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Studying dusty star-forming galaxies with Herschel-SPIRE Asboth, Viktoria 2015

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Studying dusty star-forming galaxies with Herschel-SPIREbyViktoria AsbothA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinThe Faculty of Graduate and Postdoctoral Studies(Astronomy)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)October 2015c© Viktoria Asboth, 2015AbstractObservations suggest that almost half of the total light emitted by stars in the Universeis absorbed by dust, and the emission is re-radiated at far-infrared and submillimeterwavelengths. Dusty star-forming galaxies play a significant role in the stellar mass build-up at high redshift, but their contribution to the cosmic star formation rate density atz > 4 is still unknown, due to the currently limited availability of statistically significanthigh-redshift dusty galaxy samples.In this thesis we analyze data from two large area surveys, the HerMES Large ModeSurvey (HeLMS) and the Herschel Stripe 82 Survey (HerS), observed with the Herschel -SPIRE instrument at far-infrared wavelengths of 250, 350 and 500µm. We describe theprocess of constructing maps from detector data that provide an unbiased estimate ofthe sky signal, then we use a map-based detection method to assemble a large catalog ofcandidate z > 4 dusty star-forming galaxies detected in HeLMS. The large area of thesurvey allows us to detect a significant number of sources and we are able to determinethe differential number counts of these galaxies at 500µm. We find an excess of such high-redshift galaxies compared to model predictions, and our counts suggest strong evolutionin their properties.We examine the properties of our sources at different wavelengths. Follow-up ob-servations with ALMA, SCUBA-2 and ACT strengthen our initial assumption that thedetected population consists of high-z dusty galaxies with their spectrum dominated bythermal dust emission, best fitted with an optically thick modified blackbody. Thesefollow-up observations also allow us to examine the biasing effects in our number countsdue to blending of nearby sources.We also investigate the mean dusty star formation activity in moderate redshift mas-sive galaxy clusters detected by the Atacama Cosmology Telescope. We find that, onaverage, there is an excess of far-infrared emission in the line of sight of these clusters.Finding dusty star-forming galaxies in massive clusters implies that the environment canaffect the star formation activity in galaxies.iiPrefaceDuring my doctoral studies I contributed to research done by the HerMES (HerschelMulti-tiered Extragalactic Survey) collaboration and I was also part of the SCUBA-2commissioning team, the HerS (Herschel Stripe 82 Survey) team and I was involvedin projects in the HerMES-ACT (Atacama Cosmology Telescope) joint collaboration.Throughout this thesis I summarize work done by others in these collaborations, and Idescribe in detail the analysis carried out by me.My contribution to the map-making project described in Chapter 2 was the adaptationof the SANEPIC map-maker software to work with pre-processed SPIRE data. I carriedout tests to determine the additional pre-processing steps that need to be applied to theSPIRE detector timestreams before map-making with SANEPIC (Sec. 2.4.2). I createdSANEPIC maps from the HeLMS and HerS datasets (Sec. 2.4.3) that will be part ofthe next public HerMES data release. I compared the performance of the SANEPIC andthe SHIM map-makers through various tests (Sec. 2.4.4−2.4.6). Part of this work waspublished in the article Viero et al.: ”The Herschel Stripe 82 Survey (HerS): Maps andEarly Catalog.” ApJS, 210:22 (2014). Any similarities of the text in Chapter 2 with thetext in this paper are due to the fact that the map-making sections of this article werewritten by me. Fig. 2.9 and 2.11 of this thesis are taken from this article, but these plotswere also created by me.I contributed to the high-redshift source search project described in Dowell et al.(2014), and I lead a similar project based on the new HeLMS field, this project is describedin Chapter 3. The HeLMS high-redshift source catalog and my results will be publishedin a paper lead by me, this publication is currently under internal review. The finalpublication will be a shorter version of Chapter 3, so the text and figures in this paperwill show similarities with Chapter 3. Most of the data analysis in Chapter 3 was doneby me. The ALMA spectroscopy analysis in Sec. 3.4 was carried out by Alex Conley,but the text of this section was written by me. The ACT maps used in Sec. 3.5 wereprocessed by the ACT collaboration, I used the final data products in my analysis.The SCUBA-2 telescope-time proposal that our data in Chapter 4 are based uponiiiwas written by Rob Ivison, and I was a Co-Principal Investigator of this project. I helpedin the sample selection, in the preparation of the observations and I was at the telescopesupervising part of the observing run. All data analysis presented in Chapter 4 wascarried out by me. In the analysis described in Chapter 5 I used the public ACT-selectedcluster catalog and the HeLMS and HerS maps created by me with SANEPIC. All textin this thesis was written by me and all plots except for Fig 1.2 were created by me.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Acronyms and Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Structure formation and stellar mass assembly . . . . . . . . . . . . . . . 11.2 The role of dusty star-forming galaxies . . . . . . . . . . . . . . . . . . . 41.3 Thermal emission from dust . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Observing the far-infrared/submillimeter sky . . . . . . . . . . . . . . . . 71.4.1 Number counts . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effects of gravitational lensing on the number counts . . Confusion noise . . . . . . . . . . . . . . . . . . . . . . . 111.5 The evolution of the luminosity function and the star formation rate density 121.6 Modelling the evolution of dusty star-forming galaxies . . . . . . . . . . . 161.7 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Making large maps from Herschel-SPIRE data . . . . . . . . . . . . . . 192.1 The Herschel -SPIRE instrument . . . . . . . . . . . . . . . . . . . . . . 202.2 Initial data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2.1 Deglitching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2.2 Electrical filter response correction . . . . . . . . . . . . . . . . . 23v2.2.3 Flux Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . 242.3 Map-makers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.3.1 sanepic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.3.2 shim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.4 Using sanepic with SPIRE data . . . . . . . . . . . . . . . . . . . . . . 312.4.1 The HeLMS and HerS surveys . . . . . . . . . . . . . . . . . . . . 312.4.2 Additional timeline processing . . . . . . . . . . . . . . . . . . . . 342.4.3 sanepic maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.4.4 Comparison of sanepic and shim maps . . . . . . . . . . . . . . 372.4.5 Noise properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.4.6 Transfer function . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.4.7 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 A search for high redshift dusty galaxies in the HerMES Large ModeSurvey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.1 Catalog creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.1.1 Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.1.2 Matched filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.1.3 Difference map . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.1.4 Source extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.1.5 Final catalog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.2 Number counts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.2.1 Intrinsic number counts . . . . . . . . . . . . . . . . . . . . . . . 573.2.1.1 Blending . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.2.1.2 Detection efficiency . . . . . . . . . . . . . . . . . . . . . 603.2.1.3 False detections and Eddington bias . . . . . . . . . . . 613.2.1.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . 623.2.2 Comparison to models . . . . . . . . . . . . . . . . . . . . . . . . 653.3 Colors and SED fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673.4 ALMA spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.5 Red sources in the ACT maps . . . . . . . . . . . . . . . . . . . . . . . . 753.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784 Observing SPIRE-selected “red” sources with SCUBA-2 . . . . . . . 804.1 Sample selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824.3 Data reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85vi4.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864.4.1 Daisy observations . . . . . . . . . . . . . . . . . . . . . . . . . . 864.4.2 Pong observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 984.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1025 Average dusty star-formation activity in Sunyaev-Zel’dovich-selectedgalaxy clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045.1 The ACT equatorial cluster sample . . . . . . . . . . . . . . . . . . . . . 1075.2 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1106 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119viiList of Tables3.1 Noise levels in the smoothed maps . . . . . . . . . . . . . . . . . . . . . . 523.2 Raw 500µm number counts of the detected red sources. . . . . . . . . . . 573.3 Average flux densities of sources in each 500µm flux density bin. . . . . 764.1 HerMES fields used for red source sample selection . . . . . . . . . . . . 824.2 JCMT observing weather grades . . . . . . . . . . . . . . . . . . . . . . . 844.3 Measured 250, 350, 500 and 850µm flux densities . . . . . . . . . . . . . 884.4 S850 > 3.75σ sources detected around the central red galaxy . . . . . . . 1005.1 ACT clusters in HeLMS . . . . . . . . . . . . . . . . . . . . . . . . . . . 1085.2 ACT clusters in HerS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108viiiList of Figures1.1 Negative k-correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2 Star formation rate density evolution . . . . . . . . . . . . . . . . . . . . 152.1 Auto- and cross-power spectra of bolometer timestreams . . . . . . . . . 292.2 HeLMS coverage map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.3 HerS coverage map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.4 Temperature drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.5 Cooler-burp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.6 2D power spectra of HeLMS maps made with shim and sanepic . . . . 382.7 Azimuthally averaged power spectra of HeLMS maps made with shim andsanepic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.8 Comparison of large scale structures recovered in shim and sanepic maps 392.9 Pixel flux histogram of the HerS maps . . . . . . . . . . . . . . . . . . . 412.10 Azimuthally averaged power spectra of the sky signal, the noise and thefull maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.11 Transfer function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.1 Grayscale image of the HeLMS field with the applied mask . . . . . . . . 483.2 Matched filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.3 Comparison of the final resolution of the maps using different filters . . . 503.4 Cirrus background removal in the maps . . . . . . . . . . . . . . . . . . . 513.5 Flux density recovery bias . . . . . . . . . . . . . . . . . . . . . . . . . . 543.6 Failed glitch flagging in the time ordered data . . . . . . . . . . . . . . . 553.7 Image of a cosmic ray hit in the maps . . . . . . . . . . . . . . . . . . . . 563.8 Raw 500µm differential number counts of our sample of “red” sources. . 583.9 Postage-stamp images of isolated sources and blends . . . . . . . . . . . . 593.10 Detection efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.11 Measured completeness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.12 SPIRE colors of red sources as a function of the 500µm flux density . . . 663.13 Color-color plot of red sources detected in HeLMS . . . . . . . . . . . . . 69ix3.14 MCMC contours of modified blackbody fit . . . . . . . . . . . . . . . . . 713.15 MCMC parameter distribution without applied priors . . . . . . . . . . . 723.16 Observed temperature and peak wavelength distribution of the HeLMSred sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733.17 ALMA spectra of HELMS34 and HELMS65 . . . . . . . . . . . . . . . . 743.18 (a.) ACT stacks (Bin 1-3) . . . . . . . . . . . . . . . . . . . . . . . . . . 763.18 (b.) ACT stacks (Bin 4-6) . . . . . . . . . . . . . . . . . . . . . . . . . . 773.19 Average SED of stacked sources . . . . . . . . . . . . . . . . . . . . . . . 784.1 Coverage of“daisy” and “pong-900” maps . . . . . . . . . . . . . . . . . 834.2 (a.) SPIRE and SCUBA-2 postage-stamp images of observations . . . . . 894.2 (b.) SPIRE and SCUBA-2 postage-stamp images of observations . . . . . 904.2 (c.) SPIRE and SCUBA-2 postage-stamp images of observations . . . . . 914.2 (d.) SPIRE and SCUBA-2 postage-stamp images of observations . . . . . 924.3 (a.) Modified blackbody SED fits . . . . . . . . . . . . . . . . . . . . . . 934.3 (b.) Modified blackbody SED fits . . . . . . . . . . . . . . . . . . . . . . 944.3 (c.) Modified blackbody SED fits . . . . . . . . . . . . . . . . . . . . . . 954.3 (d.) Modified blackbody SED fits . . . . . . . . . . . . . . . . . . . . . . 964.3 (e.) Modified blackbody SED fits . . . . . . . . . . . . . . . . . . . . . . 974.4 Maps of LSW28, LSW102, XMM26, XMM30 . . . . . . . . . . . . . . . . 994.5 Cumulative 850µm number counts around red sources . . . . . . . . . . 1014.6 Cumulative number of sources within different radii of the central red source1025.1 Cluster image re-binning . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105.2 Stacked SPIRE images of ACT SZ clusters . . . . . . . . . . . . . . . . . 1115.3 Radial average of SPIRE images stacked at ACT cluster positions . . . . 1125.4 Radial average of SPIRE images stacked at random positions . . . . . . . 113xList of Acronyms and SymbolsACT Atacama Cosmology TelescopeALMA Atacama Large Millimeter/submillimeter ArrayAGN Active galactic nucleusBCG Brightest cluster galaxyBLAST Balloon-borne Large Aperture Submillimeter TelescopeCIB Cosmic Infrared BackgroundCMB Cosmic Microwave BackgroundDA angular diameter distanceDL luminosity distancedex “decimal exponent”, a logarithmic unit being used in astronomy.1 dex equals a factor of 10.FIR far-infraredFWHM full-width at half-maximumHeLMS HerMES Large Mode SurveyHerMES Herschel Multi-tiered Extragalactic SurveyHerS Herschel Stripe 82 SurveyHIPE Herschel Interactive Processing EnvironmentJCMT James Clerk Maxwell TelescopeJy Jansky (1Jy = 10−26W m−2 Hz−1)L solar luminosity (L = 3.846× 1026W)LIR infrared bolometric (8− 1000µm) luminosityLIRG luminous infrared galaxyM solar mass (M = 1.99× 1030kg)M∗ stellar mass of a galaxyMpc megaparsec (1 pc = 3.26 light-years = 3.0857× 1016 m)MS main sequence mode of star formationPSF point spread functionxiPWV precipitable water vaporSANEPIC Signal And Noise Estimation Procedure Including CorrelationsSB starburst mode of star formationSCUBA-2 Submillimetre Common-User Bolometer Array-2SDSS Sloan Digital Sky SurveySED spectral energy distributionSFR star formation rateSHIM SPIRE-HerMES Iterative MapperSNR signal-to-noise ratioSPIRE Spectral and Photometric Imaging ReceiversSFR specific star formation rate (sSFR = SFR / M∗)SZ Sunyaev-Zel’dovich effectTd dust temperatureTobs observed dust temperature (Tobs = Td/(1 + z))TOD time-ordered dataULIRG ultraluminous infrared galaxyz redshiftxiiAcknowledgementsI thank my supervisor Mark Halpern for his guidance, patience and support throughoutmy graduate studies. I thank members of my supervisory committee, Sarah Burke,Gary Hinshaw and Douglas Scott for their support. I thank my collaborators in theHerMES/HerS and SCUBA-2 teams, and I thank my fellow lab-mates. In particular,thanks to Gaelen Marsden and Alex Conley for all their help and encouragement duringmy research. I thank my family and friends for always encouraging me and for believingin me even at times when I did not believe in myself. A special thank you goes to mysister, Timea Asboth, your support is invaluable, I could not have done this without you.xiiiChapter 1IntroductionOne of the key goals of astronomy is to understand how the structure of the Universeevolved from primordial density fluctuations into the galaxies and galaxy clusters we seetoday. The visible building blocks of these structures are the stars, made of luminousbaryons. Although baryons only represent a small fraction of the total mass of theUniverse, they trace the underlying dark matter distribution, and thus it is importantto understand the process of the stellar mass assembly in galaxies in order to study thestructure formation in the Universe.Stars emit most of their light in the optical and ultraviolet wavelength range, but ob-servations show that almost half of the total light emitted by stars is absorbed by dust,and this radiation is re-emitted by the heated dust grains at far-infrared and submillime-ter wavelengths. Optical surveys miss a whole population of optically faint but infrared-luminous distant dusty star-forming galaxies at the epoch when the bulk of the stellarmass in the Universe formed. Thus it is crucial to study the far-infrared/submillimetersky to gain a comprehensive view of the cosmic star formation history.In this chapter we give a broad overview of our current knowledge of the history ofstar formation, emphasizing the role of dusty star-forming galaxies, and we describe whatwe can learn from dedicated surveys of the far-infrared/submillimeter sky.1.1 Structure formation and stellar mass assemblyAccording to the current cosmological models (e.g. Bennett et al., 2013; Planck Collab-oration et al., 2014a) the Universe began ∼ 13.8 billion years ago with the Big Bang asa hot and dense plasma of baryons, electrons, and photons. As the Universe expanded,the plasma started to cool down, and eventually protons and electrons combined to formhydrogen atoms, while the photons decoupled from the matter and radiated away freely.1This recombination occurred ∼ 378,000 years after the Big Bang, corresponding to aredshift of z ∼ 1100 (The wavelength λe of the light a distant object emits increases asthe Universe expands, and it is observed at λo = (1+z)λe. The redshift z is often used todescribe cosmological distances). In the “dark ages” following the recombination, smallinitial density fluctuations in the molecular gas started to grow as the gas fell into thegravitational potential well of dark matter halos. When these over-densities became mas-sive enough to overcome the internal pressure of the gas, they collapsed, nuclear fusionbegan and the first stars were born at perhaps z ∼ 30 (Barkana and Loeb, 2001). Todaythe stars are a part of large structures, spiral, elliptical or irregularly shaped galaxies,and these galaxies form even larger structures, galaxy groups, clusters and superclus-ters. The most accepted theory describing the evolution of galaxies from the first lightin the Universe to these large structures is the hierarchical structure-formation model(Press and Schechter, 1974; White and Rees, 1978). This theory describes a “bottom-up” formation scenario, where small dark matter halos form first and larger structuresare created by merging and accretion of these smaller halos. Large N-body simulationsof the evolution of the dark matter distribution have been carried out that support thismodel (e.g. Springel et al., 2005). However, to include the star-forming processes in thesesimulations, additional complex, and often non-linear physical effects must be included,and the results of the simulations will also strongly depend on the wide range of initialconditions.There are several theories about processes that can trigger and quench star formationactivity in galaxies. The fuel of star formation is the cold molecular gas. Star formationat a moderate rate can be maintained for an extended period of time by cold gas accretionfrom the intergalactic medium and by minor mergers with gas rich dwarf galaxies (e.g.Dekel et al., 2009). Additionally, major mergers of gas rich galaxies (e.g. Li et al., 2007;Tacconi et al., 2008; Genzel et al., 2010) can trigger intense short-lived bursts of starformation. These “starburst” galaxies can form stars at a rate hundreds to thousandstimes larger than normal star-forming galaxies, but this starburst phase is expected tobe relatively short, since intense star formation uses up all of the cold gas on a shorttimescale. There is also evidence that early galaxies contained more cold gas, thangalaxies in the local Universe; thus they could form more stars even without the highstar formation efficiency of a starburst (e.g. Daddi et al., 2008, 2010; Geach et al., 2011).Many local galaxies have old, passively evolving stellar populations and do not showsignificant current star formation activity, suggesting that the star formation was stopped(“quenched”) by some process. Star formation stops if there is not enough cool gasleft in the system. The environment in which galaxies reside is suspected to play a2role in quenching star formation. In the local Universe elliptical and lenticular galaxieswith evolved stellar populations and very little star formation activity tend to reside indense environments in the cores of galaxy clusters, while star-forming spiral galaxies aremore common in the outskirts of clusters or in the field (Dressler, 1980; Go´mez et al.,2003). Observations suggest that this trend might change at higher redshifts, as moredistant star-forming galaxies are found in dense environments (Butcher and Oemler, 1978;Ellingson et al., 2001; Saintonge et al., 2008; Haines et al., 2009). This evidence suggeststhat the environmental effects arising as galaxies fall into clusters can stop the starformation activity. Interactions between galaxies in dense environments can remove coldgas, for example, through tidal effects (“strangulation”, Larson et al., 1980), disturbanceby close high-speed passes between galaxies (“galaxy harassment”, Moore et al., 1996)or ram-pressure stripping as galaxies move through the intra-cluster medium (Gunn andGott, 1972).Apart from environmental quenching, there are intrinsic processes that can removecold gas from the star-forming regions. In merging galaxies the gas can be accretedby the central black hole, creating an active galactic nucleus (AGN), which then emitsradiation that can blow away or heat up the remaining gas, thus stopping star formationactivity (Hopkins et al., 2008). To a lesser degree, feedback from stellar winds andsupernova explosions in intense starburst regions can have a similar effect. There is alsosome evidence that the quenching can depend on the stellar mass of the galaxy (Penget al., 2010) such that more massive galaxies experience quenching earlier than low massgalaxies. This is also similar to the observational trend called “downsizing” (Cowie et al.,1996; Collins et al., 2009), that suggests that more massive galaxies formed their starsearlier than smaller galaxies. The most massive local elliptical galaxies have evolvedstellar populations that must have formed much earlier than the hierarchical modelspredict. This seemingly anti-hierarchical evolution for the largest galaxies also supportsthe mass quenching scenario.Current observations cannot determine unambiguously which one of these wide rangeof processes is the most dominant in affecting the star formation history. The stellar massbuild-up in merging dark matter halos can depend on many complex, non-linear effectsthat are hard to simulate, and more observational constraints from star formation activityat different epochs are needed to fine-tune these models and to properly determine theinitial conditions.31.2 The role of dusty star-forming galaxiesWhile the dominant component of the interstellar medium is gas, it also contains dustparticles. This dust consists of irregularly shaped, sub-micron sized grains made typicallyof graphites and silicates. These dust particles can scatter and absorb the optical/UVlight emitted by stars; thus the measured intensity of the radiation is reduced. It hasbeen known for a long time that optical studies need to apply a correction factor whenmeasuring the brightness of stars to account for the dust extinction in the interstellarmedium (e.g. Trumpler, 1930). These studies, however, assume that the dust is not veryoptically thick, and the light is only partially blocked out. While the optical light ofstars is dimmed, the absorbed power of the radiation also causes the dust to warm upto typically 10s or 100s of Kelvin; thus the light is re-radiated at infrared wavelengths.The real importance of studying the dust emission was only discovered when the firstspace-based infrared telescopes were launched.The first survey to detect a large number of galaxies based on their infrared radiationwas carried out by the InfraRed Astronomy Satellite (IRAS, Neugebauer et al., 1984).The highlight of this mission was the discovery of a 60-µm-selected population of luminousinfrared galaxies (LIRGs, Soifer et al., 1984; Sanders and Mirabel, 1996) with infraredbolometric luminosities LIR > 1011L (L = 3.846 × 1026 W is the solar luminosity),and ultraluminous infrared galaxies (ULIRGs, Houck et al., 1985) with LIR > 1012L.These galaxies turned out to be very faint or undetected at optical wavelengths. Theextreme IR luminosity of these sources was attributed to emission from dust heated byintense starburst regions or active galactic nuclei, while the optical emission of the youngmassive stars is completely blocked out by the dust. Most of these local (z . 