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New methods for deblending spectral energy distributions in confused imaging MacKenzie, Todd 2015

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cefi methoys for yewlenying spextrvlenerg– yistriwutions in xonfuseyimvgingbyTodd MackenzieB.Sc., The University of Prince Edward Island, 2009M.Sc., The University of British Columbia, 2011A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinFaculty of Graduate and Postdoctoral Studies(Astronomy)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)December 2015c© Todd Mackenzie 2015VwstrvxtThe submillimetre band is ideal for studying high-redshift star-forming galaxies, but such stud-ies are hampered by the poor resolution of single-dish telescopes. Interferometric follow-up hasshown that many sources are in fact comprised of multiple sources. For many such targets,confusion-limited Hyrswhyl observations that target the peak of their far-infrared emission arealso available. Many methods for analysing these data have been developed, but most followthe traditional approach of extracting fluxes before model spectral energy distributions are fit,which erases degeneracies among fitting parameters and glosses over the intricacies of confusionnoise. We have developed a forward-modelling method in order to tackle this problem in a morestatistically rigorous way, which combines source deblending and spectral energy distributionfitting into the same procedure. We adapt our method to three independent projects, all ofwhich benefit from our improved methodology.We investigate a “giant submillimetre arc” behind a massive foreground cluster and uncoverseven multiply imaged galaxies, of which six are found to be at a redshift of z ∼ 2:9, and possiblyconstitute an interacting galaxy group. Using our new method, we disentangle the arc into itscontributing components and constrain their far-IR properties.Using confusion limited Hyrswhyl-SPIRE imaging, the far-IR properties LABOCA detectedsubmillimetre sources can be constrained. Despite such sources often breaking up in high-resolution ALMA imaging, existing studies have implemented traditional fitting methods. Weapply our new forward modelling method to re-derive constraints on the far-infrared propertiesof these sources, exploring selection effects on this sample, while highlighting the benefits ofour fitting approach.Finally, we present SCUBA-2 follow-up of 51 candidate proto-cluster fields undergoing en-hanced star-formation. With the accompanying Hyrswhyl-SPIRE observations and a realisticdust temperature prior, we provide photometric redshift and far-IR luminosity estimates for172 SCUBA-2 selected sources within the dlunwk overdensity fields. We find a redshift distribu-tion similar to sources found in cosmological surveys, although our fields are enhanced in bothdensity of sources and star formation rate density over a wide range of redshifts.iierefvxeThis work contains re-formatted pre-published work. The pronoun “we” is used throughout,as is convention in the literature, however all text has been written by myself. A breakdown ofthe work done by myself and others is given below.• Chapter 2 was published as a paper in Monthly Notices of the Royal Astronomical Society(MacKenzie et al., 2014) and has been co-authored with Douglas Scott, Andy Gibb andothers, with myself as the primary author. All work and writing was done myself withthe exception of the lens model being provided by Jean-Paul Kneib and Johan Richard.Hgh and Hyrswhyl observations were publicly available, but the SCUBA-2 observationswere performed by myself. Important feedback was provided by all co-authors.• Chapter 3 strives to improve upon the work of Swinbank et al. (2014), thus all the imagesand catalogues were publicly available. All work and writting beyond these were done bymyself, but important feedback was provided by both Douglas Scott and Mark Swinbank.• Chapter 4 is a collaborative effort to follow up high-z candidates. The dlunwk source listand Hyrswhyl observations were provided by collaborators, but the SCUBA-2 observations,analysis and the writing were performed by myself. Collaborators who have providedfeedback include Douglas Scott, Herve Dole, David Guery, Nicole Nesvadba, and DaveClements.iiiivwle of Contents4UfgeTcg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiCeefTce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTTUle bf 6bageagf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivLifg bf TTUlef . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viLifg bf 9igheef . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii4ckabwledgemeagf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix1 Iagebdhcgiba . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 7ifeagTagliag T leafed gebhc bf gTlTkief Tg z02.9 bUfeeied wigh F6U54-2 72.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Hgh and the lensing model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3 New submm imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3.1 SCUBA-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3.2 Hyrswhyl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4 A framework for fitting SEDs to confused counterparts . . . . . . . . . . . . . . 122.4.1 Model SED and image reconstruction . . . . . . . . . . . . . . . . . . . . 132.4.2 Model fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.5.1 A compact group of galaxies at high redshift . . . . . . . . . . . . . . . . 162.5.2 Physical properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 9iggiag fcecgeTl eaeegl difgeiUhgibaf gb fbhecef ia Uleaded imTgiag . . . . . 253.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 A framework for fitting SEDs to blended sources . . . . . . . . . . . . . . . . . . 263.2.1 Model SED and image reconstruction . . . . . . . . . . . . . . . . . . . . 263.2.2 Hyrswhyl -SPIRE sky residuals . . . . . . . . . . . . . . . . . . . . . . . . 263.2.3 Model fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3 Testing with simulated sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3.1 Verifying our method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3.2 The addition of a second ALMA frequency . . . . . . . . . . . . . . . . . 343.4 The properties of submm galaxies within the ALESS survey . . . . . . . . . . . 363.4.1 Comparison with Swinbank et al. (2014) . . . . . . . . . . . . . . . . . . 383.4.2 Dust temperatures and selection effects for ALESS sources . . . . . . . . 393.4.3 Contribution to the co-moving star formation rate density of the Universe 42ivhuvly of Contynts3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 F6U54n2 fbllbw-hc bf cTadidTge ClTack cebgb-clhfgeef . . . . . . . . . . . . 454.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.2 The Planck candidates follow-up . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.2.1 SCUBA-2 follow-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.2.2 Hyrswhyl SPIRE data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.3 SED model and fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.4 SED fitting results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 6baclhfibaf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.1 Summary of conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.2 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575iUlibgeTchl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594cceadik . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724 Fbhece lifgf Tad fTe-IR cebceegl gTUlef . . . . . . . . . . . . . . . . . . . . . . . 73A.1 Far-IR properties of the ALESS sample . . . . . . . . . . . . . . . . . . . . . . . 73A.2 Redshift and far-IR estimates for SCUBA-2 selected sources within the dlunwkoverdensity fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75vaist of ivwles2.1 List of images for the eight high-z galaxies. . . . . . . . . . . . . . . . . . . . . . 232.2 Lensing-amplification-corrected results from the model. . . . . . . . . . . . . . . 24A.1 The model fit parameters and credible intervals for the ALESS sample. . . . . . . 73A.2 SCUBA-2 detected sources within the dlunwk proto-cluster candidate fields. . . . 75viaist of Figures1.1 Co-moving SFR density history of the Universe. . . . . . . . . . . . . . . . . . . . 21.2 SED of a modified blackbody. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 An example of confusion limited Hyrswhyl SPIRE confusion imaging at 250m,350m and 500m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 hop lyzt: Hgh WFC3 colour-composite, clearly showing the main optical arc.hop right: Hgh image with the positions of the multiply-imaged galaxies la-belled numerically from 1 through 7 with 850m emission shown using blackcontours. Vottom: The “giant submm arc” as seen by Hyrswhyl PhotoconductorArray Camera and Spectrometer (PACS) and Spectral and Photometric ImagingReceiver (SPIRE) and SCUBA-2 over more than a factor of five in wavelengthrange. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Hgh cut-outs at the locations of the seven multiply imaged galaxies. . . . . . . . 102.3 Source plane arrangement of the z ∼ 2:9 group galaxies. . . . . . . . . . . . . . . 172.4 Dust temperature versus far-IR luminosity for several samples of galaxies. . . . . 192.5 Decomposition of the submm arc into each contributing galaxy for the best-fitmodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.6 MCMC likelihood contours for temperature and far-IR luminosity for the galaxiesthat were found to contribute to the submm arc. . . . . . . . . . . . . . . . . . . 213.1 Lyzt: SPIRE ECDFS field. fight: SPIRE ECDFS field, after source subtraction. 273.2 Results of separating the inverted covariance matrix of the Hyrswhyl-SPIRE resid-uals by angular separation and by wavelength. . . . . . . . . . . . . . . . . . . . 293.3 Results comparing the expected uncertainty in fitting a source versus MonteCarlo simulated sources injected into the data. . . . . . . . . . . . . . . . . . . . 313.4 Comparing the expected uncertainties for two standard sources separated by 5arcseconds given by our method (black contours), with the Monte Carlo simu-lated results (blue points). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.5 Comparing the expected uncertainties for a standard source using our methodand an identical method with a naive approach. . . . . . . . . . . . . . . . . . . . 333.6 Constraining power of our model as a function of redshift for our standard sourcewhile keeping peak flux density constant. . . . . . . . . . . . . . . . . . . . . . . 343.7 Constraining power of our model for the case of varying redshift uncertainty. . . 