the same but wi th the sub-mm source list determined in Chapter 4 masked out. The left panel compares the hard counts against soft, while on the right we use the ultra-hard counts. 110 the H D F region taken at the U H 2.2m telescope. The published magnitudes are 5a above the local noise threshold, and the 2579 detected objects are considered very secure. We wi l l also rely on our own photometry of these images for those cases where a fainter source seems present, and in the extended / band region where fluxes were not reported. W i t h so many sources present in the field, one requires a very small search radius in order to ensure effective matching. However, the inherent pointing uncertainty coupled wi th pointing errors due to confusion means that one cannot set an arbi-trari ly low matching radius. This is the problem al l sub-mm astronomers face when attempting to find optical counterparts; a reasonable search radius means finding several candidate objects. It is at this point when we must resort to what has al-ready been learned about S C U B A identifications in order to decrease the number of candidates. A s mentioned previously, we expect that optical counterparts are "red" due to dust extinction. From the catalogue, we isolate the 779 objects that have a detection wi th I < 24.25 and K < 20.0, which are the l imits of the survey. There are 10 objects from this sub-sample that have I — K > 4, which is the usual E R O criterion (see, for example, [124]). The stacked flux from this subset is - 0 . 1 ± 0 . 6 m J y and not at a l l indicative of a correlation. However, i f we divide the objects into three bins wi th equal numbers of objects per bin, a trend is visible. A s Figure 5.4 shows, sub-mm flux increases as the sub-sample of galaxies being stacked becomes redder. Note that the cut on increasing I — K also picks out the fainter objects in the sample, and therefore it might be that deeper N I R imaging toward S C U B A sources w i l l yield more detections. Later we wi l l show that indeed several S C U B A objects have a plau-sible E R O counterpart just below the detection level of the catalogue used here. Since there are, on average, about 5 optically detected galaxies wi th in 12" of each S C U B A source, we do not include a table of counterparts as we did for the radio and X-ray catalogues. Instead, we wi l l defer further discussion about the optical counterparts unti l we discuss individual objects later. 5.2.3.1 Optical LBG dropout surveys Their inferred high star-formation rates and co-moving number density comparable to that of present day ellipticals [125] make L B G s an interesting target for sub-mm studies. Using reasonable conversion factors based on local standards, the predicted 850 pm fluxes are expected to be on the order of 5 mJy. However, a l l sub-mm surveys to date have failed to detect L B G s except in a handful of extreme cases. Our group has performed a targeted photometry programme [126, 127] toward the 33 highest 111 • - 9 6 co TJ CD O CO - 0 . 2 h • - 3 s 0.6 \ O 0.4 0.2 CD 0.0 o CO +-> - 0 . 2 m 20 22 24 I magnitude 1 1 1 1 1 l 1 1 1 ' 1 1 1 - I X I -1 % . 1 , 1 , 1 , 1 , 1 2 -1 0 1 2 . 3 4 I - H K 5 Figure 5.4: Stacked sub-mm flux as a function of redness cut. The top panel shows the stacked 850 fim flux as a function of / band magnitude, showing a marked increase toward fainter objects. Circles denote the average sub-mm flux in each bin, the size of which is given as the horizontal bars. Triangles correspond the the same cut, but first removing the known sub-mm sources from both the 3.5 and 4.0cr S C U B A catalogues. The central left panel simply shows the distribution of I — HK values from the catalogue of Barger et al . [123]. O n the right, we plot the distr ibution of / band magnitudes (thick line) as well as the subset of / band fluxes from the reddest (thin line) and bluest (dashed) bins. This shows a slight trend for the reddest sources to be fainter. This means we cannot completely separate colour effects from brightness effects. The bottom panel plots the stacked 850 /im flux for three bins that each have the same number of objects. 112 estimated star-formers in a list compiled from observations in many fields (including the H D F ) and found only one object with detectable flux down to a 3a l imi t of 1.5 mJy. Deeper imaging revealed that the sub-mm emission was not coming from the L B G itself, but rather a very red galaxy nearby apparently in the process of merging [128]. The rest of the sample had a statistically significant mean of 0 . 5 ± 0 . 1 mJy. Altogether, these observations suggest that using optical data to predict the S F R overestimates the sub-mm flux. The C U D S S blank-field S C U B A mapping campaign [129], wi th noise levels com-parable to our photometry observations, was also used to test for flux from L B G galaxies. Their map overlaps with 86 L B G s , thus providing a larger sample. They too find a marginal detection of the sample of 0 .4±0 .2 mJy, however it should be noted that they stacked the entire sample of L B G s where in the photometry observations only those wi th the largest inferred S F R s were used. In addition, a more involved statistical analysis [100] with the original, deep Hughes et al . S C U B A observation of the H D F suggest a mean L B G flux of 0.20 ± O . O 4 m J y / M 0 y r - 1 . T H E H D F - N super-map covers much more area than these previous attempts, and contains many more known L B G s . Therefore it is worth performing a similar analysis. Images of the H D F in UGR bands were conducted by Steidel et al . [130] who found 149 L B G s in a 9' x 9' region. Each of these sources was spectroscopically verified to be at z ~ 3. The stacked flux is 0.06 ± 0.08 mJy, but goes up to 0.11 ± 0.07 m J y when we remove our known sub-mm sources (though admittedly not wi th high significance). This result is similar to that reported in Webb et al . [129], where it is suggested that the presence of al l the off-beams from the S C U B A sources conspire to decrease the correlation. This in itself is interesting, as it suggests the presence of clustering between L B G s and S C U B A detected objects. This might also help explain why the estimates for L B G flux from the H D F - N super-map are lower than those reported from other, smaller area surveys. It should be noted that in Webb et al . [129], they compared L B G fluxes from three different fields, and found a 4a stacked detection in only 2 of them. The thi rd field had only 0.01 ± 0 . 1 1 mJy average L B G flux. However, a full clustering analysis of the H D F - N S C U B A / L B G sample fails to detect a signal. The C U D S S fields also fail to detect any significant clustering signal above 3a. O f a l l 149 L B G s , only two seem co-incident wi th a S C U B A source. HDF850.2 (which we call SMMJ123656+621203) has pair of possible L B G counterparts (CC10 and M M D 2 8 ) located wi thin 6". C C 1 0 is also coincident with an X- ray and marginal radio detection. It is tempting to conclude that rapidly star-forming galaxies which are detected by 113 S C U B A are missed in the star-formation inventory discovered in the Lyman-Break technique. However this has been hard to test explicitly, since there is no sample of S C U B A galaxies with known redshifts which could be searched for using the L B G technique. 5.2.4 ISO mid-IR imaging ISO observed a ~ 4' x 5' area around the H D F - N at both 7 and 15 / /m. The data-set was difficult to analyse, and in general the 7 /mi fluxes are not trustworthy [131]. Nevertheless, we wi l l report a 7 / /m flux for each of 15 fj,m detected sources for which we find coincident wi th a S C U B A object. Al though the data were reduced separately by three different groups [132, 133, 134], the 15 / m i catalogue found i n Aussel et al . [132] is widely regarded as the best source. The catalogue is estimated to be 95% complete at its l imi t ing sensitivity of 200 / i Jy . They present a list of 49 objects wi th high S N R , and an additional 50 wi th lower confidence. The positions are accurate to wi th in 3". We present a list of our sources along with associated 15 / im fluxes in Table 5.4. Concentrating first on the 49 secure ISO 15 / im detections, we find a stacked flux of 0.65 ± 0 . 0 9 mJy, which drops to 0 . 1 6 ± 0 . 0 9 m J y after C L E A N i n g out the S C U B A sources. Even the list of 50 less secure detections gives similar results, and the overall (all 99 sources) stacked flux is significantly detected as 0.41 ± 0.06 mJy. The brightest th i rd of the ISO sources (Sis^jy = 150 — 450/xJy) have the strongest stacked flux, wi th an average value of 0.86 ± 0.13 mJy Note that since the K-correction is positive at 15 /mi , the confirmed counterparts to S C U B A galaxies must be at relatively low redshift. There is also an ambiguity introduced by A G N , which are expected to heat up at least some fraction of the dust to temperatures higher than normally associated with star-formation. This hot dust component has the effect of making the spectrum shallower short-ward of the peak. Therefore M I R measurements can be particularly useful at constraining the shape of the S E D , and hence help determine the nature of the S C U B A source. Unfortunately the sensitivity of ISO is not sufficient to enough to detect many sub-mm bright galaxies, and larger samples w i l l have to wait unt i l the launch of the SIRTF telescope in 2002. 5.3 Breakdown of each SCUBA object A r m e d wi th the information just presented, we are now i n a position to make informed guesses about possible counterparts to each of our S C U B A galaxies. A pictorial 114 CN c o o CD C J S-I O cc -S3 CJ 03 CD .Si o CD o cc ! CO fl O • r-1 > S-I CD CC O s, =2.1 t -CD > > > > > > > > C 0 O O O O O O O O / V • ^ ^ • u ^ ^ f c . o o o o o o o o Q Z Z Z Z Z Z Z Z X B. Ik CD bJO 03 SH I CJ CD H 3 CD 13 3 o I co o3 £ CD CJ S-i O CO E to • ' • • i i S ° o o o ? 2 O CO CO N CJ) i n n CO CO CO M CO 2 2 2 DH DH CU Et- &H Cc Q Q o § 3 13 r-i CN 3 3 T J , 0 to CCj C^ j J D J 3 cp * a) M CO r *• CD ^ - — CO TJ T) > n « « o 4) 4) w D 6* 6" o ffiOOZ fa S " fa a o o Q K Q Z K o o © o o o © q q © © q co cd d cd cd to CD cox WTJ" I—ICN N O CN 10 ^10 lOOl CNh- ^CO CDCN + 1+ 1+ 1+ 1+ l « a f CN IO o + l " ~ " CN 00 CN CO CO o + 1 + I 00 lO 00 t-Ol 01 CO W r-i CN r- H> | cD CO CO -H CO tO oo rn -H -H -H C N C N N » N H N _ H . H H T f C O I - H O l 1 3 ; O) ^ V V V V V V V c o V N 5 V V V V V CO lO -HCN-H rH . CN CN V rH CO IV : O) m oi - iO o Idd"?* 0 .^**?