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The most luminous galaxies in the Universe Hill, Ryley 2017

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The Most Luminous Galaxies in theUniversebyRyley HillB.Sc., The University of British Columbia, 2015A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Astronomy)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2017c© Ryley Hill 2017AbstractSubmillimetre galaxies have become essential tools in studying the high red-shift Universe. Reaching luminosities well over 1013 L, they constitute thevast majority of star formation during this early epoch. Their combinedinfrared and submillimetre emission output is comparable in energy densityto all of the optical and ultraviolet light emitted by all of the galaxies in theobservable Universe.We have used the Submillimeter Array at 860µm to observe the brightestsubmillimetre sources in 4 deg2 of the Cosmology Legacy Survey. Previousinterferometric studies have found a significant amount of multiplicity atthe bright end of the single-dish number counts, suggesting a steepeningin the drop-off brighter than 10 mJy, but these studies suffered from small-number statistics. We have targeted 75 of the brightest flux density-orderedsingle-dish SCUBA-2 sources down to approximately 10 mJy, achieving anaverage synthesized beam size of 2.4 arcsec and an average depth of 1.5 mJyin our primary beam-corrected maps, corresponding to 4σ detections ofabout 6 mJy. Our data is sufficient to distinguish between intrinsically brightgalaxies and systems that break up into two & 6 mJy galaxies with flux ra-tios less than 2 and separated by about 2 arcsec or more, corresponding toa physical distance of around 20 kpc at z= 2. We include in our study 28archival observations of similar nature, bringing our sample size to 103. Westatistically deboost our flux density measurements and use these to com-pute the cumulative and differential number counts of our sample, findingthem to be consistent with previous single-dish survey number counts withinthe uncertainties but with a systematic offset between 2 and 20 per cent. Wecompute the probability that a > 10 mJy single-dish submm source resolvesinto two or more galaxies with a brightest to second-brightest flux densityratio less than 2 to be about 15 per cent. Assuming the remaining 85 percent of the targets are ultra-luminous galaxies between redshifts 2 and 3,we find the surface density of & 500 M yr−1 sources to be 8+2−1 deg−2 and alikely volume density of 660+140−120 Gpc−3.iiLay SummaryAstronomers have recently found a particularly efficient way for selectingsome of the most actively star-forming galaxies in the Universe by lookingfor their light at special wavelengths between 0.5 and 1 mm. This newtechnique has led to the discovery of some of the most luminous galaxies inthe known Universe. In this work I have used data from a telescope withhigh angular resolution to study these incredibly bright galaxies in moredetail. I have shown that about 15 per cent of them are actually groupsof fainter galaxies so close to one another that normal telescopes could notresolve them, while the remaining 85 per cent really are among the brightestgalaxies in the Universe.iiiPrefaceIn this thesis, Chapter 2 involves work done by a collaboration of astronomers.The team members, in alphabetical order, are: Andrew W. Blain, MalcolmBremer, Edward Chapin, Scott Chapman, Chian-Chou Chen, James S. Dun-lop, Duncan Farrah, Jim Geach, Mark Gurwell, Paul Howson, Rob Ivison,Kevin Lacaille, Michal Michalowski, Ryan Perry, Glen Petitpas, DouglasScott, Ian Smail, James Simpson, Mark Swinbank, Paul van der Werf andDavid J. Wilner.Various member of this team helped write the proposal for the project(P.I. Scott Chapman), perform observations with the Submillimeter Arrayand reduce the data. Their work is outlined in Section 2.2. My contributioninvolved performing the analysis in Section 2.3 and interpreting the resultsgiven in Section 2.4, as well as coordinating the team’s work and writing thefull document. A version of this chapter is being prepared for submission toMonthly Notices of the Royal Astronomical Society.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . xiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Observing in the submm waveband . . . . . . . . . . . . . . 21.2 The spectral energy distribution . . . . . . . . . . . . . . . . 41.3 Redshift distribution . . . . . . . . . . . . . . . . . . . . . . 71.4 Driving mechanisms . . . . . . . . . . . . . . . . . . . . . . . 92 High-resolution imaging of bright submillimetre sources fromthe SCUBA-2 Cosmology Legacy Survey with the SMA . 102.1 Introduction to multiplicity in SMGs . . . . . . . . . . . . . 102.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2.1 Target selection and observations . . . . . . . . . . . 132.2.2 Source detections . . . . . . . . . . . . . . . . . . . . 142.2.3 Source IDs . . . . . . . . . . . . . . . . . . . . . . . . 162.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.3.1 Flux boosting . . . . . . . . . . . . . . . . . . . . . . 172.3.2 Astrometry . . . . . . . . . . . . . . . . . . . . . . . . 212.3.3 Flux density reliability . . . . . . . . . . . . . . . . . 22vTable of Contents2.3.4 Completeness . . . . . . . . . . . . . . . . . . . . . . 242.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . 262.4.1 Number counts . . . . . . . . . . . . . . . . . . . . . 262.4.2 Multiplicity . . . . . . . . . . . . . . . . . . . . . . . 312.4.3 Density of extremely luminous galaxies . . . . . . . . 362.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40AppendicesA Data tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58B Multiwavelength cutouts . . . . . . . . . . . . . . . . . . . . . 65viList of Tables2.1 Parameters describing our simulations, which we use to cal-culate the expected level of flux boosting in our measurements. 192.2 Completeness levels calculated for each field in our study, aswell as for the total data set. . . . . . . . . . . . . . . . . . . 27A.1 SMA sample plus archival ALMA data for the UDS field.Sources observed by ALMA in Simpson et al. (2015) are indi-cated by a b, and all other sources were observed by the SMAin this work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59A.2 SMA sample for the SSA22 field. All observations are fromthis work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61A.3 SMA sample plus archival SMA data for the COSMOS field.Sources observed by the SMA in Younger et al. (2007) are in-dicated by a c, sources observed by the SMA in Younger et al.(2009) are indicated by a d, and all other sources were ob-served by the SMA in this work. Flux density measurementsfrom Younger et al. (2007) and Younger et al. (2009) werenot deboosted. Values of N/A in the SSMA column indicatesources where our deboosting simulation was not applicable. . 62A.4 SMA sample for the LHN field. All observations are from thiswork. Values of N/A in the SSMA column indicate sourceswhere our deboosting simulation was not applicable. . . . . . 63A.5 SMA sample for the EGS field. All observations are from thiswork. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64viiList of Figures1.1 Transmission function of Earth’s atmosphere at the Llano deChajnantor Observatory on the Atacama Plateau in north-ern Chile. The elevation of the observatory is 5000 m abovesea level, crucial for minimizing the amount of water vapourabove the telescope. Strong absorption lines can be seenat 600 GHz (500µm) and 800 GHz (375µm), while observa-tional ‘windows’ are present at 850 GHz (350µm), 650 GHz(450µm), 400 GHz (750µm), 350 GHz (850µm), and 270 GHz(1.1 mm). The red, purple and green segments represent asubmm telescope’s observational bands, which roughly corre-spond to these windows. Figure taken from the ALMA Cycle5 Technical Handbook (2017). . . . . . . . . . . . . . . . . . . 31.2 Modified blackbody SED. The example shown here is forARP 220, the nearest ultra-luminous infrared galaxy to theMilky Way. The best-fit parameters in this case are T = 66.7 K,ν0 = 1.277 THz and β= 1.83. ARP 220 is thought to contain aburried active galactic nuclei, hence it has a value of T largerthan the mean of 40 K. Figure taken from Rangwala et al.(2011). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Example SMG redshift distributions, taken from Wardlowet al. (2011). The ‘robust IDs’ are SMGs with radio detectedcounterparts, which the ‘tentative IDs’ lack. This plot clearlydemonstrates that the distribution of SMGs is highly concen-trated about redshift 2.5 and is significantly different fromrandomly selected field galaxies, which peak around redshift0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8viiiList of Figures2.1 Histogram showing the deboosted flux density distribution ofthe parent SCUBA-2 CLS survey from Geach et al. (2017),our 75 targets, and our full catalogue including these 75 tar-gets and 28 archival sources from Simpson et al. (2015), Youngeret al. (2007), Younger et al. (2009) and Ikarashi et al. (2011),which are included in our counts analysis. Our sample isa nearly complete selection of single-dish SCUBA-2 sourceswith flux densities brighter than 10 mJy. . . . . . . . . . . . . 152.2 Probability distributions for the flux density of COSMOS07,a typical source in our data set. The blue curve is the prior,which is calculated by binning pixels resulting from simu-lating SCUBA-2 CLS fields and making small SMA thumb-nail images centred on the brightest sources. The red curveshows the flux density of COSMOS07 measured from ourdata, where the uncertainty is assumed to be Gaussian. Theblack curve is the posterior probability distribution, whichpeaks at a slightly lower, deboosted flux density value dueto the presence of many more faint galaxies in the simulatedsky. The deboosted flux density uncertainties given representa 68 per cent confidence interval about the peak. . . . . . . . 202.3 Radial offset of SMA-detected sources from their SCUBA-2counterparts. Where multiple counterparts are detected wesmooth the sources with the nominal SCUBA-2 beam andlocate the peak flux density and compare this to the givenSCUBA-2 position. These sources are highlighted in the fig-ure by stars. Also shown are the expected 68 per cent and95 per cent positional uncertainties as a functon of detectedS/N for SCUBA-2. . . . . . . . . . . . . . . . . . . . . . . . . 222.4 Comparison of the SCUBA-2 deboosted flux density fromGeach et al. (2017) to the ratio of our SMA deboosted fluxdensities to each corresponding SCUBA-2 flux density. Wherea single CLS source is resolved into multiple components, wehave summed each components’ flux density weighted by theSCUBA-2 beam response. These sources are shown as stars. . 23ixList of Figures2.5 Cumulative (above) and differentia (below) number countsderived from our data set. The single dish results from theCLS (Geach et al. 2017) are shown for comparison. Valuesare slightly offset from each other in each bin for clarity. Theshaded region marks where our data is no longer 100 per centcomplete. An offset between our results of 2 to 20 per centis seen in the cumulative count, although the points overlapwithin the uncertainties. . . . . . . . . . . . . . . . . . . . . . 292.6 Cumulative (above) and differential (below) number countcomparison for the UDS field. The restults from Simpsonet al. (2015), derived from a smaller sample of the full parentCLS catalogue of the UDS field, are shown in red, alongsideour more complete sample in black, where we have used onlydata from the UDS field as well. The results broadly agree,although we see evidence for less bright sources in the Simp-son et al. (2015) sample. Also shown as the shaded region iswhere our data is not 100 per cent complete; our UDS datais 96 per cent complete for S> 8 mJy. . . . . . . . . . . . . . . 302.7 Cumulative and differential number counts for the two largesingle dish submm surveys LESS (Weiß et al. 2009) and CLS(Geach et al. 2017) on the top row. On the bottom row weshow cumulative and differential number counts from Karimet al. (2013) and Simpson et al. (2015), interferometric follow-up studies of the LESS and CLS surveys, respectfully, shownalong with our SMA results and the shaded region indicatingwhere our data is no longer 100 per cent complete. Alsoshown are the models of Be´thermin et al. (2012) and Laceyet al. (2016). The black solid line shows the best-fit power toour differential distribution between 11 and 16 mJy. . . . . . . 32B.1 Multiwavelength cut-outs of 38 sources in our sample withSpitzer -IRAC 3.6µm, Spitzer -MIPS 24µm and VLA 1.4 GHzimaging. We show SMA flux contours starting from 2σ insteps of 1σ overlaid over the IR and radio data. . . . . . . . . 