0.3) LIRGsand ULIRGs were identified as major mergers between gas rich galaxies, or as galaxieswith irregular morphologies, where interaction probably triggers the very active dustystar formation phase (e.g. Murphy et al., 1996; Clements et al., 1996).Although the discovery of these LIRGs and ULIRGs showed that optical surveys po-tentially miss the most active star-forming galaxies that are heavily obscured by dust,these galaxies turned out to be very rare locally compared to normal galaxies, and theywere shown to only contribute ∼ 30% to the total local infrared luminosity (Soifer andNeugebauer, 1991). However, the discovery of the cosmic infrared background (CIB) sug-gested, that dusty star-forming galaxies should be more common at higher redshifts. Theextragalactic background light is the integrated radiation from galaxies at all distances inthe Universe. It was long predicted that the integrated background light should containa contribution from the infrared emission of galaxies (Partridge and Peebles, 1967). The4CIB was first detected by the Cosmic Background Explorer (COBE) satellite with theFIRAS instrument (Far Infrared Absolute Spectrophotometer, Puget et al., 1996; Fixsenet al., 1998) and later with the DIRBE instrument (Diffuse Infrared Background Exper-iment, Hauser et al., 1998). Surprisingly, the contribution from the infrared backgroundlight was measured to be comparable to the total integrated optical light, suggesting thatalmost half of the light emitted by stars in the Universe must be absorbed by dust and re-emitted at far-IR wavelengths (Dwek et al., 1998). Since the contribution of local LIRGsand ULIRGs cannot explain this emission, it was expected that most of the infrared lightcomes from the redshifted emission of more distant dusty star-forming galaxies.A high redshift population of dusty star-forming galaxies was first discovered atsubmillimeter wavelengths with the SCUBA instrument (Submillimetre Common-UserBolometer Array, Holland et al., 1999) at the James Clerk Maxwell Telescope (Smailet al., 1997; Hughes et al., 1998; Barger et al., 1998). These 850-µm-selected galaxieslooked like distant ULIRGs with luminosities LIR > 1012L, forming hundreds to thou-sands of stars per year. It was shown that almost all of these sources are at redshiftsz > 1, with a median at z ∼ 2.3 (Smail et al., 2000; Chapman et al., 2005; Pope et al.,2005), and based on their observed number counts their emission can account for mostof the 850µm background light (Blain et al., 1999; Barger et al., 1999).Since the discovery of the first submillimeter galaxies, further surveys at different far-infrared and submillimeter wavelengths were able to successfully resolve most of the CIB,proving that the background is really made up of individual galaxies mostly at high-z(e.g. Dole et al., 2006; Knudsen et al., 2008; Devlin et al., 2009; Marsden et al., 2009). Itwas shown that dust-obscured star formation dominates the total star formation activityat redshifts z & 1 (Le Floc’h et al., 2005); thus star formation studies based on opticaland UV data alone are expected to significantly under-predict the star formation rate atthese epochs.1.3 Thermal emission from dustThe source of the far-infrared and submillimeter emission of galaxies is thermal radiationfrom dust heated by star-forming regions or an AGN. The dominant emission comesfrom dust grains in thermal equilibrium with the local radiation field. In equilibriumthe total power absorbed by the dust is equal to the total radiated power, and the dusttemperature is determined by this balance. Typical equilibrium temperatures of localLIRGs and ULIRGs range between Td ∼ 20 K and 60 K (Sanders and Mirabel, 1996).The amount of radiation these galaxies emit at different frequencies depends on the dust5properties. The dust grains can differ in size, geometry, composition and emissivityproperties, and their spatial distribution also affects the resulting functional form of theradiation. Assuming an optically thin dust cloud, the featureless continuum emissionfrom dust grains in equilibrium can be modelled as a modified blackbody radiation, andthe spectral energy distribution (SED) can be expressed asSν ∝ νβBν(Td). (1.1)HereBν(Td) =2hc2ν3ehν/kTd − 1 (1.2)is the Planck function, describing the blackbody radiation, c is the speed of light, h is thePlanck constant, k is the Boltzmann constant, and β is the dust grain spectral emissivityindex (β ∼1-2, e.g. Hildebrand, 1983). The quantitySν =Lν′4piDL(z)2(1.3)is the observed spectral flux density of a source of luminosity L at redshift z. Herethe spectral luminosity Lν′ is the total power per unit frequency interval radiated bythe source at the rest frame frequency ν ′ = (1 + z)ν, and DL(z) is the model-dependentluminosity distance (see e.g. Hogg, 1999). Note, that in submillimeter astronomy the fluxdensity is usually expressed in units of Jansky, with 1 Jy = 10−26 W m−2 Hz−1 (hencethe notation in terms of frequency), but it is common to plot these flux density valuesas a function of wavelength as Sν(λ), where λ = c/ν.Small dust grains can be heated transiently above their equilibrium temperatures byabsorbing single photons near star-forming regions. Emission from these grains dominatesthe mid-infrared part of the spectrum. Narrow emission and absorption line featuresfrom silicates and Polycyclic Aromatic Hydrocarbons (PAHs) also contribute at thesewavelengths. The spectrum of dusty star-forming galaxies also contains emission linesfrom atomic and molecular transitions, (e.g. the CO ladder, C+, HCN and HCO+) thatcan be excited in high density regions. Spectroscopic redshift measurements are basedon the detection of such spectral lines.Apart from the fact that a significant fraction of the star formation activity at highredshift is obscured by dust, and thus it is invisible at optical wavelengths, observingsources at submillimeter wavelengths has another unique advantage. The shape of thedust emission spectrum allows us to easily observe objects in a significantly larger red-shift range than is possible at optical or radio wavelengths. The observed flux densities6101 102 103 104λ [µm]10−410−310−210−1100101102FluxDensity[Jy]z=1z=2z=3z=4z=5z=6z=7Figure 1.1: The so-called “negative k-correction” at submillimeter wavelengths illustratedwith the redshifted spectral energy distribution of a local ULIRG, Arp220. The verticallines correspond to the wavelengths we discuss in this thesis, the Heschel -SPIRE bands at250µm, 350µm and 500µm, together with the 850µm SCUBA-2 band. At far-infraredand submillimeter wavelengths the measured flux densities are not decreasing as fastwith redshift as they do in the optical range, and they remain approximately constantat 850µm.of a source with a fixed luminosity normally decrease with the square of the distance(Eq. 1.3). In the rest frame the dusty SED typically peaks around 100µm, and this peakis redshifted to λ & 200µm at z & 1. Thus FIR/submillimeter wavelengths sample theSED closer to its peak at higher redshift, and this effect can counteract the decreaseof flux density. On the long wavelength side of the SED peak, where the flux densitiesare a steeply decreasing function of λ, this can mean that the observed flux densitiesremain approximately constant at a large redshift range (z ∼1-10). This effect is alsocalled a “negative k-correction” (Franceschini et al., 1991; Blain and Longair, 1993), andis illustrated on Figure 1.1. At λ ∼200-500µm the FIR/submillimeter flux densities stilldecrease with increasing redshift, but not at the same rate as they do at optical or radiowavelengths, so even in this range we can observe higher redshift sources more easily.1.4 Observing the far-infrared/submillimeter skySince the discovery of the first submillimeter galaxies with SCUBA, a large range ofexperiments have been designed to observe the far-infrared/submillimeter sky at different7wavelengths in an attempt to resolve the cosmic infrared background into individualsources, and to investigate the properties of these dusty star-forming galaxy populations.The two biggest limiting factors when observing at these wavelengths are the opacityof the atmosphere, and the relatively large beamsizes of single dish telescopes at theobserved wavelengths. Water vapour in the atmosphere absorbs most of the infraredradiation; thus ground-based telescopes can only observe the FIR/submillimeter partof the electromagnetic spectrum through specific atmospheric windows. To overcomethis effect, balloon-borne or space-based telescopes have been built, but the resolutionof these experiments is typically limited due to the small diameters of their mirrors.Ground-based interferometric instruments can achieve much better resolution, but dueto their small fields of view they are usually better suited to carry out targeted follow-upobservations of individual sources rather than performing large area surveys.Although the physical properties of individual galaxies can be very different from oneanother, it is useful to investigate the average properties of a galaxy population as awhole. Selecting sources at different wavelengths usually selects different populations.Notable instruments that have mapped large areas of the FIR/submillimeter sky includeSpitzer -MIPS (24, 70, 160µm, Rieke et al., 2004), Herschel -PACS (70, 100, 160µm,Poglitsch et al., 2010), BLAST (250, 350, 500µm, Devlin et al., 2004), Herschel -SPIRE(250, 350, 500µm, Griffin et al., 2010), SCUBA and SCUBA-2 (450 and 850µm, Hollandet al., 1999, 2013), LABOCA (870µm, Siringo et al., 2009), and AzTEC (1.1 mm, Wilsonet al., 2008), among others.It needs to be noted, that an important wavelength-dependent selection effect arisesdue to the different dust temperatures. For example, it was shown that 850-µm-selectedSCUBA samples were biased against warmer dust galaxies and preferentially select colderdust (T ∼ 40K) objects (Eales et al., 2000; Blain et al., 2004; Kova´cs et al., 2006).BLAST and SPIRE sample the spectral energy distribution closer to the peak, and theyare less biased against warmer dust objects. Also, since the k-correction becomes verynegative above 500µm wavelengths, galaxy samples selected at longer wavelengths aremore likely to detect higher redshift galaxy populations. In the following subsections wedescribe what we can learn about populations of galaxies from large dedicated surveys,emphasizing the results from Herschel -SPIRE, the instrument used to obtain the majorityof the data analyzed in this thesis.81.4.1 Number countsMeasurements of the number of galaxies detected in a survey per unit area in differentflux density bins can provide an insight into the evolution of the selected population ofsources. Number counts are usually expressed in a differential form as dN/dS, describingthe number of objects falling into a flux density bin, or in an integral form, N(> S),corresponding to the total number of objects with flux densities above S. The observeddifferential counts are usually best fitted by either a Schechter-type function,dNdS=N0S0(SS0)−αexp(− SS0), (1.4)or a double power law,dNdS=N0S0(SS0)−α;S ≤ S0,dNdS=N0S0(SS0)−β;S > S0,(1.5)where N0, S0, α, and β are parameters of the fit.Assuming a flat Euclidean universe, the expected shape of the number counts for anon-evolving population can be easily derived. No evolution means that all sources haveluminosity L and their number density ρ is constant. For such a distribution the numberof sources in a radial shell with radius r and thickness dr can be determined asdN = ρ 4pir2dr ∝ r2. (1.6)The flux at distance r from a luminosity L object is S = L/(4pir2), and from this we canderivedSdr= − L2pir3∝ r−3, (1.7)andr =(L4piS) 12∝ S− 12 . (1.8)Combining equations 1.6, 1.7 and 1.8 we getdNdS= ρ 4pir2drdS∝ r5 ∝ S− 52 . (1.9)Thus in a flat Euclidean universe, which contains uniformly distributed sources, thecounts are expected to vary as dN/dS ∝ S−5/2, or in integral form as N(> S) ∝ S−3/2.9If the population of sources is evolving (e.g. their luminosity or number density changeswith redshift), then the slope of the observed counts will deviate from the Euclideanvalue. Note however, that number counts at submillimeter wavelengths are expected toappear steeper than the Euclidean counts, even without an evolving population, due tothe increasing negative k-correction and the larger volume sampled at higher z, but theexpected number counts for a non-evolving population can be modelled. Steep numbercounts can suggest that the number of luminous sources decreases over time. Submillime-ter number counts are known to be much steeper than predictions based on non-evolvingmodels, suggesting that the properties of these populations are strongly evolving withredshift (e.g. Borys et al., 2003; Coppin et al., 2006; Perera et al., 2008; Patanchon et al.,2009; Austermann et al., 2010; Glenn et al., 2010; Oliver et al., 2010; Be´thermin et al.,2012b; Geach et al., 2013). Effects of gravitational lensing on the number countsMassive objects between a distant source and the observer can act as lenses, bendingthe light coming from the background source. This effect is called gravitational lensing,and it can magnify and distort the image of the distant object. The magnificationof faint sources by foreground galaxies and galaxy clusters has been widely exploitedin submillimeter astronomy, since it allows the investigation of objects that would beotherwise too faint to be detected based on the typical survey flux density limits. Surfacebrightness (the flux density per unit solid angle) is conserved by gravitational lensing, soif an object is magnified by a factor of µ (meaning that the observed solid angle of thesource becomes dΩobs = µ dΩ), then its observed flux will also increase as Sobs = µS.This magnification effect can change the observed number counts (e.g. Paciga et al., 2009;Jain and Lima, 2011). Due to the magnification of the solid angle, the observed volumedecreases, so the number of sources in the same area decreases to Nobs = N/µ, thus thedifferential number counts will change asdNobsdSobs(Sobs) =1µ2dNdS(Sobs/µ). (1.10)As discussed before, the unlensed FIR/submillimeter number counts usually decreasevery steeply at the bright end, and scale as dN/dS ∝ S−α, so the observed lensed countswill be proportional to dNobs/dSobs ∝ µα−2S−αobs. Since α  2 at the bright end of thecounts, we see more bright sources than we would without lensing. Combining this effectwith the negative k-correction at submillimeter wavelengths above about 500µm suggestthat the bright end of the submillimeter counts could be dominated by high-z lensed10objects (Blain, 1996; Negrello et al., 2007). This lensed population has already beendetected with Herschel -SPIRE (Negrello et al., 2010; Bussmann et al., 2013; Wardlowet al., 2013), where objects with 500µm flux densities above ∼ 100 mJy are all expectedto be magnified by lensing. Similarly, the majority of the bright galaxies selected at1.4 mm wavelengths with the South Pole Telescope (SPT) are strongly lensed (Vieiraet al., 2013; Weiß et al., 2013). Confusion noiseOne of the limitations of FIR/submillimeter astronomy that makes it difficult to re-solve the faint sources contributing to the CIB is confusion noise (Condon, 1974; Doleet al., 2003). This noise arises due to the combination of the limited resolution of FIR-submillimeter telescopes and the steep source counts of the galaxy populations selectedat these wavelengths. The smallest angular scale θ that a telescope can resolve dependson the diameter (D) of the optics and the observed wavelength λ as θ ∼ λ/D. Since thewavelengths we want to observe are relatively large compared to the diameter of singledish telescopes, the beam sizes of these instruments are fairly wide. Due to the steepsource counts, faint objects on the sky become increasingly numerous, and below a fluxdensity limit each beam-area in the sky will contain more than one source. These sourcescannot be distinguished from each other anymore, and the sum of their flux densitiescreates an uncertainty in the maps. If the beam response function of the telescope isf(θ, φ), then the fluctuation from sources below the confusion limit Slim can be expressedasσ2conf =∫f(θ, φ)2 dθdφ∫ Slim0S2dNdSdS. (1.11)Unlike the instrumental noise, confusion noise cannot be reduced by longer observingtimes, since it is fixed on the sky.Although sources with flux densities below the confusion limit cannot be resolved,statistical methods can be used to investigate the properties of these faint galaxies. One ofthe commonly used methods is called probability of deflection analysis or P (D), which isbased on recovering the number counts based on pixel intensity histograms in FIR/submmmaps (Patanchon et al., 2009; Glenn et al., 2010). Another often used method is basedon determining the covariance between the confusion-limited maps and Spitzer -MIPS24µm selected source positions (“stacking”, Pascale et al., 2009; Marsden et al., 2009).It has been shown that 24-µm-selected catalogs are able to resolve the majority of theCIB (Papovich et al., 2004; Dole et al., 2006), and it has been assumed that these objectsare the same sources that create the confusion limit at longer wavelengths. There is a11good agreement between the P (D) and stacking results and the counts also agree wellwith the extrapolation of the resolved number counts (Be´thermin et al., 2012b), showingthat these statistical methods work well to determine the counts below the confusionlimit.Investigating the statistics of the unresolved emission in FIR/submillimeter mapscan also be useful to study the clustering properties of the sources that constitute thecosmic infrared background. A strongly clustered population will create an excess inthe angular power spectrum of the background intensity variations compared to thePoisson-term caused by unclustered sources. At small angular scales this excess powerdominantly comes from clustering of galaxies within a single dark matter halo, while onlarge angular scales the extra power is the result of the clustering of galaxies residing indifferent halos (e.g. Cooray and Sheth, 2002; Amblard et al., 2011). The one-halo termstarts to dominate above the unclustered signal at angular scales of a few arcminutes,while the transition to the two-halo term is detected at ∼ 10 arcminute angular scales(e.g. Viero et al., 2009, 2013). To detect this low spatial frequency correlated signal inthe background anisotropies it is crucial to carry out large-area surveys and to createmaps from the observed data that reconstruct these large-scale signal variations in anunbiased way. One of the main goals of the current work is to produce such maps fromlarge-area Herschel -SPIRE observations.1.5 The evolution of the luminosity function and thestar formation rate densityAs we discussed in Section 1.4.1, the observed functional form of the number countsprovides a hint to the evolution of the source population. The number of objects weare able to observe on the sky above some flux density limit is the projected numberof sources at different redshifts having different luminosities. If we know the redshiftof a source then we can calculate its bolometric infrared luminosity by integrating theobserved spectral energy distribution over the wavelength range 8−1000µm (this rangebeing the conventional choice),LIR =1000µm∫8µm4piDL(z)2Sν(λ)dλ. (1.12)12Thus if we know the redshift distribution of our sources, we can convert our numbercounts into a function φ(L) describing the number of galaxies per unit luminosity andunit volume. In flux-limited samples, high luminosity galaxies can be detected to greaterdistances than faint sources, and the luminosity function is usually determined by the1/Vmax method (Schmidt, 1968). In this method the maximum redshift zmax is found atwhich a source with luminosity LIR would still be detectable based on the flux densitylimits of the survey. Then the comoving maximum volume corresponding to this redshiftis calculated asVmax =4pi3(DL(zmax)1 + zmax)3, (1.13)where the term DL/(1 + z) is called “comoving distance” (see e.g. Hogg, 1999). After wecalculate the maximum available volume for each of our sources, the number of galaxiesin ∆L luminosity intervals can be determined asφ(L) =1∆L∑i1Vmax,i, (1.14)where the sum includes all i sources with luminosities falling into the given ∆L bin,L ≤ Li < L+∆L. The quantity φ(L) can often be parametrized as a Schechter function:φ(L)dL = φ∗(LL∗)αexp(− LL∗)d(LL∗), (1.15)where the parameters of the fit are the faint end slope α, the characteristic densityφ∗, and the break luminosity L∗, above which the number of bright sources decreasesexponentially. For an evolving population L∗ = L∗(z) and φ∗ = φ∗(z), thus the shape ofthe luminosity function changes with redshift. To investigate this evolution in an observedpopulation, the luminosity function is usually determined separately in several differentredshift bins, and L∗ and φ∗ are obtained from fitting the luminosity distribution in thegiven z range. Studies of the FIR luminosity function all show strong evolution of theseparameters, which implies that the contribution of dusty galaxies to the total luminositydensity increases towards higher redshift (e.g. Le Floc’h et al., 2005; Gruppioni et al.,2013; Magnelli et al., 2013; Burgarella et al., 2013).If we assume that the stellar light is fully reprocessed by dust, we can infer the starformation rate from LIR, as discussed in Kennicutt (1998):SFRIR = κIR × LIR, (1.16)13where the conversion factor κIR = 1.72×10−10Myr−1L−1 proposed by Kennicutt (1998)is widely used in the literature. Although the infrared luminosity only traces star forma-tion obscured by dust, observations show that in most of the massive dusty star-forminggalaxies the obscured star formation activity dominates over the unobscured contribution(e.g. Buat et al., 2010) and so LIR is a good tracer for the total star formation activityin dusty galaxies. With this relation the luminosity functions can be used to determinethe evolution of the dust-obscured star formation rate density. The infrared comovingluminosity density is determined asρL,IR(z) =∞∫LlimLφ(L, z)dL, (1.17)where Llim is the limiting luminosity of the survey at the given redshift. Using Equa-tion 1.16 we can obtain the star formation rate density asρSFR,IR(z) = κIR × ρL,IR(z). (1.18)Based on the analysis of a large range of available of multi-wavelength (both infraredand ultraviolet) datasets, Madau and Dickinson (2014) showed that the star formationactivity in the Universe peaked ∼ 3.5 Gyr after the Big Bang, corresponding to a redshiftof z ∼ 1.9, and the star formation rates declined towards both earlier and later epochs(see top of Figure 1.2). UV studies of star formation are very sensitive to reddening effectscaused by dust extinction in the interstellar medium. The bottom panel of Figure 1.2shows the contribution from the UV data uncorrected for the dust attenuation and alsofrom infrared surveys that trace the obscured star formation. The limitations in thecorrect determination of the cosmic star formation history are clearly visible. Whilethe infrared luminosity densities provide a calorimetric measure of the obscured starformation rate density, the UV data need substantial correction, and the exact valuesof this correction are quite uncertain, even in the local Universe. The IR values give aless biased result, but so far the available redshift range is limited. Currently Herschelsurveys provide the highest redshift results, as Gruppioni et al. (2013) used PACS andSPIRE data to determine the luminosity evolution up to z . 4. While several examplesof z > 4 dusty star-forming galaxies are known (e.g. Daddi et al., 2009; Coppin et al.,2009; Capak et al., 2011; Riechers et al., 2013), due to the lack of statistically significanthigher redshift samples there are no current estimates of the luminosity function at z > 4and the contribution of dusty star-forming galaxies to the high-z star formation ratedensity is still unknown. One of the main goals of this thesis is to assemble a catalog14Figure 1.2: Star formation rate density of the Universe at different redshifts. The topfigure shows the best fit to a range of datasets in the infrared, as well as ultraviolet datacorrected for dust attenuation, while the lower figure shows the IR and the uncorrectedUV values. Republished with permission of Annual Reviews, from Madau and Dickinson(2014); permission conveyed through Copyright Clearance Center, Inc.15of candidate z > 4 galaxies detected in a large area survey observed by Herschel -SPIREand to examine the number counts of these sources in order to infer their role in thestellar mass build-up in the early Universe.1.6 Modelling the evolution of dusty star-forminggalaxiesThe steep slope of the observed far-infrared and submillimeter number counts and studiesof the infrared luminosity function suggest that the properties of dusty star-forminggalaxies are strongly evolving. There are many different ways to create models thatdescribe this evolution, with the main constraint that they should be able to predict theobserved number counts and redshift distribution of the dusty galaxy populations.Backward evolution models are purely empirical. In these approaches the physicalproperties of individual sources are ignored, and instead the observed number countsare predicted by extrapolating locally observed correlations (e.g. luminosity functionsor stellar mass functions) and spectral energy distributions, assuming an evolution inredshift (e.g. Valiante et al., 2009; Be´thermin et al., 2011, 2012a). Forward semi-analyticmodels and hydrodynamical simulations are more physical. First the build-up of darkmatter halos is reconstructed, then the physical processes are modelled that can drive thebuild-up of the baryonic component. These include feedback processes, star formationrates, gas cooling physics, chemical enrichment and dust radiative transfer models (e.g.Baugh et al., 2005; Dave´ et al., 2010; Hayward et al., 2013).The widely accepted view is that dusty star-forming galaxies represent a relativelyshort phase in the evolution of local elliptical galaxies (Lilly et al., 1999; Swinbank et al.,2006). One of the popular theories of forming dusty starburst galaxies describes a mergerdriven picture, in which major mergers between gas rich galaxies trigger a short starburstperiod lasting ∼100−200 Myr (e.g. Smail et al., 2004; Greve et al., 2005; Tacconi et al.,2008), then gas depletion and feedback processes from the central AGN quench the starformation and an elliptical galaxy is formed with a passively evolving stellar population.Observations of individual submillimeter galaxies seem to support the merger-driventheory by showing disturbed morphologies (Conselice et al., 2003; Chapman et al., 2003;Kartaltepe et al., 2012); however other studies claim that there is no evidence thatmerging would be the dominant reason for the starburst activity (Swinbank et al., 2010a).Another possibility is that these galaxies are very massive, gas rich galaxies that simplycontain more molecular gas than local galaxies, so they can form more stars even without16an increased star formation efficiency (Tacconi et al., 2010; Targett et al., 2013). Localstar-forming galaxies show a tight correlation between their stellar mass and specificstar formation rate (SFR per unit stellar mass). The majority of galaxies follow thisstar formation “main sequence” (Brinchmann et al., 2004; Noeske et al., 2007), whilestarbursts show an elevated specific star formation rate compared to similar mass mainsequence galaxies. Some studies claim that the majority of the submillimeter brightgalaxies might be massive star-forming galaxies on the main sequence instead of beingstarbursts (Rodighiero et al., 2011).Since locally the most massive ellipticals can be found in the centres of large virial-ized clusters, it is reasonable to think that if dusty star-forming galaxies are indeed theprogenitors of these ellipticals at high redshift, then they could reside in a proto-clusterenvironment consisting of galaxies falling into a cluster. Some massive galaxy clustersalready contain an evolved sequence of quiescent galaxies at z > 1−2 (Cimatti et al.,2004; Gobat et al., 2011) suggesting that they should have formed the bulk of their starsmuch earlier than the epoch when the cosmic star formation rates peaked. There are sev-eral examples in the literature of z > 3−5 starburst galaxies that reside in proto-clusterenvironments (Chapman et al., 2001; Daddi et al., 2009; Capak et al., 2011), but as aa counter example, the environment of the highest redshift dusty star-forming galaxyfound to date (HFLS3; Riechers et al., 2013) does not show signs of an over-densityof star-forming galaxies around it (Robson et al., 2014). In this thesis we will investi-gate the environments of several z > 4 candidate galaxies. Finding an over-density ofstar-forming galaxies around these sources would strengthen the theory that distant star-bursts can trace proto-clusters and indicate that the environmental effects of falling intothe cluster can increase the star formation activity in galaxies. We will also investigatethe dusty star-forming activity in moderate redshift massive virialized galaxy clusters.While these clusters mostly contain galaxies with passively evolving stellar populations,finding dusty star-forming galaxies in these clusters can provide additional constraintson evolution models.1.7 Outline of this thesisThis thesis is organized as follows. In Chapter 2, we describe the process of makingoptimal large maps from Herschel -SPIRE data and we describe the two large area surveysused in this thesis. In Chapter 3, we describe a method to select z > 4 galaxies based ontheir SPIRE colors, and we investigate the statistics of the catalog created. In Chapter 4,we describe a follow-up observing campaign of high-z galaxy candidates using SCUBA-172. In Chapter 5. we investigate the dusty star formation activity in the line of sightof moderate redshift galaxy clusters selected by the Atacama Cosmology Telescope. InChapter 6. we discuss our main results and future directions and we conclude the thesis.18Chapter 2Making large maps fromHerschel-SPIRE dataWith the advancement of techniques used to observe the far-infrared sky, the importanceof designing large-area surveys will increase as well. The study of the cosmic infraredbackground, either through statistical analysis of the unresolved emission itself, or bythe investigation of the properties of individual galaxies that constitute this backgroundradiation, gives us a unique insight into the evolution of star formation and large-scalestructure in the Universe. Mapping large areas on the sky helps us to create statisticallysignificant samples of the resolved galaxy populations that contribute to the CIB andit increases our chances to find very rare objects that were not previously well studied.As we discussed in Section, we can also learn about the clustering properties andevolution of the different populations from cross-correlation studies of datasets at differentwavelengths. A large area survey allows the reconstruction of the power spectrum downto very low angular frequencies. For these studies it is crucial to create maps from theraw detector data that contain an unbiased estimate of the brightness variations in thesky on all angular scales.Far-infrared and submillimeter instruments generally contain incoherent detectors,that only measure the intensity of the incoming signal, and not the phase. In thesedetectors the power of the incoming radiation is converted into a change in voltage orcurrent compared to the detector baselines. The detectors are also sensitive to variationsin the conditions in the instrument; thus these baselines can change in time. Slowvariations, like temperature drifts in the instrument, cause an 1/f -type low frequencynoise in the detector timestreams, but short noise spikes are also often present in thedata. The main goal of map-making is to separate the observed sky signal from thesecomponents. The crucial step in recovering the large-scale variations in a field is the19correct handling of the 1/f -type correlated noise in the observed data. To create mapsthat are optimal for point-source reconstruction, the easiest approach is to use a high-passfilter that removes frequencies below the noise knee-frequency where the correlated noisestarts to dominate over the white noise level. However, this process removes any large-scale astronomical signal too, and it is not optimal to measure large-scale variations in themaps. The current far-infrared and submillimeter instruments often contain hundreds ofindividual detectors in their focal planes, and the observed data timestreams can containsignificant correlated noise between different detectors, thus the map-makers need to beoptimized to handle these noise components carefully.The main goal of the map-making project described in this chapter is to create mapsfrom observations of two wide area fields along the celestial equator carried out by theSPIRE instrument (Griffin et al., 2010) on the Herschel Space Observatory (Pilbrattet al., 2010). These two fields are the 280 deg2 HeLMS field, which is part of the HerschelMulti-tiered Extragalactic Survey (HerMES, Oliver et al., 2012) and the adjacent 80 deg2field called the Herschel Stripe 82 Survey (HeRS, Viero et al., 2014). In this chapter wedescribe the Herschel -SPIRE instrument and the main data processing steps, then wediscuss the shim and sanepic map-makers used in HerMES and HeRS to create maps.sanepic (Patanchon et al., 2008) was developed for the BLAST-telescope (Devlin et al.,2004), which was a technical and scientific prototype for SPIRE. This map-maker canhandle correlated noise between detectors to better recover the large-scale sky signal. Wediscuss the adaptation of the sanepic map-maker to work with SPIRE data; we test theperformance of recovering