353.8 Constraining power of our model for the case of two standard sources separatedby 5 arcseconds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.9 Constraining power of our model for the case of two standard sources, moved toa redshift of 4, while keeping the same peak flux density, and a separation of 5arcseconds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.10 hop: Dust temperature vs far-IR luminosity for the ALESS sample. Vottom:Far-IR luminosity vs redshift for the ALESS sample. . . . . . . . . . . . . . . . . 40viiList of Figurys3.11 A comparison of our results with those found by Swinbank et al. (2014). . . . . . 413.12 Dust temperature versus far-IR luminosity for a sample of lensed submm galaxies. 423.13 Contribution of the ALESS sources with flux densities greater than 4.2mJy tothe co-moving star formation history of the Universe. . . . . . . . . . . . . . . . . 434.1 Constraints on far-IR luminosities and photometric redshifts for the sample ofSCUBA-2-detected sources within the dlunwk overdensity fields. . . . . . . . . . . 504.2 Redshift distribution of SCUBA-2-selected sources, assuming a dust temperatureprior of 33HNP−9 K, for the dlunwk overdensity sample within the dlunwk beam. . . . 524.3 Co-moving SFR density vs redshift for SCUBA-2-detected sources with flux den-sities greater than 8mJy assuming a dust temperature prior of 33HNP−9 K. . . . . . 53viiiVxknofileygementsFirst, I would like to thank my supervisor, Dr. Douglas Scott. He has both guided me throughmy research and all the hurdles one must go through to complete both a Masters and Phd.Along with his guidance, he has also given me much independence and allowed me a muchappreciated flexible schedule.Second, I would like to thank my colleagues, Andy Gibb, Gaelan Marsden and EdwardChapin, who helped me through many technical problems, helped perform the research we haveundertaken, and with whom I have collaborated with writing my published papers (MacKenzieet al., 2011, 2014). Without them, much of this work would not have been completed.I must thank the sources of the funding I have received: my supervisor and NSERC for mysalary and conference support, the department of physics and astronomy for tuition support andtop-up bursaries, NSERC through an Alexander Graham Bell Canada Graduate Scholarshipduring my first year, UBC for a graduate fellowship during my second year, and the JointAstronomy Centre in Hawaii for my journey to finally meet “my telescope”.Finally, I must thank my parents for the support and freedom they have given me throughall my studies.Below are acknowledgements to the telescope facilities and organisations which this researchhas relied upon.The James Clerk Maxwell Telescope is operated by The Joint Astronomy Centre on behalfof the Science and Technology Facilities Council of the United Kingdom, the Netherlands Or-ganisation for Scientific Research, and the National Research Council of Canada. Data for thisthesis were taken as part of the S2SRO programme, with Project ID M09BI142.This research used the facilities of the Canadian Astronomy Data Centre operated by theNational Research Council of Canada with the support of the Canadian Space Agency.This research was supported by the Canadian Natural Sciences and Engineering ResearchCouncil and enabled through funding from the Canada Foundation for Innovation and throughthe CANFAR Programme, funded by CANARIE, Canada’s advanced Internet organisation.This work is based in part on observations made with the gpitzyr gpuwy hylyswopy, which isoperated by the Jet Propulsion Laboratory, California Institute of Technology, under a contractwith NASA.This research has made use of the NASA/IPAC Extragalactic Database (NED) which isoperated by the Jet Propulsion Laboratory, California Institute of Technology, under contractwith NASA.The Digitized Sky Surveys were produced at the Space Telescope Science Institute underU.S. Government grant NAG W-2166. The images of these surveys are based on photographicdata obtained using the Oschin Schmidt Telescope on Palomar Mountain and the UK SchmidtTelescope.The VLA is part of the US National Radio Astronomy Observatory, a facility of the NationalScience Foundation operated under cooperative agreement by Associated Universities, Inc.SPIRE has been developed by a consortium of institutes led by Cardiff University (UK)and including Univ. Lethbridge (Canada); NAOC (China); CEA, LAM (France); IFSI, Univ.ixUwknowlyxgymyntsPadua (Italy); IAC (Spain); Stockholm Observatory (Sweden); Imperial College London, RAL,UCL-MSSL, UKATC, Univ. Sussex (UK); and Caltech, JPL, NHSC, Univ. Colorado (USA).This development has been supported by national funding agencies: CSA (Canada); NAOC(China); CEA, CNES, CNRS (France); ASI (Italy); MCINN (Spain); SNSB (Sweden); STFC,UKSA (UK); and NASA (USA).PACS has been developed by a consortium of institutes led by MPE (Germany) and in-cluding UVIE (Austria); KU Leuven, CSL, IMEC (Belgium); CEA, LAM (France); MPIA(Germany); INAF-IFSI/OAA/OAP/OAT,LENS, SISSA (Italy); IAC (Spain). This development has been supported by the funding agen-cies BMVIT (Austria), ESA-PRODEX (Belgium), CEA/ CNES (France), DLR (Germany),ASI/INAF (Italy), and CICYT/MCYT (Spain).This research has made use of data from the HerMES project (hggc-//, a Herschel Key Programme utilising Guaranteed Time from the SPIRE instrument team,ESAC scientists and a mission scientist.The HerMES data were accessed through the HeDaM database (hggc-//hedam.bamc.fe)operated by CeSAM and hosted by the Laboratoired’Astrophysique de Marseille.Based on observations made with the NASA/ESA Hubble Space Telescope, obtained fromthe data archive at the Space Telescope Institute. STScI is operated by the association ofUniversities for Research in Astronomy, Inc. under the NASA contract NAS 5-26555.This work is based [in part] on observations made with the Spitzer Space Telescope, which isoperated by the Jet Propulsion Laboratory, California Institute of Technology under a contractwith NASA. Support for this work was provided by NASA.The Dark Cosmology Centre is funded by the Danish National Research Council.xChvpter FIntroyuxtionUnderstanding the star-formation history of the Universe is an appealing subject that hasgathered a lot of attention (see Fig. 1.1, e.g. Madau et al., 1996; Sanders et al., 2003; Takeuchiet al., 2003; Wyder et al., 2005; Schiminovich et al., 2005; Dahlen et al., 2007; Reddy andSteidel, 2009; Robotham and Driver, 2011; Magnelli et al., 2011; Bouwens et al., 2012; Cucciatiet al., 2012; Magnelli et al., 2013; Gruppioni et al., 2013; Schenker et al., 2013; Madau andDickinson, 2014). At the time of the Big Bang, we started with precisely zero stars, but as theUniverse expanded and cooled, over-dense regions began to collapse due to gravity, and at somepoint the Universe formed its very first star. From that point in time, the co-moving (where agiven volume encloses the same region of space, but expands with redshift due to the expansionof the universe) Star Formation Rate (SFR) density of the Universe increased until it peakedwhen the Universe was roughly 2 to 5 billion years old. The co-moving SFR density has sincebeen on the decline. The evolution of SFR density is important in astronomy and cosmology,because it is directly related to structure and galaxy formation/growth. Specifically, it shouldbe reproducible by cosmological models and/or simulations, although it does require accuratemodelling of complex physical processes important for baryons within dark matter halos, suchas the effects of stellar feedback, active galactic nuclei (AGN), supernovae and galaxy mergers.The first accurate measurements of the co-moving SFR density of the Universe were per-formed by measuring the amount of ultra-violet (UV) radiation emitted by galaxies (Lilly et al.,1996). These wavelengths of radiation are primarily emitted from galaxies by hot young massivestars. The lifetime of such stars is relatively short lived, thus if large amounts UV radiation areseen being emitted from a galaxy, one can infer that the galaxy is forming many stars. Massivestars make up a minority of stars being formed, and thus one must extrapolate to lower massesto find a total SFR, using what is known of the initial mass function of stars (e.g. Salpeter,1955). Once a galaxy stops rapidly forming stars, the hot massive stars present will quickly gosupernova, and the galaxy will stop emitting large amounts of UV radiation in a few tens ofmillions of years.The challenge of observing UV radiation is that it is absorbed by intervening dust (e.g.Whitford, 1958). This process is named “reddening” or “extinction” and can be modelled usingmulti-wavelength data (e.g. Fitzpatrick, 1999). However, in the early Universe, it is possiblethat the star-formation within a galaxy is almost completely enshrouded in dust, and will bemissed entirely in optical studies. This makes it particularly difficult to accurately measure theco-moving SFR density at redshifts greater than about 1 (Sanders and Mirabel, 1996; Hugheset al., 1998; Steidel et al., 1999).Another method to measure SFR is to observe in the far-infrared (far-IR). Ignoring thepossibility of AGN, the energy emitted by a galaxy can be crudely divided into two categories:electro-magnetic (EM) radiation emitted by stars between wavelengths around 0.1 and 8m;and EM radiation emitted by dust between around 8 and 1000m. Dust is ubiquitous in theinterstellar medium (ISM) and readily absorbs the shorter EM radiation of stars, re-emitting itat longer wavelengths. Young, hot, massive stars of a galaxy undergoing rapid star-formationwill heat the dust within the galaxy and be re-emitted at far-infrared (far-IR) wavelengths, and1Chuptyr EB Introxuwtion0 2 4 6 8Redshift0.010.1C o- Mo vi ng  S FR  De ns i ty  ( Ms olyr- 1Mp c-3 )9ighee 1.1- Co-moving SFR density history of the Universe as compiled by Madau and Dickinson(2014). A peak in SFR density is seen at z ∼ 2, although measurements at higher redshifts are highlyuncertain and subject to poorly understood systematic effects.thus the luminosity between wavelengths of 8 and 1000m will be roughly proportional to theSFR of a galaxy (see review by Kennicutt, 1998). Because dust in the ISM is optically thin atthese wavelengths, measurements of the SFR of a galaxy with this method is not affected byextinction.In the earliest studies with targeted follow-up of known sources in the near-IR, it was foundthat the far-IR luminosity of some galaxies could match or exceed the energy output in theoptical (Low and Kleinmann, 1968; Kleinmann and Low, 1970a,b). The first blind all-skysurvey in the far-IR