66xList of AbbreviationsTelescopes/Instruments/SatellitesAtacama Large Millimeter/submillimeter Array ALMAAstronomical Thermal Emission Camera AzTECBalloon-borne Large Aperture Submillimeter Telescope BLASTCosmic Background Explorer COBEDiffuse Infrared Background Experiment DIRBEFar-Infrared Absolute Spectrophotometer FIRASInfrared Array Camera IRACInfrared Astronomy Satellite IRASLarge Apex Bolometer Camera LABOCAMultiband Imaging Photometer for Spitzer MIPSPlateau de Bure Interferometer PdBISubmillimeter Common User Bolometer Array/-2 SCUBA/-2Submillimeter Array SMASpectral and Photometric Imaging Receiver SPIREUnited Kingdom Infrared Telescope UKIRTVery Large Array VLASurveys/FieldsAkari -North Ecliptic Pole Akari -NEPALMA survey of LESS ALESSCosmology Legacy Survey CLSCosmic Evolution Survey COSMOSExtended Chandra Deep Field-South E-CDF-SExtended Groth Strip EGSGreat Observatories Origins Deep Survey-North GOODS-NLABOCA E-CDF-S Submillimeter Survey LESSLockman Hole North LHNSmall Selected Area 22 SSA22UKIRT Infrared Deep Sky Survey Ultra-Deep Survey UDSxiList of AbbreviationsAstronomical termscosmic infrared background CIBcosmic optical background COBdeclination Decfull-width half-maximum FWHMinfrared IRright ascension RAspectral energy distribution SEDstar-formation rate SFRsubmillimetre galaxy SMGsignal-to-noise ratio S/Nsubmillimetre submmxiiAcknowledgementsSeveral telescope facilities were used to gather data for this thesis. TheJames Clerk Maxwell Telescope is now operated by the East Asian Ob-servatory on behalf of The National Astronomical Observatory of Japan,Academia Sinica Institute of Astronomy and Astrophysics, the Korea As-tronomy and Space Science Institute, the National Astronomical Observa-tories of China and the Chinese Academy of Sciences (Grant No. XDB09000000),with additional funding support from the Science and Technology FacilitiesCouncil of the Kingdom and participating universities in the United King-dom and Canada. The Submillimeter Array is a joint project between theSmithsonian Astrophysical Observatory and the Academia Sinica Instituteof Astronomy and Astrophysics and is funded by the Smithsonian Institutionand the Academia Sinica. The author wishes to recognize and acknowledgethe very significant cultural role and reverence that the summit of Mau-nakea has always had within the indigenous Hawaiian community. We aremost fortunate to have the opportunity to conduct observations from thismountain. This work was supported by the Natural Sciences and ResearchCouncil of Canada.xiiiChapter 1IntroductionSubmillimetre galaxies (SMGs) are the most luminous and productive galax-ies in the Universe. Understanding their nature and place in the sequenceof galactic evolution has been at the forefront of astronomical research sincetheir discovery, resulting in many key insights on the cosmic history of starformation, galaxy formation and galaxy clustering – covering nearly all scalesof structure formation.During the 1980s, the Infrared Astronomy Satellite (IRAS; Neugebaueret al. 1984) opened a new window for studying galaxies at mid- to far-infrared wavelengths. IRAS was the first instrument to catalogue a sta-tistically significant population of extremely bright extragalactic infraredsources, defined as galaxies with luminosities greater than 1011 L (Sanderset al. 2003). Equipped with samples of highly luminous, vigorously star-forming local galaxies, researchers were naturally led to predict the exis-tence of a population of highly luminous, vigorously star-forming distantand abundant galaxies, theorizing that the known luminous galaxies were infact left over from a much vaster population responsible for the majority ofstar formation in the Universe.The first hint that such a population existed came from measurements ofthe cosmic infrared background (CIB) – the sum of all infrared (IR, 1µm –200µm) and submillimetre (submm, 200µm – 1 mm) radiation emitted fromextragalactic sources averaged over the entire sky – with the Far-InfraredAbsolute Spectrophotometer (FIRAS; Mather et al. 1993) and the DiffuseInfrared Background Experiment (DIRBE; Silverberg et al. 1993) aboardthe Cosmic Background Explorer (COBE). What FIRAS and DIRBE wereable to show was that not only was the CIB comparable in energy density toits optical counterpart (the cosmic optical background, or COB), but thatmuch less than 10 per cent of it had actually been resolved into galaxieswith IRAS (Hauser et al. 1998).The implications of this observation were tremendous; a significant amountof the star-formation activity of the Universe must have taken place in verydistant, very dusty galaxies, where optical and ultraviolet light had beenabsorbed and re-emitted in the IR and submm. Detecting and character-11.1. Observing in the submm wavebandizing the population responsible for this radiation became a compliment tostudying the origins of the stars and galaxies that populate the night skytoday. This inevitably led to the development of submm astronomy, and thedetailed study of SMGs.1.1 Observing in the submm wavebandThe history of extragalactic submm astronomy is a short one, dating onlyas far back as the mid-1990s. The reason for such a late blooming of anotherwise fruitful subject can be attributed to technology. At the time itwas widely speculated that an enormous number of distant, dust enshroudedgalaxies existed in the far IR and submm. Individual high redshift objectswere already known from IRAS follow-up work, but were rare, and therewas no way to study large samples of such galaxies due to the sensitivityrequired to actually detect them.First, there is the question of resolution. The basic resolving power of adish goes as 1.22λ/D, where λ is the wavelength of light being observed andD is the diametre of the dish. To obtain something like half an arcminute ofresolution at 850µm, one must have a dish about 10 m across. This would beuseful for answering many scientific questions, but obtaining arcsecond andsub-arcsecond resolution, necessary for resolving individual SMGs, wouldrequire a dish over 30 times larger! As we shall see in the proceeding section,this problem can be addressed with a technique known as interferometry,which takes advantage of the interference patterns created by coherentlyusing an array of individual dishes.Second, one must deal with the Earth’s atmosphere, which is nearlyopaque at submm wavelengths. This is due to the abundance of watervapour, which has particularly strong absorption at these wavelengths. Thismeans either finding a consistently dry location, or performing observationsfrom space. The latter solution is the more difficultand expensive approach– imagine what would be required to place a perfectly curved, 15-m dish intoorbit, or to set up a sophisticated interferometric system in space. It is forthis reason that submm observatories are usually built high atop mountains,where the atmosphere is thin enough to permit observations through various‘windows’. These windows are bands located between the water vapourabsorption lines, and are centred around 350µm, 450µm, 750µm, 850µmand 1.1 mm, as shown in Figure 1.1.Fortunately, there is a phenomenon present that helps in the detectionof high redshift SMGs, known as the negative K-correction. A K-correction21.1. Observing in the submm wavebandChapter 4ReceiversThe ALMA front end can accommodate up to 10 receiver bands covering most of the wavelength range from10 to 0.3 mm (30–950 GHz). Each receiver band is designed to cover a tuning range which is approximatelytailored to the atmospheric transmission windows. These windows and the tuning ranges are outlined in Figure4.1. In Cycle 5, Bands 3, 4, 5, 6, 7, 8, 9, and 10 are available (see available frequency and wavelength rangesfor these bands in Table 4.1). The receivers are described in more detail in the following sections as well as inthe references listed in Table 4.2.Figure 4.1: The ten ALMA receiver bands. Receiver bands for Cycle 5 are shown in red or purple superimposedon a zenith atmospheric transparency plot at the Array Operation Site (AOS) for 0.5 mm of Precipitable WaterVapor (PWV). Band 5 (shown in purple) is newly available in Cycle 5.The ALMA receivers in each antenna are situated in a single front-end assembly (see Appendix A, SectionA.4). The front-end assembly consists of a large cryostat containing the receiver cold cartridge assemblies(including Superconductor-Insulator-Superconductor (SIS) mixers and Local Oscillator (LO) injections) and theIntermediate Frequency (IF) and LO room-temperature electronics of each band (the warm cartridge assembly,31Figure 1.1: Transmi sion functio of Earth’s atmosphere at the Llano dChajnantor Observatory on the Atacama Plateau in northern Chile. Theelevation of the observatory is 5000 m above sea level, crucial for minimizingthe amount of water vapour above the telescope. Strong absorption linescan be seen at 600 GHz (500µm) and 800 GHz (375µm), while observational‘windows’ are present at 850 GHz (350µm), 650 GHz (450µm), 400 GHz(750µm), 350 GHz (850µm), and 270 GHz (1.1 mm). The red, purple andgreen segments represent a submm telescope’s observational bands, whichroughly correspond to these windows. Figure taken from the ALMA Cycle5 Technical Handbook (2017).31.2. The spectral energy distributionis added to an object’s absolute magnitude to convert its flux density fromthe observed frame to the rest frame; it is thus useful for extragalacticobjects with significant redshifts. One generally expects the K-correction tobe positive for a given object, because it should become fainter the more itgets redshifted. But the opposite happens in the submm. This can be seenby considering thermal radiation from a cool (' 30 K) blackbody. IR andoptical emission lies on the Wien portion of the spectral energy distribution(SED), where the intensity decreases steeply with decreasing wavelength.When an object becomes redshifted, its SED is sent to larger wavelengthsin the observing frame, and so a given wavelength in the observing framenow corresponds to a much shorter wavelength in the rest frame, which hasa significantly lower intensity. K-corrections are said to be ‘positive’ if theintensity decreases with increasing redshift, hence a positive K-correctionin this case. For submm observers, these wavelengths lie on the Rayleigh-Jeans side of the SED, where instead intensity increases with decreasingwavelength. This means that in redshifting an object, it becomes brighter,and hence it has a negative K-correction. This is very beneficial for observingSMGs, which exist at high redshifts and turn out to have almost the sameapparent brightness over a wide range of redshifts.1.2 The spectral energy distributionWe learn a lot about the physical conditions in SMGs from modelling theirSEDs. From the SED of an SMG one can estimate quantities such as thestar-formation rate (SFR), the mean dust temperature and the dust mass.Here we will describe some of the more widely used models, and the physicalmotivation behind them.The modified blackbody equation is by far the most widely used modelfor the SED of an SMG (Figure 1.2). To start, this model is motivated bythe observation that the majority of radiation emitted from these galaxiesis due to dust grains. These dust grains have absorbed the majority of theoptical and ultraviolet light of the surrounding stars, and are approximatelyre-emitting this starlight as described by the Planck function Bν(T ). Thetemperature parameter T used here in the Planck function is a collectiveaverage of the temperatures of the dust grains making up the SMG (andshould not be interpreted as the true temperature of the dust).Next, to ‘modify’ the blackbody, we note that the emitted radiation mustpass through a medium with a finite optical depth τ(ν), which leads to someextinction by a factor 1− e−τ(ν). Therefore, the expression for the intensity41.2. The spectral energy distributionof an SMG takes on the formSν ∝ (1− e−τ(ν)) ν3ehν/kT − 1 . (1.1)Lastly, the optical depth is modelled as power law,τ(ν) =(νν0)β, (1.2)where ν0 is a characteristic frequency at which the optical depth is 1 (caus-ing the emitted intensity to fall by a factor of 1− e−1' 0.63) and β is knownas the spectral emissivity index. When the optical depth is small (typicallythe case in dusty galaxies) we can write 1− e−τ(ν)' τ(ν) to obtain the com-monly encountered power-law modification to Bν(T ). Of course this has thedownside of introducing two additional free parameters, but the character-istic frequency and spectral index are usually set to values around 3 THzand 1.5, respectively. These values are somewhat based on ideal theoreticalconsiderations but may vary among galaxy types; values of ν0 have beenmeasured at the 1.5 THz level (Rangwala et al. 2011), while β can rangefrom 1 to 2 if one allows it to be a free parameter (Chapin et al. 2011).Best-fit temperature values obtained from this model generally range from30 – 40 K (e.g. Chapman et al. 2005).Albeit the most common model, due to its simplicity and parameteriza-tion, other more complicated models are sometimes necessary. For example,it is known that most SMGs exhibit a mid-IR excess due to a componentof clumpy, hotter than average dust. This can be taken into account byintroducing two modified blackbodies with variable temperatures (as con-sidered, for instance, in Kirkpatrick et al. 2012), or by introducing a cutofffrequency where the modified blackbody becomes a strict power law (seeRoseboom et al. 2013, for example). Of course there are also many morenumerical fitting algorithms, which can contain all sorts of astrophysicalphenomena such as radiative transfer, chemical evolution and energy bal-ance (e.g., Siebenmorgen and Kru¨gel 2007; Rieke et al. 2009; Noll et al.2009). In detail an SED will have emission lines and various other features;however, this level of complexity is unnecessary when we are only dealingwith broad-band photometry measurements.51.2. The spectral energy distribution– 46 –! !" !"" !"""!#$!%&"'"!"'!"!'""!"'""!""'""()*+#$,-&./012!(3../012!45670.8!9:.01;..<=>;0.8/?83/9;@<AFig. 3.— Dust spectral energy distribution of Arp 220: The dot-dashed line is a modifiedblackbody model fit to the combined FTS, SPIRE-photometer and ISO-LWS data. Otherdata from the literature are over plotted for comparison and agree well with the fit. Asingle temperature component model fits the data extremely well down to 15 µm, belowwhich it breaks down. The size of the data points is approximately equal to the size of theuncertainties (random and systematic).!'B" !'BC !'D" !'DC !'E" !'EC F'""!!'F"!'FC!'G"!'GC!'H"" "#$+#!"!F&#$?I&EEJECJKDJ>LM7#!#N#!'DH>LM7#""#N#!FBB'"#O?IKC'" KC'C KK'" KK'C KB'" KB'C KD'"3#$A&!'F"!'FC!'G"!'GC!'H"" "#$+#!"!F&#$?I&EEJECJKDJ>LM7#3#N#KK'B#A>LM7#""#N#!FBB'"#O?IKD'" KC'" KC'C KK'" KK'C KB'" KB'C KD'"3#$A&!'B"!'BC!'D"!'DC!'E"!'ECF'""!EEJ ECJ KDJ>LM7#3#N#KK'B#A>LM7#!#N#!'DHFig. 4.— Modeling the dust SED yields tight constraints on a single-component dust spec-trum in Arp 220. The contours show 68%, 95% and 98% confidence levels.Figure 1.2: Modified blackbody SED. The example shown here is forARP 220, the nearest ultra-luminous infrared galaxy to the Milky Way. Thebest-fit pa ameter in this case are T = 66.7 K, ν0 = 1.277 THz and β= 1.83.ARP 220 is thought to contain a burried active galactic nuclei, hence it hasa value of T larger than the mean of 40 K. Figure taken from Rangwala et al.