^ rH H CD CD N H » CO rH 00 CO CO TP rH CO CO lO TP d rH d © d CN © O c i H -H -H -H -H -H-H -H -H-H-H o w q Gl t— CD O TP q rH od CN w cd od TP ed d d IO rH TP IO rH CN CO Ol Tf" TP CN 00 Ol H O I O I O H H O W O iO CN N CD TP I CN CN CN CN CN CN CN 1 CO CD CO CO CD CO CO " + + + + + + + ) CD CO 00 H H N TP 1 rH rH rH CN CN CN CO 1 CO CO CO CO CO CO CD ) CO CO CO CO CO CO CO + + o o . cO co c CO CO  CNCNCNCNCNCNCNCNCN CN CN CO N CO CN CO rH CN O rH TP CN 01 rH rH O rH CN CN CN CO CO CO + + + CO O rH iO © © CO S N CN IN CN CN CN CO CO + + © CN lO lO CO CO CO CO CN CN 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 C O C O C O C O C O C O C O C O C O CO CO h r ) 1 2 2 22 2 2 2 22 2 CO CO to to CO CO CN CO O rH O CO TP CN CN CN CN CD CO CO + + + CO b- CO O O rH b- b- b-CN CN CN r-J r-j r-j CO CO CO o o o o Z Z Z Z O X U IM U U J O > > > > S a. fa a s 'S » 1 1 S B ? » 1 1 O O A u ° fa ZZ a z z a OJ CD CD CP CL) CD CP > > > > • > > > o o o o o o o O CJ cj o O cj o o o o o o o o Z Z Z Z Z Z Z Ol CO 00 O CO b-O CN rH rH rH rH o d> <6 <6 d> o q Q co q q co W3 rH d 00 •<P CO Ol COO CO-H CO I- COrH CH OlQ VCO lOCO CD + i « » * r « + 1+ 1+ I H T I T I TP ko io lO b- O b- CN Ol rH TP IO rH CN CN CO TP CO V V V S V V V TP V V V TP CO TP ^ c d ^ « d d ^ CO lO 00 CN CO rH TP O TP CN O CN CN CN CN CO CO CO CO + + + + b- 00 rH 00 © O rH CN CO CD CD CD CO CO CO CO CN CN CN CN Ol © CN TP CO O TP lO CN h CO CO ^ O rH rH CN CN CN CN CO CO CO CO + ++ + lO CO 00 CN CO CO TP lO CO CO CD CO CO CO CO CO CN CN CN CN * T T ^ ^ r-J r-jr-j r-j 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 t o t o c o c o c o c o c o c o -H -H CO CN CN d CN CN CO CO + + CO Ol lO w CO CO CO CO CN CN 2 2 2 2 CO CO oo -H 01 00 CN © CN CN , CN lO CO O CN N , M H CN CO v v S V V V V 00 CO CO CO rH CO d °. cd i> TP d i> -H " -ft -H -H -H -H CD CO l-H Ol Ol 00 • CN CN CD CO + + CO Ol O rH r-co CO CN CN ) iO IO CO CN CN i O CO TP CN CO CN CN CN CN CN CD CD CO CO CO + + + + + O H CO H CO CO CO CO TP TP b- r-CO CO CO CO CO CN CN CN CN CN 2 2 2 2 2 2 2 2 2 2 2 2 2 2 CO CO CO CO CO CO CO cp CD cw iU a> > > > > > O O O O o U cj y cj o O O O O O -H-H-H -H-H O lO o o o rH O CN CN O rH rH rH CN CO CN O rH TP -H M - H c d " oi-H CN -H I d N CN Ol CN 05 CN TP O TP O rH iO O O CO CN CN CN CN CN , CO CO CD CD CO + + + + +1 Ol CN CN I- CO i-H CO O CN TP CD CO N N N CO CO CO CO CO CN CN CN CN CN CO CO CO CO CO 115 summary of each object is presented in Figures 5.5-5.11 which show postage stamp images of each target in al l the bands for which we have maps. SMMJ123607+621145 A weak radio source detected by W S R T lies wi th in 8 arc-seconds, but an inspection of the V L A map shows a 4CT peak at the position of a faint (7 = 23.2) galaxy 10" to the east of the S C U B A centre, and is likely the W S R T object. A n X-ray source 11" to the other side is coincident wi th a point source de-tected in the optical, but its separation is too far to reasonably associate it wi th the S C U B A source. There are many sources detected in the 7-band image, but without supplementary N I R data it is difficult to assign an optical counterpart to this object. The radio map is clear however, and therefore the only multi-wavelength property we choose to attribute to this object is an upper l imi t to its 1.4 G H z flux of 45 /iJy. This object was only observed i n scan-map mode wi th S C U B A . SMMJ123608+621251 Though below the threshold of the detection criterion, this source seems to lie directly on top of a very faint 7 band source (7 = 24.7). Again , we list only an upper l imit to the radio flux for this source. It too was only observed in scan-map mode. SMMJ123616+621518 W i t h i n 6" of this source lie 2 blended Chandra objects which appear coincident wi th radio sources. Neither X- ray source was detected both by the V L A and W S R T . However the V L A map does show a source where W S R T detects one, though the emission in this region appears blurred. The W S R T detected Chandra source has a very hard spectrum ([77 — S]/[77 + S] > 0.5) suggesting a heavily obscured system. This is hard to reconcile wi th the sub-mm/X-ray spectral index, but it might be that this system is dominated by star-formation though st i l l harboring an A G N core. The steep radio spectral index also argues in favour of a star-burst. The V L A source is much more X-ray soft, and the spectral indices suggest a star-bursting system if this is the correct S C U B A ID. B y eye there are two blobs in the TT-band image at the location of the two sources, though too faint to detect wi th high confidence. However, the R band flux l imi t is 25.3 and therefore undetectable at K unless R — K J> 5. It appears to be a red/blue composite system, though deeper observations are required to confirm this. No other candidate sources are in the region, and therefore we consider only this radio /X-ray pair as plausible candidates. Since both objects have comparable radio fluxes, an estimate of the redshift (which is z 2) w i l l not be affected i f only one of the sources is responsible for the sub-mm flux. Nevertheless we identify the optically faint red object ( W S R T detected) as the source of the S C U B A flux. This source had S C U B A coverage from jiggle and scan-map modes, and coincides wi th Barger-3. 116 85Qum SMMJ123607+621145 8.5GHz 1.4GHz SMMJ123618+621554 HK 8.5GHz 1.4GHz 1.1:'.. 1 ' XS TO -HK SMMJ123618+621009 8.5GHz 1.4GHz Figure 5.5: Postage stamps of the > 4a 850 pm S C U B A objects. Directions of Nor th and East on the sky run toward the top and left of the page respectively. Each sub-image is 30' on a side. Completely black stamps mean that the source is outside the map of that particular wavelength. 3.5, 4, 6, and 8a S C U B A 850 /zm contours are over-plotted on each. In images where the dynamic range is low, the image may appear "striped" (particularly the X-ray) . 117 SMMJ1236214-621254 BStytm I HK 8.5GHz 1.4GHz XS XH SMMJ123621+621712 85Qum I HK 8.5GHz 1.4GHz XS XH SMMJ123622+621618 85qum I HK 8.5GHz 1.4GHz XS XH SMMJ123637+621157 85C|Mm I HK 8.5GHz 1.4GHz XS XH Figure 5.6: Continued from previous page. 118 SMMJ123652+621227 8.5GHz 1.4GHz XS T Figure 5.7: Continued from previous page. 119 BSOjum I HK SMMJ123607+621021 8.5GHz 1.4GHz 850um I HK SMMJ123611+621215 8.5GHz 1.4GHz -«* • _ *' , • f yk km -» 3ft * . * • . * • 1 1 1 1 1 • i : O : • | i | . • • \ O : * i i i . r • - . 1 , 1 , ' r: • i i i i . I . I . 850/jm SMMJ123628+621048 8.5GHz 1.4GHz I ». It ' . I * I •<> XS XH I I t I 1 I 1 I i I 85Qam I HK SMMJ123635+621239 8.5GHz 1.4GHz I 1 I 85Qum I SMMJ123636+62070O HK 8.5GHz 1.4GHz ' • i XS XH 85Qum I HK SMMJ123648+621842 8.5GHz 1.4GHz XS XH T M ' I.' , • 1 1 1 1 • l b : I > J mil *' \j **3 : 0 • 1 1 1 1 Figure 5.8: Postage stamps of the 4a < S N R < 3.5a 850 / im S C U B A objects. These are the 17 sources from the supplementary catalogue. 120 MMjjfll SMMJ123652+621354 HK 8.5GHz 1.4GHz BBjawn HK SMMJ123659+621454 8.5GHz 1.4GHz SMMJ123706+621851 8.5GHz 1.4GHz T | i | r XS XH SMMJ123719+621109 8.5GHz 1.4GHz 7 r a SMMJ123730+621057 8.5GHz 1.4GHz XS XH jBjjwn I HK SMMJ123731 +621857 8.5GHz 1.4GHz XS Figure 5.9: Continued from previous page. 121 Figure 5.10: Continued from previous page. SMMJ123618+621009 6" to the N E lies a faint E R O (7 = 24.2,1 - K = 4) which we consider to be the only feasible detected counterpart. N o other source is present wi th in 8" of the S C U B A center. Unfortunately, this source lies outside the S C U B A contour, which stretches to the south around what appears to be an elongated region of flux terminating in an R — 24.9 galaxy. Scan and jiggle mapping were done in this region. SMMJ123618+621554 A strong V L A source (151 / i Jy) w i th a very steep spectrum is 4.5" to the south and is coincident with a very faint (R = 25.3) galaxy. The 7<~-band and 8.5 G H z images also show flux at the same position, but below the 5a detection threshold. We consider this to be the counterpart. This agrees wi th the assessment of Barger et al.[93] for this source (Barger-7). Scan and jiggle mapping were done in this region. SMMJ123621+621254 3" to the S W lies a faint optical galaxy (7 = 23.7), but no other plausible counterparts exist. We list only a radio upper l imi t for this scan-mapped only source. SMMJ123621+621712 A radio source detected by both V L A and W S R T lies 3" south of the S C U B A position, but is 2" away from the only other detected object i n the area; a 7 = 23.4 galaxy with an elongated morphology. The radio map suggests 122 SMMJ123619+621127 SMMJ123632+621542 45Cy<m I HK 8.5GHz 1.4GHz XS XH SMMJ123727+621042 45q«m I HK 8.5GHz 1.4GHz XS XH SMMJ123743+621609 450^ m I HK 8.5GHz 1.4GHz XS XH , 1 ....,.. , r - r - i — . , , , - r - 1 | 1 , T -* H i i • H ' V * / Figure 5.11: Postage stamps of the > Aa 450 /mi S C U B A objects. 123 emission from this source as well, but we attribute the sub-mm flux to the optically undetected central radio source. This object is also Barger-11 from that catalogue of radio-detected S C U B A sources. Scan and jiggle mapping were done in this region. SMMJ123622+621618 Barger associates this object (which is designated Barger-13) wi th the radio source 11" to the north. The radio source is coincident wi th an E R O (R = 25.1, R — K = 5.0) making it an appealing object for sub-mm identification. The optical image reveals a very disturbed system, suggestive of a merger process. Also , there is a 3.5tr 450 pm signal directly on top of this system. Though the offset is large, we identify this object as the sub-mm source. Note that the faint optical system very near the S C U B A centre appears to be part of a diffraction spike from a nearby star. Scan and jiggle mapping were done in this region. SMMJ123634+621409 8" to the south is a very red galaxy (R = 19.5, R-K = 4.6) which is probably too bright to be the correct identification. More compelling is the optically identified X-ray source to the North (7 = 23.8). It has a spectroscopic redshift of 3.408 and is classified as a broad line A G N . It is also oC34 from the L B G catalogue. The high redshift would explain the lack of a radio detection. This is one of two radio-unidentified sources from the survey of Barger et al . In both cases, the offsets are rather large, especially considering the 850 /jm is well above the confusion level and the S N R is high. We conclude that there is no statistically robust counterpart to the l imi t of the observations. Scan and jiggle mapping were done in this region. SMMJ123637+621157 This object has many candidates nearby. A radio detection by the W S R T (but not V L A ) is not coincident wi th two optical candidates, which both have spectroscopic redshifts. Bo th lie wi th in 4" of the S C U B A source. The first is a z = 0.779 emission line galaxy with 7 = 21.5,7 — K = 2.1. The second is a z = 0.557 galaxy wi th 7 = 21.5; 7 — K = 2.4 which also happens to line up wi th a soft X- ray source (Hardness Ra t io= —0.5). A t these redshifts, it is difficult to understand the lack of a radio detection i f one of these two objects were the counterpart. It might be that these foreground objects are lensing a S C U B A object at high redshift. Indeed, i f one assumes the 4tr is real, the C Y redshift estimator predicts z >^ 2.5. This source had observations taken in al l three S C U B A modes. SMMJ123646+621451 Though many objects are near to this S C U B A source (also called Barger-33), the identification seems clear. There is a V L A source detected in both channels which lines up with a soft X-ray source and a faint, disturbed optical system wi th R = 25.5. Th i s is the one S C U B A source where a second radio source is present wi thin 12" but in this case the first of the two is statistically more compelling. 124 Scan and photometry observations were taken in this region. SMMJ123650+621318 The most detected counterpart has measurements at both radio frequencies, 15 jum, X-ray, and optical (7 = 21.1,7 — K = 2.7) Its redshift is 0.475 and is classified by Cohen as having an intermediate type spectrum (absorption and emission lines). The redshift l imits from considering the ratios between 15//m, radio, and 850 /jm flux place the source at roughly z J> 0.5, which is consistent wi th the spectroscopic redshift, and therefore we consider this the counterpart. 