was performed by the Infrared Astronomical Satellite (IfUg, Soifer et al.,1984, 1987) and uncovered hundreds of previously unknown galaxies in the nearby Universe.This satellite was able to observe at wavelengths as long as 100m, which were previously notpossible, since from the ground, Earth’s atmospheres absorbs the majority of photons at thesewavelengths. It was found that for many of these galaxies, labeled as “starburts” or “ultra-luminous infrared galaxies” (ULIRGs), the energy emitted in the far-IR far exceeded that ofthe shorter wavelengths and were missed in optical surveys.Because the far-IR emission from a galaxy is dominated by the thermal emission of dustin the ISM, one can approximately model the far-IR spectral energy distribution (SED) of agalaxy by a modified blackbody of the formh(,P idP D) ∝ ,EPHFD2[exp(h,kBid)− 1]−NP (1.1)where h is the flux density, , is the observed frequency,  is the dust emissivity index, id isthe dust temperature, and D is the distance to the source. Fig. 1.2 shows examples of modifiedblackbody spectra, although also including the effects of redshift, as described below. This SEDshape adds just one extra term to the simple Planck distribution that describes thermal emissionof a blackbody, namely dust emissivity, . This dust emissivity is in fact a dust emissivityindex (where emissivity ∝ [,=,0]), although it is referred to colloquially in literature as thedust emissivity. This parameter, , is phenomenological, rather than physically-motivated, and2Chuptyr EB Introxuwtionis used to parameterise the effects resulting from the size distribution of dust grains, the opticaldepth of the dust at different frequencies, and actual temperature variations within the emittingregions (Draine and Lee, 1984). Typical values for dust emissivity range from 1.5 to 2. Like thedust emissivity, the dust temperature should not really be regarded as a physical parameter.Actual dust temperatures vary across galaxies depending on proximity to the galaxy centre andstar-forming regions, and the temperature of individual grains can vary dramatically with time,thus the dust temperature here should be thought of as a phenomenological parameter withthe units of Kelvin. Dust temperatures of around 35K are typical for the star-forming galaxiesthat we will consider in this work (e.g. Chapin et al., 2009; Symeonidis et al., 2013; Swinbanket al., 2014; MacKenzie et al., 2014).For distant galaxies, one must also consider the redshift of a source. This is the effect causedby space expanding and stretching the wavelength of photons, obs = (1+z)em, thus, reducingtheir energy. The consequence of redshift is such that at a redshift of z, each dimension of spacebecomes 1=(1 + z) times as big as it is today (we are at a redshift of 0). When consideringredshift, the modified blackbody becomesh(,P idP DiP z) ∝ [,(1 + z)]EPHFD2i[exp(h,(1 + z)kBid)− 1]−NP (1.2)where z is the redshift, and Di is now the “luminosity distance” (Peebles and Harrison, 1994),defined asDi = (1 + z)cH0∫ z0dz′√Ωm(1 + z′)P +Ωh(1 + z′)2 +Ω: (1.3)Here c is the speed of light, H0 is the Hubble constant, and Ωm, Ωh, and Ω are cosmologicalparameters denoting the relative densities in matter, curvature, and the cosmological constant,respectively.For a dust temperature of 35K and a dust emissivity of 1.5, our modified blackbody SEDpeaks in flux density at 92m. Beyond this wavelength, the SED falls off and enters what isknown as the “Rayleigh-Jeans” side of the SED. In this region, modified blackbodies becomenearly pure power laws. Observing at wavelengths on the Rayleigh-Jeans side is difficult becauseof atmospheric absorption in the submillimtre regime. However, the next atmospheric windowin this regime to make a significant impact in astronomy is at 850m, particularly with theSubmillimeter Common User Bolometer Array (SCUBA, Holland et al., 1999) on the JamesClerk Maxwell Telescope in Hawaii. At this wavelength, the flux density of a source is nearlyinvariant from a redshift of around 1 to 8. This is because as we go to higher redshifts, weare observing an intrinsically brighter part of the object’s SED, thus countering the effect ofthe object becoming dimmer due to distance and redshift, and is shown in Fig. 1.2. The firstdeep blind survey with this instrument was of the Hubble Deep Field (HDF) by Barger et al.(1999). They found a total of five sources, with four of them at redshifts above 2. Theirfindings showed for the first time that the SFR density at z S 2 are perhaps a factor of 5higher than previously thought from optical-based measurements. Many similar blind surveyshave since followed, with greater depths and wider fields of view (e.g. Barger et al., 1999;Eales et al., 1999; Scott et al., 2002; Cowie et al., 2002; Borys et al., 2003; Coppin et al.,2006). There are now several telescopes/instruments operating (or operated) at or near thiswavelength, including the Large Apex BOlometer CAmera (LABOCA, Siringo et al., 2009)3Chuptyr EB Introxuwtion9ighee 1.2- The SED of a modified blackbody with a dust temperature of 35K, dust emissivity of1.5, and a far-IR luminosity of 1013 L⊙, plotted for different redshifts. The transmission bands of bothHyrswhyl SPIRE and SCUBA-2 at 850m are represented by the shaded areas. Observing at 850mhas the advantage that a source’s flux density is nearly invariant with redshift.on the Atacama Pathfinder Experiment (APEX), AzTEC which was on the JCMT then theAtacama Submillimeter Telescope Experiment (ASTE, Ezawa et al., 2004), the Max-PlanckBolometer array (Kreysa et al., 1998) on the Institut de Radioastronomie Millimtrique (IRAM)telescope, and Bolocam (Glenn et al., 1998) on the Caltech Submillimeter Observatory (CSO).At shorter wavelengths, SCUBA also the exploited 450m atmospheric window, while thesecond-generation Submillimeter High Angular Resolution Camera (SHARC-2, Dowell et al.,2003) observed the sky at 350m (Kova´cs et al., 2006). The Balloon-borne Large ApertureSubmillimeter Telescope (BLAST, Pascale et al., 2008) additionally observed at 250, 350 and500m (e.g. Patanchon et al., 2009).The latest single-dish instruments/observatories, and some of the primary instruments usedin this work, include SCUBA-2 (Holland et al., 2013) on the JCMT, observing at 450 and850m, and the Hyrswhyl gpuwy cvsyrvutory (Pilbratt et al., 2010a). Hyrswhyl housed twophotometric instruments. One was was Spectral and Photometric Imaging Receiver (SPIREGriffin et al., 2010), observing at 250, 350 and 500m, and was essentially identical to thecamera used in BLAST. The other was the Photodetector Array Camera and Spectrometer(PACS, Poglitsch et al., 2010), observing at 70, 100 and 160m.One of the biggest challenges of observing in the submillimetre (submm) band is the res-olution of these single-dish instruments, which typically have a full width at half maximum(FWHM) of 15 arcseconds or more. Within such large beams there are typically dozens ofdistant galaxies, making source identification difficult. If a field is observed for long enough,every pixel in the image will contain more signal than noise, but be comprised of many sourcesall blended together. In this scenario, only the brightest sources stand out and the uncer-tainty in measuring the flux density of any individual source is dominated by the high density4Chuptyr EB Introxuwtion9ighee 1.3- An example of confusion limited Hyrswhyl SPIRE confusion imaging at 250m, 350mand 500m. The location of known infrared and radio sources are denoted by white dots. In order tofit an SED to any of the known sources, one must devise a method that addresses the confused natureof the data.of fainter sources blended together in the same region. This source of error is called “con-fusion noise”(e.g. Scheuer, 1957) and an example of such data are shown in Fig. 1.3. Evenbright submm sources have often been found to be comprised of multiple fainter sources whenfollowed-up with higher-resolution telescopes (e.g. Hodge et al., 2013), such as the AtacamaLarge Millimeter/submillimeter Array (ALMA). This problem of insufficient resolution is notunique to submm astronomy, and many methods have been developed to mitigate this problem.Using higher-resolution imaging at different wavelengths to identify contributing sources, fluxdensities for these sources can be “deblended” (e.g. Makovoz and Marleau, 2005; Roseboomet al., 2010; Elbaz et al., 2011a; Swinbank et al., 2014). However, this deblending of flux densi-ties eliminates important degeneracies with neighbouring sources. Furthermore, each wavebandis deblended independently, but confusion noise correlates both neighbouring pixels and neigh-bouring wavelengths, thus proper treatment of residuals while deblending is not trivial (seePatanchon et al., 2009; Vernstrom et al., 2014).In practice, to try to determine the properties of a submm galaxy, one combines data atseveral different wavelengths. Once all this multi-wavelength photometry is compiled and aredshift estimate obtained (perhaps from spectroscopy), it is possible to move forward to fittinga model SED. The modified blackbody given above is a popular choice, due to its simplicityand accuracy in describing the generally coarse wavelength coverage of the data. In order tomake a modified blackbody more luminous, one must either increase the dust temperature oradd more mass to the dust. For many galaxies, in practice the answer appears to be a mixtureof both possibilities and the result has been named the “a–id” relation (e.g. Chapman et al.,2005; Magnelli et al., 2012; Casey, 2012; Symeonidis et al., 2013). The relationship has beenfound to evolve with redshift, but this claim has been disputed and could instead be attributedto selection effects (e.g. Chapin et al., 2009, 2011; Casey, 2012; Swinbank et al., 2014). Inaddition, the driving force behind the high SFR in such galaxies is debated. In some cases, itappears that galaxy-galaxy mergers trigger star-formation (Sanders and Mirabel, 1996), whileother studies have suggested that the majority are simply the bright end of a galaxy “main-sequence” (Noeske et al., 2007; Daddi et al., 2007; Elbaz et al., 2011b). Again, when fitting a5Chuptyr EB Introxuwtionmodel SED, it is traditionally fitted to flux densities extracted from imaging. If these images areconfusion limited, the process of deblending flux densities will eliminate important degeneracieswith neighbouring sources, and potentially lead to biased results.Here, we have developed new methods to fit SEDs using both high-resolution imaging andconfusion limited imaging. Our method does not rely on the traditional two-step procedure ofdeblending/extracting flux densities then fitting