(2011).61.3. Redshift distribution1.3 Redshift distributionRedshifts are of utmost importance for studying galaxies, since we need thisinformation to convert observed quantities to intrinsic properties. As weknow, SMGs are typically very distant and hence seen as they were billionsof years ago. But just how young, and how distant? Did they all form aroundthe same time? When were the first SMGs? And were they different thanthe galaxies that formed later? These are questions which can be answeredby studying their redshift distribution.Redshifts come in two flavours: spectroscopic and photometric. Theformer technique relies on the detection of known emission lines, and the shiftin wavelength can be used to calculate the recessional speed (i.e. redshift).This method is always extremely precise, but expensive in telescope time.The latter technique involves assuming a rest frame SED, and calculatingthe shift from the measured SED. This method is much easier because itonly requires a few flux density measurements, but uncertainties in the SEDmodel mean that it is much less precise.On top of the lack of a priori redshift knowledge, measuring photometricredshifts of SMGs turns out to be quite difficult for two additional reasons:(1) being quite dusty by nature, SMGs obscure much of the classically brightoptical and ultraviolet emission lines; and (2) the inability of single dish in-struments to pinpoint SMGs accurately enough to locate their counterpartsat other wavelengths. Yet measuring photometric redshifts is also diffi-cult. Since the standard approach to modelling SMG SEDs is the modifiedblackbody, there is an inherent degeneracy between the temperature andthe redshift (increasing the temperature has the same effect as decreasingthe redshift, the SED moves to shorter wavelengths). But using additionalknowledge, researchers have come up with some clever ways around theseissues (e.g., Barger et al. 2012; Chen et al. 2016).Many studies have looked at the redshift distribution of SMGs (e.g.,Chapman et al. 2005; Wardlow et al. 2011; Chen et al. 2016). An exampleis shown in Figure 1.3. Results generally show a peak between z= 2 andz= 2.5, no more than 10% at z < 1, and a small tail out to z≈ 5. It isevident that there is a special peak epoch for SMGs, implying that theUniverse underwent a massive star-forming period between redshift 2 and3. This is an important clue to understanding the cosmic history of starformation.71.3. Redshift distributionFigure 1.3: Example SMG redshift distributions, taken from Wardlow et al.(2011). The ‘robust IDs’ are SMGs with radio detected counterparts, whichthe ‘tentative IDs’ lack. This plot clearly demonstrates that the distribu-tion of SMGs is highly concentrated about redshift 2.5 and is significantlydifferent from randomly selected field galaxies, which peak around redshift0.5.81.4. Driving mechanisms1.4 Driving mechanismsWith some information about their physical properties, we can then askwhat mechanism is fuelling the intense luminosities and SFRs seen in SMGs.Two scenarios dominate the discussion in the literature: (1) major mergerscause significant perturbations in the interstellar gas, which lead to excep-tional increases in SFRs; and (2) the intense luminosities observed are infact a normal part of galaxy evolution and are caused by standard accretionof intergalactic gas in the dense, early Universe.The former, major merger framework does well in that simulations ofthese events are capable of reproducing the correct IR luminosities (and, byextension, SFRs). On the downside, theoretical calculations do not predictenough major mergers to occur around redshifts 2–3 to account for the num-ber density of SMGs observed on the sky (e.g. Narayanan et al. 2010). Onthe other hand, the quiescent accretion framework does a poor job at obtain-ing high enough SFRs. But, if certain unconventional assumptions aboutthe initial conditions are made, then correct SFRs and number densities canbe obtained (e.g. Baugh et al. 2005).More recent simulations are beginning to suggest that the answer in-volves a combination of these two scenarios. It is suggested that manySMGs are made up of a few to many smaller galaxies, which, when seenthrough a single dish telescope, are merged into a single massive and highlyluminous galaxy. The smaller galaxies still have high SFRs, but these canbe duplicated through a combination of accretion of extragalactic gas andperturbations from interactions (Dave´ et al. 2010; Narayanan et al. 2015).Despite the attractiveness of this idea, there still lacks observational evidenceto back up various details.One basic question remains: how luminous can individual SMGs get?Once we have answered this we can determine wheather current theoreticalmodels are able to predict them.9Chapter 2High-resolution imaging ofbright submillimetre sourcesfrom the SCUBA-2Cosmology Legacy Surveywith the SMA2.1 Introduction to multiplicity in SMGsThe emergence of submm astronomy has led to the discovery of a cosmo-logically important population of SMGs, which appear to be among theearliest and most actively star-forming galaxies in the Universe (e.g., Blainet al. 2002; Chapman et al. 2005; Magnelli et al. 2012; Swinbank et al.2014; MacKenzie et al. 2017; Micha lowski et al. 2017; Simpson et al. 2017).While single dish observations of SMGs using facilities like the SubmillimeterCommon User Bolometer Array (SCUBA; Holland et al. 1999), SCUBA-2(Holland et al. 2013), the Balloon-borne Large Aperture Submillimeter Tele-scope (BLAST; Pascale et al. 2008), the Astronomical Thermal EmissionCamera (AzTEC; Wilson et al. 2008), the Large Apex Bolometer Camera(LABOCA; Siringo et al. 2009), and the space-based Spectral and Photo-metric Imaging Receiver (SPIRE; Griffin et al. 2010) on board the Herschelsatellite were able to greatly increase our knowledge about the evolutionof star formation in the Universe (e.g., Blain et al. 1999; Magnelli et al.2013; Gruppioni et al. 2013; Swinbank et al. 2014; Koprowski et al. 2017),their connection with today’s galaxies remains unclear, although evidence ismounting that they are progenitors of massive elliptical galaxies (e.g., Lillyet al. 1999; Scott et al. 2002; Genzel et al. 2003; Swinbank et al. 2006; Toftet al. 2014; Simpson et al. 2014; Koprowski et al. 2014; van Dokkum et al.2015; Koprowski et al. 2016; Micha lowski et al. 2017; Simpson et al. 2017).There is also debate about whether or not mergers are important for102.1. Introduction to multiplicity in SMGsSMGs. Many simulations require mergers to achieve the observed mas-sive SFRs (e.g., Narayanan et al. 2015) while others do not (e.g., Dave´et al. 2010), and on the other hand, observations of physically associatedpairs of SMGs with disturbed gas motions indicate that mergers are present(e.g., Tacconi et al. 2008; Engel et al. 2010; Chen et al. 2015), while ultra-luminous SMGs have been seen that lack such evidence (e.g., Targett et al.2013; Micha lowski et al. 2017). Progress is impeded by the sub-optimalangular resolution offered by single dish telescopes at submm wavelengths,which typically ranges between 10 arcseconds and half an arcminute. Atthese scales, source blending becomes a significant problem, and optical/IRcounterparts cannot be easily identified (with the notable exception of radio-bright SMGs; see e.g., Ivison et al. 2002, 2007; Biggs et al. 2011).Submm interferometry offers the arcsecond resolution necessary to ac-curately identify and pin-point individual submm galaxies. The Plateau deBure Interferometer (PdBI; Guilloteau et al. 1992), the Submillimeter Ar-ray (SMA; Ho et al. 2004) and the Atacama Large Millimeter/submillimeterArray (ALMA; Wootten and Thompson 2009) have greatly aided in the lo-calisation of counterparts and further characterization of SMGs. These werethe first facilities to conclusively show that many SMGs exhibit multiplicity(e.g., Iono et al. 2006; Younger et al. 2007, 2009; Wang et al. 2011; Smolcˇic´et al. 2012; Hodge et al. 2013; Simpson et al. 2015; Miettinen et al. 2015),where one bright submm source resolves into two or three individual SMGs.However, it was difficult to demonstrate this multiplicity for the most ex-treme SMGs due to their sparsity in the sky and an interferometre’s limitedfield of view.Large single-dish submm surveys (e.g., Scott et al. 2002; Greve et al.2004; Wang et al. 2004; Coppin et al. 2006; Bertoldi et al. 2007; Weiß et al.2009; Oliver et al. 2010; Valiante et al. 2016; Geach et al. 2017), followed upby interferometers, have been important for addressing the issue of multiplic-ity as they provide substantial catalogues of bright SMGs across continuouspatches of sky that interferometres can follow-up. These types of studies areprimarily driven by their sensitivity (being unable to detect, for example,very faint dwarf galaxies), but they are able to distinguish between intrin-sically bright galaxies and systems comprising of two or more galaxies withsimilar flux densities that would lead to a significant overestimation fromsingle-dish measurements. For example, Barger et al. (2012) used the SMAto observe 16 > 3 mJy sources detected with SCUBA-2 in the Great Obser-vatories Origins Deep Survey-North field (GOODS-N; Wang et al. 2004),finding that three resolved into multiple SMGs. Similarly, Smolcˇic´ et al.(2012) used the PdBI at 1.3 mm to target 28 > 5 mJy sources detected by112.1. Introduction to multiplicity in SMGsLABOCA at 870µm in the Cosmic Origins Survey field (COSMOS; Scov-ille et al. 2007), and found that six of them resolved into more than oneSMG. A larger survey of the Extended Chandra Deep Field-South (E-CDF-S; Lehmer et al. 2005) using LABOCA (the LESS survey; Weiß et al. 2009)was followed up with ALMA (the ALESS survey; Hodge et al. 2013), whoobserved 126 sources > 3.5 mJy and found that 24 out of the 69 most robustobservations showed multiple SMGs. Similar to the previous multiplicitystudies, Simpson et al. (2015) used ALMA to follow-up 30 of the bright-est (> 5 mJy) sources detected in the United Kingdom Infrared Telescope(UKIRT; Casali et al. 2007) Infrared Deep Sky Survey-Ultra-Deep Surveyfield (UKIDSS-UDS; Lawrence et al. 2007), mapped by SCUBA-2 as partof the Cosmology Legacy Survey (CLS; Geach et al. 2017), and found that18 sources break up into more than two SMGs. While these types of sur-veys have begun to reach statistically significant numbers of samples, theynonetheless lack large numbers of the brightest (> 10 mJy) single dish de-tected sources; for example, the LESS survey contained six sources brighterthan 10 mJy, and the catalogue from Simpson et al. (2015) contained fivesources brighter than 10 mJy.To date, the largest submm survey of the extragalactic sky is the com-plete CLS, encompassing 5 deg2 of the sky over seven cosmological fields,namely the UKIDSS-UDS, COSMOS, the Akari -North Ecliptic Pole (Akari -NEP; Lee et al. 2009), the Extended Groth Strip (Groth et al. 1994), theLockman Hole North (Dickey and Lockman 1990), the Small Selected Area22 (SSA22; Lilly et al. 1991) and the GOODS-N. The CLS detected over2800 submm sources above 3.5σ, about 50 of which are brighter than 10 mJy.This survey is therefore well-suited to study the properties of multiplicity inthe brightest SMGs known to exist.Here we present results from the largest yet interferometric follow-upprogramme of the brightest submm galaxies, selected from 80 per cent ofthe available area in the CLS survey. We have imaged 75 SCUBA-2 sourceswhose flux densities are & 8 mJy with 2.4 arcsec resolution using the SMAin order to measure the importance of multiplicity in this bright populationof SMGs. In Section 2.2 we describe our target selection, data reductionand source extraction procedure, in Section 2.3 we correct our flux densitymeasurements for flux boosting and compare our data to the CLS catalogueto asses the reliability of our sample, and in Section 2.4 we examine thecompleteness of our sample, present number counts, and discuss the effectsof multiplicity on the population of bright SMGs seen in our data. Theresults are summarized in Section 2.5.122.2. Observations2.2 Observations2.2.1 Target selection and observationsIn our observing programme we used the SMA in the compact configurationat 860µm to investigate bright sources in five out of the seven CLS fields,namely UKIDSS-UDS, COSMOS, the Extended Groth Strip, the LockmanHole North, and SSA22 (hereafter the UDS, COSMOS, EGS, LHN andSSA22 fields, respectively). Combined, these fields make up about 4 deg2and contain roughly 2500 SCUBA-2 sources, 40 being brighter than 10 mJy.Our initial aim was to target and resolve all sources down to 10 mJy todetermine the effects of multiplicity on the bright end of the submm num-ber count with good statistical significance. At the time these observationswere first proposed, the CLS had not yet been completed, being at that pointshallower than the final maps published in Geach et al. (2017). This led toseveral cases where either a proposed SCUBA-2 target ended up fainter thanexpected, or an originally faint SCUBA-2 source ended up being brighterthan 10 mJy. When selecting targets we only considered the measured (un-corrected) SCUBA-2 flux densities, which are believed to be boosted bypositive noise and faint background galaxies that on average add a positivebias to the flux densities and are statistically corrected for in the final CLScatalogue in Geach et al. (2017). This effect resulted in more examples ofapparently bright SCUBA-2 sources ending up being fainter in the final list.There are several submm interferometric data sets from the SMA andALMA in the literature that we did not re-observe in our programme. Inparticular, Simpson et al. (2015) carried out a follow-up campaign of 30high signal-to-noise ratio (S/N) CLS sources in the UDS field with ALMAat 870µm, and Younger et al. (2007, 2009) selected the highest significancesources in an AzTEC survey of the COSMOS field (Scott et al. 2008) forfollow-up with the SMA at 890µm. Additionally, there is a single stronggravitational lense in the UDS field, dubbed ‘Orochi’, reaching an 850-µmflux density of 52.7 mJy in the SCUBA-2 map; this source was followedup by Ikarashi et al. (2011) with the SMA at 860µm in part of a detiledmultiwavelength study. We have included 28 observations from these worksinto our analysis, which is detailed in Section 2.3.4.Our final SMA follow-up campaign sample consisted of 75 total targets;23 in the UDS field, nine in the SSA22 field, 16 in the COSMOS field, 18 inthe LHN field and nine in the EGS field. These sources were the brightestsources down to approximately 10 mJy, except in the UDS field where weprobed sources with flux densities down to about 8 mJy. In Fig. 2.1 we132.2. Observationsshow the SCUBA-2 deboosted flux density distribution from our parent CLSsample, with the distribution of our targets and the distribution of our fullcatalogue (including archival sources) overlaid. This shows the completenessof our selection, which we quantify later in Section 2.3.4.We note that we followed up two sources in the EGS field and two sourcesin the COSMOS field that ended up excluded from the final CLS catalogue.These four sources lie near the edge of the EGS and COSMOS maps, wherethe rms is higher, and were thus excluded from the area used to define thefinal CLS regions. While these four sources do not appear in our study, wenonetheless report them here for completeness.The observations were carried out over a period of two years betweenNovember 2014 and November 2016. We set up the SMA in the compactconfiguration tuned to 345 GHz and nominally used all eight available 6-mdishes. The synthesized beam achieved in this set up is about 2.4 arcsec.Flux densities were calibrated using Uranus, Neptune, Callisto or Titan,depending on availability and proximity to the given target. Our aim wasto detect 100 per cent of a target’s SCUBA-2 flux density at 4σ, requiringdepths varying from about 0.7 mJy to 2 mJy.2.2.2 Source detectionsThe data were reduced using standard CASA calibration and CLEANing rou-tines, with Briggs weighting and a robustness parameter of 0, and primarybeam corrected. The mean depth achieved in our data was 1.5 mJy (calcu-lated within 25 arcsec of the centre of the primary beam-corrected maps),varying between 0.7 mJy and 2.4 mJy, with one map at the 2.8 mJy leveland one map at the 3.2 mJy level. We set a detection threshold of > 4σpeaks in our maps. In the UDS field we detected 21 out of the 23 SCUBA-2sources we followed-up; none of these 21 sources were seen to break up intotwo components, and two sources remained undetected. Within the COS-MOS field, our SMA observations detected a total of 13 galaxies from the16 SCUBA-2 sources: one source broke up into two galaxies; and in foursources we found no peaks greater than 4σ. Of the nine SCUBA-2 sourcestargeted in the SSA22 field, four were not detected above the 4σ level inthe SMA maps, and in the remaining five we found single galaxies. In theLHN field we found 18 galaxies from our targeted sample of 18 SCUBA-2sources. Of these 18 detections two are SCUBA-2 sources that break upinto two galaxies, and in two cases we did not find any galaxies. In the EGSfield we have detected single galaxies for all nine SCUBA-2 sources. We alsoreport galaxy detections of all four of the SCUBA-2 sources we followed up142.2. Observations8 10 12 14 16SS2 [mJy]020406080100120NSCUBA-2 (Geach et al. 2016)Our targetsOur targets + literatureFigure 2.1: Histogram showing the deboosted flux density distribution ofthe parent SCUBA-2 CLS survey from Geach et al. (2017), our 75 targets,and our full catalogue including these 75 targets and 28 archival sourcesfrom Simpson et al. (2015), Younger et al. (2007), Younger et al. (2009)and Ikarashi et al. (2011), which are included in our counts analysis. Oursample is a nearly complete selection of single-dish SCUBA-2 sources withflux densities brighter than 10 mJy.152.2. Observationsoutside of the boundary of the CLS regions, and note that none resolvedinto multiples.Overall we detected 66 submm galaxies in 75 SMA pointings above a4σ depth of about 6 mJy. These detections are summarized in Tables A.1–A.5, where we provide the positions of both the SCUBA-2 sources and ourSMA detections, the measured and deboosted SCUBA-2 flux densities ofeach target as SobsS2 and SS2, respectively, and our measured flux densities asSobsSMA. For undetected sources, we report the 4σ flux density limit achievedby our observations instead. In each field, we sort sources in descendingorder of their deboosted SCUBA-2 flux density.2.2.3 Source IDsSpitzer -Infrared Array Camera (IRAC) 3.6µm, Multiband Imaging Pho-tometer for Spitzer (MIPS) 24µm and Very Large Array (VLA) 1.4 GHzimaging exists for 38 of our targets. In Fig. B.1 we show SMA contoursoverlaid over these multiwavelength data along with SMA contours. Wecan see that there are IR/radio sources coincidental with nearly all of ourSMA positions to within 1 arcsec, showing the generally high quality of ourSMA detections, complete with robustly identified conterpart galaxies. Themultiwavelength properties of these galaxies will be investigated in futurework.There are several cases where we have detected an SMA peak between3 and 4σ that matches both an IR and a radio counterpart. Specifically, wesee this with LHN11 and LHN12, where SMA flux densities were measuredto be 7.0 ± 1.8 mJy and 6.0 ± 2.0 mJy, respectively. In addition, we havefound two SMA peaks with flux densities of 5.1± 1.5 mJy and 4.5± 1.5 mJywithin 3 arcsec of LHN09, each directly overlapping with an IR counterpartand a radio counterpart. In contrast, our remaining SMA data lacking 4σpeaks do not show any peaks > 3σ overlapping with IR or radio sources. Wehave therefore included LHN11 and LHN12 in our analysis, and we reportthe detection of a triple system in LHN09. These sources are included inTable A.4, with an indication that the detections are less than our 4σ fluxdensity threshold.It is worth noting that in the COSMOS field, out of the 18 SCUBA-2sources found by Micha lowski et al. (2017) to have multiwavelength counter-parts and included in our sample, all were confirmed by our SMA imaging.In the UDS field, out of 35 SCUBA-2 sources overlapping between our twostudies, 31 were confirmed (89 per cent), consistent with the reliability of' 92 per cent measured by Micha lowski et al. (2017) based on the ALMA162.3. Analysisdata of Simpson et al. (2015). Similarly, Chen et al. (2015) was able to iden-tify multiwavelength counterparts for ' 79 per cent of the SCUBA-2 sourcesdetected in the Extended Chandra Deep Field South, consistent with ourobservations.2.3 Analysis2.3.1 Flux boostingThe effects of selection biases, particularly ‘flux boosting’, on our results arecomplicated. This is because we picked bright outliers in large SCUBA-2maps, followed them up with the SMA, and then observed them at higherresolution. Because of this complexity, we put considerable effort into sim-ulating our observing and analysis procedure. The effect of flux boostingresults from the statistical nature of measuring flux densities in a noisy mapwhere there are many more faint sources than bright ones. This effect willtend to scatter sources to higher flux densities rather than lower ones, hencethe term ‘boosting’. One approach to correct for flux boosting follows fromBayes’ theorem:P (Strue|Sobs, σobs) ∝ P (Strue)P (Sobs|Strue, σobs), (2.1)where Strue is the intrinsic source flux density, Sobs is the measured sourceflux density and σobs is the measured source uncertainty. If the sourceuncertainties are Gaussian then P (Sobs|Strue, σobs) ∝ e−(Strue−Sobs)2/2σ2obs .Here P (Strue) is the prior, which quantifies all previous knowledge that wemight have about the distribution of flux densities in our sample.To construct the prior we performed a set of simulations that reconstruct,as best as possible, our observing strategy. For each of the five fields in ourstudy we first produced a mock SCUBA-2 map with 2 arcsec× 2 arcsec pixelsby injecting sources into an area of blank sky matching the area surveyedin the SCUBA-2 CLS. The flux densities were drawn from a Schechter-typefunction of the formdNdS=(N0S0)(SS0)−γe−S/S0 . (2.2)We adopted parameters obtained by Casey et al. (2013) from a fit to thenumber counts in a roughly 0.1 deg2 portion of the COSMOS field, namelyN0 = 3300 deg−2, S0 = 3.7 mJy and γ = 1.4. While Geach et al. (2017)also fit this model to their number counts, we found that the above values172.3. Analysiswere more consistent with our data as they predicted more bright sources.Positions were randomly selected to simulate Poisson statistics, with no clus-tering. The maps were convolved with a nominal SCUBA-2 beam with aFWHM of 14.8 arcsec and a negative bowl (from Geach et al. 2017). Gaus-sian noise was added followed by a second smoothing with the SCUBA-2beam, which is the matched filter that optimizes point-source detection (seeChapin et al. 2011, Appendix A). The amplitude of the Gaussian noise issuch that, after application of the matched filter, the resulting rms is equiva-lent to the rms achieved in each fields’ actual map. We note that in practicethe SCUBA-2 noise is not Gaussian and is correlated; however, the SCUBA-2 CLS areas were covered sufficiently uniformly that our method does notintroduce significant errors.To simulate the SMA follow-ups, we found all peaks in the map brighterthan a certain cutoff, which was determined to be the faintest non-deboostedSCUBA-2 source targeted by our actual SMA observations in a given field.The mock SMA follow-ups were performed by creating 9 arcsec × 9 arcsecthumbnail images centred on a bright SCUBA-2 source’s peak pixel; wechose 9 arcsec as a characteristic thumbnail size, since beyond this radiuswe no longer expect to be seeing the source/sources that contribute to theSCUBA-2 flux density we are following up. The thumbnail images have0.1 arcsec pixel sizes and were smoothed by a 2.4-arcsec FWHM beam, whichaccurately reconstructed our actual SMA observations because most of thegalaxies in our data are unresolved. Following Coppin et al. (2005, 2006), thedistribution of pixel flux densities from all of the mock SMA observations isa good estimator for the prior, since it takes into account both resolution andselection effects present in our observations. For each of the five fields wherewe have data, we repeated our simulation a sufficient number of times toproduce 100 deg2, corresponding to over 70,000 sources brighter than 10 mJy.The parameters used in each of the five fields’ simulations are summarizedin Table 2.1.Following Eq. 2.1, we constructed a posterior probability distribution forthe intrinsic flux density of each source using priors from their respectivefields. In Tables A.1–A.5 under the column SSMA we report the deboostedflux density as the peak in the posterior probability distribution, and we giveerror bars representing 68 per cent confidence intervals. In Fig. 2.2 we showan example of this deboosting technique for a typical source, COSMOS07,which, according to our simulations, is expected to be 6.5 per cent fainterthan indicated by our maps. Note that the error bars do not necessarilyincrease, but the signal always decreases so that the S/N always decreases.Both LHN11 and LHN12, which had S/N values less than 4 but had182.3. AnalysisTable 2.1: Parameters describing our simulations, which we use to calculatethe expected level of flux boosting in our measurements.Field S2 area S2 noise S2 cutoff[deg2] [mJy] [mJy]UDS 0.96 0.9 7.8SSA22 0.28 1.2 6.7COSMOS 2.22 1.6 7.2LHN 0.28 1.1 8.1EGS 0.32 1.2 9.8good multiwavelength counterparts, had probability distribution peaks atzero flux density due to their low S/N. For these sources we report 68 percent upper limits in the SSMA column of Tables A.1–A.5. We also notethat COSMOS22, which had a S/N value of 4.0, had a probability densityfunction whose 68 per cent confidence interval overlapped with zero fluxdensity, but we keep it as a detection.Cases where a single bright SCUBA-2 source is resolved into two or morefaint galaxies are more difficult to deboost. In our simulations we do notinclude any galaxy-galaxy interactions, clustering or lensing, and we onlyfollow-up the SCUBA-2 sources brighter than a certain threshold, so we can-not use our approach to obtain deboosting fractions for those faint galaxieswhich contribute to single, bright SCUBA-2 peaks. However, should a brightSCUBA-2 source resolve into one bright SMG above our follow up thresholdand one or more faint SMGs below our follow up threshold, our boosting cor-rection would be applicable only to the bright SMG. We therefore define allfaint galaxies to be those with flux densities 1 mJy less than the cutoff usedto determine which SCUBA-2 sources were to be followed up by the SMAin our simulations in a given field. Galaxies LHN13a and LHN13b resolvedcompletely from a SCUBA-2 peak and are considered faint, while galaxiesCOSMOS11b, LHN09b and LHN09c resolved from a SCUBA-2 peak alongwith a bright companion. We did not correct the measured flux densities forthese SMGs, and we simply use the measured values throughout the paper;in the SSMA column of Tables A.1–A.5, we report a value of N/A for thesecases. We note that neglecting to deboost these faint sources will have noeffect on the bright end of the number counts.192.3. Analysis0 5 10 15 20Flux density [mJy]10-1210-810-4100ProbabilityS obsSMA =12. 4± 1. 5mJySSMA =11. 6+1. 3−1. 