3" away (though further out from the S C U B A source) lies an emission line galaxy at the same redshift. It's colours are almost a full magnitude bluer. Slightly to the south of the S C U B A source lies a z = 0.851 emission line galaxy wi th (7 = 22.3,1 — K = 2.3), but wi th no other supporting multi-wavelength detections is unlikely to be the correct ID. The faintness of this sub-mm source suggests that confusion noise may be a particular problem. Note that this source is considered as two distinct objects (HDF850.4 /HDF850.5) by Serjeant et al . This source had observations taken in al l three S C U B A modes. SMMJ123652+621227 Similar to the previous object. One location has detections at every available wavelength and is identified a,s a, z — 0.4 emission line galaxy. 7" to the east of it is another object at an identical redshift, but only having detections in 7 and K. Nearly on top of the S C U B A position is an E R O with (7 = 23.5,7 - K = 4). Though both seem like plausible candidates, it turns out to be neither. This sub-mm source, usually called HDF850.1 , has been the subject of intense scrutiny since its discovery, and we shall discuss it separately later. This source had observations taken in a l l three S C U B A modes. SMMJ123656+621203 Among al l the candidates, the most likely is a very red (7 = 23.7,7 — K = 3.8) L y m a n break galaxy that exhibits detectable X-ray flux and very faint (~ 3cr) radio flux. A very faint detected radio source lies to the north, but is coincident wi th a redshift 0.321 7 = 22.8 galaxy. The radio/sub-mm redshift indicator places the object at z = 2 i f the sub-mm flux and radio flux are coming from the same object. This object was discussed by Nandra as well who note that if at redshift 3, this galaxy is almost certainly an A G N given its X-ray luminosity. Given the positional error due to confusion, plus the lack of other plausible counterparts in the region, we suspect the L B G is responsible for the sub-mm flux. This connection was missed in the original assessment of this object, more commonly called HDF850.2 . As wi th a l l the H D F 8 5 0 objects, this was observed in al l three S C U B A modes. SMMJ123700+620912 The only contender is an optically invisible radio source (detected by the V L A in both channels) only a few arcseconds away from the S C U B A 125 centre. Designated Barger-49 as well, it was observed with jiggle and scan mapping. SMMJ123701+621148 This is a striking E R O (R = 2 5 . 3 , R - K = 5.4), that has radio detections and a spectroscopic redshift of 0.884. Th i s agrees wi th Serjeant et al . , who call this source HDF850.6 . The object near the E R O has a redshift of 0.744 and an ISO 15 / im detection. SMMJ123703+621303 Nothing stands out as a counterpart. A radio source just below the detection threshold to the west of the S C U B A source is the only thing that presents itself. We attribute only upper l imits to counterparts for this source. This source had observations taken in al l three S C U B A modes. SMMJ123707+621412 The correct identification is extremely likely to be the (R = 25.3, R — K = 4.8) radio and X-ray detected object right on top of the S C U B A source. Note that i f the redshift estimate for this source is correct (z — 3.7), the rest frame X-ray luminosity is large enough to be an A G N . This source had observations taken in a l l three S C U B A modes. SMMJ123713+621206 There are no radio, red objects, or X- ray sources nearby that are convincing enough to call a counterpart. We point out that the L B G M M D 3 1 is 9" to the north, and a R = 23.5, R — K — 3.5 X-ray source is 7" to the east, but we consider this to be a blank field object. This is the second source from the Barger et al survey that has no radio counterpart. It was observed wi th jiggle and scan mapping. SMMJ123607+621021 A n I = 24.5 radio detected galaxy is the only compelling ID. The optical emission suggests a disturbed system. There are no available N I R data. This was scan-mapped only. SMMJ123608+621433 A soft X-ray source is coincident wi th a 1.4 G H z detected radio source and an I ~ 23.5 galaxy. There is 8.5 G H z flux at the position, but fainter than the detection threshold. It was observed with jiggle and scan mapping. SMMJ123611+621215 A n extremely faint wisp of I-band emission is coincident wi th a hint of a detection in the radio. Al though deeper observations may confirm this, for now we conclude this source has no counterpart down to the l imi t of our data. Scan-map only was done in this region. SMMJ123628+621048 The counterpart is most likely the z = 1.013 E R O (I = 22.5 ,I — K = 4.0) that has detections in the optical, radio, and X-ray. No other sta-tist ically compelling candidate exists. It was observed wi th jiggle and scan mapping. SMMJ123635+621239 Th i s faint sub-mm source is called HDF850 .7 i n the Ser-jeant et al catalogue. A complex field, wi th the most appealing candidate being a z = 1.219 V R O (I = 22.3 ,I - K = 3.5). It has detections in the radio, mid-IR, and 126 X-ray. The only unfortunate thing about this candidate is that it lies 7"away from the S C U B A centre, but again this may be due to confusion noise. The redshift is compatible wi th that derived from the radio/sub-mm correlation. This source had observations taken in al l three S C U B A modes. SMMJ123636+620700 The S C U B A centre prefers a very faint 7 ~ 24 galaxy to the south, but nearby there is a very bright (presumably foreground) galaxy wi th radio emission to the north. A fainter source near it appears distorted, as i f it were being lensed. From this fainter object there is detected radio emission and hard X- ray flux. However, the radio positions are quite far away, and confusion is not an issue. We conclude there is no counterpart. Note that this was observed in scan-map only and is near the bottom edge of the map. SMMJ123648+621842 Just like the previous source, but near the northern edge of the map. Apparently a blank field to the l imi t of the observations. N o compelling counterpart is present. SMMJ123652+621354 3 moderate redshift ISO objects are in wi th in 12", but the S C U B A center lies on top of a z = 1.355 galaxy. It also has a 8.5 G H z detection from the supplementary list. A W S R T source 10" to the east is coincident wi th nothing else. The object has very blue colours (7 = 21.4,7 — K = 1.8) . Serjeant notes that this galaxy (HDF850.8) is part of an interacting pair of galaxies detected in the original HST H D F image. A l l three S C U B A observing modes were used in this area. SMMJ123653+621121 We suspect the correct counterpart is the nearby E R O (7 = 24.8,7 — K = 4.9) that has a 15 / im detection. However, the region is filled wi th sources and it is possible this is the incorrect ID. Photometry and scan-mapping observed this region. SMMJ123659+621454 8" to the east is a z = 0.762 (7 = 2 0 . 9 , 1 - K = 2.7) 1.4 G H z radio and ISO detected object. 8" to the west lies a z = 0.849 (7 = 2 1 . 4 , 7 - K = 2.9) 8.5 G H z radio and ISO detected object. This latter object has an almost detectable 1.4 G H z flux. B o t h objects have very similar radio and 15 / im fluxes, and both predict a similar redshift when using the 850 / im fluxes as a photometric redshift indicator. We cannot rule out that this is a blank field object however, and therefore only attribute an upper l imit to the radio flux. Photometry and scan-mapping observed this region. SMMJ123706+621851 It is difficult to choose among the 7 optical sources in the region, especially in the absence of any other multi-wavelength data. This too, is near the edge of the scan-map portion of the super-map. S M M J 1 2 3 7 1 9 + 6 2 1 1 0 9 There are six optically detected galaxies wi th in 8" of the 127 S C U B A position, none of which have a radio detection or K-band flux that can be used to help discern which one (if any) are the S C U B A counterpart. Jiggle-mapping and Scan-mapping were performed here. SMMJ123730+621057 A blank field aside from a possible I = 23 galaxy on the S C U B A centroid that seems to line up wi th a 3a radio blob. This is a scan-map only source. SMMJ123731-I-621857 Another blank field, very near the edge of the scan-map only region. SMMJ123736+621430 A very strong X-ray emitting, optically invisible source lies only 5" away and seems like the correct ID. Again , scan-mapping only was done in this region. SMMJ123741+621227 Though a detected radio source exists 8" to the north, the S C U B A contours prefer a very faint galaxy pair that have almost detectable radio flux. Deeper imaging is required to help determine the true counterpart. This is a scan-map only source. SMMJ123743+621325 A pair of galaxies that lie on the S C U B A contour are the best candidates, but we consider it undetermined unti l more imaging can be obtained. This is a scan-map only source. SMMJ123619+621127 The first of our 450 / im detected sources is directly on top of an I = 23 galaxy, but no other detection is obvious. This was observed wi th scanning and jiggle-mapping. SMMJ123632+621542 No compelling counterpart exists. This was observed wi th scanning and jiggle-mapping. SMMJ123702+621009 Direct ly on top of an I = 22.5 galaxy. This was observed wi th scanning and jiggle-mapping. SMMJ123727+621042 Very near a large giant ell iptical, but s t i l l too far to have it be the unambiguous ID. This is a scan-map only source. SMMJ123743+621609 No compelling counterpart exists. This is a scan-map only source. 5.4 The pathological object HDF850.1 The in i t ia l deep sub-mm survey of the H D F by Hughes et al. [91] is the single most cited S C U B A extra-galactic paper. This has helped fuel a great amount of interest in the follow up the 5 original sources, especially HDF850.1 (which we designate SMMJ123652+621227). Despite years of effort, dedicated observations, and mis-128 identifications [135],the counterpart for 850:1 has only recently been determined[114]. Al though this object is not special, or even representative of the bulk of the known S C U B A population, the amount of work being done on it warrants a short discussion. The first attempt at finding the counterpart used I R A M interferometry at 1.3mm to determine an accurate position of the source 3 [135]. Indeed, a significant detection was found coincident wi th a V L A radio source, but this was radio source was later shown not to be the same object as the S C U B A source: Extremely deep N I R imaging revealed a K = 23.5 source coincident wi th a new, very faint radio source found by co-adding V L A and M E R L I N data. This new source was then identified as the coun-terpart for both the S C U B A and I R A M source. The i f -band source was found by first removing a model elliptical galaxy light profile from an extended source in the field. Behind that source lies the faint i f -band counterpart. This el l iptical compli-cates things even further, as it possibly lenses the background object. Indeed it has long been suspected that a lens was part of the system. From the full analysis, the estimated redshift is 4.1 ± 0.5. This is constrained enough that it is possible to tune a heterodyne receiver to the appropriate frequency in order to detect redshifted C O emission. Indeed this group is currently conducting a 100 hour integration wi th the Green Bank Telescope to do just that. However, it cannot be stressed how difficult obtaining this (tentative) counterpart has been. Luckily, the majority of S C U B A ob-jects do not suffer from being in a such a complicated system, and most of the S C U B A sources we have found in the H D F - N are considerably brighter. Nevertheless, this observation only stresses the need for better angular resolution and sensitivity for sub-m m observations. Interestingly, this revised counterpart is s t i l l a radio detected E R O , which is what we would have guessed already based on the shallower observations. 