large structures by comparing the results to maps made withthe shim map-maker; we investigate the noise properties of the final maps and discusscurrent and future science projects that are based on these datasets.2.1 The Herschel-SPIRE instrumentThe European Space Agency’s Herschel Space Observatory (Pilbratt et al., 2010) wasoperational between 2009 and 2013 and observed the sky at far-infrared/submillimeterwavelengths covering the peak of the thermal emission spectrum of cold dust. Herschelhad a large aperture (3.5 m) mirror and a better sensitivity than the detectors operatingat similar wavelengths before. The satellite had three instruments on board; HIFI (Het-erodyne Instrument for the Far Infrared, de Graauw et al., 2010), PACS (PhotodetectorArray Camera and Spectrometer, Poglitsch et al., 2010) and SPIRE (Spectral and Pho-tometric Imaging Receiver, Griffin et al., 2010), which contained a three-band imagingphotometer and an imaging Fourier transform spectrometer.20The SPIRE photometer had a field of view of 4′ × 8′ and was capable of imagingthe sky simultaneously at 250µm, 350µm and 500µm wavelengths with beam sizes thatcan be approximated by Gaussian profiles with a full-width half-maximum of 18′′, 25′′and 36′′, respectively. These beam sizes result in a confusion limit of 5.8 mJy beam−1,6.3 mJy beam−1 and 6.8 mJy beam−1 at 250µm, 350µm and 500µm, respectively, ascalculated by Nguyen et al. (2010). The instrument consisted of arrays of 139 (250µm),88 (350µm) and 43 (500µm) hexagonally packed feedhorn-coupled spider-web NeutronTransmutation Doped (NTD) germanium bolometers (Turner et al. 2001; Rownd et al.2003).Bolometers are common types of thermal detectors used in infrared astronomy. InSPIRE, the light is absorbed by a spider-web shaped mesh made of silicon nitride coatedwith a thin resistive metal layer, and the generated heat is conducted to the thermistormade of NTD germanium. As the absorbed power increases, the resistance of an NTDbolometer will decrease. Each bolometer has a biasing AC-current passing through itand the voltage on the bolometers is measured. The voltage change due to the changein resistance after photon absorption is registered by the readout electronics.The SPIRE bolometers have a very low operating temperature of 0.3 K. To achievethis the arrays need to be cooled to reduce thermal fluctuation from the ∼ 85 K telescopemirror and the instrument electronics. The bolometer arrays are connected to a 3Hecooler bath (Duband, 1997) in order to keep their temperature in the operating regime.At the beginning of the cooler-cycle all of the 3He is in liquid form. As the Helium startsto evaporate, a 2 K temperature cyro-pump reduces the vapour pressure and cools theliquid. The slowly evaporating gas keeps the temperature at ∼ 300 mK. When all ofthe Helium has evaporated, the refrigerator is recycled by recondensing the Helium intoliquid form again. For this the pump first needs to be heated up to 40 K to release theabsorbed gas, then the pump is cooled down to 2 K again and a new cooling cycle starts.The stable temperature phase usually lasts for more than 46 hours, and the recyclingprocess lasts for 2 hours.Fluctuations in temperature inside the instrument can change the resistivity of thebolometers; thus they can imitate the effect of absorbed emission from the sky. Variationsin the cooler bath temperature will affect all bolometers in a similar way, creating avarying baseline for the detectors. The detector arrays can also be hit by charged high-energy particles. The detected power from these cosmic rays also has a similar effect onthe measured voltage as absorbed photons. It is therefore crucial to understand theseinstrumental and external effects and to correctly disentangle them from the sky signal.212.2 Initial data processingThe main operating mode of the telescope is scan-mapping. During this operation thefield of view of the detectors is scanned back and forth across the sky with a speed of30 arcsec s−1 (nominal mode) or 60 arcsec s−1 (fast-scan mode). During this process alarge amount of data is recorded for each bolometer as a function of time, including themeasured voltage, the pointing information, information about the telescope movementsand the instrument conditions. The bolometers are sampled with a frequency of 18.6 Hz,corresponding to a 0.05 s sampling time-interval. These time-ordered data (TOD) areuncalibrated and uncorrected. Before any map-making step we need to correct the TODsfor instrumental effects and convert the signal from Volts into flux density units in Jybeam−1 (1 Jy = 10−26 W m−2 Hz−1). These initial processing steps are carried out usingthe Herschel Interactive Processing Environment (HIPE, Ott 2010) software package.The details of the pre-processing are described in Griffin (2009).2.2.1 DeglitchingAs a first step, glitches in the timestream caused by cosmic rays hitting the detectorarrays need to be detected and removed. These cosmic rays can hit a bolometer directly,causing a large glitch in the timeline of that single detector, or they can hit the bolometerarray frame and cause a change in the signal of multiple detectors simultaneously.The pipeline first applies a concurrent deglitcher module, which finds and flags thesimultaneously appearing cosmic ray hits. First the timestream for bolometer j, dj(t)is smoothed with a boxcar filter of width 15, then this smoothed timeline dj,sm(t) issubtracted from the original timeline to find the residualsrj(t) = dj(t)− dj,sm(t). (2.1)This is repeated for all bolometers in the array, and the median of all bolometer valuesat each time index t is calculated asm(t) = medianj{rj(t)}. (2.2)The median absolute deviation from this value is determined asmad(t) = medianj{rj(t)−m(t)}. (2.3)22Now calculating the median in time we get an average number for the whole array asmmad = mediant{mad(t)}. (2.4)Finally the algorithm flags time samples withm(t) > κmmad (2.5)where κ is typically set to 4 during SPIRE map-making. To ensure that the tail of theglitch is removed too, the algorithm also flags an extra sample at the end of blocks ofconsecutive flagged samples.The next step after concurrent deglitching is to identify and flag the individual cosmicray hits that only affect a single detector. Two different methods are implemented in thereduction pipeline, a “sigma-kappa” deglitcher and a “wavelet” deglitcher. The sigma-kappa deglitcher works similarly to the concurrent deglitcher, except here we do notcombine the residuals of different detectors, but calculate a standard deviation value foreach TOD separately. The glitch detection is iterative, such that the glitches are flaggedand excluded when recalculating the standard deviation. The process is repeated untilno new glitches are flagged in the timeline.A more complex deglitching method can also be used to detect glitches in the timestreamsusing wavelet-based local regularity analysis. This assumes that these features have ashape similar to a Dirac-delta function, but the algorithm is also able to handle clippedglitches that have different shapes. The method, based on a continuous wavelet transformwith a Mexican-hat wavelet is described in detail in Ordenovic et al. (2005, 2008).2.2.2 Electrical filter response correctionDuring the readout process, AC bolometer signals are lock-in amplified at the bias fre-quency, a process that consists of a band-pass filter, a switch and a low-pass filter appliedto the switched signal. The low-pass filter imposes a time delay on the detector signals,and thus a delay between the detector signals and the signals recording telescope pointinginformation. This delay can be as long as 74 ms, which causes a 2.2′′ difference in posi-tion for nominal scan mode and 4.4′′ shift in fast scan mode. A low-pass filter responsecorrection is needed to correct for this effect. The correction happens in Fourier spaceby multiplying the timeline with a complex function whose parameters are stored in acalibration file and are based on the low-pass filter transfer function.Usually a similar correction is applied to adjust for the time response of individual23bolometers. This delay is also determined from the calibration file but this correctionstep is usually carried out after the data have been converted from voltage values to fluxdensities.2.2.3 Flux CalibrationBefore map-making the detector timelines need to be converted from units of voltage toin-beam flux density. The detailed flux calibration for SPIRE is described in Bendo et al.(2013) and Griffin et al. (2013).The spectral in-beam flux density of a source with surface brightness Iν(θ, φ) isS(ν) =∫ 2pi0dφ∫ pi0B(θ, φ)Iν(θ, φ) sin θdθ, (2.6)where B(θ, φ) is the normalized beam profile. As noted in Bendo et al. (2013) and Griffinet al. (2013) the bolometers measure the spectral response function (SRF) weighted fluxdensity, which is proportional to the power that the bolometers absorbed. If F (ν) is thespectral response function of the detector and η(ν) is the aperture efficiency then thisweighted flux density can be calculated asS¯meas =∫νS(ν)F (ν)η(ν)dν∫νF (ν)η(ν)dν, (2.7)where we integrate over the passband frequencies. Bendo et al. (2013) find that therelation between small changes in S¯meas and the voltage change across the bolometer canbe described by the functiondS¯measdV= f(V ) = K1 +K2V −K3 , (2.8)where K1, K2 and K3 are constants and are derived empirically based on internal calibra-tion sources. The conversion from measured voltage to S¯meas happens by integrating thisvalue between the operating voltage V0 of the bolometer and the measured Vm voltageafter photon absorption from sources,S¯meas =∫ VmV0(K1 +K2V −K3)dV. (2.9)To convert the data units from the SRF-weighted flux density to monochromaticspectral flux density we usually assume that the source spectrum is a power law and can24be written asS(ν) = S(ν0)(νν0)α, (2.10)where ν0 is the central frequency of the SPIRE bands corresponding to 250µm, 350µmand 500µm wavelengths. A power-law index of α = −1 is chosen in the SPIRE datareduction process in order to obtain a flat νSν spectrum across the band. CombiningEquations 2.10 and 2.7 we getS(ν) = S¯meas[να0∫νF (ν)η(ν)dν∫νναF (ν)η(ν)dν]= K4S¯meas. (2.11)The main calibrator for SPIRE is the bright and almost point like source Neptune,with a well known spectral flux density and an absolute photometric uncertainty of ∼ 4%(Moreno, 1998; Bendo et al., 2013). The measured flux densities of Neptune are comparedto the expected model values and the differences are corrected. These final pre-processedtimelines will serve as the input for different map-making software packages.2.3 Map-makersSeveral map-making software packages are capable of working with time-ordered data pre-processed by the standard SPIRE pipeline. Some of these have been developed directlyfor SPIRE and others were adapted from different instruments. Early versions of theHIPE pipeline included the Na¨ıve Mapper, which has been replaced by the Destriper.Other mappers include Scanamorphos, Unimap, HiRes and SUPREME. The descriptionand a detailed comparison of the performance of these map-makers is presented in Xuet al. (2014).Maps in the HerMES survey are usually created with the SPIRE-HerMES IterativeMapper (shim, Levenson et al., 2010, Viero et al., 2013), which is part of the SMAP pro-cessing pipeline. For the largest maps in HerMES and also for the map observed in theHeRS survey we use sanepic (Signal And Noise Estimation Procedure Including Cor-relations, Patanchon et al., 2008), a maximum-likelihood map-maker that was originallydeveloped for BLAST (Balloon-borne Large Aperture Submillimeter Telescope, Devlinet al., 2004), a telescope built effectively as a pathfinder for SPIRE. This map-makeruses the cross-correlation of noise between detector timestreams to remove correlatednoise without removing the largest scale astronomical signal from the datasets. sanepicwas developed at the University of British Columbia, and UBC also had a large involve-ment in the development of shim. In the following we focus on the shim and sanepic25map-makers, with emphasis on the optimization of sanepic to work with SPIRE data.2.3.1 sanepicsanepic (Signal And Noise Estimation Procedure Including Correlations, Patanchonet al., 2008) is a maximum likelihood map-maker developed for BLAST (Devlin et al.,2004), a balloon-borne experiment using similar detectors as the bolometers in SPIRE.sanepic can preserve large-scale signals in the sky by removing correlated noise fromthe timelines based on the cross-correlation of the timestreams of different detectors.The timestream of a bolometer indexed by i can be modeled as~di(t) =∑pAi(t, p)~s(p) + ~ni(t), (2.12)where t is the sample time, s is the signal in pixel p of the final map of the sky andAi(t, p) is the pointing matrix, which gives the weight of the contribution of the signalin pixel p to the timestream of bolometer i at time t. If our map has np pixels and theTOD has ns time-samples, then Ai(t, p) is a matrix of size ns × np. The SPIRE beamsare approximately symmetric, so we can treat ~s as the beam-convolved sky, in which casethe pointing matrix contains only zeros and ones and it simply tells us the pixel positionwhere bolometer i points on the sky at time t.If many closely-packed detectors observe the same area of the sky, then they can allfeel similar biasing effects from their environment. The noise term ni(t) can be modelledas the sum of an uncorrelated noise component n˜i(t), and a common-mode signal c(t),which is the same for all detectors, apart from a detector-dependent multiplicative factorαi:ni(t) = n˜i(t) + αic(t). (2.13)If we assume that the noise is Gaussian and stationary, satisfying 〈ni(t)〉 = 0, then wecan construct the time-domain noise covariance matrix for detectors i and j asNij(t, t′) = 〈ni(t)nj(t′)〉. (2.14)For timestreams containing ns samples, this will be a matrix of size ns×ns that will havenon zero off-diagonal elements if there is correlated noise between detector i and j. Wenote that if we have multiple bolometers nb, then in this notation ~d and ~n correspond to(ns ·nb) element column-vectors with all the detector timestreams stitched together, andthe N matrix of size (ns · nb)× (ns · nb) is built up of ns × ns sized blocks of Nij:26~d =~d1(t)~d2(t)...~dnb(t) , ~n =~n1(t)~n2(t)...~nnb(t) , N =N11 N12 . . . N1nbN21 N22 . . . N2nb....... . ....Nnb1 Nnb2 . . . Nnbnb . (2.15)The sky signal can be estimated from the detector TODs using maximum likelihoodmethods. The log-likelihood of the data islogL(~d|~s) = −12(~d−A~s)TN−1(~d−A~s). (2.16)and the maximum likelihood solution is given by~ˆs = (ATN−1A)−1ATN−1~d. (2.17)The SPIRE instrument samples the sky at 18.6 Hz, which means that we have timesamples 0.053 s apart, and many scans last for over 10 hours, creating TOD vectors thatcontain > 106 elements. For datasets this large an explicit inversion of the time-domaincovariance matrix N would be too time-intensive. Instead sanepic assumes that theTODs have no gaps and are circulant, meaning that the observations end at the sameplace where they started. If this is true, then the covariance matrix is circulant too, andits values only depend on the time separation between samples asN(t, t′) = f(|t− t′|). (2.18)The Fourier transform of a circulant matrix is diagonal and it can be constructed fromthe power spectrum of the timestreams. So if we know the power spectrum of the detectorTODs then the inverse of the time-domain covariance matrix can be calculated asN−1 = F−1[P(ω)−1], (2.19)where F−1 represents an inverse Fourier-transform and P(ω) is a matrix constructedfrom the auto- and cross-power spectra of the TODs, containing information about thecommon-mode noise between bolometers in addition to the uncorrelated noise terms.P(ω) contains diagonal blocks of Pij sub-matrices that can be expressed as the bin-averaged power spectrum between bolometers. If we divide the frequency range into27q bins with bin sizes dq, each bin containing nq samples, then the bin-averaged powerspectrum can be written asPij(ωq) =1nqωq+dq/2∑ωq−dq/2d˜∗i (ω)d˜j(ω), (2.20)where d˜i(ω) represents the Fourier-transformed TOD for bolometer i. We can also expressthe power spectrum in terms of the common-mode and uncorrelated noise componentsasPij(ω) =[αiαj〈c˜∗(ω)c˜(ω)〉+ δij〈n˜∗i (ω)n˜j(ω)〉]. (2.21)In practice the latter equation is used in the sanepic algorithm and the parametersare determined by a blind component separation method similar to the one describedin Delabrouille et al. (2003). The noise power spectra matrix of the timestreams isdetermined from the data during an iterative process. In the first iteration the algorithmassumes that the TODs contain only noise and a first realization of the sky map is created.In the subsequent iterations the current map needs to be reprojected into time-ordereddata and subtracted from the data timestreams to remove the astronomical signal. Anexample comparison of an auto- and cross-power spectrum of a bolometer TOD is shownin Figure 2.1. It can be seen that the uncorrelated white noise at high frequenciesdominantly comes from a single bolometer and the correlated noise that dominates atlow frequencies is a component that both bolometers can see. The operation N−1dcorresponds to dividing the Fourier-transformed data with the noise power spectrum,and this step removes the large-scale correlated noise from the timestreams.The inverse of the pixel-pixel noise covariance matrix, N−1pp′ = (ATN−1A)−1 is notcalculated explicitly in the map-making process. Instead the map-maker uses an itera-tive algorithm based on the conjugate gradient method with preconditioner to find themaximum likelihood solution for the map. The method works by minimizingΨ = rTN−1pp′r, (2.22)where r is defined asr = (ATN−1Asˆk − ATN−1d) = (ATN−1dk − ATN−1d). (2.23)Here sk is the map estimate at iteration k and dk = Ask is this map projected into atimestream.2810−3 10−2 10−1 100 101Frequency (Hz)10−510−410−310−210−1100Powerspectrum(arbitraryunit)Auto-PSCross-PSDifferenceFigure 2.1: Diagonal values of two sub-matrices from the power spectrum matrix P(ω).The solid line shows the diagonal values of an auto-power spectrum matrix Pii(ω) cal-culated from the TOD of bolometer i, the dashed line shows the diagonal values of thecross-power spectrum matrix Pij(ω) between two different bolometers i and j and thedotted line is the difference of the two plots. The correlated noise is seen by both bolome-ters and this information is used to de-weight the correlated noise in the timestreams.Usually a few hundred iterations are needed to reach convergence. sanepic also cre-ates an error map as an extension to the output products. This map gives an estimateof the variance of the noise in each pixel of the final map. Obtaining this error termcorrectly would require calculating the explicit pixel-pixel noise covariance matrix, butthat operation is too computationally intensive and is never carried out during the iter-ative map-making. The error map sanepic creates is a first-order estimate of this noise,computed by neglecting the off-diagonal terms in the inverse pixel-pixel noise covariancematrix, assuming that the final map only contains white noise. We note, that this methodcan result in an over-estimation of the real residual noise values in the maps, but theerror map can still be used to assign weights to each pixel in our final map.2.3.2 shimThe SPIRE-HerMES Iterative Mapper (shim, Levenson et al., 2010, Viero et al., 2013)formalism is based on an iterative baseline removal algorithm. After a median subtractionthe time-ordered data d(t) for a given detector in a given scan are passed to the map-maker where they are modelled as29~d(t) = g∑pA(t, p)~s(p) + ~bm(t) + ~˜n(t). (2.24)Like in Eq. 2.12,∑p A(t, p)~s(p) represents the reprojected signal from the sky-map ~s intoa bolometer timestream, and ~˜n(t) is the uncorrelated noise component. The baseline driftresponsible for the low frequency 1/f noise is modelled as an mth-order polynomial ~bm(t),and g is the relative detector gain, which can be changed if we assume that the beamshapes of the individual bolometers are not exactly the same. As a first iteration thegain is set to unity and the timestream is simply rebinned into a map. In the followingiteration steps the g value is first fixed to be the result from the previous iteration and the~bm(t) polynomial is fit to the timestream residual Rk(t), which is calculated at iterationk by subtracting the map calculated in the previous iteration from the timelines,~Rk(t) = ~d(t)−[gk∑pA(t, p)~sk−1(p)]. (2.25)After finding the optimal baseline, the g value can also be fitted to the data by mini-mizing Rk(t) while keeping the polynomial term fixed. The absolute detector gains forSPIRE have been determined from observations of calibration sources and these valuesare applied to the timestream during the HIPE pre-processing steps. In practice, the rel-ative gain described here will not differ significantly from unity, and the g value is oftenkept constant during map-making. At the end of each iteration the inverse variance ofthe residual timestream is assigned as a weight to the bolometer TOD aswk =[1N∑tRk(t)2]−1. (2.26)This whole process is repeated for all detector timestreams in all of the individual scansof the observation and a new map is constructed by creating a weighted mean of all ofthe samples that fall into the same pixels,sk(p) =∑∈pwk(d(t)− bmk )/gk∑∈pwk, (2.27)30where the sum runs over all samples in all bolometer timelines and all scans that maponto pixel p. The noise map is calculated from the weights asσk(p) =[∑∈pwk]−1/2. (2.28)Unlike sanepic, shim deals with the low frequency noise component individually for eachbolometer timestream, ignoring correlations between detectors. As a result, shim willnot be as efficient in reconstructing the largest angular scales in a sky map as sanepic.We will compare the performance of sanepic and shim in Section Using sanepic with SPIRE dataThe Herschel Multi-tiered Extragalactic Survey (HerMES, Oliver et al., 2012) is a “wed-ding cake” type survey containing small and deep maps and larger shallower observationsof different fields. The area of these fields varies between 0.005 deg2 and 19 deg2. In theHerMES project the native map-maker used to create the final data products is shim.shim maps are optimal for point-source detection and they also recover signals at largerangular scales than the size of the point-spread function, but the largest angular scalesare filtered out in the map-making process. The recent addition of the 280 deg2 HeLMSfield and the adjacent 80 deg2 HeRS field – which was observed in a close collaborationwith HerMES – raised the need to improve the map-making process in order to fullyexploit the large area of these maps by preserving the large scale sky signal as much aspossible.In the following we describe the HeLMS and HeRS surveys and the application ofthe sanepic map-maker to these two datasets. We compare the resulting maps to dataproducts created with shim, investigate the noise properties and the transfer function,and discuss future uses of these large area maps.2.4.1 The HeLMS and HerS surveysThe HerMES Large Mode Survey (HeLMS, Oliver et al., 2012) consists of a large areashallow observation of an equatorial field at wavelengths of 250, 350 and 500µm, obtainedusing SPIRE. HeLMS covers 280 deg2 of the sky, making it the largest area observed inthe HerMES survey. The HeLMS field spans 23h14m < RA < 1h16m and −9◦ <Dec < +9◦, an equatorial region with low contamination from heated dust clouds in31the Milky Way (Galactic cirrus). It is designed to have a large overlap with the SloanDigital Sky Survey’s Stripe 82 field, one of the most highly observed areas of the sky,with extensive multi-wavelength ancillary data coverage. The equatorial area has theadvantage that it can be observed from almost any ground-based telescope site in theworld. The HeLMS field was observed with the telescope operating in fast-scan mode(60 arcsec s−1 scan-speed) and the observations were repeated in two nearly orthogonalscan-directions in order to obtain cross-linked data. The dataset consists of 11 individualscans, out of which six cover the full HeLMS area in one scan direction and five in theother. The coverage map is shown in Figure 2.2. Since the scans corresponding to thesame scan-direction are designed to be adjacent to each other with minimal overlap, thecoverage of the map is nearly uniform. Having only two scans at each part of the mapgives shallower coverage than the deepest SPIRE maps. However, the noise is still only afew times higher than the confusion level, and the large area of the survey compensatesfor this loss in depth.The Herschel Stripe 82 Survey (HerS, Viero et al., 2014) is a field adjacent to HeLMSand although this survey is not a part of HerMES, the two analysis teams work in a closecollaboration with each other and have a substantial overlap in personnel. HerS covers79 deg2 of the sky between 0h54m < RA < 2h24m and −2◦ < Dec < +2◦. The spanin declination is smaller than that of the HeLMS field, but together HeLMS and HerScover the whole Stripe 82 region in RA. The observing strategy for HerS was similar tothat of HeLMS. This observation is made up of 21 individual scan-lines, but unlike inHeLMS, here the adjacent scans have some overlap with each other, creating areas in themap with deeper coverage. The HerS coverage map is shown in Figure 2.3.Due to the equatorial position and the full overlap with the SDSS Stripe 82 field,the HeLMS and HerS surveys have a very rich ancillary data coverage. These datasetsinclude the SDSS-III’s Baryon Oscillation Spectroscopic Survey (BOSS; Eisenstein et al.,2011), the Hobby-Eberly Telescope Dark Energy Experiment (HETDEX; Hill et al.,2008), the Spitzer -HETDEX Exploratory Large Area Survey (SHELA; Papovich et al.,2012), the Spitzer -IRAC Equatorial Survey (SpIES; Richards et al., 2012), the VLA-Stripe82 (Hodge et al., 2011), VISTA-VIKING (Emerson et al., 2004), and the HyperSuprime-Cam (HSC; Miyazaki et al., 2012) surveys, among others. In addition, HeLMSand HerS overlap with a survey of the cosmic microwave background (CMB) conductedby the Atacama Cosmology Telescope (ACT; Swetz et al., 2011) in Stripe 82. There is acollaboration between HerMES, HerS and ACT to conduct studies that involve both theHerschel and ACT datasets. Part of this map-making project is to create data productsthat facilitate cross-correlation studies between the ACT and Herschel datasets.32Figure 2.2: Coverage map of the HeLMS dataset. Dark areas have the lowest coverage,meaning that the number of detector time-samples projecting onto the map-pixel inquestion is low. The observation consists of 11 individual scans, five of which with similarscan directions span most of the RA range of the survey and the other six orthogonalscans span the total range in declination. The scans having similar detector orientationare adjacent to each other with minimal overlap, and the final map has a nearly uniformcoverage.Figure 2.3: Coverage map of the HerS dataset. HerS consists of 21 individual scans,and while the adjacent observations spanning the declination range are designed to haveminimal overlap, the scan-lines in the orthogonal scan direction overlap with each otherto some extent, creating areas with better coverage than the rest of the map. Those areasthat have been observed three times are clearly visible as light stripes in the coveragemap. The pixel-noise in these areas is smaller than the noise in the rest of the map.332.4.2 Additional timeline processingThe initial processing of the SPIRE time-ordered data segments is carried out in HIPE,as discussed in Section 2.2. Different map-makers might need to apply extra processingsteps to these timelines, depending on the data properties and the assumptions madeabout the data by the mapping algorithm.Before passing the data to either shim or sanepic, the TODs are read in by theSMAP pipeline. As discussed in 2.2.1, deglitching happens during the initial data pre-processing of the timelines in HIPE. In some cases, however, this first-level deglitchingfails, and the anomalous signal propagates into the maps. The shim map-maker appliesan iterative second-level glitch detection algorithm, using the fact that each pixel on thesky is sampled multiple times. Based on the large number of samples projecting ontothe same sky pixels, the expected flux density in that pixel can be predicted and anysamples that are more than 10σ away from this value are flagged and not included in themap-making process. This deglitching information is saved and can be re-used later. Weuse this information created from initial shim-processing of the HeLMS and HerS datato remove residual glitches from the timestreams before passing the TODs to either shimof sanepic.An astrometry correction step is also carried out in SMAP before map-making totest the reliability of the pointing information and to correct for any shifts in position.This is usually done by stacking initial maps for each observation on the positions ofSpitzer-MIPS (Rieke et al., 2004) 24µm sources. For the HeLMS and the HerS regionsMIPS catalogs are not available and the correction is based on positions of sources in theWISE survey (Wright et al., 2010). Both of the MIPS and WISE catalogs have positionalaccuracies better than 0.5′′. After stacking the SPIRE maps on these positions the sourceprofile is fitted to determine the measured position and the offsets (usually in the rangeof a few arcseconds) are applied as a correction in any later map-making process. Afterthese processing steps the timelines are exported into FITS files that correspond to thesanepic input file format.The largest component of the low frequency correlated noise between different detec-tors is the result of temperature fluctuations in the 3He cooler. As discussed in Section 2.1all bolometers in the same focal-plane are cooled to the same temperature and the cooleris recycled periodically. Although the