your model, but instead combines these twotasks into one process. By doing so, we retain a statistical description of important degen-eracies in fit parameters among neighbouring confused sources, and this allows us to performa significantly improved analysis of available data. We originally developed this method touncover and disentangle the submm emission from an interacting z ≃ 2:9 galaxy group that ismultiply lensed by the massive MS0451.6−0305 foreground cluster as described in Chapter 2.In Chapter 3, we adapt the same method to study the far-IR properties of submm galaxiesfollowed-up with ALMA, often resolving sources into multiple contributing galaxies, and im-proving upon the work done by Swinbank et al. (2014). In Chapter 4 we use the same method asin Chapter 3 to analyse SCUBA-2 and Hyrswhyl SPIRE follow-up observations of dlunwk high-zcandidates, comprised of strong gravitational lenses, potential proto-clusters and line-of-sightover-densities.6Chvpter 2Disentvngling v lensey group ofgvlvxies vt zR2CN owservey fiithhCUBVB22CF IntroyuxtionGravitational lensing has been a useful tool for enabling submm studies. The first resultsfrom the SCUBA submm camera on the James Clerk Maxwell Telescope (JCMT) (e.g. Smailet al., 1997) used “nature’s telescope” to increase the detection rate of high-redshift submmsources and effectively beat the confusion limit for single dish studies. Now Hyrswhyl (Pilbrattet al., 2010b) has found that lensing is significant for some of the brightest submm sources,with surveys such as H-ATLAS and HerMES turning up a population of sources that areboosted enough that they can be studied in great detail in follow-up observations (e.g. Negrelloet al., 2010a; Wardlow et al., 2013). However, the limited resolution of Hyrswhyl, and of non-interferometric ground-based observatories such as the JCMT, means that the effects of sourceblending are a cause of uncertainty in interpreting the results (e.g. Wang et al., 2011; Karimet al., 2013; Hodge et al., 2013), made more difficult in practice, since submm-bright sourcesare known to be typically merging or interacting systems, where disentangling the contributionto the combined spectral energy distribution (SED) is more complicated still. Even worse –while lensing is nominally achromatic, strong lensing of inhomogeneous extended sources withinfinite beams is not achromatic, since unresolved regions with different spectral properties canbe lensed by different amounts. Thus the existence of strong lensing can be a double-edgedsword, boosting the brightness of some sources, but making the detailed interpretation of theirspectral energy distributions (SEDs) problematic (Serjeant, 2012). Multi-wavelength studiesare key to understanding these complex systems.MS 0451.6−0305, a massive galaxy cluster at a redshift of 0.55, is lensing several backgroundsources and has been imaged at many different wavelengths: X-ray (Donahue et al., 2003b);optical (Gioia and Luppino, 1994; Takata et al., 2003; Kodama et al., 2005; Moran et al., 2007;Zitrin et al., 2011); near-IR (Borys et al., 2004; Wardlow et al., 2010); mid-IR (Geach et al.,2006); far-infrared (far-IR) (Oliver et al., 2012); mm/submm (Chapman et al., 2002a; Boryset al., 2004; Wardlow et al., 2010); and radio (Reese et al., 2000; Berciano Alba et al., 2010).In the optical, the previously discovered multiply-imaged sources include an extended opticalarc composed of a Lyman-Break Galaxy (LBG) with a spectroscopic redshift of z = 2:911, aswell as two extremely red objects (EROs) with a redshift of z = 2:9 ± 0:1, determined fromlensing models (Borys et al., 2004; Berciano Alba et al., 2010). The two EROs and the LBGare so close in separation (∼10 kpc in projection) that they potentially constitute an interactingsystem. A fourth multiply imaged galaxy was discovered by Zitrin et al. (2011).The steep number counts in the submm make lensing much more striking in this wavebandthan the optical – at 850m the SCUBA map of the cluster core showed a “giant submm arc,”7FBEB Introxuwtion9ighee 2.1- hop lyzt: Hgh WFC3 colour-composite (red: 1.6m / H band, green: 1.6 + 1.1m / H+ J bands, blue: 1.1m / J band), clearly showing the main optical arc (roughly vertical, at aboutRA=4h54m12:9h), offset slightly from the abundance of red images along the submm arc. The contrasthas been stretched to highlight the faint arcs and multiply imaged galaxies. hop right: Hgh image (1.6+ 1.1m / H + J bands) with the positions of the multiply-imaged galaxies labelled numerically from1 through 7, with sub-groups of images labelled as u, v and w. The galaxy discovered by Zitrin et al.(2011) is labelled as Galaxy 1 and the two EROs and the LBG discovered by Borys et al. (2004) arelabelled Galaxy 5, 6, and 7, respectively. The red contour denotes the critical line of the lensing modelfor a redshift of z = 2:911, while the black contours represent the SCUBA-2 850m emission. Galaxy8 is a singly imaged source with colours similar to those of the other multiply-imaged galaxies and hasbeen found to be important when trying to reproduce the morphology of the submm arc. Galaxy 9 isa foreground galaxy at a redshift of z = 0:157. Vottom: The “giant submm arc” as seen by HyrswhylPACS and SPIRE and SCUBA-2 over more than a factor of five in wavelength range. The red circlesplotted on the shortest and longest wavelength images mark the positions of the galaxies depicted inthe top right panel. It is obvious that this string of multiply imaged z ∼ 2:9 galaxy group sources areresponsible for generating the majority of the submm arc. However, they are too spatially confused fortraditional deblending techniques.8FBFB HST unx thy lynsing moxylby far the brightest feature in this region of the sky, with an extent of around 1 arcminute,consistent with the blending of multiple galaxy images which lie near the critical line in thelensing model. If the optical galaxies are indeed interacting, the submm arc could be attributedto triggered star formation within one or more of these galaxies. This scenario is also supportedby the radio data, as discussed in Berciano Alba et al. (2010).New observations presented here using the Wide Field Camera 3 (WFC3) on Hgh, SCUBA-2 on the JCMT, and PACS and SPIRE on HyrswhylN, shed new light on what is generating thesubmm arc. With the deeper Hgh images and a new Leaftool (Kneib et al., 1996; Jullo et al.,2007; Jullo and Kneib, 2009) lensing model, there are now syvyn known multiply-imaged galaxies(including the previously known four) in the region of the submm arc. Six of these multiply-imaged galaxies are consistent with a redshift of z ∼ 2:9 and probably constitute an interactinggalaxy group. To properly analyse the submm imaging of SCUBA-2 and Hyrswhyl, we havedeveloped a new approach to disentangle the confused components generating the submm arc,which fully exploits the multiply-imaged and differentially-magnified nature of the system, andallows us to directly estimate both the dust temperature, id, and the far-infrared luminosity,aIo, (and thus star formation rate, SFR) for each of the contributing galaxies. This allows usto investigate the id versus aIo relation for intrinsically less luminous galaxies at high-z thantraditional blank field surveys. Possible evolution of this relation with redshift allows us toprobe the properties of star formation in the early Universe (e.g. Chapman et al., 2002b, 2005;Pope et al., 2006; Kova´cs et al., 2006; Chapin et al., 2011; Symeonidis et al., 2013; Swinbanket al., 2014; Sklias et al., 2014; Smail et al., 2014). Our method significantly improves upon theconventional method of extracting sources, or smoothing and binning multi-wavelength data tothe worst resolution, before fitting SEDs (a process that destroys useful information).This Chapter is organised as follows. In Section 2.2 we introduce the Hgh optical data andthe lensing model. In Section 2.3.1 we present the SCUBA-2 data and in Chapter 2.3.2 theHyrswhyl data. In Section 2.4.1 we present the SED model and image reconstruction methodsand in Section 2.4.2 the model fitting procedure. Section 2.5.1 discusses the results and Section 5finishes with the conclusions. Throughout we employ a ΛCDM cosmology with Ω = 0:7,Ωm = 0:3, and H0 = 70 km s−NMpc−N. ΛCDM cosmology is the current leading cosmologicalmodel used to describe the expansion history of the Universe, given the current rate of expansionand density of the components that fill the Universe (matter, photons and dark energy).2C2 HST vny the lensing moyelAlthough the main motivation for our study comes from the new submm data, it makes themost scientific sense to first describe the optical data. We retrieved previously unpublishedobservations using WFC3 on Hgh from the Canadian Astronomical Data Centre (program11591, PI: Jean-Paul Kneib). The observations were taken at 1.1 and 1.6m (J and H bands,respectively) with 2400 and 2600 second exposures, respectively. A small pointing shift in thedata, with respect to Hgh data published by Borys et al. (2004) and Berciano Alba et al.(2010), was corrected by aligning to the older Hgh data in this field. These observations reveala host of new red objects in the region of the submm arc (Fig. 2.1).Leaftool (Kneib et al., 1996; Jullo et al., 2007; Jullo and Kneib, 2009) is a software pack-age used to model gravitational lensing of sources behind massive galaxy clusters. The methodinvolves modelling the gravitational effects of the most massive components of the intervening1Herschel if aa ESA fcace bbfeeiagbel wigh fcieace iafgehmeagf cebiided bl Ehebceaa-led Peiacical Iaiefgi-gagbe cbafbegia aad wigh imcbegaag caegicicagiba febm AASA.9FBFB HST unx thy lynsing moxyl9ighee 2.2- Hgh cut-outs at the locations of the seven multiply imaged galaxies listed in Table 2.1 witheach column displaying the multiple images of a single galaxy. The letters refer to the three sub-groupsof images labelled in Fig. 2.1. Image 4.b is not shown because it is obscured by foreground galaxies. Weshow a one arcsecond scale bar for all panels in the centre of the figure.galaxy cluster (the encompassing cluster sized dark matter halo and the most massive galaxysized halos) to predict the paths of photons of the background lensed sources into the imageplane. The redshifts, positions, magnitudes and shapes of the multiply imaged lensed back-ground sources are used to constrain the lensing model parameters. Using Leaftool and a newlensing model for the cluster, we were able to identify thryy new multiply-imaged galaxies withinthe Hgh images in the region of the submm arc. Table 2.1 lists the positions, amplificationsfactors, and redshift estimates derived from