5.5 Radio jet induced star formation Follow up work of the 8-mJy field has been recently been completed, and among the 30 objects recovered from that survey, a very curious source was found. Sub-mm emission was detected corresponding to a radio source wi th a very steep spectrum. Near it was another radio source with a flat spectrum, then further out along the same line another steep spectrum radio source. The radio data characterise a faint double-lobed radio source. The authors conjecture that one lobe is shocking some nearby gas and inducing star formation. A very faint / -band galaxy is also seen coincident wi th their sub-mm source. 3 IRAM observed the 2' x 2' region centred on HDF850.1, and detected only one object. 129 The V L A map of the H D F clearly shows another faint radio jet, and indeed this source has been discussed at length in Richards et al . [112]. Spectroscopic redshifts of i t and galaxies i n the area place i t at z = 1.013. A chain of galaxies at the same redshift at the top of the northern radio lobe suggests a merging system. Another hypothesis, also from the same work, is that this chain is undergoing shock induced star-formation. Interestingly, our S C U B A map has a 3.5cr detection at the top of this radio lobe, which lends some support to that theory. This source was one of two that were not considered part of our > 3.5cr detection list because it is quite near the central deep pointing, and consequently might be influenced by the off-beams of the other sources. Whether or not there is really sub-mm flux here wi l l have to wait unti l follow-up photometry work wi th S C U B A can be performed (indeed we have applied for time to do this), though it is quite a faint object and may prove too difficult to determine unambiguously. Nevertheless it is interesting to consider this class of object, as i t influences the view of the sub-mm/radio relationship. Particularly, the photometric redshift estimator is made invalid for these sources, and the two emission mechanisms are now complicated by star-formation and the radio jet. If enough of these sources exist, it would mean that targeted photometry observations of radio sources might be looking in the wrong place. VLA123644+621133 Figure 5.12: A radio jet inducing star-formation? Very faint sub-mm flux is seen coincident wi th the norther t ip of a strong radio lobe which is possibly inducing star-formation. 5.6 Redshift distribution of SCUBA sources and star formation rates We now have enough information to make crude redshift estimates of each our sources using photometric techniques. Here we concentrate on the 15 / m i sub-mm, and radio flux estimates. We have taken the model spectra shown earlier and redshifted them 130 by using Su = (l + z)Sil+z dL(z0) 2 (5.4) dL(z) where z0 is the redshift of the template (Arp220, M82, and Mkn231) and dL is the luminosity distance, which depends on a choice of cosmology (we used Q M = 0.3, Q.A — 0.7). We then calculated the predicted flux ratios as a function of redshift and plotted them in Figure 5.13 on top of our data. In general, detections at 450 /mi suggest low redshift, as past z ~ 2, the rest frame wavelength S C U B A observes at 450 jum transits over the thermal peak and stops enjoying the negative K-correct ion. Unfortunately our 450 /mi upper l imits lack the constraining power to say too much about the redshift of the sources. It is interesting to point out that the 450 /tm detections do not match any of the SEDs we use. Even if one reduces the 450 pm fluxes it is s t i l l quite difficult to fit them to local S E D templates. Indeed this is more evidence that the some of the 450 pm objects might be spurious. The 15 pm ratios drop even at low redshift since they are on the Wein side of the thermal peak, but at least we have better flux estimates. O f a l l photometric estimators, the radio/sub-mm is held i n highest regard because of the tight F I R / r a d i o correlation. Instead of calculating the expected ratio from our model spectra, we use instead the Ca r i l l i -Yun ( C Y ) estimator [47, 48] which is based on a wider range of local templates (still bracketed by the three we have used however). Since S C U B A 4 5 0 p m fluxes do not usually impose strong constraints, and since 15 pm fluxes (when available at all) can be possibly contaminated by P A H emission lines, the C Y estimator has become the standard means for deriving redshifts of radio-detected sub-mm sources. Past a redshift of 3 however, the radio/sub-mm ratio flattens out and it becomes increasingly more difficult to constrain the redshift. Therefore we shall cap the C Y redshift lower l imits to z = 3 for the sources undetected in the radio. The results are presented in Table 5.5. For the few sources that do have spec-troscopic redshifts, the photometric redshifts seem reasonable. The exception is SMMJ123650+621318, which prefers a larger redshift than what the spectroscopic measurement yields. This may mean that the identification is incorrect. 5.6.1 Star-Formation history of the Universe The major result from the last section is that the redshift distribution, though poorly constrained, is definitely concentrated past z > 1, even when using the lowest red-shift predicting estimator. The median redshift for the sources wi th stronger C Y 131 Figure 5.13: Photometric redshift estimates of sub-mm sources. The top two curves show the behavior of the 15 /mi and 450 /tm flux ratios (compared to the 850 /mi flux) for three S E D templates: Arp220 (solid), M82 (long-dashed) and Mkn231 (short-dashed). The bottom curve simply plots the Ca r i l l i -Yun relationship which is used for radio observations of 850 /mi sources. The thick solid line represents the mean of several local templates, and the thin lines are the la scatter in the redshift estimate. 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This takes us into an interesting region of time, where the star-formation rate is not well determined. Al though the conver-sion between sub-mm flux and star formation rate contains many parameters, each of which is only known to wi thin a factor of a few, it is worth estimating this quantity. To do this, we follow the prescription described in Chapter 1. We use the 850 / im flux and redshift to fix the rest luminosity at A*m. Assuming an optically th in greybody wi th T = 3 8 K , B = 1.3, (the S L U G S result [21]) we extrapolate this to estimate the rest frame 60 fxm luminosity which is then converted to a S F R . It is likely that we are underestimating the luminosities by factors of a few, because the S E D s of most known sources do not drop as fast as a Planckian spectra short-ward of the peak. The results are most strongly dependent on temperature, wi th luminosities changing by a full order of magnitude for even a factor of 2 change i n T d . S t i l l , the inferred luminosities and star formation rates are very high, placing them securely in the U L I R G category. To convert this into a star-formation rate density, we sum up the S F R for each of the our 19 > 4a and divide by the co-moving volume between z = 1 — 3. We find that the S F R D = 0.012 ± O . O O 5 M 0 y r - 1 M p c - 3 across this range. The error is based simply on Poisson statistics. Div id ing this up into smaller redshift ranges means having too few objects per bin, and therefore the estimate is quite noisy. Nevertheless we find that the value is quite constant between z =1-2, 2-3, and 3-4. This estimate is a lower l imi t , 'because we are neglecting a l l the sources fainter than our detection threshold. It also neglects the many sources we missed due to completeness, so calculating a correction factor is not straightforward. Using the source-count model from the last section, we estimate we need to mult iply our estimate by 21 in order to account for a l l sources brighter than 1 m J y The reader is free to view this result, plotted along others in Figure 5.14, wi th some skepticism (and rightly so). The major point is that, using reasonable extrapolations and conservative redshift estimates, it is difficult to conclude that the star formation rate was lower in the past than it is today. Note that the optically determined high redshift estimates are based on drop-out techniques which select only a narrow redshift range. Sub-mm observations could potentially constrain the S F R past z J> 1 i f the number of sources wi th known redshifts is increased. 134 Figure 5.14: Star formation rate density over time. We plot our result (solid cir-cle) against measurements determined by optical surveys : L i l l y et al . [136] (open triangles), Steidel et al.[137] (open circles), Connolly et al . [138] (open pentagons) and mid-IR observations from Flores et al . [139] (open triangles). The dotted line is a model prediction from Smail et al . [39] assuming luminosity evolution, and the dotted line is based on a model including merging galaxies. 