temperature is very stable for the most part of thecooler-cycle, slow temperature drifts will cause the signal of the bolometers to changeover time. These changes are usually gradual and create a baseline well represented bya low-order polynomial.Each detector array contains two thermistors that monitor the same temperature34changes that the bolometers experience. SMAP has a temperature-drift correction mod-ule nominally used before shim map-making, which removes the temperature-drifts fromthe detector timelines using the information from the thermistors. The thermistor time-lines are smoothed to remove noise on small scales and these smoothed timelines are thenfitted to the bolometer timelines and the fitted shape is subtracted. In this process themean is also subtracted from each scan.Before sanepic map-making the temperature-drift correction module in SMAP isturned off, since sanepic can handle the correlated noise in its own way. First a low-order polynomial is fit to each timeline and the result is subtracted. This step is neededbecause large gradients from variations on timescales longer than the timestream itselfare not well represented by Fourier-modes and they can cause leakage during Fourier-transformation, which introduces striping and other artifacts in our maps. An exampleTOD before and after the baseline removal is shown on Figure 2.4.Figure 2.4: The effect of gradual temperature drifts in the cooler on the detector timelines.The changing temperature has a similar effect as absorbed power from photons, so thetimestreams will have a non-zero baseline. This long variation needs to be subtractedfrom the timelines before map-making, since gradients can cause ringing during Fourier-transforms and the final maps would contain stripes. The bottom figure shows the sameTOD after the baseline has been subtracted.The order of the polynomial can be set manually and the shape of the timestreamsneeds to be investigated by eye before applying this setting. For the shorter HerS time-35lines this method works well, since the baseline is well fitted with a linear shape, butwe have to be careful because some observations are carried out shortly after a cooler-recycle process when the temperature increases abnormally. The baseline caused by these“cooler-burps” cannot be fitted by a single polynomial. This effect is frequently seen inthe very long (>11 hours) HeLMS TODs. An example of a cooler-burp is shown onFigure 2.5. To remove this effect without using a harsh high-pass filter on the data weneed to deal with the affected scans individually. These long timelines are broken up intoparts where the TOD can be fit by a simple polynomial. Some of the largest scales mightbe removed due to the subtraction of the polynomials, but these scales can be recoveredfrom the cross-scans during map-making.Figure 2.5: The effect of cooler-burps on the detector timestreams. During the recyclingof the refrigerator the temperature changes abruptly and the detector baseline cannot beremoved by a simple polynomial fit.Since sanepic assumes that each data segment is circulant, and the start and end ofthe observation is strongly correlated, we apodize the data segments at the edges over100 samples. The samples we remove this way are usually in a telescope turnaroundregion at the edges of the maps, where the coverage is sparse. These regions are usuallymasked out in any science analysis, so this process does not affect our data quality. Afterthese processing steps the data segments are ready to be passed to the map-makers.2.4.3 sanepic mapsTwo sets of maps at 250, 350, and 500µm were made in order to accommodate differentscience goals. For the first set, we used a gnomonic or tangent-plane (TAN) projectionwith pixel sizes of 6′′, 8.333′′ and 12′′ for the 250, 350, and 500µm maps, respectively.These values are typical for SPIRE maps, chosen to correspond to roughly one-third of thesize of the SPIRE beams. Since the HeLMS and HerS fields overlap with the equatorialstripe observed by the Atacama Cosmology Telescope (ACT), we also made maps using36the nominal ACT map projection, to be used for cross-analysis of the two data sets. Themotivation for matching pixels is that it avoids the reprojecting/regridding of maps thatwould be necessary to perform map-based operations, which could potentially introducesystematic uncertainties. These maps were made using a cylindrical equal-area (CEA)projection with pixel sizes of 29.7′′ in all three bands, corresponding to the nominal ACTpixel size.2.4.4 Comparison of sanepic and shim mapsTo test whether sanepic is indeed a better choice than shim to create maps from thelargest observations, we compare two sets of maps made with each of these map-makers.We select a 300 × 300 arcminute area from the HeLMS region, which is about the largestsquare area that can be selected. First we compute the 2-dimensional power spectrum,which is the square of the absolute value of the Fourier-transform of the maps, andcontains information about the power in the maps at different angular frequencies. Weshow the 2D power spectrum of the 350µm shim and sanepic maps in Figure 2.6. If theoriginal map has dimensions of npix×npix with each pixel having a size of θpix arcminutes,and the full size of the map in arcminutes is θmap × θmap, where θmap = npix × θpix, thenthe dimension of the 2D power spectrum image is still npix × npix, but the reciprocal-space pixel sizes are dk = 1/θmap, and the axes run from (−npix/2)× dk to (npix/2)× dk.The nearly isotropic power in the middle of both power spectra represents the largestscale signal in the maps. The main visible difference is extra power in the shim maps insymmetric patches at angular frequencies of k ∼ 1.5 and k ∼ 3 arcmin−1, correspondingto an angular sizes of ∼ 40′′ and ∼ 20′′, which is comparable to the beam size of 25′′ at350µm. The origin of this noise is as yet unknown, but these patches disappear in thesanepic maps.We also calculate the azimuthally averaged power spectrum by averaging all modesin the 2D spectrum that are at a certain k radius away from the center. The results areplotted on Figure 2.7. Here it is clearly seen, that while both map-makers retain similarpower at frequencies above k ∼ 10−2 arcmin−1, the power at frequencies below this limitis attenuated in the shim maps. This corresponds to physical scales larger than ∼ 100arcminutes. This filtering in shim probably comes from the mean-subtraction that isneeded to apply the temperature drift correction. While both map-makers can producesimilar quality data products for small-area observations, sanepic is clearly a betteroption to use when making very large maps.The filtering effect of the shim map-maker is clearly visible for very large-scale bright37Figure 2.6: 2-dimensional power spectrum of a 300 × 300 arcminute area selected fromthe HeLMS 350µm map. The left figure shows a power spectrum created from a mapmade with shim, and the right image shows the resulting power in the sanepic map.10−3 10−2 10−1 100 101k (1/arcmin)102103104105106107108Pk(Jy2/sr)SANEPICSHIMFigure 2.7: Azimuthally averaged power spectra for the HeLMS 350µm map createdwith sanepic and shim. shim attenuates angular frequencies below 10−2 arcmin−1,corresponding to scales larger than 100 arcminutes on the sky, while sanepic is able torecover these larger scales.38Galactic cirrus structures in the maps. Figure 2.8 shows an area of the HerS map with avery bright patch of cirrus spanning more than 150′ on the sky. The dark patches aroundthe bright structures in the shim map are the result of the filtering effect visible on theplot in Figure 2.7.Figure 2.8: A strong Galactic cirrus patch spanning ∼ 150 arcminutes in HerS. Theleft image shows the shim reconstruction and the right image shows the sanepic maps.The dark patches around the bright regions in the shim map show the filtering effect forscales larger than 100 arcminutes. The large-scale structure is visibly better recoveredwith sanepic.2.4.5 Noise propertiesTo examine the properties of the residual noise in our maps, we create so-called “jack-knife” difference maps by splitting the timestream data into two halves and making aseparate map for each half. The difference map is then made by multiplying one of thejackknifes by minus one and then averaging the two maps. This process removes theastronomical signal but retains the noise, so the jackknife difference map contains thesame instrumental noise properties as the co-added sky map.There are in principle several different ways to split the data in half, some moreeffective than others, but the shallow depth of the HeLMS and HerS observations limitour options. If the map area is observed several times in the same manner, the data canbe split by observation time. Since our fields are only scanned once in each orthogonaldirection, this option is not available for these surveys. We could split the datasets basedon the different scan directions, but we find that the resulting maps have very strongresidual correlated noise along the scan directions due to the lack of cross-linking. A thirdway to split the data is to divide up the detector focal planes, and only use every secondbolometer to make our maps. Even though this method gives the best coverage, at the39nominal pixel sizes, the resulting maps are still quite sparse, especially at 500µm wherethe sampling density is the lowest. This problem is not present in the maps made in theACT mapping configuration, since the pixel sizes are much larger and more time-samplesare projected onto the same pixels.In Figure 2.9 we plot the HerS pixel-histograms of the coadded (or sky) and differ-enced jackknife maps, showing both the standard (TAN) and ACT (CEA) projections.The coadded jackknife maps contain both instrumental and confusion noise (the latterillustrated as vertical dotted lines), and are thus wider than the differenced jackknifemaps. While the instrumental noise is the dominant contribution in the TAN maps, theinstrumental noise in the ACT-CEA maps is lower, due to their pixels being 24.5, 12.7,6.1 times larger (by area) at 250, 350, and 500µm, respectively, such that they haveapproximately equal contributions from instrument and confusion noise. We find thatthe noise is well described by a Gaussian distribution.Having two independent maps from only half of the data also allows us to comparethe pure signal and noise power spectrum of the maps. In Section 2.4.4 we investigatedthe auto-power spectrum of the map. If we instead compute the cross power-spectrumbetween the two half maps, then the uncorrelated noise is removed and the resulting powerspectrum represents the astronomical signal that is visible in both of the half maps. InFigure 2.10 we show the auto-power spectrum of the total map and the jackknife noisemap, and we also show the cross-power spectrum representing the sky-signal calculatedfrom the two half-maps. We can see that the noise is not completely white; there is someexcess correlated noise on larger scales in the maps but it is about 100 times smaller thanthe signal power at those scales. The signal spectrum reaches the white noise level onthe high frequency side due to the smoothing effect of the pixelization of the maps.2.4.6 Transfer functionTo investigate how reliable sanepic is in reconstructing sky signal on different angularscales we determine the map-maker’s transfer function through simulations. This assess-ment is made by creating simulated pure-signal maps, which are then reprojected intodetector TODs and fed back into our map-maker similarly to the real data timestreams.The transfer function is the ratio of the the azimuthally-averaged Fourier transformsof the reconstructed map and the pure-signal input map. In the ideal case the ratioshould be unity at all spatial scales. If the map-maker introduces false signal into ourmaps, or removes existing power, then the transfer function deviates from unity at thecorresponding angular scales.40Figure 2.9: Pixel flux histogram of the HerS maps in both TAN and CEA projection,determined from jackknife tests. Solid lines show the sum of two jackknife maps madefrom each half of the data. This sum represents the total map, including sky signaland detector noise. Dotted lines represent the histogram of the maps made by takingthe difference of the two jackknife maps. Taking the difference cancels out the skycontribution, so these maps can be used to investigate the properties of the residualnoise. The noise can be well fitted by a Gaussian. The instrumental noise compared tothe confusion noise is more dominant in the TAN projection maps, where the pixel sizesare smaller and thus contain fewer data samples per pixel. The excess tail in the coaddedtotal maps arises due to the log-normal nature of the confusion noise distribution. FromViero et al. (2014)4110−3 10−2 10−1 100k (1/arcmin)102103104105106107108Pk(Jy2/sr)Total MapNoiseSky signalFigure 2.10: Azimuthally averaged auto-power spectra calculated from the difference ofthe jackknife maps showing the noise (dash-dotted red line), the full map that is a sumof both halves of the data (solid blue line), and a cross power spectrum of the two halfjackknife maps (dotted green line), which shows the astronomical signal in the maps.The signal clearly dominates over the noise even on the largest scales where the noiseis not completely white. The signal spectrum reaches the white noise level on the highfrequency side due to the pixelization effects. This plot was made from the HerS CEAmaps at 350µm.We constructed 100 pure signal maps with a Monte Carlo simulation using a power-lawpower spectrum resembling that of the cosmic infrared background without the Galacticcirrus. Figure 2.11 shows the resulting transfer function for the HerS maps at 500µm.The simulated and reconstructed maps were made with the same pixel size, so the pixelwindow function does not have any effect here, and the transfer function remains unityon small scales. The transfer function only starts to drop at k ∼ 0.01 (or ` ∼ 200 inthe multipole notation usually used in power spectrum studies, where ` ≡ 2pi/λ[rad] =21600 × kθ[arcmin−1]) corresponding to a scale of 100 arcmin. In studies analyzing thepower spectrum of the sky this function can be used to correct any deviations that areless than ∼ 15 % from unity. Here this corresponds to k ∼ 0.003, or scales smaller than300 arcmin. For larger deviations the reconstruction of large scales is not reliable. Thesmallest extent of the HeRS survey is about this size, so most of the available scales arereconstructed by the map-maker.42Figure 2.11: Transfer function, T , of the sanepic map-maker at 500µm, estimated witha Monte Carlo simulation as described in Section 2.4.6. The lower axis indicates themultipole scale usually used in CMB studies and is defined by ` ≡ 2pi/λ[rad] = 21600×kθ[arcmin−1]. T is found to be approximately unity down to ` ∼ 200 (∼ 100 arcminangular scales), dropping to 0.5 at ` ∼ 30 (∼ 720 arcmin). The vertical dashed linerepresents the largest accessible scale in the HeRS survey, showing that effectively allscales available in the HeRS map are reconstructed. From Viero et al. (2014)2.4.7 ApplicationsWe showed that while the shim and sanepic map-makers work similarly well on relativelysmall angular scales, sanepic clearly shows a better performance in reconstructing thelargest structures in wide surveys. We constructed sanepic maps for the HeLMS andHerS surveys in both the nominal SPIRE projection and pixelization and also createdmaps that match the ACT equatorial maps in both projection and pixel size to helpcross-correlation studies.A very wide range of past, current and future projects are based on the analysisof the HeLMS and HerS maps. As an example, Gralla et al. (2014) investigate thethermal Sunyaev-Zel’dovich (SZ) effect (see Chapter 5) in 1.4 GHz selected radio AGNsby stacking their position on the ACT maps. They use the HeLMS and HerS maps intheir analysis to show that there is no significant contamination from dusty galaxies inthe SZ signal.Wang et al. (2015) use the HeLMS and HerS maps to cross-correlate a sample of Type1 quasars from the SDSS with the cosmic infrared background fluctuations. They detect43the submillimeter emission in the quasars and find that their star formation activity isstronger than the star formation in satellite galaxies in the outskirts of the halos thathost these quasars.An auto- and cross-frequency correlation analysis between the 250, 350 and 500µmmaps of HeLMS and HerS and also between these Herschel maps and the ACT 218 and148 GHz maps is also underway. This study is similar to the analysis described in Hajianet al. (2012) and Viero et al. (2013), and the aim is to determine the correlation betweenthe cosmic infrared background and the cosmic microwave background, and to detectthe clustering signal of dusty star forming galaxies. These studies benefit the most fromthe better large-scale signal recovery properties of the sanepic map-maker, since thisclustering signal extends to low spatial frequencies. The CIB can also act as a foregroundfor CMB measurements and these cross-correlation studies can also help in removing thebias from dusty galaxies on these very low SNR measurements.Cross-correlations with other catalogs and maps will also be possible, including theBOSS QSO sample, optical SDSS cluster catalogs, the HETDEX LAE catalog, the Planckmaps that have full sky coverage and also future instruments like ACTPol or ALMA.In the following chapters of this thesis we will also describe two specific projectsusing the HeLMS and HerS observations. In Chapter 3 we describe a project to find alarge sample of rare high-redshift dusty star forming galaxies in the HeLMS region, andin Chapter 5 we investigate the star formation activity in Sunyaev-Zel’dovich-selectedgalaxy clusters from the ACT equatorial maps that are found in the area overlappingwith HeLMS and HerS.44Chapter 3A search for high redshift dustygalaxies in the HerMES Large ModeSurveyAs we discussed in Section 1.5, our knowledge about the evolution of the cosmic starformation rate density at z > 4 is still uncertain due to the lack of statistically significantsamples of high-redshift dust obscured star-forming galaxies, and the uncertainty of theextinction-correction of the available UV luminosity functions. At lower z the redshiftdistribution of the observed samples is usually determined by calculating photometricredshifts based on available multi-wavelength datasets. However, as of now only a smallset of observed fields have sufficient ancillary data coverage, limiting the samples avail-able with known redshift distribution. Additionally, dusty galaxies at z > 4 are oftenundetectable at shorter wavelengths; thus the determination of the photometric redshiftsbecomes uncertain. To study the contribution of the high redshift dusty galaxies to thestar formation rate density we need a way to select z > 4 objects based on their propertiesin the available far-infrared/submillimeter datasets alone.Dowell et al. (2014) constructed a catalog of potentially high-z galaxies selected from21 deg2 of data from the Herschel Multi-tiered Extragalactic Survey (HerMES, Oliveret al., 2012) at wavelengths of 250, 350 and 500µm. They used a map-based searchmethod to find sources with rising flux densities towards longer wavelengths (S500 >S350 > S250), since at z & 4 the redshifted spectrum of dusty galaxies is expected to peakat λ & 500µm (see Figure 1.1). Follow-up observations of a subsample of these sourcesshowed that most of these galaxies are indeed at z > 4, and this analysis resulted in thedetection of the z = 6.34 source HFLS3 (Riechers et al., 2013), the highest redshift dustystarburst galaxy found to date, forming stars at a rate of several thousand solar masses45per year. Dowell et al. (2014) found an excess of these “500 micron riser” or “red” objectscompared to available galaxy evolution model predictions, and if the current ∼ 10 redsources with spectroscopically confirmed high redshifts are representative of the wholepopulation, then the number density of such galaxies poses a challenge to our currentknowledge about galaxy evolution, indicating that dusty star formation had a larger rolein the early universe than we predicted before. However, the Dowell et al. (2014) sampleis still relatively small and insufficient to investigate the shape of the number counts.In this chapter we describe a continuation of the program started by Dowell et al.(2014). We use a similar map-based search technique to create a large sample of poten-tially high redshift galaxies by analyzing the 280 deg2 HeLMS field (see Section 2.4.1).The instrumental noise in this map is higher than the noise in any of the previously stud-ied HerMES fields, so we will not be sensitive to the faintest objects close to the confusionlimit. However, since the observed area is much larger than before, we expect to finda statistically significant sample of brighter objects, including some very rare, stronglylensed galaxies with flux densities above S500 = 100 mJy as described by Negrello et al.(2010), Paciga et al. (2009) and others. With a sufficiently large catalog the differentialnumber counts of high redshift galaxies can be investigated, and as we discussed before,the shape of the counts could hint to the evolution of the observed population. In thefollowing we will describe the catalog creation, the observed number counts and simula-tions used to infer the corrected counts. We then discuss spectral energy distribution fitsand follow-up observations.3.1 Catalog creationWe use a technique similar to the map-based search method described in Dowell et al.(2014) to find red sources in the HeLMS field. This area of the sky lacks Spitzer-MIPS24µm data that are often used in Herschel observations as a prior to deblend sources(see e.g. Roseboom et al., 2010). Note however, that these catalogs would not be veryuseful anyway to find high-redshift sources, since z > 4 sources are often too faint at24µm to be detected in these wide area surveys. Catalogs of Herschel -SPIRE objectsare also often constructed by using the sources found in the higher resolution 250µm or350µm maps as priors, but these datasets would not be optimal for finding our typical redsources, since we expect these 500µm-riser galaxies to have low signal-to-noise ratio in the250µm or 350µm maps, and hence many of them would probably be undetected in sucha catalog. As in Dowell et al. (2014), instead of matching sources found independentlyat each wavelength, we combine our observations at different wavelengths and use the46information in the maps directly. However, as a modification to the method we use apoint source-matched filter instead of a Gaussian kernel to reduce the confusion noise inthe smoothed maps.3.1.1 MapsWe use the SHIM mapmaker described in Section 2.3.2 to create our maps. We note thatSANEPIC maps were not yet available at the time when we carried out this analysis,however, as we showed before, SHIM has a performance similar to SANEPIC on smallangular scales, so the SHIM maps are just as optimal for point source detection as theSANEPIC data products. The nominal pixel sizes at 250, 350 and 500µm are 6′′, 8.333′′and 12′′, respectively, to match one third of the full-width half-maximum (FWHM) ofthe beam in each band (18′′, 25′′, 36′′). Since we want to combine our observations, wecreate all three of our maps with matching pixel sizes of 6′′ instead. We also make surethat our maps are aligned, so that the same pixels correspond to the same coordinates.We discard the edges of the map where the telescope turned around between scansand the data are not cross-linked. This area is too noisy and the coverage is too sparse toreliably estimate the fluxes of our objects. Similarly, we discard a smaller region in themiddle of the map, where part of one of the overlapping scans had to be removed due tostray light in the telescope. The large-scale cirrus background is subtracted during thesource-finding method, but there is a a “seagull-shaped” area in the middle of the maps,where the cirrus is too strong to be easily removed and the flux estimations are biasedhigh, so we mask this region manually (see Figure 3.1). The total remaining area thatwe use in our analysis is 273.9 deg2.3.1.2 Matched filterThe convolution of a map with its point-spread function yields a map of the likelihood ofpoint sources if the noise in the original map is uniform and uncorrelated and the signalconsists of isolated sources (see e.g. Stetson, 1987). However, our maps already havesignificant confusion noise at their nominal resolution, and extra smoothing will furtherincrease this highly correlated noise component. Although the 1σ instrumental noiselevels in the raw maps (12.8, 12.5 and 15.0 mJy at 250, 350 and 500µm, respectively)are larger than the nominal confusion levels in SPIRE (5.8, 6.3 and 6.8 mJy, Nguyenet al. 2010), after we smooth the maps to the same resolution the confusion noise in thesmoothed maps will dominate over the instrumental noise. Dowell et al. (2014) smoothedthe 500µm map using a Gaussian kernel with a full-width half-maximum of 35.3′′ (the47Figure 3.1: Grayscale image of the HeLMS 250µm map with solid lines showing the areawe use in our analysis. We discard the edges of the maps, where the data lack overlappingscans, and we also discard a smaller region in the middle where part of the scan had to beremoved and our coverage is sparse. We additionally mask out a “seagull-shaped” regionof strong Galactic cirrus emission. The cirrus in this structure cannot be easily removedand biases our flux estimation of sources. The total area of the remaining dataset afterapplying the mask is 273.9 deg2.beam size in this band). This resulted in a final resolution of 49.8′′ FWHM, and the 250and 350µm maps were smoothed with a kernel so that their final resolution matched thisvalue. We decided to apply a different filter to our maps, which reduces confusion anddoes not degrade our resolution as much as a Gaussian filter would.We use an optimal filter that maximizes the signal-to-noise ratio in a map with non-negligible confusion noise. This filter is described in detail in Chapin et al. (2011). Thesignal-to-noise ratio in Fourier space after we cross-correlate our signal S with our filterF isSNR =∑k FˆTk Sˆk(∑k |FˆTk Nˆk|2)1/2 . (3.1)Here N is the noise, the hats denote the discrete Fourier transforms of our variables, the Tsuperscript refers to a transpose of our filter, and the index k corresponds to components48in the spatial frequency domain. We can derive the optimal filter by finding F for which∂(SNR)∂FˆTj= 0. (3.2)The resulting filter isFˆTj =Sˆj|Nˆj|2(∑k |FˆTk Nˆk|2∑k FˆTk Sˆk), (3.3)where Nj represents the total noise at each frequency component j. While the instru-mental noise is white and its value is constant at all frequencies, the power spectrum ofthe confusion noise will have a shape similar to the point spread function, since confusionarises from point sources in the same beam. The shape of our matched filter can be seenin Figure 3.2, compared to the 500µm beam shape and the final source profile after ap-plying the filter to our maps. Due to the smaller width of our filter, our final resolutionwill be closer to the original resolution of the 500µm map than in Dowell et al. (2014),and this can help reduce source blending effects for nearby objects (see an example inFigure 3.3).0 20 40 60 80 100 120Distance from center (arcsec)− filterSmoothed profileFigure 3.2: Shape of the matched filter at 500µm, compared to the Gaussian pointspread function (PSF) and the final source profile in the smoothed maps. The filter usedfor smoothing our maps has a smaller full-width half-maximum than the beam, so theresolution of our maps after smoothing is close to the unsmoothed resolution.After finding the optimal matched filter for the 500µm map, we need to construct thesmoothing kernels K250,350 that create the same effective source shape at 250 and 350µm49Figure 3.3: Comparison of the final resolution in our maps when using different smoothingkernels. On the left, we smoothed our map with the matched filter described in Sec. 3.1.2,while on the right we used a Gaussian filter. In addition to reducing the confusion noisefrom unresolved faint sources in our telescope beam, the matched filter also reducesblending effects between neighbouring bright sources.that we measure in the smoothed 500µm map. First we convolve the 500µm beam (aGaussian with 35.3′′ FWHM) with the matched filter to find the final source shape inour smoothed maps. If P250,350 denote the nominal beam shapes at 250 and 350µm andPmf500 is the matched-filtered source-shape at 500µm, then we can find K250,350 from theconvolutionP250,350 ⊗K250,350 = Pmf500. (3.4)Thus the smoothing kernels are determined by taking the inverse Fourier transformationof the Fourier-space ratio of the final and initial beam shapes.Before filtering the maps, we subtract a local background to remove any large-scalefluctuation from Galactic cirrus (radiation from heated dust clouds in our Galaxy), whichmight otherwise affect our flux estimation. The background removal algorithm firstbreaks up the image into 3′ × 3′ blocks and calculates the median value in each blockwhile iteratively removing sources by discarding pixels that are more than three standarddeviation away from the median of the current image. Then, the image containing these3′ × 3′ blocks with constant values is smoothed with a moving box with a size twice thesubimage size. The resulting background map is subtracted from our original maps. Wehave tested that this method removes large scale cirrus fluctuations (see e.g Figure 3.4)but does not have a significant biasing effect on point source flux density estimation.After background removal we filter our data with the matching kernels using inverse-variance weighting based on the error extension of our maps, which is an output of themapmaker and gives us the noise values in each pixel. Since the mapmaking pipeline50Figure 3.4: A patch of the HeLMS image containing extended cirrus emission, before(left) and after (right) background subtraction.does not correct for the effects of pixelization, we create our filters on an oversampledgrid, and then rebin them to our final pixel-size. We also apply our filters to our errormaps to find the typical instrumental noise values in our pixels after smoothing. We testthis filtering method by injecting fake sources with known flux density values into ourraw maps, and find no significant bias in the recovered flux distribution after subtractingthe background and applying our filter.3.1.3 Difference mapBecause the sources responsible for the confusion noise in the maps emit at all threeSPIRE wavelengths, one can produce a difference map that has a substantially reducedconfusion limit. It will be much more effective to search for bright 500µm sources insuch a difference map (D) than in the raw 500µm maps (M500). Dowell et al. (2014)have found that the differenceD =√1− k2M500 − kM250 (3.5)reduces confusion, while red sources remain bright in the D map. By carrying outextensive simulations using different coefficients, they demonstrated that the value k =0.392 works well empirically to maximize D/σconf in the maps. They also experimentedwith creating linear combinations using all three maps, but they have found that includinga 350µm term does not improve the efficiency of the source selection. We find that thissame choice of coefficients also works well for our HeLMS maps.Our final difference map is constructed as D = 0.920M500−0.392M250. We also com-bine the error maps and measure the resulting instrumental noise levels. After measuring51the total variance of our map we calculate the confusion noise in our final map asσconf =√σ2total − σ2instr. (3.6)The noise levels in our smoothed maps and the difference map are listed in Table 3.1.