our model for of each of the seven multiply-imagedgalaxies within the region of the submm arc. Fig. 2.1 shows the close positional arrangement ofthe multiple images with respect to the “giant submm arc” and the available submm data. En-larged cut-outs of the multiply imaged galaxies are shown in Fig. 2.2. Borys et al. (2004) havealready suggested that Galaxies 5, 6 and 7 are likely to be an interacting group at z ∼ 2:9. Ournew model supports their analysis and adds Galaxies 2, 3, and 4 to the same group, expandingit to a group of at least six galaxies at z ∼ 2:9. Galaxy 1 is found to have a slightly higherredshift of z = 3:11 ± 0:03 derived from the lensing model, and thus is not likely associatedwith the interacting group.Galaxy 8 is not multiply imaged, but has similar colours to the rest of the multiply-imagedgalaxies and has a disturbed morphology. If it is at the same redshift as the interacting group,our lensing model predicts no multiple images, consistent with the observations but yieldingno additional constraints on its redshift from the lensing model. However, we have found thatsubmm emission originating from near its position is important for reproducing the morphologyof the submm arc (see Section 2.5.1), and thus we have included it in our model (see Section 2.4).Galaxy 9 is a foreground galaxy at z = 0:157 and has associated Multiband Imaging Photometerfor Spitzer (MIPS) 24m (not described here) and PACS emission (see Section 2.3.2), thus itis also included in our model as a possible source of submm emission.The lensing model consists of a cluster-sized dark matter halo, followed by 68 smaller masshalos to represent the most massive of the cluster galaxies. The parameters of the lensingmodel, such as the dark matter halo and galaxy masses, are constrained by the positions,relative magnitudes, ellipticities, and angles on the sky of the multiply imaged backgroundsources. A total of 12 multiply imaged sources are known for this cluster, all of which aretriply imaged, except for one source which is imaged five times with a confirmed spectroscopic10FB3B byw suvmm imugingredshift S 4. The model is fit using a Monte Carlo Markov chain (MCMC) method (Metropoliset al., 1953; Hastings, 1970), and is therefore able to provide uncertainties in the redshift andmagnification estimates. The uncertainties provided do not include sources of error, such as anincomplete lensing model. More details concerning the Leaftool modelling will be presentedin a forthcoming paper by Kneib & Richard (in prep.).For our purposes, we are only interested in the redshift and magnification estimates providedby the lensing model. Along with the positions of the multiple images from the Hgh images,these will provide the backbone of the modelling described below. Because the uncertaintiesin redshift and magnification are small, we treat these values as fixed in order to reduce thecomplexity of the modelling described below. This does not significantly affect our resultsbecause our main source of uncertainty is the relatively low-resolution of the submm data andthe confused nature of the Hyrswhyl-SPIRE imaging. However, we are vulnerable to the possibleexistence of fainter sources not detected in the Hgh imaging that may be contributing the thesubmm-arc, as was the case in Borys et al. (2004). Because we are able to reproduce thesubmm-arc as seen across all the available submm wavelengths with a high degree of fidelity(see Section 2.5.1), we do not believe we are missing any such missing component.It is apparent that the nature of the submm arc is significantly more complicated thanpreviously thought and is likely a combination of several of the galaxies described above.2C3 cefi suwmm imvging2C3CF hCUBVB2The cluster was observed with SCUBA-2 (Holland et al., 2013) on the JCMT during commis-sioning, as part of “Guaranteed Time” for the instrument team. A total of 12.7 hours in grade2 weather between February of 2010 and February of 2012 achieved an rms error of 15mJy perbeam at 450m using 2 arcsecond pixels and 1.2mJy per beam at 850m using 4 arcsecondpixels. Since the submm arc had already been observed at 850m using SCUBA (Borys et al.,2004), the motivations for the new observations were: (1) to confirm the bright lensed structurewith SCUBA-2, without the complications introduced by SCUBA’s requirement to chop (Boryset al., 2004); and (2) to detect the lensed structure at 450m, at a resolution better by about afactor of two, with the hope of resolving the submm arc into individual sources. The data werereduced using a configuration file optimized for blank fields using the fmhef data reductionsoftware for SCUBA-2 (Chapin et al., 2013).At 850m, the submm arc is detected at high signal-to-noise by SCUBA-2 (see Fig. 2.1).Its brightest part is elongated roughly north-south, and at the southern end curves to thewest, just as in the original SCUBA image. The higher-resolution 450m data trace a largelysimilar structure, but at a lower relative sensitivity, with a signal-to-noise ratio of about 3 aftersmoothing with the beam, for the brightest portion of the lensed emission. The SCUBA-2 dataare constrained by both resolution at 850m and sensitivity at 450m, and thus only limitedconclusions can be obtained from these two channels alone. Fig. 2.1 shows the SCUBA-2 dataalongside the Hyrswhyl SPIRE and PACS images for comparison, while Fig. 2.1 shows smoothed850m contours plotted over the Hgh imaging.2C3C2 HerschelConfusion-limited images of MS 0451.6−0305 using Hyrswhyl SPIRE (Griffin et al., 2010; Swin-yard et al., 2010) were taken as part of the guaranteed time program HerMES (the Hyrswhyl11FB4B U frumywork for tting gEDs to wonfusyx wountyrpurtsMulti-tiered Extragalactic Survey, Oliver et al., 2012). The cluster was imaged at the threeSPIRE wavelengths of 250, 350 and 500m with FWHM beam sizes of 18.1, 24.9 and 36.2arcseconds, respectively (Griffin et al., 2010). A total of 18.3 hours of observation reached anrms of 1.5, 1.5 and 1.7mJy per beam at 250, 350 and 500m, respectively, with pixel sizes of6, 8.3, 12 arcseconds. A detailed description of the map-making procedure is given in Levensonet al. (2010), and the most recent updated method described in Viero et al. (2013). To ensureaccurate astrometry, we have stacked on the positions of over 900 gpitzyr MIPS 24m sourcesthat overlap with the field and have corrected a 1.3 arcsecond shift in RA and 0.4 arcsecondshift in Dec. The uncertainty in this correction is 0.2 arcseconds, calculated by bootstrappingthe 24m source list.Two PACS (Poglitsch et al., 2010) observations taken as part of the PACS EvolutionaryProbe key program (Lutz et al., 2011) are also available and were processed using the “mul-tiple obsid scanMapDeepSurvey” pipeline within hice 10 (Ott, 2010). The default units wereconverted from Jy pixel−N to Jy beam−N by multiplying by the beam area and dividing by thepixel area. The beam area for the 160m point spread function (PSF) was found to be 180arcsecond2 and was computed by integrating over the beam profile provided by the NASAHyrswhyl Science Center. A total of 5.2 hours of observation reached an rms of 2mJy per beamusing 3 arcsecond pixels. The FWHM at 160m is 11.6 arcseconds. For galaxies at z ∼ 3,70m PACS data are expected to be dominated by warm dust, which is not well reproducedby the simple SED model adopted in Section 2.4, and are therefore not used in this study.The submm arc is detected across all the available submm bands (see Fig. 2.1), but with thelarge number of multiply-imaged galaxies (seen in Fig. 2.1) that are strung along the submmarc, it is unclear which galaxies are contributing. The morphology of the submm arc seen ineach image is a function of both the telescope PSFs and the SEDs of the contributing galaxies.In addition to determining which galaxies are contributing, we would also like to constraintheir physical properties. With the lensing model well constrained by the Hgh observations(see Section 2.2) and this wealth of multi-wavelength data, it is clear that a comprehensivemodelling approach is required.2CI V frvmefiork for tting hEDs to xonfusey xounterpvrtsBoth Borys et al. (2004) and Berciano Alba et al. (2010) performed limited modelling of theoptical and radio counterparts, respectively, in an attempt to reproduce the observed submmarc. Their approach of smoothing different plausible components with the SCUBA 850mbeam showed that the LBG and two EROs are likely contributors, but neither could fullyreproduce the observed submm arc. With new SCUBA-2 and Hyrswhyl observations, we areable to expand on this approach and have developed a framework for fitting SEDs to theconfused optical counterparts, fully exploiting the strong gravitational lensing of this system.While source plane reconstruction of multiply-imaged galaxies is an effective approach forhigh-resolution imaging (e.g. Kochanek and Narayan, 1992; Colley et al., 1996), it fails in theconfused regime. Because the galaxies blend together in the submm, it is impractical to tracephotons back through the lensing potential and into the source plane, since much of the photonpositional information has been lost due to the large telescope beams. Instead, we use the high-resolution Hgh imaging to identify candidate counterparts to the submm galaxies in the optical,and use their positions as priors for the origin of any submm emission. We then forward-modelthe galaxy SEDs through the telescope filters, and use the amplification factors derived from thelensing model for each galaxy image, to reproduce the submm arc in each wavelength channel12FB4B U frumywork for tting gEDs to wonfusyx wountyrpurtsseparately. Essentially, we are fitting SEDs of galaxies directly to the data, without the needfor first deblending and extracting sources or smoothing and re-binning our data to the worstresolution (a process that destroys useful information).Our method is complementary to that employed by Fu et al. (2012), where they forward-model a single submm source through the gravitational lens, allowing the position to vary, toreproduce the observed morphology of their Submillimetre Array (SMA) and Very Large Array(VLA) observations. With their model, they were able to show that the source of the gas anddust emission was offset from the optical counterpart. However, the gravitational lensing inthis case is galaxy-galaxy lensing and the observations have much higher resolution than eitherthe SCUBA-2 or Hyrswhyl observations presented here. The gravitational lensing presentedhere is for a group of galaxies being lensed by a foreground cluster and thus the set of multipleimages subtends a much larger area on the