135 5.7 Summarizing the SCUBA population Using the analyses in the previous section, we are now able to summarize the entire set of S C U B A sources we have detected in the H D F - N (see Table 5.6). Concentrating on the secure (> 4cr) S C U B A sources, we find a ~ 50% overlap between S C U B A sources brighter than ~ 5 mJy and radio detected sources brighter than ~ 45/ iJy. This is in line with results from Ivison et al . [140], Chapman et al. [95], and Barger et al . [93]. In almost each case the radio source is detected in the optical, and contrary to popular belief some of them are bright enough to obtain spectra using ground based 8-m telescopes [140, 95]. This fact is only recently being exploited to obtain redshifts for this subset of sources. Significant improvements in radio sensitivity are required in order to detect the fainter S C U B A sources. Only ~ 25% of our S C U B A sources have identified X-ray counterparts, and 2/19 (~ 10%) are likely A G N based on estimates of the rest frame X-ray luminosities of these sources ( > 1 0 3 9 W ) . A s noted in Ivison et al . [140] based on the fraction of A G N energy emitted between 0.5-8 keV, the A G N contribution to the F I R flux is insufficient to explain the observed sub-mm results [141]. Therefore star-bursts must be responsible for the bulk of F I R energy budget even i f many (or all) S C U B A galaxies have a supermassive black hole at their core. Indeed, the stacking results seem to verify the presence of dust obscured A G N activity in our S C U B A detections. The stacking analysis of optically detected sources clearly demonstrates a trend wi th increasing redness. A s with the 8-mJy results[140], roughly one-third of our S C U B A objects seem to have an E R O counterpart. Results from [40] show that the surface density oi K > 19.5 E R O s is ~ 2400 d e g - 2 . We have seen in the previous chapter that the 850 / im number counts give a similar density of S C U B A objects for N(^3 mJy) , which consist of 3% of al l S C U B A sources brighter than 0.1 mJy. Therefore currently detected E R O s wi th S C U B A counterparts account for only 1% of the entire sub-m m population. It is interesting to note that sub-mm observations of 27 E R O s in a photometry programme wi th S C U B A failed to detect any of them at 850 / /m [38]. Th i s is difficult to reconcile wi th the results from the H D F - N survey presented here, as well as many other recent observations. O f course we may have biased our indentifications by our prejudice that E R O s are S C U B A bright, and therefore the fraction of true identifications is much lower. S t i l l , the low surface density of E R O s means that it is difficult to find a nearby counterpart by chance. Results from other surveys find a similar relationship between S C U B A sources and E R O s , so the case is strengthening that a real correlation exists. More observations are required to fully 136 T3 '111 0000 •AT , 3. >, IS 6 • i-H O O IDf cot cS IS . \ CO j oi B! fa .2 i, a a o n CO -p-. tfOO » O H J CL. o •> <•> ^ — fa J** fa CO o* t i g j , ^ ^ H Z O O I O B O B faOoSoSo.oS.2oS.iS 0 < H > 0 H O > O O X o o s o c s o OS OS o o OS OS o o o OS X OS OS TP TP TP TP TP TP "TP Tp TP TP Tp | 6 ® d d c 5 6 6 6 d 6 ^ 2 0 ^ 0 0 0 ^ V C N V W W W V O 0 V d V V V r II II II O C N o © o <? <° o o O O O + I © o CN CN CN © CN CN o © o © CN CN V V V co W V V V f ~ i O i o © T p w c N i i b - © r -| C l C i C O © c O 0 0 b - ~ © T p T p v v v v v v v S v v v V V V V V V V V co CO . . . 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Almost half of our sources have an undetermined counterpart, clearly demonstrating how difficult i t is to make secure identifications. It can be argued that some of the identifications we have made here are wrong, but at least the radio/sub-mm results lead to the same conclusion that S C U B A sources are typically at high redshift. 138 6: Discussion The previous chapters represent the cutting edge of research for sub-mm astronomy. Though we have demonstrated the importance that this population of objects has on our understanding of the Universe, there is clearly a great deal more to accomplish. In this chapter, we wi l l apply everything presented thus far and recast it in the context of future work. We wi l l follow the order that this thesis has taken, by first commenting on the more technical issues related to sub-mm data and S C U B A in particular. Next we wi l l review the properties of the S C U B A sources, and speculate on the nature of the sub-m m population we have detected. From there, we wi l l address the next generation of sub-mm observations being planned or in some cases already underway. In particular, by the time this thesis is in press, a major venture wi l l have started wi th S C U B A to address issues that we have not yet been able to do wi th surveys as small as the one presented here. A s clearly demonstrated in this thesis, measurements at sub-mm wavelengths alone are insufficient to understand these objects, and therefore we shall discuss several new ground- and space-based observatories that have the necessary wavelength coverage and sensitivity to directly apply their results to the study of dusty galaxies. 6.1 SCUBA/sub-mm data collection and analysis 6.1.1 Sky correction Meaningful deep observations at sub-mm wavelengths are possible only when atmo-spheric effects are removed properly. A t the hardware level this necessitates the chopping and nodding procedure to contend wi th the strong emission on scales of the array. This works, but at the expense of a more complicated data set. For some of the new sub-mm cameras being developed, it is hoped that chopping can be bypassed altogether; essentially the array is rapidly jiggled such that several pixels see the same patch of sky. W i t h fast enough readout rates, and efficient real-time firmware, the hope is that the flux from the source and sky can be separated using matr ix tech-niques such as those described in Chapter 3. This was attempted (unsuccessfully) several years ago for S C U B A (i.e. the D R E A M mode[142]). 139 In software, extinction is corrected for by using the best guess at the opacity. Cur-rently, this is done by interpolating C S O tau measurements taken every ten minutes, at another wavelength, in a different area of sky, and extrapolating them to the 450/850 /mi frequencies. It would be very desirable to have instantaneous sampling of the opacity directly along the line of sight of the observations. To that end, the J C M T has commissioned a water vapour monitor due to be in operation near the end of 2002 [143]. This is a total power radiometer mounted at the top of the secondary mirror, and is sensitive to a water line at 183 G H z . Provided a relationship between this and the extinction factor at S C U B A wavelengths can be found (as was done for wi th the C S O ) , this device would assist wi th observations which would otherwise be difficult to perform (eg. ultra-long scans, which pass through a large swath of sky, and polarisation, which requires extinction correction accurate to the few percent level). However, it is worth noting that extrapolating observations at 1 8 3 G H z to 350 G H z (850 /im) and 650 G H z (450 /tm) wi l l possibly be subject to the same scatter (or worse) as seen between the C S O (225GHz) and S C U B A channels. We already know that there are times when even the 450 and 850 /tm noise levels do not corre-late well at a l l even though the extinction estimates show less scatter. In any case, since this device wi l l point in the same direction as the science data is being taken, it should prove very useful in monitoring the sky conditions during an observation. 6.1.2 On Scan-mapping versus Jiggle-map mosaics for large surveys This thesis describes the most carefully analysed S C U B A scan-map data ever taken, and thus it is important to discuss the lessons learned wi th this observing mode. Most extra-galactic sub-mm surveys previously done use a series of jiggle-maps to fully sample a large area of the sky. To ensure uniform noise coverage, the number of integrations on a particular jiggle-map field has to be adjusted according to the weather at the time of observation. Even so, overlap regions between neighbouring pointings mean that some parts of the map wi l l be more heavily sampled than others. The noise level across a scan-map composed of individual scans is very uniform, since each pixel is sampled by many different bolometers, whose noise is close to constant throughout a scan. One advantage of jiggle-mapping is that it is the most heavily used S C U B A observing mode and thus is already well understood. Also, it is known that the observing efficiency, e (the ratio of time spent collecting data to elapsed real time) for the jiggle-map mode is higher than for scan-mapping, but this is a slightly misleading measure for reasons discussed below. 140 6.1.2.1 Efficiency for point sources In Section 3.3 we described how to measure fluxes of point sources by fitting the beam pattern to the map. We denote the reduction i n noise by fitting the beam pattern, as opposed to fitting the positive beam alone, by £. In the case of scan-mapping, where the beam weights are +1 and —1, we have fs = V2. The beam weights for jiggle-mapping, —0.5, +1, —0.5 lead to £j = \JZ/2. We have determined that the observing efficiencies are ej ~ 0.77 and es — 0.52 for jiggle and scan-mapping respectively (using standard sizes and chops). The nature of the loss of efficiency in both modes is related to the time needed to read out data after each exposure, and set up the next one. One factor is that in the scan-map mode, the sky is sampled 8 times more often than in jiggle-mode, and hence the readout time is longer. Other reasons for the efficiency difference are st i l l being explored. The overall sensitivity to point sources is oc £ e ~ 0 ' 5 and, given the numbers above, the jiggle-map and scan-map mode are found to be almost equally sensitive for detecting point sources. 6.1.2.2 Source recovery rate A t the 3o~ = 8 mJy level, one recovers approximately one source per 8 hour observing shift in a jiggle-map observation. Thus one is able to begin the lengthy process of multi-wavelength follow-up after only a short time. In scan-map mode, one finds sources in order of brightest to faintest, thus the recovery rate is non-linear (essentially tracking the number counts curve). One requires a significant investment in observing time before even the brightest sources are found. A t the end of the programme, a jiggle map and scan map campaign wi l l produce essentially the same number of objects, since the same area and depth w i l l be reached in a similar amount of time. 6.1.2.3 Scan/Jiggle-map Comparison The advantage of using scan-mapping over jiggle-maps in studies of the clustering of S C U B A sources is that the latter mode is completely insensitive to scales larger than the array size. This , coupled with the uniform noise level and nearly equivalent effective sensitivity should make scan-mapping the preferred mode when planning large field surveys. O n top of that, the increased sampling rate allows for the possi-bi l i ty of more fully characterising the temporal behaviour of the sky in order to more effectively remove it. It is also worth noting that the efficiency of the scan-map mode 141 may possibly be increased by at least 25% by introducing a double-buffer scheme that allows scan data to be read out from one scan while another is in progress. The S C U B A engineers are currently investigating this. From the results of the work presented here, we conclude that the scan-mapping mode is a reasonable one to use: There seem to be no pointing problems introduced by the rapid motion of the telescope across the sky (though it does effectively l imi t the pixel scale to 3"). 1/f type noise induced by scanning the telescope across different patches of sky are manageable by standard sky subtraction and a simple base-line removal from each scan. The situation at 450 fim is more complicated, as it is more sensitive to changes in atmospheric emission. However, more sophisticated analysis methods, where the power spectrum of the noise is also estimated, may improve things here as well. This latter point is an important one, since most of new sub-mm cameras being buil t are expected to use scan-mapping as their primary observing mode. Hence it is worth keeping an open mind to the amount of effort which might be required to adequately reduce such data. 6.1.3 Observing strategies Almost a l l groups that have performed survey work wi th S C U B A realize that using a single fixed chop complicates the source extraction process. In the in i t ia l surveys, using a single chop was justified, since just finding sources was difficult, and uncov-ering an unambiguous multi-beam pattern was re-assuring. However, now that we are more comfortable with the data S C U B A produces, it is possible (and desirable) to employ multiple chop configurations in order to deconvolve the map and recover sources unambiguously. Not only that, it w i l l allow information to be extracted from the faint, undetected sources that fill in the space between sources. Indeed, this philosophy is being applied toward the next (and possibly last) major survey to be conducted by S C U B A , the Half-Degree Fie ld Survey. This is one contribution this thesis has made to the community: based on the map-making techniques developed here, this survey wi l l employ a well-connected chop configuration that w i l l allow a robust deconvolution to be performed. 