7mJyP (Strue)P (Sobs|Strue, σobs)P (Strue|Sobs, σobs)Figure 2.2: Probability distributions for the flux density of COSMOS07,a typical source in our data set. The blue curve is the prior, which iscalculated by binning pixels resulting from simulating SCUBA-2 CLS fieldsand making small SMA thumbnail images centred on the brightest sources.The red curve shows the flux density of COSMOS07 measured from our data,where the uncertainty is assumed to be Gaussian. The black curve is theposterior probability distribution, which peaks at a slightly lower, deboostedflux density value due to the presence of many more faint galaxies in thesimulated sky. The deboosted flux density uncertainties given represent a68 per cent confidence interval about the peak.202.3. Analysis2.3.2 AstrometryThe accuracy with which SCUBA-2 sources can be localized is well under-stood to be a function of observed S/N (assuming no multiplicity), and isapproximated as (equation B22 in Ivison et al. 2007)∆α = ∆δ = 0.6 FWHM [(S/N)2obs − (2β + 4)]−1/2, (2.3)where ∆α is the uncertainty in right ascension (RA), ∆δ is the uncertaintyin declination (Dec), FWHM is the full-width half-maximum beamsize ofSCUBA-2 and β is the local slope of the cumulative number count used asa prior to correct the observed flux densities for boosting. To examine thepositional accuracy of our sample we computed the radial distance betweenour interferometrically-detected sources and those of the parent SCUBA-2 catalogue as a function of the detected S/N from Geach et al. (2017).For cases where multiple SMA/ALMA sources are detected, we simulated asimple (noiseless) SCUBA-2 image by convolving point sources at the SMApositions with a nominal SCUBA-2 beam with a FWHM of 14.8 arcsec (thebest-fitting model from Geach et al. 2017, resulting from stacking 322 pointsources of > 5σ in the UDS map) and calculated the location of the peakintensity, which is then compared to the reported SCUBA-2 source position.We took into account offsets between the SMA and SCUBA-2 referenceframes on a field-by-field basis by subtracting the mean difference in RAand Dec from each calculated offset.In Fig. 2.3 we plot the radial separation of our SMA positions relative tothe SCUBA-2 positions (except for the 12 sources where we did not detecta galaxy) as a function of detected S/N. Also shown are theoretical 68 percent and 95 per cent contours, derived using Equation 2.3 with β = 2.4. Toobtain the radial probability density we integrate re−r2/2σ2 , so 68 per centand 95 per cent contours are are actually at 1.51σ and 2.50σ, respectively.Six sources lie above the 95 per cent contour, corresponding to about 10 percent of the sources in our sample. While this may be more than expected,we note that in our simple simulations used to estimate the peak flux densityposition seen by SCUBA-2 using the SMA positions are priors, we did notinclude any SCUBA-2 noise. There also appears to be one outlier with a9 arcsec offset. This outlier is LHN09, which we have identified as a tripletwith one bright galaxy and two faint companions. The large offset seen hereis directly attributed to LHN09a, the bright galaxy, and the peak of the fluxdensity seen by SCUBA-2 in our simulation lies almost on top of it. Lookingat Fig. B.1, we can see that LHN09 is a rather complicated system, withseven IR galaxies and five radio galaxies all within the SCUBA-2 beam. It212.3. Analysis4 8 12 16 20SCUBA-2 S/N2468Separation[arcsec]UDSSSA22COSMOSLHNEGSFigure 2.3: Radial offset of SMA-detected sources from their SCUBA-2 coun-terparts. Where multiple counterparts are detected we smooth the sourceswith the nominal SCUBA-2 beam and locate the peak flux density and com-pare this to the given SCUBA-2 position. These sources are highlighted inthe figure by stars. Also shown are the expected 68 per cent and 95 per centpositional uncertainties as a functon of detected S/N for SCUBA-2.is therefore possible that our SMA data has resolved out some of the fluxdensity seen by SCUBA-2, which would in turn lead to the large offset weare seeing.2.3.3 Flux density reliabilityNext we compare the interferometric flux density observations to those fromSCUBA-2 to check the reliability of the flux densities in our data set. We usethe boosting-corrected flux densities reported by Geach et al. (2017) and ourboosting-corrected flux densities. When comparing the cases where a singe-dish source is resolved into multiple components, we take into account the222.3. Analysis5 10 15 20SS2 [mJy]0.51.01.52.0SS2/SSMAUDSSSA22COSMOSLHNEGSFigure 2.4: Comparison of the SCUBA-2 deboosted flux density from Geachet al. (2017) to the ratio of our SMA deboosted flux densities to each cor-responding SCUBA-2 flux density. Where a single CLS source is resolvedinto multiple components, we have summed each components’ flux densityweighted by the SCUBA-2 beam response. These sources are shown as stars.232.3. AnalysisSCUBA-2 14.8 arcsec beamsize. To do this, for each component, we multiplythe flux density by a 14.8-arcsec FWHM Gaussian, representing the SCUBA-2 beam, evaluated at the angular separation between the component and thelocation of the peak flux density seen in the SCUBA-2 map. Summing upthese weighted flux densities is a better approximation to what was observedby SCUBA-2. The results are shown in Fig. 2.4, where we have plotted SS2versus SSMA/SS2 and removed from our comparison the twelve sources wherewe only have upper limits on the flux density.The mean value of the ratio SSMA/SS2 is 1.05 ± 0.03, where the uncer-tainty is the standard error of the mean. While this result does not provideevidence for missing flux from faint sources in our maps with detections, itis likely that there are faint sources below the the noise levels in our mapslacking detections – when we add these observations to the calculation ofthe mean value of SSMA/SS2 we get 0.87± 0.05.2.3.4 CompletenessHere we discuss in detail the completeness of our observations with respectto the parent SCUBA-2 CLS survey. Since our targets were selected basedon early CLS maps with higher noise, it is important to understand oursample in terms of the final, published maps. In addition, we have to decidehow many sources from other experiments (i.e. Younger et al. 2007, 2009;Simpson et al. 2015) we wish to include in our sample, since they will affectour completeness.The latter question is important because we have not specifically targetedany sources below the given flux density limit (which depends on the field);however, images from Younger et al. (2007, 2009) and Simpson et al. (2015)extend much deeper, and in several cases a faint source that would have beenomitted from our study turned out to be bright enough to affect the brightend of the number counts when observed by the SMA or ALMA. Includingsources like this could potentially bias our results, since our survey wouldthen not really be ‘blind’, rendering the analysis much more difficult tointerpret.Our approach to this problem involves two steps. First, we incorporateinto our catalogue all sources from Younger et al. (2007, 2009) and Simpsonet al. (2015) that have SCUBA-2 deboosted flux densities greater than thefaintest source we targeted in our observations in a given field (see Table 2.1,under the ‘S2 thresh’ column). These sources are included in Tables A.1–A.5, and we have used the numbering conventions given in their respectivepapers. There are seven sources from Younger et al. (2007), four sources242.3. Analysisfrom Younger et al. (2009) and 16 sources from Simpson et al. (2015), for atotal of 27 archival sources. We note that the flux densities from Youngeret al. (2007, 2009) have not been corrected for flux boosting, so we use theirdirect measurements and give the deboosted flux densities under the SSMAcolumn as N/A; the flux densities from Simpson et al. (2015) have beencorrected for flux boosting, which are given under the SALMA column, andwe use these values for further analysis. We also include in our work theSMA observation of Orochi from Ikarashi et al. (2011), the gravitationallense in the UDS field. This brings the total number of interferometricsamples in our analysis to 103.Next, we calculate a completeness level for that field by dividing the totalnumber of SCUBA-2 sources targeted in our sample by the total number ofSCUBA-2 sources in the parent sample in a given flux density bin. Welooked at bins above 8 mJy with widths of ∆S = 1 mJy. In this way we areeffectively treating the external sources as if we had targeted them ourselves,indroducing as little bias as possible, while still using all of the data. Wecan then use the calculated completeness values in each bin to correct forthe missing sources introduced in the final, deeper CLS SCUBA-2 maps.In the UDS field, we have targeted sources down to SCUBA-2-deboostedflux densities of 7.2 mJy. After introducing the sources from Simpson et al.(2015) with deboosted SCUBA-2 flux densities greater than 7.2 mJy, we findthat our catalogue reaches a completeness of 96 per cent for S > 8 mJy, wherethe unobserved 4 per cent of sources are cases where a SCUBA-2 flux densitywas scattered to a higher value with the additional exposure time. At fainterflux densities our completeness falls below 80 per cent, which we deem tobe too low to be used reliable, and in the brighter regime of S > 9 mJywe have 100 per cent completeness. A similar analysis performed for theALMA sources observed by Simpson et al. (2015) resulted in completenesslevels of 50 per cent for S > 8 mJy, 56 per cent for S > 9 mJy, and 73 percent for S > 10 mJy, which shows that our observations offer a significantimprovement in this field owing to the fact that our targets were selectedfrom later versions of the CLS maps.In the SSA22 field we have followed up 100 per cent of the sources with adeboosted SCUBA-2 flux density greater than 10 mJy. In this field there areno sources with SCUBA-2 deboosted flux densities between 9 and 10 mJy,and below 9 mJy our data do not cover enough sources to allow us to reliablyestimate the number counts. Despite the fact that we have targeted fiveadditional sources less than the 10 mJy level, two sources scattered up toabout 8 mJy in the deeper SSA22 CLS map after our targets were selected,and so our completeness for S > 8 mJy is only 71 per cent.252.4. Results and discussionIn the COSMOS field, only about 50 per cent of the total area wasmapped to a nominal depth of 1.6 mJy in the published CLS maps used inour study, and the remaining half is currently being completed (S2COSMOS:Simpson et al. in prep); our completeness calculation for this field is basedon the current data available in Geach et al. (2017). We find that, withthe addition of the observations from Younger et al. (2007, 2009) downto 7.1 mJy, our faintest target, we have completeness of 89 per cent forS > 10 mJy, and 100 per cent completeness for S > 11 mJy. Below 10 mJyour sample becomes very sparse. There are two sources with deboostedSCUBA-2 flux densities of 10.0 and 10.1 mJy that have not been observedwith the SMA in our campaign, nor in the work of Younger et al. (2007,2009), due to their low S/N in earlier SCUBA-2 and LABOCA maps.We have fully probed the LHN field down to 7.5 mJy, achieving 100 percent completeness. Below this we targeted one source whose correspondingdeboosted SCUBA-2 flux density is 7.3 mJy, but we do not try to probenumber counts this low.Lastly, our sample does not include any EGS members below 9 mJy,while above 9 mJy we have resolved all of the available CLS sources, andthus every detection is statistically significant for estimating the counts inthis field.We now consider the completeness of our total data set. We have ob-served nearly all sources down to 10 mJy in these five cosmological fields,reaching a completeness level of 95 per cent for S > 10 mJy. As describedabove, there are two SCUBA-2 sources with deboosted flux densities of 10.0and 10.1 mJy that have no interferometric data, both in the COSMOS field.When considering our full data set, these two sources comprise 5 per centof the total number of sources with flux densities above 10 mJy. In Table2.2 we summarize our completeness calculations for each field, for S > 8 mJyand S > 10 mJy.2.4 Results and discussion2.4.1 Number countsWe now estimate the cumulative number counts of our sample of interferometrically-detected SMGs. Our calculations are restricted to counts within the com-pleteness regimes discussed above. The areas for each field are given inGeach et al. (2017) and are 0.96 deg2 for the UDS field, 0.28 deg2 for theSSA22 field, 2.22 deg2 for the COSMOS field, 0.28 deg2 for the LHN fieldand 0.32 deg2 for the EGS field, totalling 4.06 deg2 for our complete survey.262.4. Results and discussionTable 2.2: Completeness levels calculated for each field in our study, as wellas for the total data set.Field Completeness Completeness> 8 mJy > 10 mJyUDS 96% 100%SSA22 71% 100%COSMOS 54% 89%LHN 100% 100%EGS N/A 100%Total 77% 95%We calculate the cumulative number count in bins of ∆S = 1 mJy by simplycounting the total number of sources >S and dividing by the total area.To correct for the incompleteness due to the two COSMOS sources lackingSMA data in the S> 10 mJy bin, we first identify all sources in our cataloguethat have a SCUBA-2 deboosted flux density within ± 0.5 mJy of the miss-ing sources’ flux densities, and then we average over our corresponding SMAdeboosted measurements. For the missing 10.0 mJy COSMOS source we get10.2 mJy, and for the missing 10.1 mJy COSMOS source we get 10.5 mJy.These two values are then used for calculating the number counts.For the twelve observations where only upper limits were obtained forthe SMA counterparts we use the upper limit flux density as the deboostedSMA flux density; all 4σ upper limits we have measured constrain the fluxdensities of these sources to be less than 10 mJy, below the regime wherewe have good completeness, so we are not introducing any bias in the fluxdensity region studied in this work by doing this. The source SSA22-04is however an exception, where we have constrained the flux density to beless than 12.6 mJy but the corresponding SCUBA-2 flux density is 10.0 mJy.Since our SMA observations of this source have not been able to provide anyfurther information, we adopt the same method used for the two missingCOSMOS sources and use a flux density of 10.2 mJy for calculating thenumber counts. Lastly, for plotting purposes, we remove all repeated points,that is, points where there is no change in the cumulative number count intwo adjacent bins because there are no sources between S and S + ∆S.The results for the cumulative number count are shown in Fig. 2.5. Theerror bars are calculated as 68 per cent confidence intervals from Poissonstatistics (see Gehrels 1986). In addition, we show the CLS cumulativecount results from Geach et al. (2017) for comparison. We have also shaded272.4. Results and discussionthe boundary marking the 100 per cent completeness of our sample.We then compute the differential number counts in each field, followingthe same procedure as above. The results are shown in Fig. 2.5, beside ourcumulative number counts and together with the CLS differential countsfrom Geach et al. (2017) and the region marking the boundary of 100 percent completeness.In Fig. 2.6 we show our cumulative and differential number counts forthe UDS field alone compared to those derived by Simpson et al. (2015),along with the shaded region indicating our 100 per cent completeness limit.There seems to be a slight lack of sources at S& 10 mJy seen by Simpsonet al. (2015), but this is probably due to incompleteness in their data; thereare three SCUBA-2 sources (UDS03, UDS08 and UDS09) that were nottargeted in their work as they did not appear to among the brightest 30 UDSsources in the earlier, shallower CLS maps used to design their follow-upALMA programme. Also shown in Fig. 2.6 is the cumulative and differentialcount from the SCUBA-2 data in Geach et al. (2017). By including thethree bright UDS sources to the number counts we find no strong evidencefor diagreement between the single-dish measurements from Geach et al.