σtot σinst σconf(mJy) (mJy) (mJy)250µm 15.61 7.56 13.66350µm 12.88 6.33 11.21500µm 10.45 7.77 6.98D 8.54 7.75 3.5Table 3.1: 1 σ noise levels in our smoothed 250, 350 and 500µm maps and in the differencemap.3.1.4 Source extractionTo find red sources in our maps we first search for the brightest peaks in our differencemap and then we select the 500µm riser objects from the resulting list. We apply alocal-maxima search algorithm to our D map, which finds the positions of the pixels thathave greater values than their eight adjacent pixels. We create a list of these peaks witha cutoff at 4σtotal which corresponds to D = 34 mJy in the difference map.To select red sources from this list we simply require that S500 > S350 > S250. However,to evaluate this we need to extract the actual flux densities from our single wavelengthmaps at these D-peak positions. It is not trivial to determine if it is optimal to use oursmoothed maps to measure these values or to go back to the nominal resolution mapsand find the sources there. Due to a typical positional uncertainty of ∼ 6′′ betweenbands, extracting the fluxes at the precise D position biases our flux estimation at 250and 350µm. To address this we could re-fit our peaks in each of the smoothed mapsto find the actual peak position in each band and extract the fluxes there. However, atypical red source has an S500/S350 flux density ratio that is close to 1, and hence adjacentsources often boost our 350µm flux density above S500, even if in the nominal maps weclearly detect our source as a red source. This is an important issue at the bright end,where the source counts decrease rapidly, and even in our very large area field we expectonly to find a handful of such objects.52After careful consideration, we decided that for this last step it is better to measure thefluxes from the less confused nominal resolution maps, but instead of doing photometryat the measured D-position, we find the best-fit source after taking into account ourpositional uncertainty. To achieve this we move around our D-peak position in sub-pixelsteps, allowing the search radius to change corresponding to our typical uncertainty, andwe calculate the Pearson correlation coefficient r between our data d and the beam shapeP at each position byr =Npixels∑i=1(di − d¯)(Pi − P¯ )Npixels∑i=1(di − d¯)2)1/2 Npixels∑i=1(Pi − P¯ )2)1/2. (3.7)We pick the position where the correlation is the largest, and we extract the flux densityat this position using inverse variance weighting:S =Npixels∑i=1diPi/σ2iNpixels∑i=1P 2i /σ2i. (3.8)We test the validity of this method by injecting artificial sources on a grid with knownflux densities in the raw maps, and we run our source extraction pipeline on these maps.We inject 66 874 objects into the map, using the same mask as we used for source finding.These artificial sources are spaced 37.586 pixel away from each other, corresponding to225.516′′ angular separation. This spacing is deliberately not an exact multiple of the 6′′pixel size, so the source centres will not always coincide with the pixel centres, similarly toour real sources. We generate an oversampled Gaussian point spread function accountingfor the corresponding sub-pixel shifts, then we re-bin this PSF to have 6′′ pixels. This waywe can generate sources with their peaks not always located the centre of the pixel. Thenwe run our detection pipeline and we compare the injected and measured flux densities.In Figure 3.5 we show an example of the distribution of measured flux densities after weinject sources into our three maps with flux densities S500 = 80 mJy, S350 = 70 mJy andS250 = 50 mJy. Since we smooth our maps to match the resolution at 500µm, in this bandall three methods give similar results. In the other two bands, however, fixing the peakposition to the D-peak clearly under predicts the real flux densities. Finding the peaks in5340 50 60 70 80 90 100 110 120S500 (mJy) 40 50 60 70 80 90 100 110SS350 (mJy) 20 30 40 50 60 70 80 90S250 (mJy) 3.5: Histogram of the measured flux densities for injected sources with S500 =80 mJy, S350 = 70 mJy, S250 = 50 mJy. The blue dashed line shows the distribution offlux densities measured in the smoothed maps at the fixed D-peak position, the dottedblack line is the distribution of flux densities measured in the smoothed maps after re-fitting the peak positions in each band, and the red solid line represents the recoveredflux densities in the nominal resolution maps using the positions in each band where thecorrelation with the PSF is the largest.each band and measuring the smoothed map flux densities at these peak positions doesa better job in recovering the actual flux densities, but a small bias still exists, and dueto the larger confusion noise in the smoothed maps, the recovered distribution is widerthan what we measure in the nominal resolution maps, reducing the efficiency of findingsources that have flux densities close to our selection limits. Measuring the flux densitiesfrom the nominal resolution maps is clearly the best choice, and we conclude that themethod described above reduces the bias due to positional uncertainties.3.1.5 Final catalogBefore finalizing our high-z catalog we need to address the radio source contaminationof our sample. Flat spectrum radio quasars can have colors similar to those of our high-redshift dusty galaxy candidates, but these objects can be easily identified from availableradio surveys. We compare our catalog to the 21 cm radio catalogs from the NRAO VLASky Survey (NVSS, Condon et al., 1998) and the FIRST survey (Becker et al., 1995) andwe flag 17 of our sources that show up in these catalogs with a radio flux density brighterthan 1 mJy. We do not use these sources in any further analysis.Our catalogs could be contaminated by cosmic ray hits or other spikes in the detector540 2 4 6 8 10 12 14Time (s)− 3.6: Example of incorrect glitch detection in the detector timestreams. The shadedarea shows the part of the data that is masked out and not used in further processing.In this case, the large spike, usually caused by a cosmic ray hitting the detector array, isonly partially masked out, and the long tail of the fluctuation is not removed.timestreams that are not properly removed by the initial deglitching process describedin Section 2.2.1. Figure 3.6 shows an example of a very large spike in the time-ordereddata, where incorrectly only half of the feature is masked out during data pre-processing,and the long tail of the glitch is included in the further map-making steps. A spike leftin the 500µm array data would mimic a 250 and 350µm dropout source. During theiterative mapmaking process for ordinary SPIRE data, isolated spikes are recognized asoutliers among the samples associated with a given pixel, and are removed from the dataas described in Section 2.4.2. However, the HeLMS maps are sparsely sampled and theremay be too few samples near a given pixel for this recognition procedure to be reliable.The result is a “hot” pixel or a stripe of a few very bright pixels in the map from onearray, while the neighbouring pixels show values consistent with the instrumental noiseand no spike is present in the other arrays. After smoothing the map with our matchedfilters, these corrupted pixels appear like bright sources in the 500µm map. An exampleof such a spurious source can be seen on Figure 3.7.A common method to detect these objects is to create two maps, each from onehalf of the data. The false sources only show up in one of the maps. However, dueto the very shallow depth of our observation these half-maps are sparsely sampled, andthey contain new artifacts due to the lack of cross-linking. In the case of the HeLMS55Figure 3.7: Example image of an undetected cosmic ray hit in our maps. The top rowshows the raw images, with a stripe of very bright pixels showing up in the 500µmmap, while the other two maps show only noise. The bottom row shows the smoothedmap, where the cosmic ray is detected as a very bright source at 500µm, that has nocounterparts in the shorter wavelength maps.observations this method does not reliably remove cosmic rays from the maps. Insteadwe turn to a different approach. We compare the raw and smoothed maps in a 5 × 5pixel region around each source, and discard all candidates if any pixel shows a largedifference, (Sraw − Ssmooth) > 5σraw. Most cosmic rays produce outlier pixels almost10σ away from the smoothed values, and this method works well to discard these falsesources. Nonetheless, we still use the images from each half of our data as a consistencycheck when there were no obvious artifacts in those maps, and we find that we correctlydiscard the bright outlier pixels caused by cosmic rays. In our final catalog we adopta 5σ cut of S500 > 52 mJy to protect from fainter cosmic rays that this technique maynot have recognized. After discarding these cosmic rays and the radio sources, the finalnumber of objects in our catalog with S500 > 52 mJy, D > 34 mJy, and red colors, is 477.3.2 Number countsWe measure the raw 500µm differential number counts of the red sources in our finalcatalog in nine logarithmic bins between 52 mJy and 195 mJy. The uncorrected numbersare listed in Table 3.2 and plotted on Figure 3.8. In practice, raw number counts need tobe corrected for completeness and flux-boosting effects, and the expected number of false56Smin Smax Smean Nbin dN/dS(mJy) (mJy) (mJy) (×10−4 mJy−1deg−2)52.0 60.2 56.1 225 998.6± 66.660.2 69.8 65.0 154 590.1± 47.569.8 80.8 75.3 55 181.9± 24.580.8 93.6 87.2 27 77.1± 14.893.6 108.4 101.0 9 22.2± 7.4108.4 125.5 117.0 4 8.5± 4.3125.5 145.4 135.4 1 1.84 + 8.41− 1.79145.4 168.4 156.9 1 1.58 + 7.26− 1.55168.4 195.0 181.7 1 1.37 + 6.27− 1.33Table 3.2: Raw 500µm number counts.detections needs to be subtracted from the binned data in order to examine the under-lying true source distribution. When measuring number counts at a single wavelengththese corrections usually only depend on the flux density and signal-to-noise ratio, andthey are relatively easy to simulate when we are investigating sources with flux densitiesfar above the confusion limit. Our catalog, however, has a more complicated selectionfunction, and the correction factors will also depend on the colors of our sources, withthese colors having a very large scatter due to the low signal-to-noise ratio at our shorterwavelengths. Additionally, these corrections require us to assume an intrinsic shape forour number counts based on model predictions and previous observations, but due to thesmall sample sizes the slope of the red source counts has not been measured before. Herewe do not explicitly correct our estimated counts for these biases, but instead, in thenext subsection, we describe a simulation where we attempt to predict the most likelyshape of our intrinsic source counts.3.2.1 Intrinsic number countsThe raw source counts can provide a biased estimator of the intrinsic source distributionthrough a number of effects. In the following we describe the biases that change theshape of the observed distribution, and we describe a self-consistent simulation where weattempt to determine the shape of the intrinsic counts accounting for all these biases.57102S500 [mJy]10−510−410−310−210−1100dN/dS[mJy−1deg−2]Raw ”red” countsClements et al. 2010B12 mock ”red” catalogB11 mock ”red” catalogred sim.: injectedred sim.: measuredFigure 3.8: Raw 500µm differential number counts of our sample of “red” sources. Filledblue circles represent the raw counts with 1σ Poisson error bars, except for the highestthree flux density bins, where due to the very small number of objects we plot the95% upper confidence limits. The green diamonds shows the total Herschel 500µmnumber counts measured by Clements et al. (2010). The dotted blue line representsthe expected observed counts from an intrinsic distribution shown by the solid blueline. These two lines are derived from the simulations described in Section 3.2.1 whichaccount for blending, Eddington bias, false detections and completeness. The cyan starsconnected with a dashed line are binned data from creating a simulated catalog basedon the earlier Be´thermin et al. (2011) model, and selecting objects with the same criteriaas we do for our catalog. The red crosses connected with a dashed line show the samewith a catalog drawn from Be´thermin et al. (2012a) model. The model comparisons arediscussed in Section BlendingThere may be a bias in our counts that arises from the variation of our angular resolutionwith wavelength. There will be closely adjacent sources that appear blended into oneobject at 500µm and resolved into several at 350 or 250µm. If one of these sources isvery red, but not bright enough for catalog inclusion, and the other(s) neither very brightnor very red, the sum may well appear both bright enough and red enough for inclusion.This results in a fairly red but slightly faint object in the catalog. Examples of sourcesthat appear to be a single object in the 500µm map and in the difference map are shown58Figure 3.9: Postage-stamp images of three sources detected in our catalog that appearto be a single object in the 500µm map and in D. From left to right we show thenominal resolution 250µm, 350µm and 500µm map, and the difference map, respectively.Example A shows a source that is isolated and has a clear counterpart in each band.Example B shows an object that clearly breaks up into two sources in the 250µm and350µm maps, but is blended at 500µm. Example C shows a complex blend with noclearly identifiable counterparts that could be used for Figure 3.9. During source selection we only require that our objects are detected as apoint source at the 500µm resolution, and appear red in the maps, but we do not requirea detection at 250 and 350µm, because that could bias our selection against the reddestobjects. We note that the photometry method we described in Section 3.1.4 will biasour flux density estimation at these shorter wavelengths if our sources clearly break upinto multiple component in these bands. In some cases the components of the blend areclearly identifiable in the 250 and 350µm maps and their positions can in principle beused to deblend the 500µm flux density, but most of the time we only see a very confusedregion with low signal-to-noise ratio and no clear detectable peak positions, so we cannotextract individual flux densities for these faint objects. We examined our objects by eyein the higher flux density bins, and determined that about 33 % of our detected sourcesin each bin have an unreliable photometry due to blending or nearby sources. We stillinclude these sources in our analysis, because simply discarding these objects by eye ishighly subjective. We include the correlation values in our catalog to show how reliable59our flux estimation is in each band. We note that the simulation we describe in thefollowing takes the effects of blending into account. Detection efficiencyIn an ideal case we would be able to determine the true flux densities of our sourceswithout measurement errors, thus we would detect every source with a flux densityabove a given catalog cut with 100 % efficiency. In practice, however, the measuredflux densities can be scattered below this cutoff by noise. If we want to investigate thestatistics of our catalog, we need to account for the sources that we potentially missduring source extraction. The completeness of a catalog at a given flux density is theratio of the number of sources recovered with the source detection pipeline to the realnumber of objects with that intrinsic flux density in the map. The measured raw numbercounts are usually divided by the mean completeness in each flux density bin to accountfor sources that are missed during source extraction. Calculating the completeness in acatalog of sources selected at a single wavelength is straightforward, since the detectionefficiency only depends on the signal-to-noise ratio of these sources. Having an extracolor-constraint leads to a very large variation in the completeness at each 500µm fluxdensity bin, since even at high 500µm signal-to-noise ratio the measured colors of sourceswith S500 & S350 or S350 & S250 are often not red due to the noise scattering.To investigate how the detection efficiency changes with color, we create a 3-dimensionalgrid of flux density triplets, we determine the detection efficiencies at each grid-point,then we determine the efficiency of finding a source with a particular color using cubicinterpolation between these grid points. To do this we inject sources into our raw mapsas described in Section 3.1.4. In all three bands we create a separate map for injectedflux densities ranging from 10 mJy to 200 mJy in 10 mJy steps. Then we combine thethree maps of our different bands in all possible variations to calculate the efficiencies forall the flux density triplets corresponding to our grid points. We find, that if we fix theflux densities in any two bands, the detection efficiency of the source will be a smoothlychanging function of the third flux density value, thus we can estimate the efficienciesfrom our three dimensional grid using axis-wise cubic interpolation. On Figure 3.10 weillustrate the smooth change in efficiency with the flux density at one particular SPIREwavelength, while fixing the flux density values in the other two bands. It is clearly seen,that even sources detected with high signal-to-noise ratio in the 500µm map can havea low detection efficiency if the 350µm flux density is close to S500 or S250, so unlesswe know the exact color distribution in our bins, we cannot correct our 500µm numbercounts with an average completeness value.600 20 40 60 80 100 120S5000., S350=60mJy0 20 40 60 80 100 120S3500., S500=90mJy0 20 40 60 80 100 120S2500., S500=90mJyFigure 3.10: Detection efficiency as a function of flux density at a particular wavelengthwhile the flux densities at the other two SPIRE wavelength are fixed. These fixed valuesare illustrated with vertical grey lines. The smooth change allows us to find the efficiencyvalues between the grid points using axis-wise cubic interpolation. For a source with afixed 500µm flux density the detection efficiency drops to ∼ 50% if S500 ≈ S350 orS350 ≈ S250, thus the completeness in a given 500µm bin is not constant.This effect is also illustrated on Figure 3.11, where we plot what the detection ef-ficiency of each of our catalog sources would be if the measured flux density valuescorresponded to their true flux densities. In each 500µm bin there is a large scatter inactual detection efficiencies. Dowell et al. (2014) calculated these efficiency values foreach catalog source and used these values as a correction factor in the number countsmeasurement, but due to the large uncertainties of the flux density measurements ofthese sources this method is not optimal. False detections and Eddington biasOn Figure 3.10 it can be seen that sources that have flux densities where the S500 >S350 > S250 relation does not apply can still have nonzero detection efficiencies due tothe noise in the flux density measurements. To correctly determine the number of suchfalsely detected non-red sources, a correct model describing the population with almostred colors is needed, but current models are trained to describe the monochromaticnumber counts, not the color distribution of the SPIRE sources.If the intrinsic source counts are a steep function of source brightness, or the fluxuncertainties are large, a larger number of faint sources may accidentally appear to satisfyour catalog selection criteria than the number of acceptable sources that accidentally6160 80 100 120 140 160 180 200S500 [mJy] 3.11: Detection efficiency calculated for each of our catalog sources, assumingthat their measured flux density corresponds to their true flux density. The detectionefficiency is not constant in our 500µm bins; the actual values also depend on the 250and 350µm flux density values for each source.appear not to. This so-called “Eddington bias” (Eddington, 1913) may be present at thecuts where we require S500 > 52 mJy, D > 34 mJy, S500 > S350 and S350 > S250, and thiswill affect the observed slope of the number counts. In order to calculate the expectedcorrection for this effect, we would need to know the shape of the intrinsic red sourcecounts, but as we mentioned before, this has not been measured yet. SimulationsThe shape of our final measured number counts is a complex combination of the abovementioned effects, so instead of correcting for them separately, we take a self-consistentapproach that incorporates all of these biases. We use the Be´thermin et al. (2012a) modelto create simulated maps at all three wavelengths that contain no red sources, then weadd the measured instrumental noise to these maps and we inject artificial red sourcesinto this dataset drawn from a parametric power-law distribution, and by using MonteCarlo simulations we fine-tune the parameters of this distribution until the measuredcounts in these simulated maps look similar to our real measured red source counts.The Be´thermin et al. (2012a) model is an empirical model that extrapolates locallyknown correlations of different galaxy properties to high redshift, without using physicalinformation about the modelled population. The model’s predictions agree well with theobserved monochromatic SPIRE number counts, so we draw sources from this model tocreate our simulated sky maps. The model is based on the evolution of main-sequence and62starburst galaxies and uses a simple SED template where the dust gets slightly warmerwith increasing redshift. The first ingredient of the model is the stellar mass functionof star-forming galaxies that evolves with redshift and can be described by a Schechterfunction asΦM∗ =dNdlog(M∗)dV= Φb(z)×(M∗Mb)−0.3× exp(−M∗Mb)× ln(10), (3.9)where M∗ is the stellas mass of the galaxy, Mb = 1011.2 M is the characteristic mass, andthe characteristic density Φb(z) is constant for z < 1 (Φb,z<1 = 10−3.02 Mpc−3, Sargentet al. 2012), and decreases at z > 1 aslog(Φb(z)) = log(Φb,z<1) + 0.4× (1− z). (3.10)We can calculate the co-moving volume element dV asdV = DH × D2L(1 + z)2√Ωm(1 + z)3 + 1− ΩmdzdΩ, (3.11)where DH = c/H0 is the Hubble distance, c is the speed of light, DL is the luminositydistance, and the cosmology parameters used are H0 = 70 km s−1Mpc−1, Ωm = 0.27,Ωk = 0. Combining this relation with the mass function we can get an expression forthe number of galaxies in intervals of redshift and logarithmic stellar mass per unit solidangle asdNdlog(M∗)dzdΩ= ΦM∗ × dVdzdΩ. (3.12)We draw (z,M∗) value pairs from this distribution, finding the total number of sourcesper unit solid angle by integrating Equation 3.12 with respect to our whole z and log(M∗)range.The main sequence (MS) specific star formation rate for each source can be determinedassSFRMS(z,M∗) = sSFRMS,0 ×(M∗1011M)−0.2× (1 + min(z, zevo))3 (3.13)where sSFRMS,0 = 10−10.2 yr−1 is the specific star formation rate for an M∗ = 1011Mgalaxy at z = 0, and zevo = 2.5 represents the redshift where sSFRMS stops to evolve. Theactual specific star formation rate for galaxies will scatter around sSFRMS, and starburst(SB) galaxies will have highly elevated sSFR values compared to the main sequence.The probability for a galaxy with known redshift z, stellar mass M∗ and correspondingsSFRMS value to have a certain sSFR specific star formation rate can be described by a63double log-normal distribution (Sargent et al., 2012) asp(log(sSFR) |M∗, z) ∝ exp(−(log(sSFR)− log(sSFRMS))22σ2MS)++ rSB(z)× exp(−(log(sSFR)− log(sSFRMS)−BSB)22σ2SB)∝ pMS + pSB,(3.14)where σMS = 0.15 dex, σSB = 0.2 dex (Salmi et al., 2012) are the standard deviation ofthe log-normal MS and SB distributions, BSB = 0.6 dex describes the boost in sSFR forstarbursts compared to main sequence galaxies, and the redshift evolution up to zSB = 1is coded inrSB(z) = 0.012× (1 + min(z, zSB)). (3.15)We first assign an MS or SB type for each of our drawn galaxies based on thepMS/(pMS + pSB) and pSB/(pMS + pSB) probability ratios, then we draw an sSFR valuefrom the double log-normal probability distribution centered on sSFRMS for our mainsequence objects or on sSFRMS+BSB for the starbursts.Having drawn values of stellar mass and specific star formation rate for each of oursources, we can calculate the total star formation rate as SFR = sSFR×M∗. The infraredstar formation rate can be converted to infrared luminosity LIR based on Kennicutt (1998)asSFRIRLIR= 1.7× 10−10Myr−1L−1 . (3.16)In lower mass dusty galaxies not all of the star formation is obscured by dust, and thetotal SFR is the sum of the infrared and UV star formation rates, with the mean ratioof these components depending on the stellar mass asr = 2.5 log(SFRIRSFRUV)= 4.07× log(M∗M)− 39.32, (3.17)adopting the relation in Pannella et al. (2009). Combining equations 3.16 and 3.17 andusing SFR = SFRIR + SFRUV we can convert our generated SFR values to infraredluminosity asLIR =SFR1.7× 10−10Myr−1L−1× 100.4r1 + 100.4r. (3.18)With a redshift and LIR value in hand for each simulated source, we determine theflux densities of these objects at the three SPIRE wavelengths using the infrared SEDtemplates from Magdis et al. (2012).After we determine the 250, 350 and 500 µm flux densities of our generated sources,64we inject these sources into an empty map at random positions, then we add instrumentalnoise that resembles the noise measured in our real maps. We discard any sources thathave red SPIRE colors in this simulated dataset, then we inject artificial red sources intoour newly created sky maps. To do this we first draw 500µm fluxes from a power-lawdistribution of the shape dN/dS = N0× S−α, then we fix the color ratios of our injectedobjects to the median of the color ratios measured in our catalog, S500/S250 = 1.55 andS500/S350 = 1.12. We note that the actual colors of our objects are not constant, butdue to the large uncertainties in the color measurements it is not straightforward todetermine the underlying color distribution. In Figure 3.12 we plot the measured colordistribution in our 500µm bins. The largest scatter is in the lowest two bins, where manyof the objects with high color ratios are either blends or have very low signal-to-noiseratio counterparts at 250 and 350µm. After injecting our artificial red sources we runour detection pipeline in the same way as we do for our real maps and we compare themeasured counts from this simulated data with our raw numbers. In an iterative processwe change the input parameters N0 and α until the output counts resemble the measuredraw number counts in our real data. In Figure 3.8 we show the result of a simulationwith an area of 1500 deg2. The blue solid line represents a power law dN/dS = N0 × Sαwith α = −5.6 and logN0 = 8.6, while the dotted blue line shows the measured numbercounts for simulated objects with 500µm flux densities drawn from this distributionand with fixed color ratios. The simulations are in good agreement with our observedcounts, suggesting that assuming a power-law model without a break is adequate for ourpurposes.3.2.2 Comparison to modelsWe compare our observed number counts to mock “red” catalogs created from theBe´thermin et al. (2011, B11) and the Be´thermin et al. (2012a, B12) models. We generate1000 deg2 simulations from both of these catalogs, and then select sources the same wayas we do for our observed sample (S500 > 52 mJy, D > 34 mJy, and red S500 > S350 > S250colors). These two models predict the total Herschel number counts very well, but asDowell et al. (2014) already showed, they both under-predict the number of red sourcesin the HerMES fields. The resulting counts from these simulations are plotted on Fig-ure 3.8. We can see that B11 predicts more red sources; however, they are mostly atz < 3, and since all of our red objects with measured redshift are at z > 3 we know thatthis model’s predictions are not correct. The B12 model predicts even fewer red sourcesthan the B11 model, but in this sample all of the objects lie above z = 3, agreeing with6560 80 100 120 140 160 180 200S500 [mJy]12345S500/S25060 80 100 120 140 160 180 200S500 [mJy] 3.12: Measured SPIRE colors of red sources in our catalog as a function of the500µm flux density. The vertical lines show the edges of the flux density bins we usedto measure the differential number counts. The horizontal lines at S500/S250 = 1.55 andS500/S350 = 1.12 show the median colors of our sample. The sources with anomalouslylarge colors are mostly blends or objects without clear 250 and 350µm detections.66our follow-up results. We note that both of these models are empirical and are basedon extrapolation of the properties of lower redshift starburst galaxies, such as the lumi-nosity function (B11) or the stellar mass function (B12), instead of the actual physics ofthese galaxies; however, at present none of the physically-motivated models have beenfine-tuned to properly describe the observed Herschel number counts.In Fig. 3.8 we also show the total SPIRE 500µm counts measured by Clements et al.