6.2 What we have learned about sub-mm sources In this section we review the major conclusions from Chapter 4 and 5 and use them to discuss the role S C U B A galaxies play in helping us understand galaxy evolution. 142 The reader may wish to review Section 1.6 which outlined the goals that sub-mm surveys wish to accomplish. 6.2.1 Resolving the FIR background into sources The F I R background is constrained by the F I R A S data from C O B E , which surveyed the sky between 100-5000 /xm. Starting with the calibrated F I R A S data, the C M B , which is t ightly constrained by the data to be a 2.728 K e l v i n blackbody, is removed. The residual is a combination of the F I B plus galactic emission. Different groups [10, 11, 12] use different assumptions to estimate the contribution from our galaxy. A warm, diffuse galactic component could be mistaken for an extra-galactic background, and hence al l the fits to the F I B may be too large. Alternatively, i f the F I B spectrum is close to the shape of the galactic spectrum, it w i l l have been subtracted out and estimates of the F I B would be too low. The reported error bars to the F I B are statistical only, and do not reflect these extreme cases. Therefore it is useful to report the background derived by S C U B A independently of the F I R A S background. However, based on the currently favoured estimates from F I R A S , our sources brighter than 2 m J y account for ~40% of the energy from the F I B . We stress that there is s t i l l significant uncertainty in both the numerator and denominator, and this should be used only as a rough guide. Reasonable extrapolations of the number counts to roughly 0.1 m J y could reproduce the background entirely. The 850/ im number counts, if better constrained, could place a l imit on the F I B to rival F I R A S . It is interesting to note that the number of sources detected here (i.e brighter than 2 mJy) account for only 2% of the sources brighter than 0.1 mJy. The 450 / im background is less constrained. From the review by Hauser and Dwek [4], we expect the integrated 450 / im background to be (5.8 ± 2 . 0 ) x 10 4 m J y d e g - 2 . Based on the crude estimate of the counts determined in Chapter 4, we recover only 0.2% of the 450 / im background, clearly demonstrating the importance of making detectors sensitive to shorter sub-mm wavelengths. Nevertheless these detections, along wi th their estimated redshifts and implied lumi-nosities verify that there are more U L I R G S in the past than there are today. S C U B A sources are a therefore an important piece in theories of galaxy evolution. 6.2.2 How does the star formation rate change over time? Before describing how better constraints on sub-mm redshifts are important to fully characterise the population, we discuss what we have learned already based on our 143 more crude estimates. Firs t , using primari ly the Ca r i l l i -Yun redshift estimator, we estimate a median red-shift of ~ 2 for the sub-mm sources detected in this survey. In some cases photometric information from other wavelengths and/or spectroscopically determined optical red-shifts confirm the results. Note than in many cases, determining the redshift bound on a source depends on the non-detection of a 850 pva. source i n another band. It w i l l be necessary to improve the sensitivity of radio and sub-mm instruments to counter the positive K-correction at other wavelengths and detect these distant sources. Using these crude redshifts, we calculated the star-formation rate density implied by our S C U B A sources, and showed that it was consistent wi th other high redshift estimates determined from optical surveys. In Chapter 1 we indicated that finding out when most of the stars in the Universe were formed is one of the things sub-mm surveys wish to answer. B y re-arranging the Madau plot shown in Figure 5.14, we obtain a means to do just that. In Figure 6.1 we plot what essentially amounts to the number of stars produced in a given epoch. The curve peaks somewhere between a redshift of 1-2, indicating that most stars were formed in that time. The data is not sufficiently constrained to draw detailed conclusions, but i t appears that perhaps up to 30% of al l stars in the Universe were formed in S C U B A galaxies. Differing evolutionary models that describe the role of S C U B A galaxies cannot cur-rently be discriminated against due to our ignorance of the precise form of the redshift distribution. To overcome this requires a method better than those described in this thesis for determining redshifts. The approach thus far is to either constrain the red-shift photometrically, v ia sub-mm or radio fluxes, or to identify an optically bright counterpart for which one can obtain a spectrum. The former is biased by our extrap-olation of local S E D templates to the high redshift Universe, and the latter is biased toward objects that are optically detectable. To make further progress effectively requires both increased sensitivity for the multi-wavelength data and finer angular resolution of the sub-mm maps in order to unambiguously identify the counterparts. Nevertheless, unti l we can do better, photometric estimation is the only option. A great deal of effort is being directed toward this end, and is the focus of much current debate. The procedure, as described in Hughes et al . [46] involves estimating the redshift using each of several S E D templates drawn from the local Universe. The scatter in these estimates is used as an error estimate, and it has been shown to be on the order of ± 0 . 5 in z. There is an an obvious possible bias here: Are the local templates representative of the high redshift Universe? Unfortunately to answer this question, one requires the redshift and SEDs of distant galaxies to compare wi th , but 144 1 h 0.1 10 Present Epoch (Gyr) Figure 6.1: History of star production. We have altered Figure 5.14 to roughly measure the number of stars produced in S C U B A galaxies. The horizontal error bars are suppressed for clarity. Al though the data is quite scattered, the number of stars produced by S C U B A galaxies is significant when compared wi th those produced recently (below redshifts of 2). 145 that is exactly what photometric redshift estimation is meant to do in the first place. Progress is being made by obtaining optical spectra for a subset of the S C U B A population that have (reasonably likely) optical counterparts. However the subset of these sources which are optically bright enough for spectroscopy may also be a biased group. Despite these reservations, comparing the spectroscopic redshift against sub-m m and radio fluxes, should allow us to get a handle on how dust properties evolve wi th cosmic time (if they do at all), and thus improve the templates. A more productive, and direct approach is to measure C O (or other) spectral lines in the sub-mm. Currently this is quite difficult because the bandwidth of heterodyne receivers is quite narrow. In some cases where the redshift is constrained by the F I R / r a d i o estimator, the number of receiver tunings required to cover the redshift range is small, and one can attempt to measure these lines. To date, less than a dozen S C U B A sources have a measured C O detection. However, this is likely to increase given the increasing interest in pinning down the S C U B A redshift distribution and the availability of new detectors. 6.2.3 Are high redshift IR bright sources the progenitors of modern day ellipticals? The star-formation rates derived in Chapter 5 are large enough to generate massive ell iptical galaxies provided the burst lasts for ~1 G y r . The redshifts of these sources also imply that the systems that evolve from S C U B A galaxies w i l l be old by z ~ 1. This , and the crude equality of the volume densities imply that the S C U B A sources we observe wi l l evolve into elliptical galaxies. This argument, discussed in Scott et al . [54], is something we mentioned in Chapter 4, but which we can strengthen here wi th the redshift constraints derived in Chapter 5. Note that the connection wi th E R O s is also involved here. Recall that E R O s are either a z ~ l el l iptical galaxy, or a heavily obscured star-burst galaxy. Our results show a general increase in sub-mm flux as a function of optical redness. Indeed, roughly a thi rd of our sources appear to have an E R O counterpart. S t i l l , many of the E R O s in our survey area are undetected in the sub-mm, implying that they have li t t le or no dust emission. If S C U B A galaxies are the progenitors of ellipticals, one would expect to see both of these results. A useful study would be to target a large sample of E R O s wi th known (and diverse) redshifts. 146 6.2.4 Do sub-mm sources cluster? Measuring a clustering signal from S C U B A sources is also needed to secure the ellip-t ical progenitor hypothesis. Because ellipticals are observed to be clustered, S C U B A sources must be as well since they formed in the same peaks of the density field. To do this requires a survey that contains an order of magnitude more sources than those detected here in order to lower the errors. It also requires the abili ty to crudely sepa-rate sources into redshift bins. There is no apparent correlation between sub-mm flux and redshift from our results, which is expected due to the negative K-correct ion. Wi thout separating sources, the projection of sources across a wide redshift range wi l l "wash-out" the signal. It is also important to increase the angular resolution of sub-mm surveys. The scale at which significant clustering exists for E R O s and L B G s is roughly 30", which is close to the size of the S C U B A beam. This w i l l not strongly influence determinining a cross-correlation between S C U B A galaxies and other samples, such as the X-ray analysis presented in Chapter 5. There we found, after a very careful treatment of systematic effects, that S C U B A sources and X-ray detected objects in the H D F - N are not clustered wi th eachother. This is at odds with results from A l m a i n i et al . [119] who detect a signal and conclude that S C U B A sources and X- ray sources are tracing out the same large scale structure. To resolve this issue requires a larger survey area which contains more sources in which to perform these statistical tests. 