(2017), the measurements from Simpson et al. (2015) and our work withinthe uncertainties.Similar single dish counts were also obtained by the LESS survey (Weißet al. 2009), which was a 0.35-deg2 870-µm survey of the Chandra DeepField South carried out with LABOCA, which has a FWHM of 19.2 arcsec.The LESS survey detected a total of 126 submm galaxies to a noise level ofapproximately 1.2 mJy. Following this, a high-resolution follow-up campaignwas carried out by Hodge et al. (2013) using ALMA, and the number countswere presented by Karim et al. (2013). They found no sources brighterthan about 9 mJy despite there being 12 LABOCA sources in this regime,implying a cut-off to possible FIR luminosities and star-formation rates.We compare our results to these earlier works in Fig. 2.7, where on thetop row we have plotted the cumulative and differential number counts fromLESS and the CLS (i.e. two single dish submm surveys), and on the bottomrow we have plotted the cumulative and differential number counts fromKarim et al. (2013), Simpson et al. (2015) and our work (i.e. high angularresolution follow-up studies); the shaded region indicating where our datais no longer 100 per cent complete is shown as well. We see no evidencefor a lack of high flux density sources, as hinted at by the results of Karimet al. (2013), and instead see the number count carrying on at a relativelyconstant slope to around 15 mJy. In this plot we have included the num-ber counts from models of evolving star-forming galaxies, specifically the282.4. Results and discussionFigure 2.5: Cumulative (above) and differentia (below) number counts de-rived from our data set. The single dish results from the CLS (Geach et al.2017) are shown for comparison. Values are slightly offset from each otherin each bin for clarity. The shaded region marks where our data is no longer100 per cent complete. An offset between our results of 2 to 20 per cent isseen in the cumulative count, although the points overlap within the uncer-tainties. 292.4. Results and discussionFigure 2.6: Cumulative (above) and differential (below) number count com-parison for the UDS field. The restults from Simpson et al. (2015), derivedfrom a smaller sample of the full parent CLS catalogue of the UDS field,are shown in red, alongside our more complete sample in black, where wehave used only data from the UDS field as well. The results broadly agree,although we see evidence for less bright sources in the Simpson et al. (2015)sample. Also shown as the shaded region is where our data is not 100 percent complete; our UDS data is 96 per cent complete for S> 8 mJy.302.4. Results and discussionempirical model from Be´thermin et al. (2012) and the GALFORM modelfrom Lacey et al. (2016). While the model from Lacey et al. (2016) ap-pears to be a better fit to our data, it is worth noting that the model fromBe´thermin et al. (2012) contains much less assumptions and no tuneableparameters (such as active galactic nuclei feedback and an adjustable initialmass function).Lastly, we fit a power law to our differential count in order to quan-titatively compare our results with these other works. We fit only pointsbetween 11 and 16 mJy, since our flux density coverage for smaller valuesis not 100 per cent complete, and beyond 16 mJy the differential numbercount begins to flatten, likely due to gravitational lensing not captured bya simple power law. Our model is of the formdNdS= N0S−γ , (2.4)and we find best-fit parameters of γ = 4.1 ± 1.9 and N0 = (0.4 ± 1.8) ×105 mJy−1 deg−1. This best-fit curve is plotted alongside our data in Fig. 2.7.We then compute the χ2 value between our model and the two data pointsbetween 11 and 16 mJy from Simpson et al. (2015), finding a value of 0.34.Taking the number of degrees of freedom to be 1, this corresponds to a p-value of 0.56. A similar analysis for the five data points (so 4 degrees offreedom) from Geach et al. (2017) between 11 and 16 mJy results in a χ2value of 3.99 and a p-value of 0.41. These p-values, being much greater thanthe commonly used threshold of 0.05, do not suggest that the differentialmeasurements from Simpson et al. (2015) and Geach et al. (2017) differsignificantly from our best-fit power law model within the flux density rangeof 11 to 16 mJy, although it is worth noting that we have not incorporatedthe uncertainty of the best-fit parameters in this analysis.Even though this simple calculation shows that our results and thosefrom the parent CLS sample are largely consistent, it should be noted thatthe two data sets are entirely correlated, being observations of the exact samegalaxies. Thus any differences at all in the counts, even if they are withinthe Poisson errors, still carry importance. In particular, the cumulativedistribution in Fig. 2.5 suggests a systematic offset of a few up to about 20per cent for all flux density bins.2.4.2 MultiplicityThe importance of galaxy interactions and mergers for the intense star-formation rates observed in many submm galaxies is a hotly debated topic.312.4. Results and discussion105 6 7 8 9 20S [mJy]10-1100101102dN/dS[mJy−1deg−2]LESS (Weiss et al. 2009)CLS (Geach et al. 2016)Bethermin et al. 2012Lacey et al. 2015This work105 6 7 8 9 20S [mJy]10-1100101102dN/dS[mJy−1deg−2]ALESS (Karim et al. 2013)Simpson et al. 2015This workBethermin et al. 2012Lacey et al. 2015This work105 6 7 8 9 20S [mJy]10-1100101102N(>S)[deg−2]LESS (Weiss et al. 2009)CLS (Geach et al. 2016)Bethermin et al. 2012Lacey et al. 2015105 6 7 8 9 20S [mJy]10-1100101102N(>S)[deg−2]ALESS (Karim et al. 2013)Simpson et al. 2015This workBethermin et al. 2012Lacey et al. 2015Figure 2.7: Cumulative and differential number counts for the two largesingle dish submm surveys LESS (Weiß et al. 2009) and CLS (Geach et al.2017) on the top row. On the bottom row we show cumulative and differ-ential number counts from Karim et al. (2013) and Simpson et al. (2015),interferometric follow-up studies of the LESS and CLS surveys, respectfully,shown along with our SMA results and the shaded region indicating whereour data is no longer 100 per cent complete. Also shown are the models ofBe´thermin et al. (2012) and Lacey et al. (2016). The black solid line showsthe best-fit power to our differential distribution between 11 and 16 mJy.322.4. Results and discussionHere we discuss the multiplicity seen in our large sample of bright, 850-µm-selected galaxies at a resolution of about 2 arcsec, and contrast our observa-tions with previous works.There is first the question of how to precisely define a multiple; withenough sensitivity, due to the steep rise in number counts at fainter flux den-sities, one could start to detect very faint background sources that are not infact associated. Our observations, being sensitive only down to about 6 mJy,would not suffer from this problem, but, for example, Lambas et al. (2012)defined multipes by their flux ratio, and pairs with brightest to second-brightest ratios less than 3 were considered multples, since this value pro-vides a reasonable cut-off for finding single dish sources whose flux densitieshave been seriously affected. Our observations are not able to detect ratiosas high as 3 but we have probed the regime of ratios less than 2, where singledish flux densities are the most seriously affected; in the following discussionwe use this as a working definition for multiplicity in our sample.In the UDS field, we found that none of our 23 observed SCUBA-2sources break up into two components, while the ALMA follow-up resultsof Simpson et al. (2015) reported 18 single dish sources breaking up intomultiple components in 30 observations, a fraction of 0.60± 0.14, where theuncertainty is calculated as the square root of the number of multiples di-vided by the sample size. It is hard to directly compare these two results forseveral reasons. First, Simpson et al. (2015) targeted most of the S > 10 mJysources in this field, while we have followed-up those in the fainter 8–10 mJyregime, and we might expect brighter SCUBA-2 sources to have a higherchance of being composed of multiple galaxies. Second, the typical rms levelobtained in the ALMA images was about 0.2 mJy, compared to our SMAimages, which have about 1.5 mJy of noise. For example, in cases where asingle bright SCUBA-2 source is composed of one bright galaxy and severalfainter (. 5 mJy) galaxies below the detection limit of the SMA, we mightexpect to see one detection with the SMA and multiple detections withALMA. Third, the synthesized beam of the ALMA pointings was about0.35 arcsec, much smaller than the 2.4 arcsec synthesized beam we achievedwith the SMA. We could therefore still be blending sources together, butonly if they are genuinely close on the sky – Simpson et al. (2015) foundonly two cases with equally bright galaxies separated by less than the SMAbeamsize.In the COSMOS field we found that one SCUBA-2 source resolved intotwo components. Including AzTEC11 from Younger et al. (2009), also amultiple, we obtain a multiplicity fraction of 0.07 ± 0.05 out of 27 SMAobservations. We note that the full catalogues published in Younger et al.332.4. Results and discussion(2007, 2009) contained two multiples, one of which is not included in ourobservations since its SCUBA-2 counterpart was not detected in the CLS.In the LHN field we found that, of the 18 SCUBA-2 sources followed-up,two break up into two galaxies, and one breaks up into three galaxies, whichis a multiplicity fraction of 0.17±0.10. This field represents the highest suchfraction in our sample; however, it still does not approach the multiplicityfraction seen in the Simpson et al. (2015) sample. The remaining fields,SSA22 and EGS, did not show any multiple-galaxy SCUBA-2 sources.The fact that we did not robustly detect any sources in twelve of ourpointings may in several cases be attributed to faint multiples being washedout by the noise level in our SMA observations. Using more sensitive ALMAobservations, Simpson et al. (2015) found four cases of bright, 7–11 mJySCUBA-2 sources resolving into multiple < 5 mJy sources, which would notbe detected in most of our SMA pointings. It is thus plausible to attributesome of our null-detections to cases where the SCUBA-2 blended source iscomposed of multiple faint sources that are lost in the noise; however, wemust be careful with this interpretation as there are instances where the fluxdensity threshold in our SMA maps is greater than the flux density of theSCUBA-2 source we are trying to detect. In these cases we cannot claimevidence for detecting multiplicity. Specifically, UDS14, UDS15, SSA22-03,COSMOS06, COSMOS17, LHN11 and LHN12 each have SMA flux densitylimits less than their observed SCUBA-2 counterpart flux densities, andso may be composed of multiple galaxies below our 4σ limit, whereas forSSA22-04, SSA22-07, SSA22-09, COSMOS23 and COSMOS25 we are notable to say anything about the galaxies contributing to the SCUBA-2 fluxdensity. Under the interpretation that undetected sources constrainted byour SMA observations to be fainter than their SCUBA-2 measurements arein fact multiples, we actually have observed seven more of these systems.This interpretation would change the multiplicity fraction in the COS-MOS field to 0.15 ± 0.07, and the multiplicity fraction in the LHN field to0.28±0.12, while in the SSA22 field we can calculate a fraction of 0.11±0.11.In the UDS field, in order to properly incorporate the ALMA observations(taking into account the difference in sensitivity compared to the SMA) weinclude multiples from Simpson et al. (2015) where two or more sources haveflux densities greater than 6 mJy or where all multiples are less than 6 mJy,which assumes a mean 1.5 mJy noise level and a 4σ cut. This includes fourmultiples: UDS156.0 and UDS156.1; UDS57.0 and UDS57.1; UDS286.0,UDS286.1, UDS286.2 and UDS286.3; and UDS199.0 and UDS199.1. Then,incorporating the two non-detections from our SMA observations, we find amultiplicity fraction of 0.15± 0.06, which agrees well with the other fields.342.4. Results and discussionThe GOODS-N field, a smaller, 0.07 deg2 part of the CLS, has also beenprobed with the SMA. In particular, Barger et al. (2014) provided a compi-lation of 28 SMA observations of known SCUBA-2 sources, 11 of which hadflux densities brighter than 8 mJy. The mean noise obtained by these SMAobservations was 1.1 mJy. In this work, after application of a 4σ cut, noneof these brighter sources