(2010), which is in good agreement with other SPIRE total number counts measurements(Oliver et al., 2010; Glenn et al., 2010; Be´thermin et al., 2012b). We can see that theinferred corrected slope of our counts is very steep, suggesting a strong evolution of ourpopulation of red sources. Negrello et al. (2010) predicted that the number counts ofunlensed galaxies at 500µm are rapidly decreasing and reach zero at S500 ∼ 100 mJy.Every bright object with flux densities above this value is expected to be strongly lensed,and the number counts are expected to have a bright tail due to this lensed population.We have found several red objects with bright 500µm flux densities, but their low num-bers in our flux density bins do not allow us to see an actual departure from the steeppower-law shape of red sources at lower flux densities.Our inferred number counts do not show any significant differences compared withthe Dowell et al. (2014) findings, although we now have much better statistics. TheDowell et al. (2014) sample consists of red sources with S500 > 30 mJy and D > 24 mJy,and they found the total corrected cumulative counts to be 3.3 ± 0.8 sources per deg2.If we assume that the shape of our distribution can be described by the power law, thatwe found in Section 3.2.1, and that it does not have a break between 30 mJy and 52 mJy,then integrating this power law above 30 mJy gives us a total number of more than 10red sources per deg2. However, this comparison is not straightforward, since many ofthese objects at lower 500µm flux densities would be discarded by the D cut used in theDowell et al. (2014) analysis. Integrating our power law for S500 > 40 mJy (where thetwo samples have a larger overlap) results in 2.8 objects per deg2, which is closer to theDowell et al. (2014) result.3.3 Colors and SED fitsThe interpretation of our red color-selection as leading to a catalog rich in high-z galaxiesrelies on the assumption that galaxies with rising flux densities towards longer wave-lengths are at high redshifts. Although some observations suggest that the temperatureof starburst galaxies could be rising slightly towards high z, it does not rise as fast as(1+z), and the observed temperature Tobs = Td/(1+z) drops with redshift. This behavior67is evident in the catalog of 25 strongly-lensed galaxies selected at 1.4 mm with the SouthPole Telescope (Weiß et al., 2013; Vieira et al., 2013), where the apparent temperature isfit by Tobs = [11.1− 0.8(1 + z)] K. This pattern is consistent with examining the spectralenergy distributions (SEDs) of several known lower redshift dusty starburst galaxies, andmeasuring their expected flux-ratios at the SPIRE wavelengths for different redshifts.In Figure 3.13 we present the color-color plot for our objects with S500 > 60 mJy. Asa comparison we also show the redshift tracks for two starburst galaxies, as well as thecolors of our two red sources that have ALMA spectroscopic redshift measurements andfour spectroscopically confirmed z > 4 galaxies from the Dowell et al. (2014) sample.We have examined the SPIRE images of our S500 > 60 mJy sources by eye and flaggedobjects that look blended at higher resolution. As discussed before, we include possibleblends in our catalog, since although we are not able to deblend the flux densities ofthe components, we assume that at least one component is a red source. We includedthis effect in the number counts simulation, but when we are investigating the colorsof individual objects, we need to note that blending effects can result in boosted fluxdensities that are not well fitted by a modified blackbody SED. We plot the positions ofthese confused sources in our color-color space with a different symbol on Figure 3.13 toillustrate how the anomalous colors that are very distant from the typical redshift tracksare often the result of blending.In Section 1.3 we discussed that the spectral energy distribution of submillimetergalaxies is often modelled as an optically thin modified blackbody. Dowell et al. (2014)show that most of the red sources in their sample are better fit with an optically thickmodel described asSν = (1− e−τν )Bν(Td)Ωs, (3.19)where Bν(Td) is the Planck function, Ωs is the solid angle of the source, andτν = (ν/ν0)β (3.20)is the optical depth term. Here β is the dust grain spectral emissivity index as discussedbefore (β ∼ 1−2) and ν0 defines the frequency at which the optical depth equals unity.At frequencies larger than ν0, where τν > 1, the dust cloud becomes optically thick.This usually corresponds to rest-frame frequencies of ν0 ∼1.5−3 THz or wavelengthsof λ ∼100−200µm (Draine, 2006; Conley et al., 2011). Dowell et al. (2014) appliedan optically thick model to fit the SED of several dusty galaxies with well-sampledspectra, including three sources from their red sample, and they have found that therest frame wavelengths where the dust cloud becomes optically thick are in the range681.0 1.5 2.0 2.5 3.0S350/S2500. 3.13: Color-color plot of our red sources with S500 > 60 mJy. Blue filled circlesrepresent the objects that look isolated in the nominal resolution maps, while open blacksquares show the more confused sources that we have flagged by eye to illustrate thatanomalous colors are usually the result of blending. The green dashed line represents theredshift-track for the starburst galaxy Arp220 and the dotted black line for SMMJ21352–102 (Cosmic Eyelash, Swinbank et al. 2010b), with the labels on these curves showing theredshifts. Red filled diamonds show two sources from the catalog discussed in our paperthat have ALMA spectroscopic redshift measurements. From left to right: HeLMS65 withz = 4.997 (or z = 3.798, see discussion in Section 3.4); and HeLMS34 with z = 5.162. Forthese two sources we show the typical errors in their color measurements. The black opendiamond symbols represent four sources from the Dowell et al. (2014) red source samplethat have spectroscopic redshift measurements. From left to right: FLS1 (z = 4.3); FLS5(z = 4.4); LSW102 (z = 5.3); and FLS3 (z = 6.3).190µm< λ0 < 270µm.We use the affine invariant Marcov chain Monte Carlo (MCMC) code described inDowell et al. (2014) to fit an optically thick modified blackbody to our SPIRE flux den-sities. When fitting the redshifted SED in the observed frame, the fitted parametersbecome Tobs = Td/(1 + z) and λ0,obs = λ0(1 + z). Since we only have three data points,and four parameters to fit (Tobs, β, λ0,obs and an amplitude), we apply a broad Gaussianprior to the parameters that are not well constrained by our SPIRE data alone. FollowingDowell et al. (2014) these constraints are β = 1.8 ± 0.3 and λ0,obs = (1100 ± 400)µm(assuming a typical redshift of z ∼ 4.5 for red sources). An example of the parameterdistribution of the MCMC samples for one of our sources (HELMS34) is shown in Fig-69ure 3.14. As shown on the marginal histograms, although β and λ0,obs are not fixed, theyare narrowed down and are only allowed to vary between the Gaussian limits given above.Figure 3.15 shows the observed temperature parameter distribution of the MCMC chainsfor the case when we do not apply a prior on λ0,obs. The very large and small λ0,obs valuescorrespond to a long tail of the fitted temperature distribution, corresponding to valueswith low probability, thus applying the prior will not bias our results significantly.The resulting observed temperature distribution for our isolated sources is plottedin Figure 3.16. We also show the distribution of λmax, the observed wavelength wherethe SED peaks. The mean observed temperature is (11.03 ± 1.91) K. This is coolerthan Tobs for SPIRE-selected galaxies in general (e.g. Amblard et al., 2010; Casey et al.,2012). At the same time, this is warmer than the (8± 2) K mean apparent temperatureseen for galaxies in the 1.4-mm selected SPT sample. Since only a small fraction ofour sample has very bright 500µm flux densities (S500 > 100 mJy), the majority of oursources are not expected to be strongly magnified by gravitational lensing and are thusintrinsically very luminous. Heating from intense star formation can explain these warmerdust temperatures. The SPT sample, however, contains very strongly lensed galaxiesand we can assume that they select intrinsically fainter and colder objects than thetypical red sources we find. This can explain the difference in the apparent temperaturedistributions. We have to be very careful however, when comparing temperature valuesquoted in the literature. Applying an optically thin model, where λ0 → 0, the fitted Tobsvalues can decrease by ∼ 15%, so the observed temperatures can have a different meaningdepending on the SED model applied. Using the same parameters as Dowell et al. (2014),our observed temperature distribution is similar to their measurements, showing that weselect a similar population of sources in our maps. Red sources with known redshifts havea very warm inferred intrinsic dust temperature. The three sources with spectroscopicredshift estimations listed in Dowell et al. (2014), FLS1 (z = 4.29), FLS5 (z = 4.44)and LSW20 (z = 3.36) have dust temperatures of 63 K, 59 K and 48 K, respectively, andRiechers et al. (2013) quote Td = 56 K for the z = 6.3 source HFLS3. The observedSED peak wavelength λmax is more directly constrained by the data than Tobs. For asimilar λmax distribution as the one we measure, Dowell et al. (2014) estimates a meanphotometric redshift of z = 4.7 by determining priors of the rest-frame peak wavelengthbased on different comparison samples. While we did not carry out a similar analysis,based on the similar selection function and measured λmax and Tobs distribution of oursample, we can assume that our catalog also consists of mostly high-redshift objects.700.β05001000150020002500λ0,obs[µm]8 10 12 14 16Tobs [K]8090100110120130140S500[mJy]1.5 2.5β1000 2000λ0,obs [µm]80 100 120 140S500 [mJy]Figure 3.14: Parameter distributions for MCMC samples. We show joint distributionsof two different variables, with arbitrary density contours, and also show marginal his-tograms of the given parameter. The black dashed line in the β and λ0,obs histogramsshows the Gaussian prior applied to these parameters.716 7 8 9 10 11 12 13 14 15Tobs [K]050010001500200025003000Frequencyλ0,obs < 700µmλ0,obs > 1800µm700µm < λ0,obs < 1800µmFigure 3.15: Histogram of the posterior temperatures from the MCMC chain when thereis no prior applied to λ0,obs. The black line shows the total distribution. Small and largeλ0,obs values contribute to low probability tails of the temperature distribution, showingthat applying a prior on λ0,obs will not change the fitted results significantly.3.4 ALMA spectroscopyFollow-up observations of red sources have already shown that we can indeed successfullyselect high-redshift dusty galaxies based on their red SPIRE colors. To further increaseour sample of sources with confirmed spectroscopic redshift estimations we observedtwo of our red sources (HeLMS34 and HeLMS65) using the Atacama Large Millime-ter/submillimeter Array (ALMA) during the Cycle 2 operational phase. These sourceswere selected based on their very red colors and we already have photometric redshiftestimates for these two sources, zphot = 5.15± 0.12 and zphot = 5.24± 0.27, respectively(Asboth et al. in prep.). The observations were carried out in Band 3, covering frequen-cies between 84 and 116 GHz, which contains the redshifted CO rotational lines typicallybelow the J = 6− 5 transition.The observed spectra are shown in Figure 3.17. In the spectrum of HeLMS34 wedetect two lines, unambiguously identified as the CO(5 − 4) and CO(6 − 5) transitions.These correspond to a redshift of z = 5.162 that is in very good agreement with thephoto-z estimate of 5.15.Only a single strong line is seen in the spectrum of HeLMS65. There are several726 7 8 9 10 11 12 13 14 15Tobs = Td/(1 + z)[K]01020304050N350 400 450 500 550 600 650 700 750 800λmax[µm]01020304050607080NFigure 3.16: Distribution of the observed temperature Td/(1 + z), and the observed SEDpeak wavelength λmax of our red sources, measured by fitting an optically thick modifiedblackbody spectrum to our SPIRE flux densities, as described in Section 3.3.7385 90 95 100 105 110 1150.[mJy]CO(5-4) CO(6-5)HeLMS34: z = 5.16285 90 95 100 105 110 115Frequency (GHz)[mJy]CO(5-4)/CO(4-3)?[CI]?HeLMS65: z = 4.997 / 3.798?Figure 3.17: ALMA spectrum for two red sources in our catalog. In the spectrum ofHeLMS34 we detect two CO lines and their observed frequencies correspond to redshiftz = 5.162. HeLMS65 has only one high signal-to-noise line in its spectrum and theredshift can be either z = 4.997 or z = 3.798, depending on whether the low signal-to-noise ratio spectral feature at 102.6 GHz is only a noise fluctuation or a faint [CI] spectralline. See the discussion in Section 3.4 for details.spectral lines that could fall into this region. We can discard the possibility that theobserved line is CO(6 − 5) or a higher transition, since then we would always detectother CO rotational lines in the observed spectrum. If we identify the detected line asthe CO(5 − 4) transition, then the redshift of this source is z = 4.997 and we wouldnot see any other lines in the observed spectral range; this is consistent with the photo-zestimate. If, on the other hand, the detected line corresponds to the CO(4−3) transitionthen the redshift is z = 3.798 and we should be able to detect a [CI] line at 102.6 GHz.There is a possible low signal-to-noise peak near to this frequency, but the spectral featurein question is not larger than a dozen other spikes in the observed spectrum, and hencethe identification is not definite. We note that we have seen cases where the photo-zestimate is not consistent with later spectroscopic data, and so from this measurementalone we cannot determine the redshift unambiguously. Additional follow-up observationsare planned to determine the actual redshift of this source.74Together with follow-up observation results of sources from the Dowell et al. (2014)sample we now have more than ten red sources with spectroscopically confirmed high-redshift, with the majority being at z > 4, and the rest at z > 3, strengthening the initialassumption that our search method selects high-redshift dusty galaxies.3.5 Red sources in the ACT mapsSince red sources have increasing flux densities towards longer wavelengths, with theirSED peaking close to 500µm, we expect that these galaxies should also be detected atmillimeter wavelengths. As we discussed in Section 2.4.1, there is an overlap between theHeLMS region and equatorial observations made by the Atacama Cosmology Telescope(ACT; Swetz et al., 2011). ACT is a 6-m off-axis Gregorian telescope located in theAtacama Desert. It observes the sky in three frequency bands, at 148 GHz, 218 GHz and277 GHz corresponding to wavelengths of 2000µm, 1400µm and 1100µm, respectively.The ACT beams at these frequencies have a FWHM of 84′′ (2000µm), 60′′ (1400µm) and54′′ (1100µm). These beams are much larger than the SPIRE beams, so the ACT datacannot be used to refine the positions of our sources, but detecting millimeter emissiontowards these red galaxies would confirm their thermal nature.We use the available 1400µm and 2000µm equatorial maps (Du¨nner et al., 2013) tofind our red sources in the overlapping region. To improve point-source detectability, themaps are matched filtered with the ACT beams (Hasselfield et al., 2013b) as described inMarsden et al. (2014). The resulting maps have typical uncertainties of 3.3 and 2.2 mJyat 1400µm and 2000µm, respectively.We find that only a small fraction of our sources are detected in the ACT maps witha signal-to-noise ratio larger than three, so instead of measuring the individual sourceflux densities, we define 10 mJy wide intervals of 500µm flux density values, and westack the ACT maps at the positions of all of our sources in the overlapping area withS500 falling into the given interval. This method increases the signal-to-noise ratio in theACT dataset and we are able to detect the average flux densities of the sources that aretoo faint to be detected individually. The stacked images are shown on Figure 3.18 andthe average SPIRE and ACT flux density values for the sources falling into the different500µm flux density bins are listed in Table 3.3. The errors are determined by dividingthe standard deviation of the pixel values in the individual images at the position of thestacked peak by the square root of the number of objects that belong to the stack.It is encouraging to find that all the stacked images (except for the 2000µm stackcorresponding to 90 mJy > S500 > 80 mJy) show a clear point source at the position of75Figure 3.18: (a.) ACT stacks using the red source positions in different 500µm fluxdensity bins (bin 1: S500 > 100 mJy, bin 2: 90−100 mJy, bin 3: 80−90 mJy).S500 range 〈S250〉 〈S350〉 〈S500〉 〈S1400〉 〈S2000〉(mJy) (mJy) (mJy) (mJy) (mJy) (mJy)1 > 100 86.69± 11.75 118.76± 13.01 132.34± 13.74 19.13± 2.41 5.55± 1.532 90−100 56.10± 4.33 80.16± 4.65 94.27± 1.28 8.66± 2.64 3.55± 0.413 80−90 57.82± 1.81 72.90± 1.68 82.92± 0.47 3.30± 0.99 0.29± 0.724 70−80 46.49± 1.89 64.01± 1.62 74.84± 0.52 5.24± 1.16 1.66± 0.415 60−70 38.80± 0.97 52.83± 0.82 64.58± 0.25 2.20± 0.44 0.85± 0.336 52−60 30.79± 0.72 44.06± 0.60 55.80± 0.19 2.51± 0.33 0.95± 0.24Table 3.3: Average 250µm, 350µm, 500µm, 1400µm and 2000µm flux densities of thesources falling into different 500µm flux density bins.our red sources. The average colors of our brightest sources with ACT detections areS500/S1400 = 7.1 and S500/S2000 = 21.5. The average flux densities we detect in thestacked maps are lower than what we would expect from the S500 values. However, the76Figure 3.18: (b.) ACT stacks using the red source positions in different 500µm fluxdensity bins (bin 4: 70−80 mJy, bin 5: 60−70 mJy, bin 6: 52−60 mJy).ratios mentioned above are typical for isolated sources, and as we discussed before, sourceblending is a significant biasing effect in our catalog, and it is possible, that a fraction ofred sources in each of these stacks have a lower S500 flux density than what we measure. Ifthe other component of the blend is a non-red source, then this component will probablybe too faint to be detected in ACT, and it is possible that the millimeter emission wesee is from the fainter, but red component of the blend. Additionally, we only detect thebrightest sources in ACT individually, and these rare sources might be lensed but lessluminous sources with different SED properties, than the majority of our sources in thecatalog.In Figure 3.19 we plot the average SED of the sources belonging to our different S500bins. Except for Bin 3 all average SEDs follow a similar shape, showing that the sourcesin different bins have very similar properties. Our bin corresponding to 90 mJy > S500 >80 mJy shows higher 250µm and lower longer wavelength flux densities than what wewould expect based on the average SED in the other bins. To test whether this anomalous77103λ[µm]100101102Fluxdensity[mJy]Bin 1Bin 2Bin 3Bin 4Bin 5Bin 6Figure 3.19: Average spectra of the sources falling into the different S500 bins listed inTable 3.3.behavior is caused by some extreme outliers, or by sources with different SED propertiesthan the rest of our red sources, we will need to investigate the sources belonging inthis bin individually. We note, that due to the very steep 500µm source counts, the binscorresponding to higher S500 values contain significantly fewer galaxies than the lower fluxdensity bins, thus these bins can be more biased by outliers. The successful detectionof our sources in the ACT bands indicates that it is worth pursuing high-resolutioninterferometric follow-up observations of these sources at millimeter wavelengths. Thesefollow-up observations would help us in several ways. Interferometric observations give amuch more accurate position for our sources, which is crucial for spectroscopic redshiftobservations. Additionally the higher resolution and better sensitivity would allow us toinvestigate in more detail the biasing effects of blending on our number counts.3.6 SummaryWe used a map-based detection method similar to Dowell et al. (2014) to search for“red”(S500 > S350 > S250), potentially z > 4 dusty star-forming galaxies in the HeLMSfield. The HeLMS survey has a significantly larger area than the HerMES fields studiedbefore, and this allowed us to assemble a catalog of red sources 15 times larger than the78catalog we had before. Spectral energy distribution fits to the SPIRE flux densities ofthe HeLMS red sources resulted in observed dust temperature and SED peak-wavelengthdistribution similar to what we measured in the Dowell et al. (2014) sample, showingthat we were able to detect a similar population of sources in the HeLMS map. The totalnumber of detected HeLMS red sources confirms previous findings, that there is an excessof luminous dusty star-forming galaxies at high redshifts compared to model predictions.Our large sample, however, also allowed us to investigate the functional form of thedifferential number counts of these high-z galaxy candidates for the first time. The verysteep slope of the 500µm differential counts of our sources suggests that the propertiesof these galaxies are strongly evolving, and they possibly have a significant role in thestellar mass build-up of massive galaxies in the distant Universe. The very high redshiftof two of our sources was confirmed by ALMA spectroscopic follow-up observations. Sofar, all red sources selected for follow-up observations either from the Dowell et al. (2014)sample, or the new HeLMS red galaxy sample described in this thesis, were proven tobe indeed at high-z, the majority of them at z > 4 − 5, and the lowest redshift sourceis still very distant (z > 3). The detection of millimeter-wave emission from our sourcesin the ACT maps also shows that long-wavelength interferometric follow-up observationsof red sources are worth pursuing. In the future, we will extend our spectroscopicallyconfirmed subsample of high-z red sources, and multi-wavelength photometric follow-up observations will allow us to determine the photometric redshift distribution of ourpopulation. This will help in the construction of the z > 4 infrared luminosity function,and thus we will be able to determine the contribution of these luminous dusty galaxiesto the high-z cosmic star formation history.79Chapter 4Observing SPIRE-selected “red”sources with SCUBA-2We observed a sample of HerMES-selected “red” (S500 > S350 > S250, as discussed inChapter 3) sources with the SCUBA-2 instrument (Submillimetre Common-User Bolome-ter Array–2; Holland et al., 2013) on the James Clerk Maxwell Telescope (JCMT) operat-ing at the summit of Mauna Kea in Hawaii. SCUBA-2 is a bolometer camera containing10,000 detectors and it observes the sky simultaneously in two atmospheric windows at450 and 850µm. Due to the telescope’s large 15-m diameter dish, the images observedwith SCUBA-2 have significantly better resolution than the SPIRE images obtained byusing the 3.5-m diameter Herschel mirror. The SCUBA-2 beams have a full-width halfmaximum of 7.5′′ and 14.5′′ at 450 and 850µm, respectively.There are several advantages of observing our sources with SCUBA-2. First, obtainingsubmillimeter flux densities at 850 µm – the long-wavelength side of the peak of thedusty spectral energy distribution – can confirm the thermal nature of the emission andthus can constrain the dust temperature, infrared luminosity, star formation rate andother physical properties of the sources. SCUBA-2 images have larger resolution andlower confusion limits than the SPIRE maps, which allows us to potentially detect over-densities of faint galaxies around these bright red objects. Detecting such over-densitieswould strengthen the idea that distant dusty starburst galaxies possibly reside in proto-cluster environments (see discussion in Section 1.6).Our observational campaign had two tiers. First we observed a relatively large sampleof red sources at 850µm to a depth of 4 mJy RMS, well above the confusion limit (σconf <1 mJy). Then we selected four of our reddest galaxies, and we mapped a large areafield down to 2 mJy RMS around these sources in order to examine their environments.Although the telescope observes the sky simultaneously at both 450µm and 850µm80wavelengths, the transmission of the atmosphere at 450µm is only about half the 850µmvalue; thus in order to obtain high signal-to-noise ratio data at 450µm excellent weatherquality and very long integration times are needed. Due to the limited telescope timeavailable, we decided to design our observing proposal with the goal to reach the requireddepth at 850µm, and due to the shorter integration times the 450µm data we obtainedwere too noisy to be used in any further analysis.In this chapter we describe our sample selection, the observations and the data re-duction, and we summarize the early results of this observing campaign.4.1 Sample selectionOur sample of red sources was selected from three HerMES fields (Lockman-SWIRE,Bootes and ELAIS-N1), which were visible from the JCMT during the observing semester.The location of these fields and their SPIRE detector noise levels are listed in Table 4.1.We selected a total of 54 red sources from these fields detected with the map-basedsearch method described in Section 3.1. We required that they look like point-sourcesat the 500µm resolution, and that their SPIRE flux densities follow the relation S500 >S350 > S250. We also required that their flux density at 500µm should be greater than5×σ500 but at the same time less than 100 mJy. Above S500 = 100 mJy the relativelikelihood that a source is strongly lensed, rather than intrinsically luminous, increasesdramatically (Negrello et al., 2010). The focus of our study is to find sources with themost intense star formation activity, while finding the bright, lensed ordinary sourcesis part of a separate program. Since the instrumental noise levels in these HerMESobservations are lower than in the HeLMS maps, many of the selected sources are fainterat 500µm than 52 mJy (the flux density cutoff in our HeLMS catalog), with the faintestsources having flux densities of S500 ∼ 30 mJy, but due to the thermal shape of thespectral energy distribution we expect to measure 850 µm flux densities in the range of0.3 to 1.0 × S500, so they should be visible in these SCUBA-2 maps with flux densitiesat a level of > 3σ.In the second part of this observational campaign we observed four sources namedLSW28, LSW102, XMM30 and XMM26. We required that these sources are “ultra-red”,meaning that their flux densities obey the S500/S250 > 1.5 criterion in the smoothedmaps. The SPIRE flux densities of the observed sources are listed in Section 4.4 alongwith the SCUBA-2 flux density measurements.81Field RA Dec Area σ250 σ350 σ500(deg) (deg) (deg2) (mJy) (mJy) (mJy)Lockman-SWIRE 162.20 58.16 16.1 9.1 (4.9) 8.9 (4.9) 10.8 (5.7)Bootes 218.15 34.17 10.6 5.3 (3.4) 5.1 (3.4) 6.1 (4.2)ELAIS-N1 242.55 54.33 3.3 3.4 (2.7) 3.2 (2.8) 3.9 (3.2)Table 4.1: Location, area and 1σ SPIRE detector noise values for the HerMES fieldsincluded in the red source sample selection. The noise values are measured in mapscreated with the nominal SPIRE pixel sizes of 6′′, 8.333′′ and 12′′ at 250, 350 and 500µm,respectively, and the values in parentheses denote the noise values in point-source filteredmaps.4.2 ObservationsThe observations were carried out in April and December 2012. In the first part of theproject in order to quickly obtain 850µm flux densities we observed our sources usinga constant velocity “daisy” pattern (Holland et al., 2013). In this observing mode thetelescope moves in a precessing ellipsoidal pattern around the observed source, giving adeep coverage in the central 3 arcminute region of the ∼12 arcminute wide image (seeleft panel in Fig. 4.1). In the second part of the project we used the rotating “pong-900”pattern (Holland et al., 2013) to obtain large and deep maps with uniform coverage. Thisobserving mode results in a uniformly mapped area with a diameter of 15′ around thesource (see right on Fig. 4.1).The optimal integration time for each source depends on the requested depth, thesize of the fields, the scanning pattern used and the weather quality at the time of theobservation. The integration time to reach a given 1-σ850 [mJy] depth is calculated astintegr =1f[(aT850− b)1σ850]2, (4.1)where T850 is a weather-dependent atmospheric transmission factor, f is a sampling factor,(a, b) = (189, 48) for the “daisy” observations and (a, b) = (407, 104) for the “pong-900”pattern.SCUBA-2 is a ground-based detector, so any signal with intensity I0 needs to travelthrough a volume of air; thus the measured intensity Im will be attenuated compared toI0. T850 describes the atmospheric transmission and it is calculated as the ratio of the82Figure 4.1: Coverage map of the “daisy” (left) and “pong-900” (right) scanning patternsof the JCMT. Bright colors correspond to areas with deep coverage.measured and incident intensities,T850 =ImI0= e−τ850A, (4.2)where A is the airmass (the optical path length through Earth’s atmosphere for lightfrom a source