sky than galaxy-galaxy lensing. The optical imagingprovides positions which are more than adequate for our purposes, since, with the resolutions ofSCUBA-2 and Hyrswhyl, any small offset of the submm emission from their optical counterpartswill not have a strong effect on the morphology of the submm arc; the strongest effect of anoffset would be seen in the relative amplifications of the multiple images. Our method is novelin that we reproduce the morphology of the submm emission across multiple wavelengths, whilesimultaneously fitting source SEDs, thus tying together the multi-wavelength data. These twocomplementary techniques (detailed source plane reconstruction and forward modelling SEDsat fixed source positions) could be combined in the future, given the proper observations.2CICF boyel hED vny imvge rexonstruxtionThe first ingredient we need is an SED model for our galaxies in the submm. For the longerwavelength channels of SCUBA-2 and Hyrswhyl SPIRE, the SED of a galaxy is well representedby a modified blackbody with a single temperature:h(,P id;iP ziP Xi) = Xi(,(1 + zi),0) (,(1 + zi))P [exp(h,(1 + zi)kBid;i)− 1]−NP (2.1)where h is the flux density, , is the observed frequency, ,0 = 1:2THz = c=(250m),  is the dustemissivity, id;i is the dust temperature, zi is the redshift, Xi is a normalization factor, and thesubscript i denotes the galaxy. We have virtually no constraining power on the dust emissivity,primarily due to the confused nature of the data, and we therefore fix it to a nominal value of1.5. Due to the high redshifts of our galaxies, the shorter wavelength channels of Hyrswhyl aredominated by hot dust and are better represented by a power law on the Wien side, i.e.,h(,P id;iP ziP Xi) ∝ ,−P (2.2)where the power law amplitude and the frequency at which to switch between the power lawand modified blackbody are chosen so that the transition is smooth (i.e. the two functions andtheir first derivative are continuous); such a model has been used by Pascale et al. (2009), forexample. For the same reason that we fix the value of the dust emissivity, we fix  to a nominalvalue of 2.0 as found by Casey (2012). We then propagate the individual galaxy SEDs througheach telescope bandpass filter:h¯b(id;iP ziP Xi) =∫h(,P id;iP ziP Xi)ib(,)d,∫ib(,)fb(,)d,P (2.3)13FB4B U frumywork for tting gEDs to wonfusyx wountyrpurtswhere h¯b is the galaxy flux density, as would be measured by the instrument for channel b, ib(,)is the transmission for channel b, and fb(,) is a calibration parameter. This calibration factorarises from the fact that bolometers respond to energy input and not flux density, and detailscan be found in Griffin et al. (2013). For Hyrswhyl, fb(,) = ,0=,, due to assuming a power lawSED shape for observed sources, where ,0 is equal to c=(160m), c=(250m), c=(350m), andc=(500m) for 160, 250, 350 and 500m, respectively. We assume a constant calibration factor,fb(,) = 1, for SCUBA-2, since the bandpass filters are relatively narrow and we are firmly onthe Rayleigh-Jeans side of the spectrum.Using the lensing model, the SCUBA-2 and Hyrswhyl images are reconstructed as follows:bb(x) =∑i∑jAijh¯b(id;iP ziP Xi)P,(x− rij) +Bb: (2.4)Here bb(x) is the flux at position x for frequency channel b, Aij is the amplification factorfor image j of Galaxy i derived from the lensing model, P,(x − rij) is the response function(i.e. the telescope beam), with rij denoting the position of image j of Galaxy i, and Bb is theimage background. We assume all sources can be accurately represented by point sources at thepositions of their optical counterparts. This assumption may be incorrect and tidal interactionsmay have created tails and bridges between the group members where the star formation isoccurring, although the fidelity of our more simplistic model in Fig. 2.5 suggests that a morecomplex model is not needed here.The response functions for the Hyrswhyl SPIRE channels are approximated as Gaussianswith FWHM of 18.1, 24.9 and 36.2 arcseconds at 250, 350 and 500m, respectively, and 11.6arcseconds at 160m for Hyrswhyl PACS. Due to the high-pass filtering of the SCUBA-2 data,we need to ensure that we have an accurate model of the effective response function, thuswe simulate point-sources, for the 450 and 850m data, respectively, within the fmhef data-reduction software, and approximate the effective response function by fitting double Gaussiansto their resulting shapes. The result for the 450m response function is a Gaussian with FWHMof 6.86 arcseconds and an amplitude of 0.893, plus a second Gaussian with FWHM of 34.6arcseconds and amplitude of −0.015. The result for the 850m response function is a Gaussianwith FWHM of 13.9 arcseconds and a amplitude of 0.869, plus a second Gaussian with FWHMof 25.9 arcseconds and amplitude of −0.077.2CIC2 boyel ttingThe SED model adopted is non-linear and due to the confused nature of this system, we expectthere to be some degeneracies between fit parameters. To obtain uncertainties for each fitparameter, determine the degeneracies between them, and efficiently explore the large parameterspace required, the model is fit to the data using an MCMC Metropolis-Hastings algorithm(Metropolis et al., 1953; Hastings, 1970) with Gibbs sampling (Geman and Geman, 1993, whereonly one model parameter is varied per MCMC chain point instead of all parameters,). Thismethod has become widely used in Astronomy, especially for fitting cosmological parameters(Lewis and Bridle, 2002). The method requires a likelihood function to be defined to whichthe model is fit. Since the SCUBA-2 450 and 850m and PACS 160m data are limited byinstrumental noise, the log likelihood functions for these data are calculated as follows:− logab = Xb +∑k(Db(xk)−bb(xk)=cb)222b;kP (2.5)14FB4B U frumywork for tting gEDs to wonfusyx wountyrpurtswhere subscript b denotes the band, Db(xk) are the data, xk denotes the position of pixel kin the image, 2b;k is the instrumental noise for pixel k, cb is the instrument calibration factor(with a mean value of unity), and Xb is a constant.The log likelihood function for the Hyrswhyl SPIRE data is more complicated, since we arelimited by extragalactic confusion noise as opposed to instrumental noise. The confusion limitin each channel is 5.8, 6.3 and 6.8mJy at 250, 350 and 500m, respectively (Nguyen et al.,2010). In short, we cannot determine the flux density of a given source to greater accuracythan these confusion limits without using additional information from another sources (suchas a prior position catalogue of all the sources within the field or flux density estimates fromanother telescope at a comparable wavelength). This means that the residuals after subtractingthe model will be: (i) much larger than instrumental noise; (ii) correlated spatially with thebeam; and (iii) correlated across wavelengths. This is because confusion noise is real signalgenerated from many faint sources that are all blending together to produce an unknown andcorrelated variable background. Taking confusion into account, the log likelihood function forthe Hyrswhyl SPIRE data is therefore− logapmIob = XpmIob + 12RTC−NRP (2.6)where R is a one-dimensional list of the residuals, and contains all three channels of SPIREdata (R = {D2R0(xk)−b2R0(xk)=c2R0P DPR0(xk)−bPR0(xk)=cPR0P DR00(xk) −bR00(xk)=cR00}), and C−N is the inverse covariance matrix for theresiduals. The covariance matrix, C, is estimated using the GOODS-North HerMES field, alsoobserved with Hyrswhyl SPIRE. This is the largest blank Hyrswhyl field with instrumental noisesimilar to that of the MS0451.6−0305 data, and has an area of 0.1 deg2. To estimate thecovariance matrix, we extract cut-outs from the GOODS-North field, with the same dimensionsas the MS0451.6−0305 data, and calculate the covariance between all the pixels. We then aver-age the covariance matrices of each set of cut-outs to obtain an estimate of the true covariancematrix, ignoring regions with standard deviations greater than twice the confusion limit in anychannel to avoid regions with significantly bright sources. One could smooth the covariancematrix using the assumption that the sky is homogeneous and isotropic, but this may lead tosingular matrices. Any standard method to invert the matrix may be used here. The total loglikelihood is thenlogatotal = logaUR0 + loga4R0 + logapmIob + logaNS0: (2.7)This however assumes that the confusion noise on the sky is Gaussian and does not account forthe possibility that the sky may hold non-Gaussian bright objects in our field of view, conspiringagainst our efforts to disentangle this galaxy group.Flux calibration uncertainties, cb, are taken into account during the fitting procedure bysetting priors on cb for each band. The flux calibrations of the 160, 450 and 850m data are5%, 2.5% and 5%, respectively (Muller et al., 2011; Dempsey et al., 2013). SPIRE wavebandcalibrations are correlated, with a covariance matrixX =0:001825 0:0016 0:00160:0016 0:001825 0:00160:0016 0:0016 0:001825 P (2.8)15FBIB fysults unx xiswussionwhere the calibration is normalised to unity (Bendo et al., 2013, 4% correlated uncertaintybetween bands plus 1.5% uncorrelated between bands). The calibration uncertainties are asmall effect when compared to the instrumental and confusion noise within the observations.We set no prior (or a flat prior) on the amplitude of the modified blackbodies or eachunknown image background. A hard prior, i S 10K, is motivated by the fact that neitherDale et al. (2012) nor Amblard et al. (2010) found any colder Hyrswhyl galaxies in either thenearby or distant Universe, respectively. While we have corrected the relative pointing ofHyrswhyl and Hgh, we are unable to find any significant pointing shift in the JCMT due to thelower signal-to-noise in the map than what is available in the Hyrswhyl SPIRE observations. Thenominal pointing accuracy is 1.5 arcseconds, and thus we include this as a prior and marginaliseover any possible pointing offset along with the image backgrounds.Table 2.1 lists the possible contributing galaxies in our model. This consists of the sevenmultiply-imaged galaxies, one singly-imaged red galaxy (Galaxy 8) with disturbed morphology,and one foreground galaxy (Galaxy 9) with associated MIPS 24m and PACS 160m emission.This brings the total to nine possible contributing galaxies. Their positions are derived fromthe Hgh data and their amplification factors are derived from the lensing model. The redshiftof Galaxy 8 is set to a nominal value of z = 2:9 and we report the lensed far-IR luminosity andSFR for this galaxy. Galaxy image positions, amplification factors and redshifts are held fixedduring the fitting procedure since their