were seen to break up into multiple components,but three fainter SCUBA-2 sources did break up. While this sample is notsufficiently complete to calculate number counts, Chen et al. (2013) pointedout that the single-dish counts were not significantly affeced by multiplicity.Considering our entire catalogue, we have a total of 16 multiples in 102observations (removing the gravitational lens Orochi), which results in amultiplicity fraction of 0.16 ± 0.04. It is worth noting once more the as-sumptions we have made to get to this number. First, we have assumedthat undetected sources with flux density constraints less than what wasobserved by SCUBA-2 are multiples, but this might not be true if an intrin-sically faint SCUBA-2 source were to lie on a rather large positive noise peak.Second, we have assumed that there are no multiples where we have not beenable to gain any interferometric information due to large amounts of noise,which might not be true in particular for SSA22-04, a 10 mJy SCUBA-2source which could potentially be resolved into two similarly bright galaxiesdetectable by the SMA.Our data therefore suggest that about 15 per cent of single dish submmsources brighter than 10 mJy will be seen as multiple SMGs with brightestto second-brightest flux density ratios less than 2 when viewed with anangular resolution of 2.4 arcsec. This multiplicity fraction can be thought ofas depending on three parameters: the minimum flux densities targeted, thesensitivity of the interferometric observations, and the angular resolution ofthe interferometric observations. In targeting brighter sources, we expectto observe more multiples (when strong lensing is not considered), and inaddition, more sensitive instruments with better angular resolution, likeALMA, should also observe more multiples.The question of wheather the multiplicity seen in our SMA images cor-respond directly to galaxy mergers is difficult to address with our data.First, we note that the physical scale being probed by the SMA’s resolu-tion, namely 2.4 arcsec, at a fiducual redshift of 2 is about 20 kpc, whichis around the same separation seen with major-mergers in the local Uni-verse (e.g. Lambas et al. 2012, who examined a set of about 2000 galaxypairs at z <0.1). On the other hand, it has been suggested that line-of-sightprojections could account for a significant fraction of the multiplicity seenin bright SMGs (Cowley et al. 2015), although larger sample sizes will be352.4. Results and discussionrequired to better understand this fraction over larger scales. But the factthat we hardly see any multiples may be useful for detecting galaxy clustersin formation. Under the assumption that these multiples are in fact phys-ically associated, merging galaxies, one could reasonably expect that thefew instances of multiplicity where both galaxies are equally bright are mas-sive galaxy cluster cores in the midst of formation, being such rare events.However, the sensitivity of our SMA observations only allows us to detectup to two galaxies per single SCUBA-2 source (there is no way to divide a12 mJy source into three parts brighter than 6 mJy, the typical noise levelin our data – the two faint companions to LHN09 technically fall below ourS/N threshold of 4), which may be too few to be the progenitor of today’smassive galaxy clusters. Nonetheless, the fact that we do not observe verymany equally bright pairs may help future work constrain massive clusterformation.2.4.3 Density of extremely luminous galaxiesOur sample of galaxies represent some of the most luminous and intenselystar-forming sites in the Universe. The SEDs of SMGs are well describedby a modified blackbody function (e.g., Dale and Helou 2002; Blain et al.2004):S(ν, Td, C, z) = C (ν(1 + z))β (ν(1 + z))3ehν(1+z)/kBTd − 1 , (2.5)which depends on a dust temperature Td, the redshift z, a normaliza-tion constant C. The spectral emissivity index β, which is the power lawthat ‘modifies’ the blackbody, is usually fixed at 2 based on physical ar-guments (Draine 2011). We can estimate the IR luminosity for a typical10 mJy source in our sample by setting β= 2, z= 2, Td =30 K and normal-izing to 10 mJy at 860µm then integrating this model from 8 to 1000µm(which is the definition of the IR luminosity). This calclation results in6× 1012 L, and this can be converted to a SFR using the relationshipfrom Kennicutt (1998) modified for a Chabrier IMF (Chabrier 2003) (i.e.SFR[M yr−1] = 9.5×10−11 LIR/L) to get 550 M yr−1.Using the above result we can recast our number counts in terms ofintrinsic SFRs. Since we see a surface density of galaxies brighter than10 mJy of 8+2−1 deg−2, this is a good approximation for the number of galaxieswith SFRs & 500 M yr−1. Here we are assuming that none of our sourcesare being gravitationally lensed, which would reduce their intrinsic SFRs;we will address the fraction of gravitaionally lensed galaxies in our sample362.5. Summaryin future work. Assuming all of our sources lie between z= 2 and z= 3 andusing the cosmological parameters from Planck Collaboration XIII (2016),this implies a likely volume density of 660+140−120 Gpc−3. With our data we arenot able to determine the number of nearby foreground galaxies that do notactually possess such high SFRs or that do not fall into the redshift rangeused for our volume calculation, but such a correction should not be largerthan a factor of a few.2.5 SummaryUsing the SMA we have followed-up 75 of the brightest SCUBA-2 CLSsources spread across 4 deg2 in five fields. We have also included in ouranalysis 28 archival SMA and ALMA observations of similar nature to bringour total sample size to 103. The synthesized beam of our observationswas on average 2.4 arcsec FWHM and the noise 1.5 mJy as calculated fromthe primary beam-corrected images, sufficient to resolve the majority ofthe SMGs contributing to the flux density peaks seen by the SCUBA-2instrument. Altogether, we detected 66 SMGs above 4σ, and saw threeexamples of a single SCUBA-2 peak breaking up into two or more SMGs.We also found that ten of our pointings did not detect any SMGs, whichmay result from a SCUBA-2 peak breaking up into two or more SMGsfainter than our 4σ detection limit, which is on average 6 mJy. We foundfour more sources with 3σ SMA peaks coincident with IR/radio data, twoof which are counterparts to a brighter SMA galaxy while the other two areindividual galaxies, which we include in our work to bring the number ofgalaxy detections to 70.We simulated SCUBA-2 maps and SMA follow-up pointings using thesame selection criteria as for our observations in order to estimate and cor-rect for flux boosting in our measurements. Upon applying these corrections,we found that the posterior probability distributions of two sources peakedat 0 mJy, so we can only constrain 68 per cent upper limits on their flux den-sities. We tested our positional accuracy by calculating the radial distancefrom the peak flux density positions in our SMA images to those in the CLSmaps, finding the spread to be consistent with the expected spread given theS/N values. We also compared our deboosted flux density measurements tothe deboosted flux density measurements published in the CLS, and foundthe mean ratio to be SS2/SSMA = 1.05± 0.03.Assessing completeness, our sample consists of 95 per cent of the sourceswith S > 10 mJy with respect to the reference fields in the CLS, and we372.5. Summarycalculate the number counts for this regime. We compare our number countsto what was found in our parent sample, finding general agreement; however,we do find a systematic offset between 2 and 20 per cent. We also compareour counts to those from Simpson et al. (2015), who followed-up most of thebright sources in the UDS field of the CLS with ALMA, and we show thatthe two estimations are in agreement.While multiplicity is evidently not uncommon in most of the brightsingle-dish sources, the effects appear not to severely steepen the brightend of the number counts. We estimate an upper limit of 15 per cent tothe multiplicity fraction of single dish submm sources brighter than approxi-mately 10 mJy, defined as groups of SMGs with brightest to second-brightestflux density ratios less than 2. Instead, the most common situation involvesbright single dish submm sources resolving into one slightly less bright SMGand several much fainter ones with much larger flux density ratios, whichonly slightly lowers previous estimates of the number of bright SMGs.Lastly we calculate the surface density of galaxies with SFRs greater thanapproximately 500 M yr−1 to be 8+2−1 deg−2, and assuming all redshifts arebetween 2 and 3, a volume density of 660+140−120 Gpc−3.38Chapter 3ConclusionSMGs have proven to contain a wealth of information regarding the highredshift Universe; since their discovery in the late 1990s, they have contin-uously been a prolific area of research. It has become very clear that SMGsrepresent a population of galaxies in the very early Universe, with a redshiftdistribution peaking between 2 and 2.5, which translates to a time when theUniverse was only about 3 billion years old. They have incredibly bright IRluminosities, which average to about LIR ≈ 1012 L. Since LIR is expectedto be directly proportional to the SFR, SMGs must also be some of the mostintensely star-forming sources of their epoch – values well over 1000 M yr−1have been observed.New telescopes with high resolution and improved sensitivity are begin-ning to break up some of the brightest submm sources into multiple SMGs.This has been important when considering number counts and resolving theCIB. The improvements in resolution are important when considering the-oretical models and numerical simulations of SMG formation. The sheernumber of ultraluminous SMGs seen on the sky is very difficult to repro-duce. Major mergers require more inter-halo collision in the early Universethan permitted by theoretical calculations, while standard galactic evolutionthrough gas accretion has been shown through simulations to be incapableof reaching large enough luminosities. If it turns out that the majority ofSMGs break up into smaller, less luminous components, models and simu-lations will not have to duplicate such extreme scenarios.There remain many unanswered questions; this is still a highly activefield of research. Some of the most pressing issues include determiningwhether or not SMGs represent a common stage of galaxy evolution, re-vealing the physical mechanisms behind their incredible luminosities, anddeveloping a comprehensive theory to describe the formation of SMGs – aremergers the primary drivers behind their development, or does the answer liecloser to the classic view of galaxy formation through accretion? 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Kawabe, D. H. Hughes, I. Aretxaga, T. Webb,A. Mart´ınez-Sansigre, S. Kim, K. S. Scott, J. Austermann, T. Perera, J. D.Lowenthal, E. Schinnerer, and V. Smolcˇic´. Evidence for a Population ofHigh-Redshift Submillimeter Galaxies from Interferometric Imaging. As-trophysical Journal, 671:1531–1537, December 2007. doi: 10.1086/522776.J. D. Younger, G. G. Fazio, J.-S. Huang, M. S. Yun, G. W. Wilson, M. L. N.Ashby, M. A. Gurwell, A. B. Peck, G. R. Petitpas, D. J. Wilner, D. H.Hughes, I. Aretxaga, S. Kim, K. S. Scott, J. Austermann, T. Perera,and J. D. Lowenthal. The AzTEC/SMA Interferometric Imaging Surveyof Submillimeter-selected High-redshift Galaxies. Astrophysical Journal,704:803–812, October 2009. doi: 10.1088/0004-637X/704/1/803.57Appendix AData tablesHere we provide data tables detailing our interferometric sample. Each ofthe five fields used in our study are summarized in a single table. Thecolumns give the source name, the SCUBA-2 position, the SMA (or ALMA)position, the SCUBA-2 observed flux density, the deboosted SCUBA-2 fluxdensity, the SMA (or ALMA) observed flux density and the SMA deboostedflux density. For SMA pointings that did not detect any galaxies above4σ we provide flux density upper limits. For sources that were deboostedto 0 mJy, we also provide 4σ upper limits. All sources are sorted by theirdeboosted SCUBA-2 flux density. We have used ALMA data from Simpsonet al. (2015) for some of the sources in the UDS field; these sources aremarked with a b. We have also used SMA data from Younger et al. (2007)and Younger et al. (2009) for some of the sources in the COSMOS field;these sources are marked with a c and a d, respectively.58Appendix A. Data tablesTable A.1: SMA sample plus archival ALMA data for the UDS field. Sources observed by ALMA in Simpson et al.