on the sky) and τ850 is the extinction coefficient or opacity at 850µm. Theairmass A for a source at declination δ during transit can be expressed asA =10.9 cos[pi180(δ − 19.823)] . (4.3)As described in Dempsey et al. (2013), the opacity is determined based on the amountof precipitable water vapor (PWV, in units of mm) in the atmosphere asτ850 = 0.179[PWV/(1mm) + 0.337]. (4.4)The PWV values are measured with the JCMT’s water vapor monitor (WVM) at 183 GHzalong the line-of-sight of the telescope. The neighbouring Caltech Submillimeter Obser-vatory (CSO) has a radiometer that measures the zenith opacity at 225 GHz. Althoughthe WVM has better time resolution than the CSO radiometer, and in general gives abetter measurement of the opacity even when the atmosphere is unstable, during stable83Weather Grade PWV τ225Grade 1 <0.83 mm <0.05Grade 2 0.83−1.58 mm 0.05−0.08Grade 3 1.58−2.58 mm 0.08−0.12Grade 4 2.58−4.58 mm 0.12−0.20Grade 5 >4.58 mm >0.20Table 4.2: Weather grades defined at the JCMT. PWV means the amount of precipitablewater vapor in the atmosphere in units of mm, and τ225 is the opacity measured at 225GHz at the Caltech Submillimeter Observatory (CSO).weather conditions the 225 GHz opacity determined from PWV values measured at thezenith with the WVM as τ225 = 0.04PWVzen + 0.017 are in excellent agreement with theCSO τ225 measurements (Dempsey et al., 2013). In practice, the quality (or “grade”) ofthe weather during JCMT observations is defined based on the CSO τ225 values. Thecorresponding PWV and opacity values are listed in Table 4.2.The f value in Equation 4.1 is a sampling factor corresponding to the map-makingoptions for SCUBA-2 data. The nominal pixel size of SCUBA-2 maps at 850µm is 4′′,and the noise in each pixel depends on the number of samples that are projected ontothe given pixel. If we know in advance that we want to use pixel sizes different from thenominal size, the final pixel noise will change, and we need to take this into account inthe integration time calculation by applying a correction factor f , determined asf = (used pixel size/default pixel size)2. (4.5)Additionally, if we are planning to use a point source matched filter during the analysis ofthe maps, which increases the signal-to-noise ratio in the final products, then the requiredintegration time to reach a given sensitivity will decrease by a factor of f = 5 at 850µm.To carry out the shallower “daisy” observations we applied for telescope time withGrade 3 weather conditions, and we intended our observations to reach an RMS ofσ850 = 4 mJy. This is well above the confusion limit, but since most of our objectsare brighter than 30 mJy at 500µm, we expect to detect these objects at a level of atleast 3σ in the 850µm SCUBA-2 maps if their spectral energy distribution is indeeddominated by thermal dust emission. Using the matched-beam factors, we calculatedobserving times of 12−15 minutes per source depending on the declination of the target.The deeper “pong” observations were carried out during Grade 2 weather conditions,and we needed 2.5−3 hours of integration time per source to reach 2 mJy RMS (> 3σabove the confusion limit) with the matched-beam factors.84The success of any observational campaign depends on the weather conditions duringthe allocated observation periods, and due to bad weather not all of the proposed sourceswere observed. In the first part of the project we obtained data for 28 out of 54 sources,and out of the four deep maps XMM30 was only observed for a fraction of the proposedtime, so that particular observation did not reach the required RMS.4.3 Data reductionThe SCUBA-2 data reduction pipeline uses components of the Starlink Software Envi-ronment (Warren-Smith and Wallace, 1993; Jenness et al., 2009). There are two ways toreduce the raw telescope data. The ORAC-DR data reduction pipeline (Cavanagh et al.,2008) creates maps quickly with the most optimal settings for the given observation type.Additionally, one can use a combination of SMURF (Sub-Millimetre User Reduction Fa-cility; Chapin et al., 2013) and KAPPA (Kernel Application Package; Currie and Berry,2013) commands directly for more advanced customization options. Post-processing ofthe maps happens in PICARD (Pipeline for Combining and Analyzing Reduced Data;Gibb et al., 2012).The maps are constructed with the Dynamic Iterative Map-Maker (DIMM, Chapinet al., 2013), which is part of the SMURF package. We use a configuration file that isoptimized to reduce observations of blank fields containing only faint sources. In thisconfiguration the map-maker applies a harsh high-pass filter to the detector timelinesat the beginning of data processing to remove fluctuations on spatial scales larger than200′′. Since we are not interested in recovering any large scale structure in these maps,this recipe applies a noise-removal method to each bolometer time stream independently,ignoring any possible correlations between detectors. An extinction correction is alsoapplied during map-making to correct for the signal attenuation caused by the atmo-sphere. In this step a time varying scaling factor is applied to the data based on PWVmeasurements with the JCMT waver vapor monitor.DIMM and the associated pipeline produces a map in units of pW (pikowatt). Orac-DR automatically uses the standard flux conversion factors (FCFs) to convert the maps tounits of Jy. These FCFs are determined based on observations of bright calibrator sourceswith known flux densities (e.g. Uranus). The standard value at 850µm is FCF850 = 537±24 (Jy pW−1), as measured in Dempsey et al. (2013). During the actual observations,calibrator sources close to the target have been observed to make sure that the calibrationfalls within 5% of the standard value.Our final maps have pixel sizes of 4′′. Very long observations are always split into85shorter timelines. Maps are made from these smaller datasets separately, and in PICARDwe can co-add these images using inverse noise-weighting. The most important post-processing step is the application of a point-source matched filter. In this step thealgorithm first smooths the image with a broad Gaussian kernel with a FWHM of 30′′,and subtracts this map from the original image to remove any large-scale background fromthe maps. The 850µm beam is also smoothed with the same Gaussian, and a weightedconvolution is carried out with this modified beam in order to increase the point-sourcedetectability. For a raw map M(x, y) and an error map σ(x, y) the convolution with thebeam P (x, y) is calculated asMfilt(x, y) =[Mraw(x, y)/σ2(x, y)]⊗ P (x, y)[1/σ2(x, y)]⊗ [P 2(x, y)] , (4.6)and after filtering the variance map becomesσ2filt(x, y) =1[1/σ2(x, y)]⊗ [P 2(x, y)] . (4.7)In the resulting filtered maps the flux density of the detected sources is determined bytheir peak pixel values.4.4 Results and discussionHere we present the results of our two observing campaigns and our early findings, whilea more detailed analysis of this dataset will be part of future projects, that also includefollow-up data from several other telescopes at different wavelengths.4.4.1 Daisy observationsThe SPIRE 250, 350 and 500µm flux densities, and the SCUBA-2 850µm flux densityvalues of our observed sources are listed in Table 4.3, and postage-stamp images of theseobjects are shown on Figure 4.2 (a,b,c,d). The SPIRE flux densities are measured fromthe nominal resolution matched-filtered maps, except for the sources that appear to beblends of several sources in the 250 and/or 350µm maps. These sources are flaggedwith a star symbol in Table 4.3, and the quoted SPIRE flux densities of these objectscorrespond to the values in the maps that are smoothed to the 500µm resolution. We didnot discard any blends from our initial sample, since we expect that even blended objectsshould contain at least one red source if they appear to be red in the smoothed maps. We86note, that the observed sample was selected in the early stages of the red source searchproject, when we categorized sources as being red based on their smoothed flux densities.As we discussed in Section 3.1.4, the flux densities measured in the nominal resolutionmaps are less biased by the positional uncertainties, so whenever possible, we quote thelatter values here. This is the reason why some of the sources listed in Table 4.3 have amaximum flux density at 350µm.To check whether the measured 850µm flux densities of these sources are in agreementwith the values predicted from the SPIRE fluxes alone, we fit a modified blackbodyspectrum to the measured SPIRE and SCUBA-2 flux densities. As in Section 3.3, we usean optically thick SED model,Sν = (1− e−τν )Bν(Td)Ωs, (4.8)where Bν(Td) is the Planck function, Ωs is the solid angle of the source, τν = (ν/ν0)β is theoptical depth, β is the dust grain spectral emissivity index, and ν0 is the frequency whereτν = 1 and the dust becomes optically thick. As we discussed in detail in Section 3.3 wemarginalize over the Gaussian priors β = 1.8 ± 0.3 and λ0(1 + z) = (1100 ± 400)µm .The fitted curves are shown on Figure 4.3 (a, b, c, d, e).From Figure 4.2 and Table 4.3 it is clearly seen that most of our sources with a > 3σdetection in SCUBA-2 (LSW20, 28, 31, 36, BOOTES17, 23, 24, 28, 29, 33, 50, ELAIS-N11) have bright and isolated counterparts in the SPIRE maps. Figure 4.3 shows thatthe measured SCUBA-2 fluxes of these sources are in good agreement with the SPIREflux density values, thus we can confirm that the luminosity of these sources is dominatedby thermal dust emission and their SED is best fitted with an optically thick modifiedblackbody curve, similarly to the red sources selected in the HeLMS maps. We note,that many of these isolated sources have slightly higher 500µm flux densities than ourfitted values. Since we only select sources with S500 > S350, we are introducing a biasbecause were are more likely to find objects with their 500µm flux densities scatteredhigher than the real value. The number counts simulations we describe in Section 3.2.1take this effect into account.Our sources that look blended in the SPIRE maps typically show anomalously high500µm flux densities compared to the measured SCUBA-2 flux. Our reason to includethese sources in the catalog is that we expect that at least one of the components ofthe blend should be red in order to produce red colors in the smoothed maps. Themeasured 500µm flux density of such a source will be the co-added flux density of allcomponents of the blend. If we assume that red sources are rare enough that they87Name S250 S350 S500 S850 SNR850(mJy) (mJy) (mJy) (mJy)LSW19? 27.4± 7.6 42.3± 6.9 41.9± 6.5 10.6± 3.9 2.7LSW20 17.6± 4.4 36.6± 4.8 43.9± 5.5 30.0± 4.0 7.5LSW22? 22.2± 5.4 36.8± 5.2 43.4± 6.3 9.1± 4.0 2.3LSW28 33.4± 5.2 55.9± 4.7 60.0± 5.1 40.5± 4.0 10.1LSW31 43.3± 4.7 58.6± 5.2 52.3± 5.3 26.1± 4.0 6.5LSW36 55.3± 6.2 63.6± 6.8 62.5± 7.0 21.8± 3.5 6.2LSW37? 26.9± 5.0 45.3± 4.6 48.7± 6.2 8.2± 3.9 2.1LSW38? 25.3± 7.8 37.9± 7.1 47.2± 7.6 0.6± 3.7 0.2LSW40? 49.0± 6.8 51.0± 5.8 53.7± 7.5 −0.1± 3.7 0.0LSW41 26.9± 8.6 28.8± 6.3 45.2± 9.2 11.7± 4.1 2.9LSW42 19.1± 5.2 43.3± 4.8 44.4± 6.1 11.3± 4.0 2.9LSW43? 35.7± 4.7 45.9± 4.7 49.8± 6.2 4.8± 3.6 1.3LSW44 28.6± 5.4 36.7± 5.3 45.2± 5.9 11.7± 4.2 2.8BOOTES17 25.8± 4.9 38.1± 5.1 43.8± 5.9 14.5± 3.6 4.0BOOTES21? 12.8± 4.1 36.2± 4.4 49.5± 4.6 15.4± 3.7 4.2BOOTES23 33.9± 5.1 51.2± 5.0 52.5± 6.0 21.7± 3.6 6.0BOOTES24 28.7± 4.9 49.6± 5.0 55.8± 5.9 15.8± 3.8 4.2BOOTES25? 18.3± 4.8 36.2± 5.1 44.1± 6.2 11.9± 4.1 2.9BOOTES27 24.6± 5.2 30.0± 5.6 36.9± 5.5 4.2± 3.8 1.1BOOTES28 64.1± 4.9 87.4± 5.0 75.4± 5.7 15.4± 3.6 4.3BOOTES29 64.0± 5.3 74.5± 5.1 64.8± 5.5 17.6± 4.3 4.1BOOTES33 53.9± 2.7 57.6± 2.7 47.4± 3.0 12.5± 3.7 3.4BOOTES34 23.6± 5.2 34.7± 5.2 37.2± 6.3 6.8± 3.7 1.8BOOTES37 24.3± 5.2 27.2± 5.0 43.3± 5.9 11.3± 4.0 2.8BOOTES39 15.3± 5.0 29.6± 5.1 28.3± 5.5 6.1± 3.7 1.7BOOTES42 32.7± 3.9 46.1± 4.3 35.4± 4.8 9.7± 3.4 2.9BOOTES50 16.9± 5.3 28.1± 5.3 36.9± 6.1 14.4± 3.7 3.9ELAISN11 19.2± 2.9 24.3± 2.9 27.6± 3.4 11.1± 3.3 3.3Table 4.3: SPIRE 250, 350 and 500µm and SCUBA-2 850µm flux densities and the850µm signal-to-noise ratio of our observed sources. The SPIRE flux densities aremeasured from the nominal resolution maps, except for the sources marked with astar symbol, where the flux densities could not be determined due to blending effects.Here we quote the flux density values we measured from maps smoothed to the sameresolution.88+ + + +LSW19+ + + +LSW20+ + + +LSW22+ + + +LSW28+ + + +LSW31+ + + +LSW36+ + + +LSW37Figure 4.2: (a.) Postage-stamp images showing 1.8′ × 1.8′ area around our sources ob-served with “daisy” scans. From left to right we show the SPIRE 250, 350 and 500µmimages and the SCUBA-2 850µm image, respectively. The SPIRE images are scaledbetween −5σ and +10σ, and the SCUBA-2 images are scaled between −3σ and +4σ forbetter visibility.89+ + + +LSW38+ + + +LSW40+ + + +LSW41+ + + +LSW42+ + + +LSW43+ + + +LSW44+ + + +BOO17Figure 4.2: (b.) Postage-stamp images showing 1.8′ × 1.8′ area around our sourcesobserved with “daisy” scans. From left to right we show the SPIRE 250, 350 and 500µmimages and the SCUBA-2 850µm image, respectively. The SPIRE images are scaledbetween −5σ and +10σ, and the SCUBA-2 images are scaled between −3σ and +4σ forbetter visibility.90+ + + +BOO21+ + + +BOO23+ + + +BOO24+ + + +BOO25+ + + +BOO27+ + + +BOO28+ + + +BOO29Figure 4.2: (c.) Postage-stamp images showing 1.8′ × 1.8′ area around our sources ob-served with “daisy” scans. From left to right we show the SPIRE 250, 350 and 500µmimages and the SCUBA-2 850µm image, respectively. The SPIRE images are scaledbetween −5σ and +10σ, and the SCUBA-2 images are scaled between −3σ and +4σ forbetter visibility.91+ + + +BOO33+ + + +BOO34+ + + +BOO37+ + + +BOO39+ + + +BOO42+ + + +BOO50+ + + +ELA11Figure 4.2: (d.) Postage-stamp images showing 1.8′ × 1.8′ area around our sourcesobserved with “daisy” scans. From left to right we show the SPIRE 250, 350 and 500µmimages and the SCUBA-2 850µm image, respectively. The SPIRE images are scaledbetween −5σ and +10σ, and the SCUBA-2 images are scaled between −3σ and +4σ forbetter visibility.920 200 400 600 800 1000Wavelength [µm]0102030405060FluxDensity[mJy]LSW19T0=13.1λ0=788.0β=1.9χ2=2.070 200 400 600 800 1000Wavelength [µm]0102030405060FluxDensity[mJy]LSW20T0=9.6λ0=1123.0β=1.8χ2=0.050 200 400 600 800 1000Wavelength [µm]0102030405060FluxDensity[mJy]LSW22T0=12.3λ0=758.0β=1.9χ2=3.40 200 400 600 800 1000Wavelength [µm]010203040506070FluxDensity[mJy]LSW28T0=10.6λ0=1218.0β=1.8χ2=0.370 200 400 600 800 1000Wavelength [µm]010203040506070FluxDensity[mJy]LSW31T0=13.3λ0=1092.0β=1.8χ2=0.040 200 400 600 800 1000Wavelength [µm]01020304050607080FluxDensity[mJy]LSW36T0=14.4λ0=896.0β=1.8χ2=0.96Figure 4.3: (a.) Modified blackbody SED fits to the SPIRE 250, 350 and 500µm andSCUBA-2 850µm flux densities.930 200 400 600 800 1000Wavelength [µm]0102030405060FluxDensity[mJy]LSW37T0=12.2λ0=649.0β=1.9χ2=5.210 200 400 600 800 1000Wavelength [µm]−100102030405060FluxDensity[mJy]LSW38T0=14.6λ0=627.0β=1.9χ2=10.530 200 400 600 800 1000Wavelength [µm]−10010203040506070FluxDensity[mJy]LSW40T0=17.0λ0=592.0β=2.0χ2=12.420 200 400 600 800 1000Wavelength [µm]0102030405060FluxDensity[mJy]LSW41T0=13.5λ0=974.0β=1.8χ2=2.360 200 400 600 800 1000Wavelength [µm]0102030405060FluxDensity[mJy]LSW42T0=11.0λ0=668.0β=1.9χ2=3.510 200 400 600 800 1000Wavelength [µm]0102030405060FluxDensity[mJy]LSW43T0=14.2λ0=637.0β=2.0χ2=7.64Figure 4.3: (b.) Modified blackbody SED fits to the SPIRE 250, 350 and 500µm andSCUBA-2 850µm flux densities.940 200 400 600 800 1000Wavelength [µm]0102030405060FluxDensity[mJy]LSW44T0=13.0λ0=870.0β=1.9χ2=2.350 200 400 600 800 1000Wavelength [µm]0102030405060FluxDensity[mJy]BOO17T0=12.5λ0=894.0β=1.8χ2=1.30 200 400 600 800 1000Wavelength [µm]0102030405060FluxDensity[mJy]BOO21T0=9.4λ0=650.0β=1.9χ2=3.810 200 400 600 800 1000Wavelength [µm]010203040506070FluxDensity[mJy]BOO23T0=12.2λ0=909.0β=1.8χ2=0.520 200 400 600 800 1000Wavelength [µm]010203040506070FluxDensity[mJy]BOO24T0=11.3λ0=705.0β=1.9χ2=2.990 200 400 600 800 1000Wavelength [µm]0102030405060FluxDensity[mJy]BOO25T0=10.9λ0=727.0β=1.9χ2=2.74Figure 4.3: (c.) Modified blackbody SED fits to the SPIRE 250, 350 and 500µm andSCUBA-2 850µm flux densities.950 200 400 600 800 1000Wavelength [µm]01020304050FluxDensity[mJy] BOO27T0=14.5λ0=807.0β=1.8χ2=4.360 200 400 600 800 1000Wavelength [µm]020406080100FluxDensity[mJy]BOO28T0=12.3λ0=536.0β=2.0χ2=5.560 200 400 600 800 1000Wavelength [µm]0102030405060708090FluxDensity[mJy]BOO29T0=14.8λ0=750.0β=1.9χ2=1.960 200 400 600 800 1000Wavelength [µm]010203040506070FluxDensity[mJy]BOO33T0=16.4λ0=810.0β=1.9χ2=1.50 200 400 600 800 1000Wavelength [µm]01020304050FluxDensity[mJy] BOO34T0=13.7λ0=762.0β=1.9χ2=2.960 200 400 600 800 1000Wavelength [µm]0102030405060FluxDensity[mJy]BOO37T0=12.2λ0=863.0β=1.8χ2=3.14Figure 4.3: (d.) Modified blackbody SED fits to the SPIRE 250, 350 and 500µm andSCUBA-2 850µm flux densities.960 200 400 600 800 1000Wavelength [µm]0510152025303540FluxDensity[mJy] BOO39T0=13.1λ0=818.0β=1.8χ2=2.190 200 400 600 800 1000Wavelength [µm]0102030405060FluxDensity[mJy] BOO42T0=13.9λ0=710.0β=1.9χ2=1.840 200 400 600 800 1000Wavelength [µm]01020304050FluxDensity[mJy] BOO50T0=11.3λ0=963.0β=1.8χ2=0.790 200 400 600 800 1000Wavelength [µm]0510152025303540FluxDensity[mJy] ELA11T0=13.0λ0=1038.0β=1.8χ2=0.33Figure 4.3: (e.) Modified blackbody SED fits to the SPIRE 250, 350 and 500µm andSCUBA-2 850µm flux densities.are most likely to be blended with a non-red source, then it is possible that at longerwavelengths the contribution from this non-red object will become negligible, and themeasured emission from the red source will be fainter than what the biased 500µm fluxdensity would suggest. The fact that we often see a 2−3σ source in the SCUBA-2 imagesat the positions of these confused objects seems to support this scenario, and while themeasured SPIRE flux densities are biased high, we cannot simply discard these objectsas spurious detections. This result agrees with our findings in Section 3.5, where weshow that even if we include the possible blends in our stacks we still detect a source atmillimeter wavelengths. To examine the detailed properties of blended galaxies higherresolution images are needed, but both our SCUBA-2 and ACT measurements suggest97that these blends indeed contain at least one red source.4.4.2 Pong observationsThe matched-filtered “pong” maps of LSW28, LSW102, XMM26 and XMM30 are shownon Figure 4.4. Each map has a diameter of 15′ (a 1 arcmin angular scale corresponds toa ∼ 0.39 Mpc physical scale at z ∼ 5), so they cover an area of 177 arcmin2 around thecentral bright red source. These pong maps are typically created from five observationsof the same field, each ∼ 40 minutes long, and these scans are co-added in PICARD usinginverse-variance weighting. Since the weather conditions are not always stable during longobservations, and since the separate scans of the same field are often observed on differentdays, the final noise values will be different in each of these observed fields. Additionally,XMM30 was only observed two times, so the noise in that map is much higher than inthe other three fields. The noise levels in the central region of the matched-filtered mapsare σLSW28 = 2.1 mJy, σLSW102 = 2.5 mJy, σXMM26 = 2.3 mJy and σXMM30 = 3.3 mJy. Asexpected, our central sources are detected in each of these maps with a very high signal-to-noise ratio: SLSW28 = 34.8 mJy (17σ), SLSW102 = 72.8 mJy (29σ), SXMM26 = 18.5 mJy(8σ) and SXMM30 = 32.8 mJy (10σ).To investigate whether there are over-densities of fainter sources around these galaxies,we create a signal-to-noise ratio map from our observations, and we search for peaks withSNR > 3.75 in these maps. This SNR cut is needed in order to reduce the chance offalse detections (e.g. Geach et al., 2013; Casey et al., 2013; Chen et al., 2013). Thedetected sources are highlighted with white circles on Figure 4.4, and their measuredSCUBA-2 flux densities along with their separation from the central red source are listedin Table 4.4. We also list the SPIRE flux densities for the sources that are visible in theHerschel maps. We check the possibility of false detections by creating two separate mapsfor each field from only half of the data, and we examine the positions of the detectedsources in these maps. All of our sources are visible in both halves of the data, thus weconclude that they are not noise peaks. Note, that the SNR> 3.75 cut corresponds todifferent flux density limits in the four maps. We detect eight sources around LSW28with flux densities S850 & 7.8 mJy, six sources around LSW102 with S850 & 9.4 mJy,seven sources around XMM26 with S850 & 8.6 mJy, and one source around XMM30 withS850 & 12.3 mJy.To improve our statistics, we combine the results for our three fields with similarnoise levels (LSW28, LSW102 and XMM26), and we investigate the average number ofsubmillimeter-detected galaxies around these red sources. On Figure 4.5 we plot the98Figure 4.4: 850µm “pong” observations of our sources LSW28, LSW102, XMM26,XMM30 (highlighted with red square symbols). The maps are matched-filtered, andthe sources detected around our targets with flux densities above 3.75σ are highlightedwith white circles.cumulative number counts of the combined fields and we compare our results to theCoppin et al. (2006) source densities measured in a blank field survey. The resultingnumber counts shows no obvious evidence for an over-density of faint galaxies aroundour red sources. Additionally, we can also see from Table 4.4 that the observed colorsof the sources that have a counterpart in the SPIRE maps are usually not red, which99ID S850 SNR850 Distance S250 S350 S500(mJy) (arcmin) (mJy) (mJy) (mJy)LSW280 34.8± 2.06 16.92 0.0 33.38 55.86 59.981 15.69± 2.05 7.65 1.7 64.52 73.43 46.272 13.49± 2.05 6.58 1.8 28.10 38.86 26.603 12.39± 2.10 5.90 5.0 45.49 57.56 55.384 11.49± 2.05 5.61 0.9 30.22 43.14 35.255 8.4± 2.07 4.06 4.4 - - -6 8.53± 2.26 3.77 6.3 30.79 18.79 14.267 9.25± 2.46 3.75 6.7 20.53 14.42 -8 9.48± 2.53 3.75 7.0 10.55 12.87 21.54LSW1020 72.80± 2.51 29.04 0.0 49.71 118.14 140.401 11.43± 2.82 4.05 6.4 - - -2 10.86± 2.72 3.99 6.1 - - -3 9.83± 2.53 3.88 4.0 - - -4 9.79± 2.53 3.87 3.5 - - -5 9.56± 2.51 3.81 4.1 - - -6 9.48± 2.53 3.75 4.0 - - -XMM260 18.48± 2.31 8.01 0.0 38.09 58.89 69.711 10.48± 2.30 4.56 3.8 36.99 39.72 35.672 11.02± 2.69 4.10 7.1 29.62 22.62 12.633 9.58± 2.37 4.04 5.4 10.14 7.97 13.514 9.17± 2.28 4.01 3.7 - - -5 9.19± 2.32 3.97 4.5 - - -6 10.7± 2.71 3.94 7.0 16.78 20.16 -7 9.61± 2.51 3.83 6.3 - - -XMM300 32.79± 3.41 9.61 0.0 23.77 39.11 55.591 20.58± 3.35 6.15 3.5 35.40 54.35 55.32Table 4.4: Sources detected with S850 > 3.75σ around LSW28, LSW102, XMM26 andXMM30. ID = 0 refers to the central red source in all cases. See also Figure 4.4might suggest that they are at a different redshift and are not physically associated withthe central source. The one really bright source we find 3.5′ away from XMM30 has redcolors similarly to the central source, which could suggest that these two sources might be100101S850 [mJy]101102N(>S)[deg−2]Figure 4.5: Cumulative 850µm number counts of the three combined 177 arcmin2 fieldsmapped around our sources LSW28, LSW102 and XMM26. The black symbols representour raw counts with Poisson errorbars. The blue solid line shows the Coppin et al. (2006)blank-field number counts with the shaded region corresponding to ±1σ uncertainties ofthese counts.physically related to each other. Unfortunately the signal-to-noise ratio of the XMM30map is too low to find a larger number of faint sources, so this one detection alone is nota strong indicator of an over-density; however, the close proximity of another bright redsource makes this galaxy an ideal target for future follow-up observations.On Figure 4.6 we plot the cumulative number of sources detected within differentradii of the central red source, and we compare this to the distribution we would expectto observe if our sources were distributed in an unclustered fashion within the observedarea. We do not see any strong deviation from the expected shape that would suggestangular clustering of the detected sources.Several high redshift dusty starburst galaxies are known to reside in over-dense regions(e.g. Chapman et al., 2001; Daddi et al., 2009; Capak et al., 2011), and it was expected,that the red sources we select could also trace proto-clusters. The lack of observedover-density around our red sources is similar to the result described in Robson et al.(2014), who mapped the region around HFLS3 (Riechers et al., 2013), the z = 6.34 redsource found with our map-based search method during our analysis of the FLS field. One1010 1 2 3 4 5 6 7 8Distance from center [arcmin]05101520NumberofsourceswithindistanceFigure 4.6: Cumulative number of sources within different radii of the central red sourcefor the combined fields around LSW28, LSW102 and XMM26. The solid blue line showsthe expected distribution from an unclustered source distribution.might argue, that the possible companion galaxies might be even fainter than our currentflux limits, or that they contain smaller amount of dust than expected. Laporte et al.(2015) carried out an analysis to search for Lyman-break galaxies (an unobscured high-zgalaxy population) in the vicinity of HFLS3 , but they also came to the conclusion thatthe environment of HFLS3 shows no evidence of an over-density of similar redshift starforming galaxies. Robson et al. (2014) show that current large-scale structure simulationswould predict that we should find an over-density around such a luminous source. But,on the other hand, our current observations of three red sources suggest, that it is notuncommon to find distant starburst galaxies without a clear over-density around them.This shows how important it is to obtain more observational constraints when modellingthe evolution of star formation in the large-scale structures in the Universe.4.5 SummaryWe described a follow-up observational campaign for SPIRE-selected “red”(S500 > S350 >S250) galaxies with the SCUBA-2 instrument at 850µm. We found that the observed850µm flux densities of sources that appear isolated in all three SPIRE wavelengths are102consistent with the values we would predict by fitting a thermal modified blackbodySED to the SPIRE flux densities alone. Together with other multi-wavelength follow-upobservations in the future these additional photometry points will allow us to determinethe photometric redshifts and constrain some physical properties of these sources (e.g.LIR, dustmass, star formation rate). The observation of sources that appear to be a singleobject at the 500µm resolution, but break up into multiple components in the higherresolution SPIRE maps resulted in lower signal-to-noise ratio 850µm detections than wewould have expected based on the 500µm flux densities alone. At the position of mostof these blends we still see a faint SCUBA-2 source; this suggests that at least one of thegalaxies in the blend is a red source, although its 500µm flux density is boosted high. Thisresult shows that the higher-resolution of the SCUBA-2 instrument can help us assessthe biasing effect of blending on our 500µm number counts of red sources described inChapter 3. We also examined the environment of four of our red sources. On average,we cannot see an over-density of fainter submillimeter galaxies around these sources thatcould suggest that these galaxies reside in a proto-cluster environment. This can suggestthat environment has a smaller role in triggering extreme star formation events thanpreviously predicted, or that these high-redshift dusty galaxies do not always reside in aproto-cluster environment, as previously thought.103Chapter 5Average dusty star-formationactivity inSunyaev-Zel’dovich-selected galaxyclustersStudying the star formation history of galaxy clusters – the largest gravitationally boundstructures in the Universe – can help us assess whether the environment in which galaxiesreside plays a role in triggering or quenching star formation activity. As we discussedin Section 1.1, in the local Universe there is no observational evidence for significantstar formation activity in the cores of massive virialized structures; only galaxies inthe outskirts of these clusters form new stars at a moderate rate. There is an ongoingdebate whether this locally observed morphology-density relation universally holds at allredshifts, or whether there is a reversal in this relation in the high-z Universe. Thereis observational evidence both for and against the theory that at higher redshifts starformation happens in denser environments.Galaxy clusters can contain hundreds to thousands of individual galaxies, but thedominant baryonic component of these structures is the intra-cluster gas, having a masslarger by a factor of ten, than the total mass of the cluster-member galaxies (e.g. Kravtsovand Borgani, 2012). This hot, ionized gas is in hydrostatic equilibrium in the deeppotential well of the cluster, and it is heated to a temperature of 107−108 K. Due tothe very hot temperature, the gas emits X-rays in the form of thermal bremsstrahlungradiation. Apart from identifying clusters by their optical richness (e.g. Abell, 1958;Gunn et al., 1986), the detection of this X-ray luminosity is one of the most widely usedmethods to find clusters of galaxies. The biggest limitation of this technique is, however,104the decrease of the intensity of the X-ray radiation with increasing distance, limiting therange of redshifts where these large clusters can be detected.A redshift-independent way of finding massive galaxy clusters is based on the de-tection of the Sunyaev-Zel’dovich effect (Sunyaev and Zel’dovich 1972, and see reviewse.g. in Birkinshaw 1999; Carlstrom et al. 2002) in cosmic microwave background (CMB)measurements. The cosmic microwave background radiation originates from the epochof recombination, when photons decoupled from the matter in the Universe and startedto propagate freely. This background radiation has a remarkably uniform temperature