uncertainties are small.By assuming the UV radiation of hot young stars is completely absorbed and re-radiatedat longer wavelengths by intervening dust, as well as assuming an initial mass function anda starburst model, it is possible to estimate a rough conversion factor between bolometricluminosity and SFR (e.g. Lehnert and Heckman, 1996; Meurer et al., 1997; Kennicutt, 1998).Here, we convert far-IR luminosities, calculated by integrating the rest-frame SEDs from 8 to1000m, to SFRs using the relation estimated by Murphy et al. (2011):SFR = 1:49× 10−N0M⊙yr−NacIo=L⊙: (2.9)When reporting the uncertainties in our SFR values for each galaxy in our model, we consideronly the uncertainty in far-IR luminosity and do not include any uncertainty in this relation.2C5 gesults vny yisxussion2C5CF V xompvxt group of gvlvxies vt high reyshiftAll galaxies listed in Table 2.1 are included in our model and when fitted, we can clearly identifyGalaxies 2, 6, 7, 8, and 9 as the sources of submm emission generating the submm arc. Fig. 2.3shows the positional arrangement of the z ∼ 2:9 galaxy group in the source plane with squareshighlighting the galaxies responsible for generating the majority of the submm arc. Fig. 2.5shows the data, the best-fit model, and the residuals after subtracting the model from the data.Also included in the figure is a decomposition of the submm arc into the unique contributionsof each galaxy to the total best-fit model. Fig. 2.6 shows the MCMC likelihood contours fortemperature and far-IR luminosity for these five galaxies, and Table 2.2 lists the results alongwith SFRs and upper limits for Galaxies 1, 3, 4, and 5. It is apparent in the MCMC likelihoodcontours that there is a strong degeneracy between the far-IR luminosities of Galaxies 6 and 7.Fig. 2.6 shows a degeneracy between the luminosity of Galaxy 6 versus Galaxy 5 in ourmodel, due to their close proximity. While our model prefers emission from Galaxy 6, Berciano Alba16FBIB fysults unx xiswussion9ighee 2.3- Source plane arrangement of the z ∼ 2:9 group galaxies. Galaxies 2 through 7 are consistentwith being at this redshift. Galaxy 1 lies at a slightly higher redshift, while Galaxy 8 is assumed tobe part of the z ∼ 2:9 group. The galaxies found to be generating the majority of the submm arc arehighlighted with red backgrounds and scale with their measured far-IR luminosity. The galaxies arespread over no more than ∼ 100 kpc in projection, with many components separated by ∼ 10− 20 al. (2010) found that Galaxy 5 has associated radio emission, and hence we might considerthat the submm emission attributed to Galaxy 6 in our model actually originates from Galaxy5. We can test this hypothesis using the far-IR-to-radio correlation to predict a luminosity forGalaxy 5 and by also removing Galaxy 6 from our model and perform the fitting procedureagain (thus forcing our model to attribute a portion of its luminosity to Galaxy 5), and thencomparing the results. When doing so, we find that Galaxy 5 is attributed a luminosity of(4:5 ± 0:9) × 10NN L⊙ by our model (i.e essentially all the luminosity of Galaxies 5 and 6 to-gether). Using the peak flux density measurements of Berciano Alba et al. (2010) at 1.4GHzand the amplification factors in Table. 2.1, the unlensed 1.4GHz flux density for Galaxy 5 is(11±1)Jy. With these two measurements, we can calculate the logarithmic ratio of the far-IRflux to radio flux density, qIo = logN0[(hIo=3:75× 10N2Wm−2)=(hN:4=Wm−2Hz−N)]. We assumea power law for the radio SED, hradio ∝ ,, with  = −0:8, and we correct for the effectsof redshift. We find qIo = 1:67 ± 0:09, which is 2- below the relation found by Ivison et al.(2010b) for high-z galaxies, qIo = 2:3 ± 0:3. This indicates that Galaxy 5 may have excessradio emission, suggesting contribution from an AGN, rather than radio emission associatedwith star formation. For this reason, we tend to follow the results which come from our modelfitting, i.e. that Galaxy 6 dominates the far-IR emission. Nevertheless, it remain the case thatinterpretation of this pair is difficult with existing data.Using ALMA to obtain high-resolution imaging, Hodge et al. (2013) recently showed thatmany of the submm galaxies (SMGs) previously detected in the LABOCA ECDFS Submil-limeter Survey (LESS) are in fact composed of multiple fainter sources. The group of galaxiesbehind MS0451.6−0305, consisting of Galaxies 2 through 8, is another good example of SMGsbeing composed of several sources. Unlensed, this z ∼ 2:9 group would appear as a pointsource to any of the current single-dish submm telescopes, with flux densities of 3:8± 0:5 mJy,8:5± 0:9 mJy, 10:4± 1:1 mJy, 8:0± 0:9 mJy, 8:9± 1:0 mJy, and 2:5± 0:3 mJy at 160, 250, 350,500, 450 and 850m, respectively. This would put the group below the LESS survey detection17FBIB fysults unx xiswussionthreshold of 4.5mJy at 870m, hence we are seeing evidence of submm source multiplicitydue to physically associated groupings, as opposed to chance alignment, extending to fainterflux densities. On account of the frequency of submm source multiplicity, Hodge et al. (2013)suggest that many are likely to be physically associated. Our findings support this claim andsuggest that these systems could be part of larger groups, many of which are too faint to bedetected in the submm at current depths. The coincidence of being highly magnified by amassive foreground cluster allows us to study this group in much greater detail than wouldotherwise be possible, but we cannot infer how rare such SMG groups might be.Although not as striking, a few analogues of our lensed star-forming galaxy group are foundin the literature. First of all SMM J09431+4700, a SCUBA selected hyperluminous infraredgalaxy behind A851 at z = 3:35 (Cowie et al., 2002; Ledlow et al., 2002). It is accompanied byan optically selected galaxy, DG 433, (Trager et al., 1997), separated by 400 km s−N in redshiftand 1Mpc in projection. Secondly there is SMM J16359+6612, a faint SCUBA selected galaxybehind A2218 at z = 2:5165 (Kneib et al., 2004; Sheth et al., 2004). It is accompanied by twooptically selected galaxies, separated by only 100 km s−N in redshift and 130 kpc in projection.With more unlensed analogues of groups and recent mergers in the literature (e.g. Ivison et al.,1998; Frayer et al., 1998; Borne et al., 2000; Tacconi et al., 2008; Ivison et al., 2010a, 2013) andthe ALMA multiplicity results from Hodge et al. (2013), it is clear that mergers and interactionsplay an important role for many SMGs. These distant galaxy groups are akin to nearby compactgroups (Hickson, 1982), with the z ∼ 2:9 galaxy group presented here reminiscent perhaps toStephan’s Quintet (Stephan, 1877), due to the remarkable number of galaxies associated withthis submm source. There are surely more such systems to be discovered.However, we believe that situations like we found here are fairly rare, and it is possible thatwhat we have described in this chapter is the largest compact group that is lensed by a richgalaxy cluster on the entire sky. Although a detailed estimate of the probability is clouded bythe usual problems with a posteriori statistics (i.e., if we only consider systems exactly like wefound, then the probability would be arbitrarily small), we can carry out a crude estimate asfollows. The MS0451 cluster has a mass of around 10NRM⊙ (Donahue et al., 2003a) and anEinstein radius of around 30 arcseconds (where strong lensing is possible). Conservatively taking3×10N4M⊙ as the limit for rich clusters, surveys (like the Planck catalogue of Sunyaev-Zeldovichsources, Planck Collaboration XXIX, 2013) suggest there are around 2000 such clusters on thesky, and hence the sum of the areas covered by their Einstein radii is about 10−R of the sky.Assuming that a compact group has a mass of at least 3 × 10NPM⊙, then the Press-Schechterformalism (Press and Schechter, 1974) suggests a comoving density of about 10−SMpc−P atz = 3 for such groups. The Press-Schechter formalism is a model used to predict the abundanceof massive halos in a given volume of the Universe, given a mass range. Taking a volumethat covers ∆z = 1 centred on z = 3, we estimate 500,000 such groups on the sky. Finally,multiplying this by the fraction of the sky that might be strongly lensed by rich clusters, wefind that there will only be a handful of such objects lensed by a rich cluster. Given a groupradius of 45Kpc, the group crossing time is of the order 30Myr. The merging timescale for agalaxy group is on the order of ten crossing times (Barnes, 1984; Navarro et al., 1987; Kodairaet al., 1990; Cavaliere et al., 1991; Hickson, 1997), thus the merging time of the galaxy groupis on the order of 0.3Gyr. This timescale is about a tenth the age of the Universe at a redshiftof 2.9, and given that only a small percentage of 3× 10NPM⊙ objects are compact groups (andeven smaller for merging groups Hickson, 1997), it may seem surprising that this group hasbeen found. However, the numerical argument presented here should be considered to be veryapproximate, and hence no strong conclusions can be drawn.18FBIB fysults unx xiswussion9ighee 2.4- Dust temperature versus far-IR luminosity for several samples of galaxies. The solidline shows the trend found by Symeonidis et al. (2013) using Hyrswhyl for z ∼0–1.5 galaxies, with thedashed lines showing the dispersion of the sample. The green squares are the LESS SMGs followed upby Swinbank et al. (2014) with ALMA and Hyrswhyl, with z ∼1-6. The blue squares are the results ofstacking on narrow-band [Oii] emitters (left) and MIPS+radio sources not detected in SPIRE/SCUBA-2(right) for a z = 1:6 cluster (Smail et al., 2014). The red squares are a sample of lensed SMGs discoveredwith Hyrswhyl (Sklias et al., 2014) with z ∼1.5–3. The black circles are the four z ∼ 2:9 group galaxiesthat compose the submm arc of MS 0451.6−0305. Both Swinbank et al. (2014) and Symeonidis et al.