(2015) are indicated by a b, and all other sources were observed by the SMA in this work.Source RA/Dec SCUBA-2 RA/Dec SMA SobsS2 [mJy] SS2 [mJy] SobsSMA [mJy] SSMA [mJy](SobsALMA) (SALMA)Orochia 02:18:30.77 −05:31:30.8 02:18:30.68 −05:31:31.7 52.7 ± 0.9 52.7 ± 1.2 90.7 ± 20.7 N/AUDS156.0b 02:18:24.33 −05:22:56.8 02:18:24.14 −05:22:55.3 16.7 ± 0.9 16.4 ± 1.3 9.7 ± 0.7 9.7 ± 0.7156.1b 02:18:24.33 −05:22:56.8 02:18:24.24 −05:22:56.9 16.7 ± 0.9 16.4 ± 1.3 8.5 ± 0.7 8.5 ± 0.7UDS57.0b 02:19:21.19 −04:56:52.5 02:19:21.14 −04:56:51.3 13.0 ± 0.9 12.8 ± 1.7 9.5 ± 0.6 9.5 ± 0.657.1b 02:19:21.19 −04:56:52.5 02:19:20.88 −04:56:52.9 13.0 ± 0.9 12.8 ± 1.7 6.0 ± 0.9 5.8 ± 0.957.2b 02:19:21.19 −04:56:52.5 02:19:21.41 −04:56:49.0 13.0 ± 0.9 12.8 ± 1.7 1.8 ± 0.6 1.5 ± 0.657.3b 02:19:21.19 −04:56:52.5 02:19:21.39 −04:56:38.8 13.0 ± 0.9 12.8 ± 1.7 2.7 ± 1.0 2.1 ± 1.0UDS03 02:15:55.41 −05:24:56.2 02:15:55.10 −05:24:56.6 12.8 ± 1.3 12.0 ± 1.8 13.7 ± 1.4 13.1+1.2−1.5UDS361.0b 02:16:48.08 −05:01:30.7 02:16:47.92 −05:01:29.8 11.5 ± 0.9 11.3 ± 1.7 11.8 ± 0.6 11.8 ± 0.6361.1b 02:16:48.08 −05:01:30.7 02:16:47.73 −05:01:25.8 11.5 ± 0.9 11.3 ± 1.7 2.6 ± 0.7 2.0 ± 0.7UDS286.0b 02:17:25.81 −05:25:36.9 02:17:25.73 −05:25:41.2 11.4 ± 0.9 11.2 ± 1.7 5.2 ± 0.7 5.1 ± 0.7286.1b 02:17:25.81 −05:25:36.9 02:17:25.63 −05:25:33.7 11.4 ± 0.9 11.2 ± 1.7 5.1 ± 0.6 5.0 ± 0.6286.2b 02:17:25.81 −05:25:36.9 02:17:25.80 −05:25:37.5 11.4 ± 0.9 11.2 ± 1.7 2.7 ± 0.6 2.6 ± 0.6286.3b 02:17:25.81 −05:25:36.9 02:17:25.52 −05:25:36.7 11.4 ± 0.9 11.2 ± 1.7 1.7 ± 0.6 1.4 ± 0.6UDS269.0b 02:17:30.50 −05:19:22.9 02:17:30.44 −05:19:22.4 11.0 ± 0.9 10.7 ± 1.4 12.9 ± 0.6 12.9 ± 0.6269.1b 02:17:30.50 −05:19:22.9 02:17:30.25 −05:19:18.4 11.0 ± 0.9 10.7 ± 1.4 2.6 ± 0.7 2.1 ± 0.7UDS08 02:15:56.03 −04:55:10.3 02:15:55.95 −04:55:08.6 10.9 ± 1.0 10.5 ± 1.3 10.1 ± 1.7 8.9+1.6−1.6UDS204.0b 02:18:03.04 −05:28:42.9 02:18:03.01 −05:28:41.9 10.7 ± 0.9 10.4 ± 1.2 11.6 ± 0.6 11.6 ± 0.6204.1b 02:18:03.04 −05:28:42.9 02:18:03.01 −05:28:32.5 10.7 ± 0.9 10.4 ± 1.2 2.9 ± 0.9 2.2 ± 0.9UDS202.0b 02:18:05.71 −05:10:50.9 02:18:05.65 −05:10:49.6 11.0 ± 0.9 10.4 ± 1.5 10.5 ± 0.5 10.5 ± 0.5202.1b 02:18:05.71 −05:10:50.9 02:18:05.05 −05:10:46.3 11.0 ± 0.9 10.4 ± 1.5 3.9 ± 0.9 3.5 ± 0.9UDS09 02:17:38.95 −04:33:37.0 02:17:38.82 −04:33:34.1 10.9 ± 1.3 10.1 ± 1.2 13.9 ± 0.8 13.6+0.9−0.7UDS11 02:16:43.77 −05:17:54.7 02:16:43.72 −05:17:53.5 10.1 ± 0.9 9.8 ± 1.4 10.0 ± 1.8 8.6+1.7−1.5UDS306.0b 02:17:17.23 −05:33:26.8 02:17:17.07 −05:33:26.6 9.9 ± 1.0 9.7 ± 1.3 8.3 ± 0.5 8.3 ± 0.5306.1b 02:17:17.23 −05:33:26.8 02:17:17.16 −05:33:32.5 9.9 ± 1.0 9.7 ± 1.3 2.6 ± 0.4 2.3 ± 0.4306.2b 02:17:17.23 −05:33:26.8 02:17:16.81 −05:33:31.8 9.9 ± 1.0 9.7 ± 1.3 3.0 ± 0.9 2.3 ± 0.9UDS14 02:16:30.77 −05:24:02.6 Undetected 9.6 ± 0.9 9.4 ± 1.2 < 6.1UDS15 02:18:03.57 −04:55:26.9 Undetected 9.6 ± 0.9 9.4 ± 1.3 < 5.1UDS16 02:19:02.24 −05:28:56.6 02:19:02.05 −05:28:56.7 9.5 ± 1.0 9.3 ± 1.4 6.5 ± 1.5 6.1+1.3−1.6UDS18 02:17:44.29 −05:20:08.9 02:17:44.22 −05:20:09.8 9.3 ± 0.9 9.1 ± 1.3 8.9 ± 1.5 8.1+1.3−1.4UDS13 02:19:27.31 −04:45:08.5 02:19:27.17 −04:45:06.1 9.8 ± 1.1 9.0 ± 1.6 15.3 ± 1.1 14.9+1.0−1.2UDS109.0b 02:18:50.32 −05:27:22.7 02:18:50.07 −05:27:25.5 9.4 ± 0.9 9.0 ± 1.5 7.7 ± 0.7 7.6 ± 0.7109.1b 02:18:50.32 −05:27:22.7 02:18:50.30 −05:27:17.2 9.4 ± 0.9 9.0 ± 1.5 4.3 ± 0.6 4.2 ± 0.6UDS48.0b 02:19:24.66 −04:53:00.5 02:19:24.57 −04:53:00.2 8.9 ± 0.8 8.9 ± 1.3 7.5 ± 0.5 7.5 ± 0.548.1b 02:19:24.66 −04:53:00.5 02:19:24.62 −04:52:56.9 8.9 ± 0.8 8.9 ± 1.3 1.6 ± 0.5 1.4 ± 0.5Continued on next page59Appendix A. Data tablesTable A.1 – continued from previous pageSource RA/Dec SCUBA-2 RA/Dec SMA SobsS2 [mJy] SS2 [mJy] SobsSMA [mJy] SSMA [mJy](SobsALMA) (SALMA)UDS20 02:17:30.51 −04:59:36.9 02:17:30.61 −04:59:36.8 9.1 ± 0.9 8.7 ± 1.4 9.0 ± 1.4 8.2+1.3−1.3UDS199.0b 02:18:07.31 −04:44:12.9 02:18:07.18 −04:44:13.8 9.2 ± 0.9 8.5 ± 1.4 4.3 ± 0.6 4.2 ± 0.6199.1b 02:18:07.31 −04:44:12.9 02:18:07.19 −04:44:10.9 9.2 ± 0.9 8.5 ± 1.4 2.5 ± 0.5 2.4 ± 0.5UDS22 02:16:11.81 −05:00:54.5 02:16:11.72 −05:00:54.0 9.0 ± 0.8 8.5 ± 1.2 15.0 ± 1.4 14.1+1.5−1.3UDS160.0b 02:18:23.79 −05:11:40.9 02:18:23.73 −05:11:38.5 8.8 ± 0.9 8.4 ± 1.4 7.9 ± 0.6 7.9 ± 0.6UDS110.0b 02:18:48.43 −05:18:06.7 02:18:48.24 −05:18:05.2 8.4 ± 0.9 8.2 ± 1.4 7.7 ± 0.6 7.7 ± 0.6110.1b 02:18:48.43 −05:18:06.7 02:18:48.76 −05:18:02.1 8.4 ± 0.9 8.2 ± 1.4 2.5 ± 0.8 2.0 ± 0.8UDS21 02:19:34.14 −04:44:40.4 02:19:34.15 −04:44:38.1 9.0 ± 1.2 8.2 ± 1.5 10.3 ± 1.0 9.9+0.9−1.0UDS337.0b 02:16:41.11 −05:03:52.7 02:16:41.11 −05:03:51.4 8.4 ± 0.9 8.0 ± 1.2 8.1 ± 0.5 8.1 ± 0.5UDS29 02:17:39.87 −05:29:18.9 02:17:39.78 −05:29:19.1 8.3 ± 0.9 8.0 ± 1.3 11.6 ± 1.1 11.2+1.0−1.2UDS79.0b 02:19:10.09 −05:00:08.6 02:19:09.94 −05:00:08.6 8.1 ± 0.9 7.9 ± 1.4 7.7 ± 0.5 7.7 ± 0.5UDS30 02:17:55.27 −04:47:22.9 02:17:55.05 −04:47:22.9 8.3 ± 0.9 7.8 ± 1.2 7.4 ± 1.1 7.1+1.0−1.0UDS28 02:19:42.53 −05:18:04.3 02:19:42.45 −05:18:03.6 8.4 ± 1.1 7.6 ± 1.6 9.0 ± 1.0 8.6+0.9−1.0UDS36 02:17:12.19 −04:43:18.9 02:17:12.21 −04:43:16.5 8.0 ± 0.9 7.6 ± 1.2 8.5 ± 1.4 7.8+1.3−1.2UDS34 02:17:42.15 −04:56:28.9 02:17:41.92 −04:56:29.8 8.0 ± 0.9 7.6 ± 1.3 7.9 ± 1.2 7.6+1.0−1.3UDS35 02:16:40.43 −05:13:38.7 02:16:40.40 −05:13:35.9 8.0 ± 0.9 7.6 ± 1.3 7.1 ± 1.4 6.6+1.3−1.4UDS37 02:16:38.44 −05:01:22.7 02:16:38.33 −05:01:21.4 7.9 ± 0.9 7.5 ± 1.3 8.4 ± 1.3 7.8+1.2−1.2UDS39 02:16:40.57 −05:11:00.7 02:16:40.59 −05:10:58.8 7.9 ± 0.9 7.5 ± 1.4 7.9 ± 1.0 7.6+0.9−1.0UDS40 02:17:27.43 −05:06:44.9 02:17:27.29 −05:06:42.8 7.8 ± 0.9 7.5 ± 1.2 6.9 ± 1.1 6.6+1.1−1.0UDS168.0b 02:18:20.46 −05:31:44.8 02:18:20.40 −05:31:43.2 8.2 ± 0.9 7.5 ± 1.4 6.7 ± 0.6 6.7 ± 0.6168.1b 02:18:20.46 −05:31:44.8 02:18:20.31 −05:31:41.7 8.2 ± 0.9 7.5 ± 1.4 3.0 ± 0.6 2.8 ± 0.6168.2b 02:18:20.46 −05:31:44.8 02:18:20.17 −05:31:38.6 8.2 ± 0.9 7.5 ± 1.4 2.0 ± 0.7 1.6 ± 0.7UDS33 02:15:46.99 −05:18:52.2 02:15:46.70 −05:18:49.2 8.1 ± 1.2 7.4 ± 1.4 10.3 ± 1.0 9.9+1.0−1.0UDS218.0b 02:17:54.87 −05:23:22.9 02:17:54.80 −05:23:23.0 7.6 ± 0.9 7.2 ± 1.3 6.6 ± 0.7 6.6 ± 0.7UDS38 02:16:46.07 −05:03:46.7 02:16:46.17 −05:03:48.9 7.9 ± 0.9 7.2 ± 1.3 6.9 ± 1.6 6.3+1.5−1.5a From Ikarashi et al. (2011) using the SMA at 860µm.b From Simpson et al. (2015) using ALMA at 870µm, following the naming convention in their paper.60Appendix A. Data tablesTable A.2: SMA sample for the SSA22 field. All observations are from this work.Source RA/Dec SCUBA-2 RA/Dec SMA SobsS2 [mJy] SS2 [mJy] SobsSMA [mJy] SSMA [mJy]SSA22-01 22:17:32.50 +00:17:40.4 22:17:32.43 +00:17:44.1 14.5 ± 1.1 14.5 ± 1.4 12.2 ± 1.8 10.6+1.9−1.8SSA22-03 22:16:56.10 +00:28:44.4 Undetected 11.1 ± 1.2 10.7 ± 1.4 < 8.7SSA22-02 22:16:59.96 +00:10:40.4 22:16:59.83 +00:10:37.1 10.8 ± 1.1 10.2 ± 1.5 9.3 ± 1.6 8.2+1.5−1.6SSA22-04 22:16:51.43 +00:18:20.4 Undetected 10.4 ± 1.1 10.0 ± 1.4 < 12.6SSA22-08 22:18:06.63 +00:05:20.4 22:18:06.60 +00:05:20.5 10.0 ± 1.3 8.8 ± 1.8 9.5 ± 1.6 8.2+1.7−1.3SSA22-07 22:17:18.90 +00:18:06.4 Undetected 8.5 ± 1.1 7.9 ± 1.3 < 8.5SSA22-06 22:18:06.36 +00:11:34.4 22:18:06.48 +00:11:34.7 8.3 ± 1.1 7.7 ± 1.5 9.9 ± 1.3 9.2+1.3−1.3SSA22-05 22:17:34.10 +00:13:52.4 22:17:33.90 +00:13:52.3 7.9 ± 1.1 7.3 ± 1.1 11.7 ± 2.0 9.9+2.0−1.8SSA22-09 22:17:42.23 +00:17:00.4 Undetected 6.7 ± 1.1 6.0 ± 1.4 < 8.561Appendix A. Data tablesTable A.3: SMA sample plus archival SMA data for the COSMOS field. Sources observed by the SMA in Younger et al.(2007) are indicated by a c, sources observed by the SMA in Younger et al. (2009) are indicated by a d, and all othersources were observed by the SMA in this work. Flux density measurements from Younger et al. (2007) and Youngeret al. (2009) were not deboosted. Values of N/A in the SSMA column indicate sources where our deboosting simulationwas not applicable.Source RA/Dec SCUBA-2 RA/Dec SMA SobsS2 [mJy] SS2 [mJy] SobsSMA [mJy] SSMA [mJy]AzTEC1c 09:59:42.89 +02:29:36.5 09:59:42.86 +02:29:38.2 16.7 ± 1.5 16.0 ± 3.0 15.6 ± 1.1AzTEC2c 10:00:08.11 +02:26:12.6 10:00:08.05 +02:26:12.2 15.4 ± 1.4 14.7 ± 2.3 12.4 ± 1.0COSMOS05 09:59:22.99 +02:51:36.4 09:59:22.99 +02:51:36.4 14.0 ± 1.5 13.0 ± 1.7 13.7 ± 2.3 11.3+2.4−2.2COSMOS06 09:58:42.40 +02:54:42.2 Undetected 14.0 ± 1.5 13.0 ± 2.1 < 8.1COSMOS10 10:00:15.72 +02:15:48.6 10:00:15.72 +02:15:48.6 12.9 ± 0.8 12.9 ± 1.2 16.8 ± 1.5 15.8+1.7−1.5COSMOS07e 09:58:37.92 +02:14:06.3 09:58:37.99 +02:14:08.5 13.2 ± 1.0 12.4 ± 1.5 13.8 ± 2.8 10.7+2.4−3.1COSMOS09e 10:00:57.22 +02:20:12.6 10:00:57.22 +02:20:12.6 13.0 ± 1.5 12.1 ± 2.2 12.5 ± 2.5 9.7+2.5−2.3AzTEC9d 09:59:57.44 +02:27:28.6 09:59:57.25 +02:27:30.6 12.4 ± 1.4 11.8 ± 1.9 9.0 ± 2.2COSMOS08 09:59:10.31 +02:48:54.4 09:59:10.34 +02:48:55.5 13.1 ± 1.6 11.7 ± 2.1 12.7 ± 2.0 11.3+1.6−2.3COSMOS11a 09:58:45.89 +02:43:26.3 09:58:45.95 +02:43:29.1 12.5 ± 1.6 11.5 ± 2.0 8.6 ± 1.1 8.0+1.1−1.011b 09:58:45.89 +02:43:26.3 09:58:46.06 +02:43:31.5 12.5 ± 1.6 11.5 ± 2.0 5.1 ± 1.1 N/ACOSMOS15 09:57:49.03 +02:46:15.9 09:57:48.93 +02:46:19.9 11.8 ± 1.5 11.2 ± 2.1 11.2 ± 2.0 9.7+1.6−2.2AzTEC5c 10:00:19.86 +02:32:04.6 10:00:19.75 +02:32:04.4 12.0 ± 1.4 11.2 ± 2.2 9.3 ± 1.3COSMOS14 10:00:13.46 +01:37:04.7 10:00:13.47 +01:37:04.3 12.0 ± 1.5 11.0 ± 1.8 12.2 ± 1.2 11.7+1.0−1.3COSMOS17 10:00:04.78 +02:30:44.6 Undetected 11.2 ± 1.4 11.0 ± 1.8 < 8.4AzTEC12d 10:00:35.34 +02:43:52.6 10:00:35.29 +02:43:53.4 11.6 ± 1.3 10.9 ± 2.0 13.5 ± 1.8COSMOS18 09:58:40.46 +02:05:14.4 09:58:40.28 +02:05:14.5 11.1 ± 1.5 10.4 ± 2.1 10.9 ± 1.7 9.7+1.6−1.7AzTEC8d 09:59:59.44 +02:34:38.6 09:59:59.34 +02:34:41.0 10.9 ± 1.4 10.1 ± 1.8 19.7 ± 1.8AzTEC7c 10:00:17.99 +02:48:30.5 10:00:18.06 +02:48:30.5 10.8 ± 1.4 9.7 ± 2.0 12.0 ± 1.5COSMOS21 09:59:07.63 +02:58:36.3 09:59:07.49 +02:58:39.3 10.6 ± 1.5 9.5 ± 2.0 9.9 ± 1.9 8.3+1.8−1.8AzTEC3c 10:00:20.79 +02:35:20.6 10:00:20.70 +02:35:20.5 9.2 ± 1.3 8.6 ± 1.5 8.7 ± 1.5AzTEC11.Nd 10:00:08.91 +02:40:10.6 10:00:08.91 +02:40:09.6 9.3 ± 1.4 8.3 ± 1.8 10.0 ± 2.111.Sd 10:00:08.91 +02:40:10.6 10:00:08.94 +02:40:12.3 9.3 ± 1.4 8.3 ± 1.8 4.4 ± 2.1COSMOS23 10:00:10.12 +02:13:34.6 Undetected 8.4 ± 0.9 8.2 ± 1.4 < 9.3AzTEC6c 10:00:06.64 +02:38:34.6 10:00:06.50 +02:38:37.7 8.9 ± 1.4 8.0 ± 1.8 8.6 ± 1.3AzTEC4c 09:59:31.68 +02:30:42.5 09:59:31.72 +02:30:44.0 9.3 ± 1.5 7.9 ± 1.9 14.4 ± 1.9COSMOS22 09:59:33.55 +02:23:46.5 09:59:33.55 +02:23:46.5 8.5 ± 1.2 7.8 ± 1.6 8.9 ± 2.2 7.2+2.0−7.2COSMOS24 09:59:12.08 +02:09:54.5 09:59:12.17 +02:09:57.1 7.9 ± 1.1 7.2 ± 1.3 8.1 ± 1.7 7.0+1.6−1.6COSMOS25 10:00:23.73 +02:19:14.6 Undetected 7.2 ± 1.0 7.1 ± 1.1 < 9.3COSMOS01f 10:02:09.77 +02:36:33.9 10.6 ± 1.2COSMOS02f 10:02:49.19 +02:32:55.3 18.6 ± 0.7c From Younger et al. (2007) using the SMA at 890µm, following the naming convention in their paper.d From Younger et al. (2009) using the SMA at 890µm, following the naming convention in their paper.e Also detected with PdBI in Smolcˇic´ et al. (2012).f Source is found in the CLS maps but outside the area defining the CLS catalogue, and hence not used in our analysis.62Appendix A. Data tablesTable A.4: SMA sample for the LHN field. All observations are from this work. Values of N/A in the SSMA columnindicate sources where our deboosting simulation was not applicable.Source RA/Dec SCUBA-2 RA/Dec SMA SobsS2 [mJy] SS2 [mJy] SobsSMA [mJy] SSMA [mJy]LHN01 10:46:45.01 +59:15:39.8 10:46:45.00 +59:15:41.6 12.3 ± 1.2 12.3 ± 1.8 10.3 ± 1.9 8.8+1.8−1.7LHN02 10:46:35.78 +59:07:48.0 10:46:35.91 +59:07:48.1 12.0 ± 1.0 11.9 ± 1.2 12.2 ± 1.9 10.4+2.0−1.7LHN03a 10:47:27.66 +58:52:14.6 10:47:27.97 +58:52:14.1 10.4 ± 1.1 9.9 ± 1.3 8.1 ± 1.8 7.3+1.5−1.803b 10:47:27.66 +58:52:14.6 10:47:26.52 +58:52:12.8 10.4 ± 1.1 9.9 ± 1.3 8.0 ± 1.9 7.1+1.6−1.9LHN06 10:45:55.19 +59:15:28.1 10:45:55.24 +59:15:28.6 9.7 ± 1.1 9.7 ± 0.9 7.2 ± 1.8 6.6+1.5−6.5LHN04 10:48:03.37 +58:54:22.9 10:48:03.57 +58:54:21.5 10.1 ± 1.3 8.9 ± 1.4 14.1 ± 2.4 11.7+2.2−2.5LHN08 10:47:00.03 +59:01:07.5 10:47:00.18 +59:01:07.5 9.2 ± 1.0 8.9 ± 1.6 10.4 ± 1.6 9.4+1.4−1.6LHN11* 10:45:22.55 +59:17:21.7 10:45:22.28 +59:17:25.6 8.6 ± 1.4 8.8 ± 1.7 7.0 ± 1.8 UndetectedLHN07 10:45:35.23 +58:50:49.9 10:45:34.98 +58:50:49.9 9.3 ± 1.1 8.7 ± 1.4 9.6 ± 1.6 8.8+1.3−1.6LHN10 10:45:54.58 +58:47:54.1 10:45:54.50 +58:47:55.6 8.8 ± 1.1 8.3 ± 1.5 8.2 ± 0.8 8.1+0.7−0.8LHN05 10:43:51.48 +59:00:57.7 10:43:51.21 +59:00:58.1 10.0 ± 1.5 8.2 ± 2.1 10.9 ± 2.4 8.8+2.0−2.3LHN09a 10:45:23.87 +59:16:25.7 10:45:23.11 +59:16:18.6 9.0 ± 1.3 8.2 ± 1.5 9.4 ± 1.5 8.6+1.3−1.409b* 10:45:23.87 +59:16:25.7 10:45:25.01 +59:16:25.7 9.0 ± 1.3 8.2 ± 1.5 5.1 ± 1.5 N/A09c* 10:45:23.87 +59:16:25.7 10:45:23.71 +59:16:31.9 9.0 ± 1.3 8.2 ± 1.5 4.5 ± 1.5 N/ALHN12* 10:46:32.85 +59:02:12.0 10:46:32.80 +59:02:14.4 8.6 ± 1.0 8.1 ± 1.3 6.0 ± 2.0 UndetectedLHN13a 10:47:25.25 +59:03:40.7 10:47:25.47 +59:03:36.7 8.5 ± 1.1 7.9 ± 1.4 5.5 ± 0.8 N/A13b 10:47:25.25 +59:03:40.7 10:47:25.13 +59:03:41.5 8.5 ± 1.1 7.9 ± 1.4 3.9 ± 0.8 N/ALHN14 10:46:31.68 +58:50:54.0 10:46:31.58 +58:50:55.7 8.5 ± 1.1 7.9 ± 1.4 7.1 ± 0.8 7.0+0.7−0.8LHN15 10:46:57.26 +59:14:57.6 10:46:57.30 +59:14:58.6 8.5 ± 1.2 7.9 ± 0.9 5.5 ± 0.7 5.5+0.6−0.8LHN16 10:44:56.86 +58:49:59.0 10:44:56.74 +58:49:59.7 8.3 ± 1.1 7.6 ± 1.4 16.9 ± 2.5 13.9+3.0−2.2LHN17 10:44:47.69 +59:00:36.6 10:44:47.68 +59:00:35.6 8.1 ± 1.1 7.5 ± 1.3 5.6 ± 0.7 5.5+0.7−0.7LHN18 10:47:20.57 +59:10:40.9 10:47:20.54 +59:10:43.4 8.1 ± 1.1 7.3 ± 1.3 7.0 ± 0.8 6.9+0.7−0.7* Source falls below the 4σ threshold in the SMA data, but a > 3σ peak has excellent positional alignment with IR and radiocounterparts.63Appendix A. Data tablesTable A.5: SMA sample for the EGS field. All observations are from this work.Source RA/Dec SCUBA-2 RA/Dec SMA SobsS2 [mJy] SS2 [mJy] SobsSMA [mJy] SSMA [mJy]EGS01 14:19:51.56 +53:00:44.8 14:19:51.33 +53:00:46.4 16.3 ± 1.2 16.3 ± 1.4 13.2 ± 0.9 12.9+0.9−0.8EGS02 14:15:57.62 +52:07:11.1 14:15:57.53 +52:07:12.7 12.7 ± 1.3 12.1 ± 1.2 13.8 ± 1.4 12.9+1.5−1.2EGS03 14:15:47.46 +52:13:47.2 14:15:47.09 +52:13:48.6 10.8 ± 1.0 10.5 ± 1.1 16.4 ± 2.8 12.9+2.9−2.4EGS05 14:19:20.35 +52:56:08.9 14:19:20.08 +52:56:09.1 10.7 ± 1.0 10.1 ± 1.4 20.0 ± 0.9 19.7+1.0−0.8EGS06 14:17:40.55 +52:29:04.7 14:17:40.34 +52:29:06.7 10.0 ± 1.0 9.8 ± 2.3 9.8 ± 2.0 8.9+1.7−1.8EGS08 14:19:00.37 +52:49:45.3 14:19:00.24 +52:49:48.3 10.4 ± 1.1 9.8 ± 1.5 8.6 ± 1.5 8.1+1.5−1.4EGS04 14:19:14.54 +53:00:33.6 14:19:14.32 +53:00:33.8 10.5 ± 1.4 9.3 ± 1.6 11.1 ± 1.5 10.5+1.2−1.6EGS10 14:17:44.09 +52:21:22.4 14:17:43.38 +52:21:21.7 10.2 ± 1.5 9.2 ± 2.3 8.3 ± 1.6 7.7+1.6−1.5EGS11 14:17:41.73 +52:22:04.6 14:17:41.41 +52:22:07.9 9.8 ± 1.4 9.2 ± 1.4 7.2 ± 1.5 6.7+1.6−1.3EGS07f 14:18:22.04 +52:54:02.0 7.7 ± 1.5EGS09f 14:20:52.55 +52:54:00.3 6.1 ± 1.4f Source is found in the CLS maps but outside the area defining the CLS catalogue, and hence not used in our analysis.64Appendix BMultiwavelength cutoutsHere we provide Spitzer -IRAC 3.6µm, Spitzer -MIPS 24µm and VLA 1.4 GHzcutouts of the 38 sources for which these two images are available. Overlaidare SMA contours starting from 2σ in steps of 1σ.65Appendix B. Multiwavelength cutoutsUDS08UDS20UDS22UDS29UDS30UDS28UDS34UDS37Figure B.1: Multiwavelength cut-outs of 38 sources in our sample withSpitzer -IRAC 3.6µm, Spitzer -MIPS 24µm and VLA 1.4 GHz imaging. Weshow SMA flux contours starting from 2σ in steps of 1σ overlaid over theIR and radio data.66Appendix B. Multiwavelength cutoutsUDS39UDS40COSMOS05COSMOS08COSMOS11COSMOS15COSMOS14COSMOS18Figure B1 (Cont.)67Appendix B. Multiwavelength cutoutsCOSMOS22COSMOS24COSMOS25LHN01LHN02LHN03LHN06LHN08Figure B1 (Cont.)68Appendix B. Multiwavelength cutoutsLHN11LHN07LHN10LHN05LHN09LHN12LHN13LHN14Figure B1 (Cont.)69Appendix B. Multiwavelength cutoutsLHN15LHN16LHN17LHN18EGS06EGS08Figure B1 (Cont.)70

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