of2.725 K. Very small fluctuations of this temperature trace the primordial matter densityperturbations, but secondary anisotropies can also emerge due to the CMB photons prop-agating through structures along the line of sight. As the CMB photons pass through thehot intra-cluster gas in the core of massive galaxy clusters, the hot electrons in the gascan scatter these photons through inverse Compton scattering. As a result, the tempera-ture and thus the energy of the CMB photons increases, and the blackbody spectrum ofthe cosmic microwave background becomes distorted, since photons are scattered fromthe long wavelength Rayleigh-Jeans side of the peak of the spectrum to the shorter wave-length Wien side. This distortion is called the Sunyaev-Zel’dovich (SZ) effect, and inpractice it is observed as a relative change in the CMB temperature as∆TSZTCMB= fSZ(x) y = fSZ(x)∫nekBTemec2σTd`, (5.1)where x = hν/(kBTCMB) is a dimensionless frequency, y is called the Compton y-parameter, ne is the electron number density, σT is the Thomson scattering cross-section,Te is the temperature of the electrons in the hot gas, kB is the Boltzmann constant andd` represents the the line of sight extent of the cluster. The frequency dependence of thedistortion is given by the function fSZ(x) asfSZ(x) =(xex + 1ex − 1 − 4)(1 + δSZ(x, Te)). (5.2)Here δSZ(x, Te) is a relativistic correction that cannot be ignored when we are lookingfor massive clusters containing very hot gas. The result of this frequency dependenceis an observed decrement in the CMB temperatures below frequencies ν ∼ 220 GHz(corresponding to wavelengths greater than λ ∼ 1.3 mm), and an increment for largerfrequencies (shorter wavelengths). A similar relation can be applied to the observed in-tensity of the background radiation, where the change in the intensity is also proportionalto the Compton y-parameter (∆I0 ∝ y I0).105The amplitude of the thermal distortion is independent of redshift, but it depends onthe line of sight extent of the cluster; thus SZ surveys are limited by the cluster massand are usually able to select only the most massive structures. Apart from the thermalSunyaev-Zel’dovich effect, a distortion in the CMB temperature can also occur due tobulk motion of the electrons in the hot gas, but the amplitude of this so-called “kineticSZ-effect” (Sunyaev and Zeldovich, 1980) is much smaller than the distortion caused bythe inverse Compton scattering of CMB photons. The thermal distortion is already verysmall (< 1 mK), so the kinetic SZ effect can be essentially ignored in cluster surveys.Recently, large cluster samples have been assembled using the Sunyaev-Zel’dovichdetection technique by the Atacama Cosmology Telescope (Marriage et al., 2011; Has-selfield et al., 2013a), the South Pole Telescope (Vanderlinde et al., 2010; Reichardt et al.,2013) and the Planck satellite (Planck Collaboration et al., 2011, 2014b). The ACT andSPT telescopes operate at millimeter wavelengths, where a cluster can be detected asa decrement in the intensity of the cosmic microwave background. At far-infrared andsubmillimeter wavelengths the thermal SZ effect causes an increment in the observedbackground intensity, which has been detected at 350 and 500µm with Herschel (Zem-cov et al., 2010) and at 850µm with SCUBA (Zemcov et al., 2003), as well as with Planck.In this wavelength range sources behind the cluster that are magnified by gravitationallensing can also contribute to the excess measured FIR/submillimeter flux density to-wards these clusters, as well as dusty star-forming galaxies that reside inside the observedcluster. While these point sources are treated as contaminants in the Sunyaev-Zel’dovicheffect measurements, these objects are a focus of several different studies. Exploitingthe lensing magnification allows us to study dusty galaxies with flux densities below ourdetection limits, and investigating the rare star-forming galaxies inside clusters can helpus understand the interaction between environment and star formation activity.In this chapter we exploit the large overlap of our HeLMS and HerS regions with anequatorial field observed by the Atacama Cosmology Telescope. We investigate dustygalaxy emission towards massive Sunyaev-Zel’dovich-selected galaxy clusters found withACT. Due to the low resolution available with the large SPIRE beams, as well as theshallow depth of our HeLMS and HerS maps, we do not attempt to investigate the farinfrared emission towards each of these clusters individually and we do not focus onthe cluster member galaxies. Instead we stack the Herschel maps on the positions ofthe centers of the clusters determined from the Sunyaev-Zel’dovich effect to increase oursignal-to-noise ratio, and we investigate the average far-infrared emission towards thesemassive galaxy clusters.1065.1 The ACT equatorial cluster sampleThe ACT Sunyaev-Zel’dovich-selected equatorial cluster sample (Hasselfield et al., 2013a)consists of 68 galaxy clusters detected at 148 GHz with a signal-to-noise ratio SNR > 5.1.All of the cluster candidates have been confirmed to be actual clusters based on opticalor infrared data (Menanteau et al., 2013). As a first step in this confirmation process thebrightest cluster galaxy (BCG) is identified in each candidate cluster using mainly SloanDigital Sky Survey (SDSS) data. The BCGs are usually the most massive cluster-membergalaxies and reside in the centers of the clusters. The next step is to find the so-called redsequence around this central galaxy. The red sequence consists of elliptical and lenticular(“early-type”) galaxies that have a very tight color-magnitude relation with the reddergalaxies being brighter. This population can be found in all galaxy clusters and theidentification of this red sequence is often used as optical cluster-detection technique(Gladders and Yee, 2000). A candidate is confirmed as a cluster if it contains more than15 galaxies within a projected 1 Mpc area of the center of the cluster. The redshifts ofthese clusters are determined from follow-up observations, or – if available – from alreadyexisting SDSS spectroscopy data of cluster-member galaxies.The clusters were selected from a 504 deg2 field along the celestial equator spanning20h16m00s < RA < 3h52m24s and −2◦07′ < Dec < 2◦18′. This area has ∼ 100 deg2overlap with our HeLMS field, and contains the full HerS region (see Section 2.4.1). Inour analysis we select all clusters from the Hasselfield et al. (2013a) sample that fall intoour HeLMS and HerS fields. We find 15 ACT SZ clusters in HeLMS and 11 clusters inour HerS region. The redshift range of these clusters is 0.21 < z < 1.11 and their typicalmasses are ∼ 5 × 1014 M. The ACT IDs, locations and redshifts of these clusters aresummarized in Table 5.1 for HeLMS and in Table 5.2 for HerS.5.2 Data analysisOur goal is to investigate the mean far-infrared emission measured towards galaxy clustersas a function of the distance from their centers determined by the Sunyaev-Zel’dovicheffect. This can be done by stacking our SPIRE maps on the ACT cluster positions, andinvestigating the radially-averaged flux density distribution. A simple co-addition of ourmaps, however, does not take into account the changing angular extent of these clustersat different redshifts.We can define the characteristic physical radius of a cluster to be 1 Mpc (e.g. Koesteret al., 2007; Hasselfield et al., 2013a; Menanteau et al., 2013). Here we adopt similar107ACT ID RA Dec z DA θ1Mpc(deg) (deg) (Mpc) (arcmin)ACT-CL J0022.2 – 0036 5.5553 −0.6050 0.805 1576.4 2.2ACT-CL J0059.1 – 0049 14.7855 −0.8326 0.786 1563.0 2.2ACT-CL J2337.6+0016 354.4156 0.2690 0.275 869.5 4.0ACT-CL J0014.9 – 0057 3.7276 −0.9502 0.533 1316.3 2.6ACT-CL J0044.4+0113 11.1076 1.2221 1.110 1721.9 2.0ACT-CL J0058.0+0030 14.5189 0.5106 0.760 1543.8 2.2ACT-CL J2351.7+0009 357.9349 0.1538 0.990 1678.0 2.0ACT-CL J0018.2 – 0022 4.5623 −0.3795 0.750 1536.1 2.2ACT-CL J0104.8+0002 16.2195 0.0495 0.277 874.0 3.9ACT-CL J0017.6 – 0051 4.4138 −0.8580 0.211 712.9 4.8ACT-CL J0051.1+0055 12.7875 0.9323 0.690 1485.8 2.3ACT-CL J2327.4 – 0204 351.8660 −2.0777 0.705 1499.1 2.3ACT-CL J0045.2 – 0152 11.3051 −1.8827 0.545 1331.5 2.6ACT-CL J0026.2+0120 6.5699 1.3367 0.650 1448.2 2.4ACT-CL J0008.1+0201 2.0418 2.0204 0.360 1045.7 3.3Table 5.1: ACT Sunyaev-Zel’dovich-selected clusters in the HeLMS region. Based on theredshift, we calculate the angular diameter distance DA and the corresponding observedangular size θ1Mpc of a cluster with a physical size of 1 Mpc.ACT ID RA Dec z DA θ1Mpc(deg) (deg) (Mpc) (arcmin)ACT-CL J0206.2 – 0114 31.5567 −1.2428 0.676 1473.0 2.3ACT-CL J0218.2 – 0041 34.5626 −0.6883 0.672 1469.3 2.3ACT-CL J0215.4+0030 33.8699 0.5091 0.865 1614.6 2.1ACT-CL J0127.2+0020 21.8227 0.3468 0.379 1080.8 3.2ACT-CL J0119.9+0055 19.9971 0.9193 0.720 1511.8 2.3ACT-CL J0058.0+0030 14.5189 0.5106 0.760 1543.8 2.2ACT-CL J0219.8+0022 34.9533 0.3755 0.537 1321.4 2.6ACT-CL J0139.3 – 0128 24.8407 −1.4769 0.700 1494.7 2.3ACT-CL J0104.8+0002 16.2195 0.0495 0.277 874.0 3.9ACT-CL J0152.7+0100 28.1764 1.0059 0.230 761.8 4.5ACT-CL J0156.4 – 0123 29.1008 −1.3879 0.450 1199.4 2.9Table 5.2: ACT Sunyaev-Zel’dovich-selected clusters in the HerS region. Based on theredshift, we calculate the angular diameter distance DA and the corresponding observedangular size θ1Mpc of a cluster with a physical size of 1 Mpc.108standard flat cosmology parameters as used in Hasselfield et al. (2013a), with Ωm = 0.27,Ωλ = 0.73 and H0 = 70 km s−1Mpc−1. If we know the physical size x of an object atredshift z, the observed angular size θ can be determined from the angular size-redshiftrelation for small angles asθ =xDA(z), (5.3)where DA(z) is the angular diameter distance, a commonly used distance measure inastronomy. In a flat (Ωk = 0) universe DA(z) can be expressed asDA(z) =cH0(1 + z)∫ z0dz′√Ωm(1 + z′)3 + 1− Ωm. (5.4)This relates to the quantity DL used in Chapter 3 as DA = DL/(1 + z)2 (see e.g. Hogg,1999). Using these relations we calculate DA(z) and θ1Mpc values for each cluster. Thesevalues are listed in Table 5.1 and 5.2. It can be seen that there is a large variation in theangular size of our clusters, since a 1 Mpc physical size corresponds to an angular size ofθ1Mpc ∼ 5′ at z ∼ 0.2 and θ1Mpc ∼ 2′ at z ∼ 1.1. If our sample was larger, these clusterscould be binned based on their angular size, and stacks could be created in each of thesebins in order to investigate the star formation activity on a physical scale. Instead, dueto the relatively small number of clusters in our sample we create a single stacked imagefrom all of our 26 clusters, while we resize our individual images so that the pixel sizes inthe SPIRE images corresponds to similar physical extent. We choose to scale all of ourimages to match an image where 2′ corresponds to a 1 Mpc physical scale. Our nominalSPIRE pixel sizes at 250, 350 and 500µm are 6′′, 8.333′′ and 12′′, respectively, so 2′corresponds to 20.0, 14.4 and 10.0 pixels in each band. In practice as a first step in eachSPIRE band we create 50′×50′ postage-stamp images centered on the position of each SZcluster. After we convert our θ1Mpc values in Tables 5.1 and 5.2 from units of arcminutesto pixels in the corresponding band (θ250, θ350, θ500), the re-binning factors for each of ourpostage-stamp images are calculated as 20.0/θ250, 14.4/θ350 and 10.0/θ500. After this stepwe trim the edges of each image so that all of our postage-stamp images have the samedimensions. As a result, our final cut-out images have pixel sizes corresponding to 50 kpc(250µm), 69 kpc (350µm) and 100 kpc (500µm) (see Figure 5.1). Due to the negativek-correction at FIR/submm wavelengths we do not expect a significant decrease in fluxdensity for objects at higher redshifts, so the observed flux densities are not rescaledduring this analysis.We create a stack from all the postage-stamp images in HeLMS and HerS by cal-culating their weighted mean. After re-binning the noise-per-pixel values will change109Figure 5.1: Result of re-binning the SPIRE images of ACT clusters at different redshifts.A physical radius of 1 Mpc corresponds to an angular scale of θ ∼ 5′ at z ∼ 0.2 and θ ∼ 2′at z ∼ 1.3, as shown with white circles. Before re-binning, the pixel sizes correspondto 6′′ (250 µm), 8.333′′ (350 µm) and 12′′ (500 µm) angular size. After re-binning, thenew pixel sizes correspond to a physical extent of 50 kpc (250µm), 69 kpc (350µm) and100 kpc (500µm).in our images and we re-scale our noise values based on the ratio of the noise in there-binned maps to the original cutouts. The final stack of all 26 cluster images is shownin Figure 5.2, with white circles illustrating the characteristic 1 Mpc cluster radius.5.3 Results and discussionWe calculate the radial averages of our stacked images in 100 kpc bins in each band. Theresults are plotted in Figure 5.3. Since some of the 26 clusters contain bright objectsthat we did not remove, we have to investigate how these outliers affect the mean weobserve. We re-calculate the mean and standard deviation using a bootstrap method.First we randomly select 20 clusters from our sample of clusters, and we calculate theradial average of the stacked image created from these 20 clusters. We then repeat thisprocedure 1000 times, always selecting a different random set of 20 clusters. We calculatethe mean and standard deviation of the resulting curves of all these different realizations,and these results are also plotted on Figure 5.3. We can see that the full sample of 26sources appears to contain some outliers, but the resulting radial average curve is still lessthan 2σ away from the mean calculated by the bootstrap method. We also investigate110Figure 5.2: Stacked image of the 26 ACT Sunyaev-Zel’dovich selected cluster positionsin HeLMS and HerS at 250, 350 and 500µm (left to right). The white circles correspondto a physical radius of 1 Mpc.stacks made from random positions in the map that do not correspond to cluster centres.Figure 5.4 shows the result of the mean and standard deviation of 1000 realizations ofpicking 26 random positions in our maps and calculating the radial average similarly tothe red curve on Figure 5.3.Our results show that excess far-infrared emission is seen in Fig. 5.3 in all threebands towards the centers of the clusters compared to the results obtained from stackingrandom positions in the maps. This excess is visible up to a distance of ∼ 1.5 Mpc fromthe center of the clusters. As we discussed before, an excess of FIR/submm emissiontowards clusters could be a result of the SZ increment, or it can be a contribution fromdusty star-forming galaxies inside the cluster, and distant, lensed galaxies behind thecluster.Zemcov et al. (2010) measured a Sunyaev-Zel’dovich increment of ∆I0 = 0.268 MJy sr−1in the 500µm surface brightness. The amplitude of the increment depends on the line-of-sight extent of the clusters that the CMB photons need to travel through, and thisis encoded in the Compton-y parameter (Eq. 5.1). Zemcov et al. (2010) quote an av-erage of y = 3.46 × 10−4 for their observed clusters. From Hasselfield et al. (2013a)we determine that our sample has an average y ' 0.95 × 10−4, and since ∆I0 ∝ y, weexpect to find an increment of ∆I0 ≈ 0.073 MJy sr−1 in the 500µm surface brightness,which corresponds to flux densities of ∆S500 ≈ 2.5 mJy beam−1. The SZ increment inthe 250µm and 350µm is expected to be below our detection limits, thus the excess wesee in these bands should be the result of dusty galaxy emission along the line of sight tothe clusters. Typical dusty galaxies are brightest in the 250µm or 350µm SPIRE bandsand faintest at 500µm. Our observed flux densities in Figure 5.3 are at a similar levelin all three bands. This result is consistent with detecting dusty galaxy emission in theline of sight of the cluster, while the measured 500µm flux densities are boosted high by1110.0 0.2 0.4 0.6 0.8 0.0 0.5 1.0 1.5 2.0−1012345250 micron0.0 0.5 1.0 1.5 2.0−1012345350 micron0.5 1.0 1.5 2Distance from center (Mpc)−1012345500 micronFigure 5.3: Radial average of SPIRE images stacked at ACT cluster positions. Theradial average of the stacked image containing all 26 clusters is shown with a red line.The central blue line corresponds to the mean radial profile calculated from a bootstrapmethod, by averaging 1000 realizations of radial profiles created from stacking 20 randomcluster positions from our full sample of 26 clusters. The blue contours correspond tothe ±1σ and ±2σ errors determined from the bootstrap method.the SZ increment. A similar effect is shown in Gralla et al. (2014, Fig. 2.) where thestacked flux densities of radio AGN would normally decrease towards 500µm but the SZincrement increases the measured S500 flux density.As discussed in Zemcov et al. (2007) and Zemcov et al. (2013), lensing magnification1120.0 0.2 0.4 0.6 0.8 0.0 0.5 1.0 1.5 2.0−1.0− micron0.0 0.5 1.0 1.5 2.0−1.0− micron0.5 1.0 1.5 2Distance from center (Mpc)−1.0− micronFigure 5.4: Radial average of SPIRE images stacked at random map positions. Theblue curves and the contours represent the mean and ±1σ standard deviation of 1000realizations of radial profiles created by stacking 26 randomly-selected positions in themap that do not correspond to cluster centers.of sources is more likely to happen at some distance from the geometrical center of theclusters, since sources that fall directly behind the center of the lensing mass are distortedinto an Einstein ring and the flux at their centers should decrease. Thus towards thecenters of massive clusters a deficit is expected in the cosmic infrared background surfacebrightness, which has been detected in Zemcov et al. (2013). The flux in our stacked113images consistently increases all the way to the center of the clusters in our 250µm and350µm bands, so it is likely that lensed galaxies only contribute partially to the excessflux density, and that we see dust emission from cluster member galaxies, possibly evenfrom the brightest cluster galaxies at the centers of these massive structures.To determine whether these point sources are star-forming galaxies falling into thecluster, or lensed dusty galaxies behind the clusters, more detailed analysis is needed.High signal-to-noise measurements with large resolution instruments can help resolve theindividual galaxies that contribute to this emission. Determining the redshifts of thesesources will unambiguously confirm whether these galaxies are part of the cluster or not.Additionally, stacking the maps on cluster members identified in optical surveys can tellus how much dusty star formation exists in these clusters.Regardless of whether our excess FIR emission emerges from cluster member galaxiesor lensed sources, our results show that the contribution of dusty star-formation towardsthese SZ selected galaxy clusters cannot be ignored. Any survey based on the detectionof the SZ distortion needs to take the contribution of these dusty sources into account.These galaxies could be faint enough at millimeter-wavelengths, that they are not de-tected individually, but their flux densities can partially fill in the SZ decrement, thusbiasing SZ cluster surveys against finding galaxy clusters containing dusty star-forminggalaxies. The clusters already identified can have an even deeper decrement, thus a largermass than predicted without identifying the contamination from such dusty sources. Thisshows the importance of cross-frequency studies in cluster detection surveys and the needto correctly model and disentangle all components that act as contaminants in these sur-veys. As we mentioned before, a much smaller amplitude distortion in the backgroundintensities can arise due to the relative motion of the galaxy clusters compared to theuniform Hubble flow. Measuring this kinetic SZ effect (Sunyaev and Zeldovich, 1980) isan important part of understanding the velocity field of our Universe, and these measure-ments are also very sensitive to contamination from dusty sources. While in the abovementioned studies of the CMB the dusty galaxies act as a source of contamination, we canalso learn important insights from cross-correlation studies of the far-infrared emissionand the CMB temperature. Currently we are not able to directly detect the first galaxiesthat contributed to the reionization of the early Universe, but we can still learn aboutthese objects by investigating the temperature changes of the CMB photons that passthrough the gas that these first galaxies ionized with their radiation. Thus CIB-CMBcross correlation studies can help us learn more about the timing of the reionization ofthe Universe (e.g. Atrio-Barandela and Kashlinsky, 2014).114Chapter 6ConclusionsIn this thesis we investigated the role of dusty star formation at different redshifts and indifferent environments. Studying the evolution of the cosmic star formation history andthe role of the galaxy environment in triggering and quenching star-forming processes iscrucial in order to understand the evolution of large-scale structures in the Universe. Ithas been known that dusty star-forming galaxies play a significant role in the stellar massbuild-up at high redshifts, but the currently available samples are limited by observedsky area and accurate redshift measurements; thus their contribution to the cosmic starformation rate density at z > 4 is still unknown.Our main datasets analyzed in this thesis included two recent large area surveys, theHerMES Large Mode Survey (HeLMS) and the Herschel Stripe 82 Survey (HerS) ob-served at far-infrared wavelengths by the SPIRE instrument aboard the Herschel SpaceObservatory. To fully exploit the spatial extent of these observations it is important tocreate maps that provide an unbiased estimate of the brightness variations in the skyon all angular scales. We created maps for both the HeLMS and HerS field with twomapmaker software packages, SHIM and SANEPIC. SANEPIC was designed to workwith BLAST data, a pathfinder instrument for SPIRE. After we adapted the SANEPICmapmaker to work with SPIRE data, we carried out an analysis to compare the perfor-mance of the two algorithms. We concluded that at small angular scales both mapmakersperform similarly well, but the largest angular scales are better recovered by SANEPIC.Our final data products have been and will be the base of many multi-wavelength studies.The large areas of these surveys allow for the detection of statistically significant numbersof the galaxies that constitute the cosmic infrared background, including the rarest ob-jects on the sky. The power spectrum of the background emission from unresolved faintgalaxies also contains critical information about the underlying galaxy populations, andcross-correlation studies with other maps at different wavelengths can provide important115constraints on the evolution of the large-scale structure of the Universe.The main result of our work is the creation of a large catalog of candidate z > 4luminous dusty star-forming galaxies detected in the HeLMS survey. We used a map-based search method to locate galaxies with increasing flux densities towards longerSPIRE wavelengths. This method has been shown to select high-redshift actively star-forming objects. In a previous analysis of smaller area HerMES maps we have foundan excess of these “red” galaxies, but the small samples only allowed us to measure thetotal number of sources above some flux density limit. In this work we applied our searchmethod to the HeLMS field and we created a catalog of 477 red sources. This catalogis large enough that for the first time we were able to infer the shape of the differentialnumber counts of these high-redshift galaxy candidates. After carefully investigating thedifferent biasing effects, we determined the differential number counts of our sources at500µm. While the total number of sources confirmed the excess we have seen before, thevery steep slope we found for our number counts suggests that this population is stronglyevolving and that massive luminous dusty galaxies were more important in the past thanpopular galaxy evolution models predict. Current simulations are not able to reproducethe massive gas reservoirs at such early times, which are needed to fuel the very activestar formation.We determined the spectroscopic redshift for two of our reddest sources with ALMA.These redshifts are z = 5.126 and z = 4.994 (or z = 3.798). Including these results wenow have more than ten red sources with a confirmed z > 4 redshift, and the lowestredshift red source we have found so far was still at z > 3. In the future the sampleof sources with confirmed redshift will be extended, and knowing the exact redshiftdistribution of these sources will allow us to construct the infrared luminosity functions atz > 4 and to infer the evolution of the star formation rate density at these high redshifts.Our current knowledge of the evolution of the star formation history at these epochscomes from high-z UV data sets that measure unobscured star formation rates, and arein need of significant and yet quite uncertain corrections due to dust extinction. Theaddition of our high redshift far-infrared sample will play a crucial role in understandingthe stellar mass build-up at z > 4.We designed a follow-up project to measure the 850µm flux densities of a sample ofred sources with the SCUBA-2 instrument. Based on the SPIRE flux densities alone,the spectrum of the red sources is usually better fit with an “optical-depth-modified”blackbody curve than an optically thin model. In this case the dust becomes opticallythick for rest frame wavelengths λ < 200µm. Our measured SCUBA-2 850µm fluxdensities of sources that are isolated in all three SPIRE bands confirm this trend. Due116to the large beamsize in our 500µm SPIRE band some of the red sources we find breakup into several components in the higher resolution 250µm and 350µm maps. Ourassumption was that at least one component of these blends should still be a red source,although with its measured 500µm flux density statistically biased high. Our observedSCUBA-2 sample contained such blended sources, and we have found that many of theseblends are still detected with SCUBA-2, although with an anomalously high S500/S850ratio. This suggest that our initial assumption, that these blends contain a red source iscorrect, and while the non-red component of the blend becomes undetectable, the fainterred source still shows emission at these longer wavelengths.In a different analysis we stacked the positions of our HeLMS selected red sourceson maps obtained by the Atacama Cosmology Telescope at wavelengths of 1400µm and2000µm. We created stacks of sources with 500µm flux densities belonging to differentbins, and in almost all of our bins we have detected a source in the stacked ACT maps.The average flux density of these sources is lower than we would expect based on theiraverage 500µm flux densities, but all of our stacks contained blended objects too, whichhave been shown to have anomalous colors. The successful detection of isolated sourceswith SCUBA-2 and the fact that we can see emission at long wavelengths at the posi-tion of blended objects shows the importance of future follow-up campaigns with betterresolution millimeter-wave interferometric instruments. We were also successful in get-ting telescope time to observe all of our sources in the HeLMS catalog with SCUBA-2.The HeLMS sources all have S500 > 50 mJy flux densities, so we expect a large detec-tion fraction at 850µm. This new dataset will help us reduce the bias in the numbercounts caused by blending effects and it will help to better constrain the spectral energydistributions of the red sources.We also mapped a larger area around four red sources with SCUBA-2 to investigatetheir environments. Our goal was to search for over-densities of fainter star-formingsubmillimeter galaxies near these starbursts, similar to what was observed for severalwell-studied high redshift dusty galaxies. Such an over-density might indicate that thesegalaxies reside in a proto-cluster environment. Our measurements show no obvious over-density in the vicinity of our red sources. We cannot rule out that the other proto-cluster members are simply too faint to be detected in our survey, perhaps becausethey contain smaller amount of dust than the central red source and are less luminous.Nevertheless, our results are consistent with environmental studies of the highest redshiftdusty starburst galaxy, the z = 6.34 red source HFLS3, where studies have found no over-density of either submillimeter emitting or optical Lyman-break galaxies. This suggeststhat there are different physical processes triggering extreme star formation apart from117environmental effects, but in order to create better constraints on the current evolutionmodels, more observations will be needed.To exploit the large overlap between the equatorial field mapped by the AtacamaCosmology Telescope and our HeLMS and HerS surveys, we investigated the averagedusty galaxy emission in the line of sight of moderate redshift massive galaxy clustersdetected by ACT, based on the decrement in surface brightness caused by the Sunyaev-Zel’dovich effect. We stacked our SPIRE maps at the positions of the 26 clusters that arefound in the overlapping area, and we detected excess submillimeter emission in all threeSPIRE bands. The observed amplitudes of this excess are similar in all three bands, andthis suggests that the excess emission comes from dusty galaxies inside the clusters orlensing magnified clusters that are located behind the cluster, and since the flux densityof these sources should decrease towards 500µm, the flux we see at 500µm is a possibledetection of the expected SZ increment. While the current signal-to-noise ratio andthe available resolution are not sufficient to investigate this excess in detail, this resultsuggests that there might be more dust-obscured star formation happening in massivevirialized clusters at higher z than in local clusters. 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