6.2.5 What are the multi-wavelength properties of sub-mm sources? Even wi th C O line detections, increased angular resolution would allow us to isolate counterparts at other wavelengths and consequently let us explore the l ink between S C U B A sources and other high redshift classes of objects. The only way to accomplish this is through interferometry, though at present the only facility that really has the required sensitivity is the I R A M array operating at 1.3 mm. W i t h i n the next 10 years however, at least two more sub-mm arrays wi l l be on-line. Improvements in radio interferometry wi l l help as well: for example, since radio emission from A G N is confined to the region directly around the black hole, while star-bursts generate diffuse radio emission on kpc scales, we would be able to better understand the power sources for the sub-mm luminosity i f we could resolve the galaxy. Here we review the issues associated with counterpart identification in current sub-m m surveys. S C U B A positions are influenced by the S N R and confusion, wi th the latter affecting mainly the faint sources. We have shown that offsets as large as 30% 147 of the F W H M of the beam can be expected for 850 pm S C U B A surveys near the confusion l imit . Increased sensitivity and angular resolution are the only ways to mitigate these effects. A n important question to address is whether or not other phenomenon might in-fluence the determination of a S C U B A counterpart. Recently, Chapman et al . [144] have investigated the effect of galaxy-galaxy lensing on the bright S C U B A popula-tion. The idea is that sub-mm sources along the line of sight of a foreground galaxy wi l l be amplified, making them easier to detect, and then incorrectly associated wi th the foreground. If a redshift of this counterpart were determine spectroscopically, an incorrect, and low, value wi l l be tagged to the sub-mm source. More work needs to be done to fully characterise this, but they estimate that up to 5% of a l l > 10 m J y S C U B A sources are lensed by a foreground source. We have also investigated how clustering between S C U B A sources and those at other wavelengths may influence our counterpart choice. Recall ing that the probabili ty over random of finding a nearby source goes as 1 + w{6), we can adjust our P-stat ist ic given the highest value for w(6). In the cases of the X- ray and L B G population, the null (or at least very low) detection of w(9) suggests that these determinations are not influenced by clustering. The radio band is quite different in this respect, as 50% of our sources have a radio counterpart. To determine unambiguously that radio and S C U B A emission are coming from the same object requires better angular resolution. Final ly , one might expect that merger events could lead to ambiguity i f one of the pair was optically invisible. Indeed this has already been seen in a handful of L B G galaxies where the S C U B A flux was later found to be coincident not wi th the L B G , but rather a nearby optically faint red galaxy. The sources found in this thesis exhibit a wide range of properties. Is there a way to unify these different classes of S C U B A objects into a common framework? It may be that a l l S C U B A galaxies evolve in similar ways, but without knowing the redshifts and multiwavength properties of sources it is difficult to tell at present. 6.3 Current or upcoming Sub-mm programmes Over the past five years, tremendous progress has been made in understanding the dust-obscured high redshift Universe. This has inspired the course of new observa-tions and new detectors, which are coming into fruition now. S C U B A , though s t i l l the instrument primari ly driving the field, is now sharing the spotlight wi th a host of new detectors and telescopes dedicated to the sub-mm. In this section, we describe 148 a series of observations being taken by S C U B A and others that are geared toward advancing our understanding of these IR luminous galaxies. 6.3.1 SCUBA multi-wavelength observations It has been unfortunate that the longer wavelength channels S C U B A provides have been dysfunctional throughout almost the entire lifetime of the instrument. Though they are single element photometers, the sky at 1.1, 1.3, and 2.0 m m is much more transparent than at 850 /xm. Mapping of sources is difficult, but following up known sources would provide a stronger constraint on their redshifts and dust properties. O n the shorter end, the 450/xm array has not been able to provide particularly useful data for the low S N R work described here. Not only is the array more sensitive to atmospheric conditions, but the beam response is also highly dependent on the surface accuracy of a dish that changes shape over the course of an evening. The flux calibration is only 30% accurate, and coupled wi th an uncertain beam-shape combining data over several observations becomes very difficult. Note that for bright objects that do not require lengthy integrations, the 450 /xm data are much better behaved. Recognizing this, the S C U B A designers have decided to repair the filter wheel during the scheduled upgrades programme in July 2002. If successful, S C U B A wi l l be able to provide al l of its specified photometric channels. The upgrades also promise to modestly increase the overall sensitivity for al l channels. 6.3.2 The Half-Degree Field BLAST/SCUBA Survey A n extended survey of the Lockman Hole and Subaru Deep F ie ld is about to be conducted wi th S C U B A . The total coverage wi l l be 0.5 square degrees wi th an R M S point-source sensitivity of 2-3 mJy. Observations commence in August of 2002, and completion of the survey is anticipated in 2005. This represents a factor of ~15 increase in area compared to the H D F - N survey presented in this thesis. It w i l l be the largest extra-galactic sub-mm survey ever conducted, and has over 50 scientists involved. A m o n g the primary goals of the survey is to unambiguously measure a clustering signal in the 850/xm sources. In order to secure the massive amounts of time require to do the survey, the project agreed not to use the best grade of weather. 850 /xm observations can be conducted quite reasonably in grade 2 or 3 weather 1 . Thus 1 Weather grades range from 1 through 5, with the higher numbers representing more water vapour in the atmosphere. SCUBA at 850 /mi can be used in grades 1-3 weather, but 450 /xm observations 149 the survey wi l l lack the short wavelength fluxes from S C U B A that would be necessary to constrain the redshift distribution of the nearly 250 sources that are estimated to be uncovered. To that end, the Balloon-Borne Large-Aperature Sub-mm Telescope ( B L A S T ) [145] wi l l provide 500 pm fluxes. B L A S T is expected to have at least 4 flights using the bolometer array which is the prototype for the S P I R E instrument on Herschel. The first of which wi l l host a 2.0m mirror and operate at 550 pm only. Later flights wi l l be long-duration, employing circumpolar winds to stay afloat for several days (even weeks). These flights w i l l also use the full multi-spectral camera, able to take measurements at 250, 350, and 550 pm, and possibly using a larger (~ 3.0 m) mirror. The number of bolometers for each of the arrays is 144, 96, and 48 respectively, wi th a F W H M beam size of 34", 47"; and 73". The major advantage in flying from a balloon is that one is above the atmospheric water vapour which is the primary source of noise for these observations. B L A S T claims to be able to provide a N E F D of only ~ 1 5 0 m J y H z - 0 - 5 , thus allowing it to reach the confusion l imi t quickly. In a typical 6 hour flight, B L A S T is expected to significantly detect over 360 galaxies in a 3 square degree patch. It is interesting to compare that value to S C U B A , which has found roughly the same number of galaxies over the past 4 years. 6.3.3 SHARCII The C S O is currently commissioning the S H A R C I I bolometer array [146]. This em-ploys Sil icon Pop-Up Detector ( S P U D ) technology to provide a filled array. The array and telescope, which has exceptional surface accuracy, is optimised for use at 350 pm. Provided the weather allows for an extended observing programme, S H A R C I I should be able to provide short wavelength fluxes to compliment the known S C U B A 850 pm sources. Coupled wi th spectroscopically determined redshifts, the sub-mm fluxes can be used to constrain dust temperatures and emissivities, and therefore determine how these properties evolve wi th time. The importance of such observations cannot be understated: al l current models or photometric redshift estimators rely on S E D templates derived from the local galaxies. If SEDs are different in the past, these assumptions become invalid and introduce a bias. In principal, B L A S T can do the same thing much faster, but S H A R C I I provides smaller beams (11") and can run year round depending on the weather. S H A R C I I wi l l attempt a "no-chopping" mode of operation. If this technique proves too difficult, it w i l l resort to classical chopping can only be performed efficiently in grade 1. 150 strategies. 6.3.4 BOLOCAM and MAMBO Also on the C S O is the B O L O C A M instrument [59]. Th i s is a 144 element array that is sensitive to longer wavelengths (2.1, 1.4, or 1.1mm). After in i t ia l engineering difficulties, B O L O C A M is now running, and is beginning to produce results. In particular, measurements are being made of the SZ effect for several galaxy clusters. M A M B O [57] is a very similar instrument wi th the same number of array elements and wavelength ranges. It is currently working at the I R A M 30 m telescope, and scientific results beginning to come out now. 6.3.5 IRAM Interferometry The Plateau de Bure Interferometer has demonstrated an abil i ty to obtain high res-olution 1.3mm maps for the brightest of S C U B A sources ( ^ 8mJy) . In a number of cases this has provided the much needed positional constraint required to identify a S C U B A counterpart. However, the sensitivity is st i l l quite poor, and only a handful of S C U B A sources have been detected wi th I R A M . Nevertheless, interferometry is absolutely required in order to overcome the large beam sizes current telescopes are restricted to. 6.4 Future Sub-mm instruments Since results from S C U B A highlighted the importance that dust plays on our un-derstanding of cosmology, bolder new instruments and telescopes were proposed to achieve the beam-sizes and sensitivities required to significantly make progress. These are long time-scale projects that require years of development and construction. Here, we provide a terse overview of the many projects actively underway, even though they w i l l not be available for several years. 6.4.I JCMT and SCUBA2 Bui ld ing on the reputation, impact, and lessons learned from S C U B A , a next genera-t ion sub-mm camera is being built to succeed it . S C U B A 2 wi l l be a wide-field (8' x 8') camera that uses a dual fully sampled bolometer array wi th several thousand pixels to measure the sky at 450 and 850 pm. Of course the beam size, which is dependent on the diameter of the telescope, is the same, but the time saving gained by not having 151 to jiggle means that S C U B A 2 can reach the confusion level faster than S C U B A . The atmosphere is s t i l l the l imi t ing factor, but S C U B A 2 hopes to employ the same rapid-jiggle (non-chopping) mode that S H A R C I I is testing. Overall , S C U B A 2 promises a factor of 1000 in mapping speed (source recovery rate) over the original. S C U B A 2 , should be on the telescope in late 2006, which is compatible wi th the time-lines for many of the other major telescopes/instruments being built . 6.4-2 The Large Millimetre Telescope A 50-m telescope is currently being built atop the 16,000 foot volcano Le Negra, near Puebla Mexico. The L M T is a joint project between UMass and the I N A O E . The telescope is being optimised for work at millimetre wavelengths, and a host of new instruments are being developed to take advantage i f it. B O L O C A M , and later B O L O C A M 2 are meant to be the continuum mapping in-struments. The designers claim that the original 50-hour jiggle-map integration on the H D F - N wi th S C U B A can be done in 1 minute wi th the L M T to the same sensi-tivity. In a l l , the L M T promises to be able to detect 1000 times as many sources as S C U B A in an equivalent amount of time. A n ultra-wide band heterodyne receiver, called "The Redshift Machine" is also being developed. It is a special purpose line receiver wi th 35 G H z bandwidth to be used solely for the detection of high redshift C O lines. Past a redshift of ~ 2, the 115 G H z spacing between C O lines is compressed to < 35 G H z , meaning that the redshift machine w i l l always be able to see at least one line. Whether or not that line is actually strong enough to be detected is another issue, but such an instrument is clearly a step in the right direction. W i t h its large dish, the L M T beam-size wi l l be on the order of 6", meaning the confusion l imi t w i l l be much lower than for S C U B A . One disadvantage to the L M T is the site: the summer months are particularly wet, thus rendering the atmosphere opaque across the L M T observing bands. The L M T is meant to be taking data in 2005-2006. 6.4-3 Interferometry with SMA/ALMA The Atacama Large Mil l imeter Array ( A L M A ) is the most ambitious mm/sub-mm telescope project ever devised. 64 12-meter antennas w i l l be used to image the sky between 350 psm and 10 m m with a resolution measured in units of milli-arcseconds. The site is located at Llano de Chajnantor, Chile, at an elevation of 16,400 feet, and 152 provides stable and dry atmospheric conditions almost year round. This telescope w i l l allow us to probe the dust properties on sub-galaxy size scales, and w i l l provide unambiguous identifications of counterparts. However, we have to wait unt i l at least 2010 before A L M A is operational. In the meantime, the Smithsonian Mil l imeter Array ( S M A ) atop Mauna Kea , is nearing completion and should be taking data by 2005. Consisting of 8 6 - m dishes, the S M A w i l l cover the wavelength range 350/ /m-1 .3mm with a resolution ranging from 0.1 "-5.9" depending on baseline and wavelength. There are additional plans to l ink it wi th the C S O and J C M T , which would enhance its collecting area and baseline coverage considerably. 6.44 SIRTF/SOPHIA The M i d - I R wi l l experience an influx of data when the Space Infrared Telescope Facility is launched i n early 2003. This is the last of four N A S A "great observatories", and considerable expense and effort have been directed toward providing the best mid-infrared data ever obtained. O f particular interest to the issues this thesis has touched is the M I P S instrument, which is sensitive to 24, 70, and 160 / im. Combined wi th X- ray and sub-mm data, SIRTF can address the AGN/s ta r -bu r s t problem. N A S A is also modifying a Boeing 747 to host a 2.5 m mirror that w i l l operate in the mid-far Infrared well above the layer in the atmosphere responsible for the bulk of the absorption at these wavelengths. This telescope is named S O P H I A (Stratospheric Observatory for Infrared Astronomy), and together wi th SIRTF these two missions wi l l help understand a frequency range that has remained largely unexplored since IRAS. 6.4.5 Herschel(FIRST)/Planck The Herschel Space Observatory (formerly known as F I R S T ) w i l l use three instru-ments to take images and spectra of sources emitting radiation between 60-670 /xm. The S P I R E instrument has already been mentioned via the discussion about B L A S T , which is flying the S P I R E bolometer array prototypes. S P I R E also consists of an imaging Fourier transform spectrometer, thus offering medium resolution spec-troscopy of selected targets. S P I R E is the most directly relevant instrument for extra-galactic sum-mm astron-omy. The other two systems are P A C S , which is another imaging and spectrometer device (sensitive to 75-170 /xm) and HIFI , a high spectral resolution heterodyne re-153 ceiver operating between 160-625 pm. The restriction to fly small mirrors (in this case 3.5 m) means that the beams wi l l be large, but the unprecedented sensitivity wi l l offset that disadvantage. Herschel wi l l be launched after 2007 and wi l l take up orbit at the Earth-Sun L2 point, which should provide an extremely low background environment. Planck is an all-sky C M B experiment that is going to be launched wi th Herschel in the same rocket. Its primary mission is to obtain full sky maps at wavelengths relevant to the understanding of small-scale C M B anisotropics. However one of these channels w i l l be at 850 pm. Though the sensitivity (la ~ 20mJy) and 5' beam-size w i l l not be optimal for sub-mm motivated cosmology, Planck w i l l nevertheless provide a complete sky sample of every bright S C U B A source. 6.5 The Future of the HDF-N The H D F - N has proven to be an excellent region of sky to study in order to understand the high redshift Universe [90]. After seven years of intense scrutiny by almost every major telescope, the H D F - N is st i l l being targeted. Chandra is about to take another Msec exposure of the region, thus making the X-ray constraints even tighter. The new HST Advanced Camera for Surveys (ACS) instrument is about to take a deep exposure across U B V I R bands to a depth across the entire flanking field region rivaling that of the original 2' x 2' HST image that started everything going in the first place. 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D . thesis, C a m b r i d g e / M R A O , 1998. [144] S. C . Chapman, I. Smail , R . J . Ivison, and A . B la in , M N R A S , submitted, (2002). 162 [145] M . Devl in , in Deep millimeter surveys : implications for galaxy formation and evolution, Edited by James D. Lowenthal, and David H. Hughes. (2001), p. 59. [146] C . D . Dowell et al., American Astronomical Society Meeting 198, 1 (2001). 163 A: SCUBA Analysis Notes Here we present some supplementary information regarding the pre-map making analysis of data collected with S C U B A . W i t h a few exceptions, the prescription is similar to that found in the S U R F manual [61]. A.l Converting raw data into a calibrated time-stream For each observation, we perform the S U R F task R E D U C E - S W I T C H . This takes the difference data from each of the two nod positions and combines it to provide the three-beam data (see section 2.2). For scan-map data (which uses only a single nod), this task has no effect1. A t periodic intervals, the S C U B A operators measure the response of the bolometers to a uniform thermal load. The sensitivity of each bolometer compared to the central one on the array is then derived and stored in a "flat-field" file. The S U R F task F L A T - F I E L D multiplies the data from each bolometer by the appropriate factor to correct the gain. Al though it is possible to change the flat-field file, we never had a reason to; there is no reason to suspect that the gain values were incorrect for any of the data we have taken. The E X T I N C T I O N task is then run to correct the data for atmospheric opacity. For each file, an estimate of the r is provided, and S U R F corrects the data accordingly. One can specify the r before and after an observation, and S U R F w i l l linearly in-terpolate the opacity throughout the file. The data collected here was obtained in conditions where the r did not vary significantly enough from file to file to justify this additional complication. The E X T I N C T I O N task also breaks up the data into two new files, one corresponding to the 450 /xm data and the other for the 850 /xm. It is at this point where we diverge slightly from the S U R F analysis. Using the tasks SCUBA2MEM and N D F 2 F I T S , we convert the files into the more common F I T S format, which we can then read in using our own software. The data is presented as a data cube, wi th one axis for time, one for bolometer number, and the third for data. The data vector contains the corrected signal, and the ra/dec offsets for each 1 This is not entirely true. Depending on how exactly the data was taken, the notion of which of the two beams is "positive" can be reversed during each scan. REDUCE_SWITCH sorts this out. 164 of the three positions the bolometer observed. For scan-map data, the th i rd pair of offsets is the midpoint between the chop positions, and we never use it. Our software then performs a despiking operation. For each bolometer, the R M S is calculated and any data point that is greater than 4 times this value is nagged as bad. The procedure is repeated to find additional spikes shadowed by the larger ones. Typical ly, only a small number of points are lost from despiking (< 0.01%). For scan-map data, we now isolate each strip and remove a linear baseline from each bolometer. This step is v i ta l , as each bolometer has a D C offset associated wi th it that is normally removed v ia nodding. A mean sky is calculated at each time-step based on the mean of the bolometers, and subtracted. Here we exclude bolometers that are excessively noisy from the sky estimate. Final ly , we can mult iply the data by the calibration factor, and then proceed to make the map using the routines described in Chapter 3. A.2 Estimation of sub-mm atmospheric opacity-Opacity estimation from relations with the C S O tau meter have replaced skydips in performing extinction corrections. The conversion factors have changed slightly over time, so for completeness we report the values used throughout this dissertation. They are taken from [56, 69]. f a r r o w = 3 . 9 9 ^ + Q.004 ' ( A . l ) r 4 N 5 * r r o w = 23.5rcso + 0 . 0 1 2 r ™ d e = 4.02TCSO + 0.001 (A.2) r 4 ™ d e = 26.2rcso + 0.014 A single value of r was applied to each observation file. Recently, polynomial fits to a night's worth of C S O tau measurements have been used to interpolate the opacity wi thin each observation. For the data used in this thesis, the opacity varied modestly from file to file, and therefore this added complication was not required. The J C M T is currently testing a water vapor monitor which, if successful, w i l l allow opacity estimates along the line of sight of the target to be estimated in real time. This 165 would greatly assist low S N R observations as well as those that require stable signal levels (polarisation for example). 166 

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