(2013) found that high-z galaxies are on average cooler than the z = 0 relation, while Sklias et al. (2014)and our results report warmer than average results for high-z galaxies. The dotted red line representsthe SPIRE 250m detection limit as a function of dust temperature for z = 2:9 galaxies, illustratingthe usefulness of gravitational lensing, to push to fainter objects, when studying high-z SMGs.2C5C2 eh–sixvl propertiesThe SED fits within our model allow us to investigate the physical conditions of each componentof the submm arc. Fig. 2.4 plots id verus aIo for the four z ∼ 2:9 galaxies constrained by ourmodel with trends and data found by Symeonidis et al. (2013), Swinbank et al. (2014), Skliaset al. (2014), and Smail et al. (2014). As described in Symeonidis et al. (2013), studying therelation between these two quantities gives insight into the nature of star-formation withingalaxies: a flat relation with id = constant implies that star formation regions become moreextended when increasing far-IR luminosity, while something close to the Stefan-Boltzmannlaw, aIo ∝ i 4, would imply constant star formation region size (for optically thick star-formingclouds). Symeonidis et al. (2013) used Hyrswhyl SPIRE and PACS to probe this relation andfound the trend plotted as a solid black line in Fig. 2.4, with dashed lines showing the dispersion.When comparing low and high redshift galaxies, they found that the later were up to 10K coolerthan their low redshift counterparts, suggesting evolution with redshift towards more extended19FBIB fysults unx xiswussion9ighee 2.5- Decomposition of the submm arc into each contributing galaxy for the best-fit model, thetotal emission for the best-fit model, the data, and the residual after subtracting the model from thedata. The columns display the contributions for individual galaxies across the six wavelength channels.Due to the differential amplification and unique positions of the multiple images, the emission from eachgalaxy is morphologically unique and this is what enables us to disentangle their contributions. Thedata and residual components for the SCUBA-2 channels have been smoothed with the FWHM for eachrespective wavelength. The pixel sizes are 3, 6, 8.3, 12, 2, and 4 arcseconds at 160, 250, 350, 500, 450,and 850m, regions in the early universe. Swinbank et al. (2014) found a similar trend withhigh redshift galaxies being on average 2–3K colder than low redshift galaxies. Smail et al.(2014) found that stacking on narrow-band [Oii] emitters and MIPS+radio sources within az = 1:6 cluster (intrinsically faint sources) found no evidence of evolution, although their directdetections with SPIRE and SCUBA-2 (thus intrinsically luminous sources) were also found tobe cooler in temperature. A recent study by Sklias et al. (2014), used gravitational lensingto examine intrinsically fainter galaxies at high redshifts. Although limited by small numberstatistics, they found the opposite trend for high redshift galaxies. When adding the four z ∼ 2:9galaxies constrained by our model, our results appear to support those found by Sklias et al.(2014). This suggests that selection effects and/or biases are present in the different studies.As has been pointed out before (e.g. Chapman et al., 2005; Chapin et al., 2011) selectioneffects can be extremely important when studying the correlation between id and aIo. TheSwinbank et al. (2014) sample of SMGs were selected at 870m and thus may be biased towardslower dust temperatures, and those of Sklias et al. (2014) were formally selected at 160m, andthus could be biased towards warmer dust temperatures. It should be noted that the submmarc in MS0451.6−0305 was first discovered at 850m (Chapman et al., 2002a) and thereforeunlikely to be biased towards the warmer dust temperatures that we find.In addition to the selection biases inherent in focusing on a single distinctive source, thereare also a number of systematic uncertainties that could be present in our modelling approach.20FBIB fysults unx xiswussion9ighee 2.6- MCMC likelihood contours for temperature and far-IR luminosity for the galaxies thatwere found to contribute to the submm arc. The contour levels are 68%, 95% and 99.7% confidenceintervals. Because of the morphological uniqueness of the lensing for each individual galaxy, there arefew degeneracies here, despite the images of the system being spatially confused. The most obviousdegeneracy is between the far-IR luminosity of Galaxy 6 and Galaxy 7. hop right: The likelihoodcontours for the model show a degeneracy between Galaxy 5 and Galaxy 6 in far-IR luminosity. Galaxy5 has associated radio emission, but it exceeds that expected from SFR alone, thus suggesting an AGNcomponent.21FB6B ConwlusionsMost importantly, we have fixed the amplification factors for the galaxy images. Any errors inamplification can affect our results in several ways. For example, since the contributions to thesubmm arc from Galaxies 7 and 8 (See Fig. 2.5) are mostly point-like, then any uncertaintyin amplification predominantly affects their measured far-IR luminosities and SFRs. This isespecially true for Galaxy 7, because two of its images lie very close to the critical line (theregion in the image plane with the greatest amplification), and thus its amplification is highlysensitive to any offset between optical and submm components of the galaxy. The uncertaintyin relative amplification between galaxy images likely affects which galaxies are preferred by thedata. For example, the images of Galaxies 5 and 6 are spatially very close, thus the differentrelative amplifications between their respective images probably contributes to Galaxy 6 beingpreferred by the model fits.It is possible that the simple SED model we have adopted may not accurately approximatethe true SEDs of the galaxies in the lensed system. The dust emissivity, , is known to bepartially degenerate with dust temperature and we have fixed it to a nominal value of 1.5, thusthe uncertainties reported for dust temperatures are likely too small. Furthermore, althoughthis newer Hgh data is both deeper and at a longer wavelength, it is possible that we are missingfainter group members, as was the case in previous studies (Borys et al., 2004; Berciano Albaet al., 2010). If any of the galaxies are not at z ∼ 2:9, their reported far-IR luminosities andthus SFRs will be affected, since the distances to the galaxies are used in these calculations.This is especially true for Galaxy 8, as we have no constraints on its actual redshift and ouranalysis has assumed it to be part of the z ∼ 2:9 group.Despite these reservations, the model we have adopted appears to provide a reasonably goodfit to the data across a wide range of wavelengths. Higher resolution submm data would beneeded to further investigate the nature of the z ∼ 2:9 galaxy group.2C6 ConxlusionsWith our new modelling approach, we have overcome the confused nature of this complexsystem by fully exploiting the differential amplification across the galaxy group and the multipleimaging caused by the strong gravitational lensing. This has allowed us to tackle the challengeof disentangling and fitting SEDs to multiple components of the submm arc. We have shownthat the submm arc is predominantly generated by four of the seven galaxies that probablycomprise a group at a redshift of z ∼ 2:9, with star-formation likely triggered by the galaxiesundergoing a merger. It is therefore not necessary to have a hidden region of dust-enshroudedstar formation (as postulated by Berciano Alba et al., 2010) to explain the morphology of thesubmm arc. This method also demonstrates the power of a broad multi-wavelength approachto fully understanding the nature of the submm arc: Hgh imaging gives us the priors on galaxypositions, as well as providing the constraints for the lensing model; Hyrswhyl samples thepeak of the far-IR SED, as well as providing the high-resolution far-IR imaging at 160m; andSCUBA-2 850m data samples the long wavelength portion of the FIR SED at a resolutionthat closely matches that of the 160m imaging.This is a unique system that gives us a glimpse into the formation of structure and starsin the early Universe, and no other submm lens discovered to date can match the number ofseparate galaxies lensed from the same redshift. Spectroscopy and high-resolution follow-upwith new interferometer observatories will be the key to confirming and unravelling the natureof this high-z merging galaxy group.22FB6BConwlusionsTTUle 2.1- List of images for the eight high-z galaxies, as well as one low redshift interloper at z = 0:157. The galaxy IDs denote each galaxy, as shownin Fig. 2.1, and the letters indicate the multiple images of each galaxy (with a being the most Northern images in each case, and c being the mostsouthern images). The position of image 4.b, as inferred from the lensing model, is obscured by foreground cluster galaxies. The amplification factorsare derived from the Leaftool modelling in Section 2.2. The redshift of Galaxy 8 is unknown, but has similar colours to the other high-redshiftmultiply imaged galaxies, a disturbed morphology, and was found to be important for reproducing the SW extension of the submm arc, thus weassume a nominal redshift of 2.9. The superscript letters on the redshifts denote the method by which they were derived: u for redshifts derived fromthe lensing model, v for a spectroscopic redshift, and w for a nominally chosen value. The reported magnitudes for the F160W and F110W Hgh filtersare AB magnitudes.Gal ID R.A. Dec. F160W F110W Amplification Redshift NotesJ2000 J2000 (Mag) (Mag)1.a 04:54:13.42 −3:00:43.0 21:94± 0:01 23:26± 0:01 3:80± 0:06 3:11± 0:03a (Takata et al., 2003; Zitrin et al., 2011)1.b 04:54:12.65 −3:01:16.5 20:91± 0:01 22:27± 0:01 20± 1 (Takata et al., 2003; Zitrin et al., 2011)1.c 04:54:12.17 −3:01:21.4 21:86± 0:01 23:18± 0:01 7:3± 0:1 (Takata et al., 2003; Zitrin et al., 2011)2.a 04:54:13.15 −3:00:38.4 24:15± 0:03 24:74± 0:05 2:86± 0:04 2:91± 0:04a2.b 04:54:12.58 −3:01:11.9 23:62± 0:03 24:25± 0:05 8:1± 0:42.c 04:54:11.79 −3:01:20.2 22:88± 0:02 23:85± 0:04 6:1± 0:13.a 04:54:13.04 −3:00:39.2 24:98± 0:04 26:28± 0:07 3:19± 0:05 2:94± 0:04a3.b 04:54:12.68 −3:01:09.1 23:27± 0:02 24:09± 0:05 2:98± 0:053.c 04:54:11.46 −3:01:21.7 24:27± 0:04 25:49± 0:06 4:31± 0:084.a 04:54:12.82 −3:00:39.3 24:82± 0:05 26:39± 0:08 3:57± 0:06 2:94± 0:04a4.b DHNIHNE2BIG −GNDENDHBI 26:64± 0:07 27:50± 0:09 6:2± 0:2 Lensing model position4.c 04:54:11.03 −3:01:22.4 24:70± 0:05 25:90± 0:07 3:36± 0:065.a 04:54:12.81 −3:00:44.4 21:73± 0:01 23:51± 0:01 5:3± 0:1 2:89± 0:03a ERO-B(Borys et al., 2004)5.b 04:54:12.69 −3:01:01.5 21:81± 0:01 23:47± 0:01 6:4± 0:1 ERO-B(Borys et al., 2004)5.c 04:54:10.93 −3:01:24.6 21:97± 0:01 23:78± 0:02 2:89± 0:04 ERO-B(Borys et al., 2004)6.a 04:54:12.81 −3:00:47.5 22:62± 0:02 24:55± 0:06 8:2± 0:2 2:86± 0:03a ERO-C(Borys et al., 2004)6.b 04:54:12.72 −3:00:59.6 24:41± 0:04 26:60± 0:15 4:98± 0:08 ERO-C(Borys et al., 2004)6.c 04:54:10.88 −3:01:25.8 22:85± 0:02 24:67± 0:09 2:76± 0:04 ERO-C(Borys et al., 2004)7.a 04:54:12.95 −3:00:54.8 21:80± 0:01 22:26± 0:01 33± 2 2:911± 0:003b LBG(Borys et al., 2004)7.b 04:54:12.93 −3:00:57.5 22:29± 0:01 22:76± 0:01 45± 3 LBG(Borys et al., 2004)7.c 04:54:11.11 −3:01:26.6 23:66± 0:02 24:23± 0:03 2:87± 0:04 LBG(Borys et al., 2004)8 04:54:10.55 −3:01:27.3 22:77± 0:02 23:50± 0:03 1:73± 0:04 2:9c Singly imaged9 04:54:12.85 −3:01:09.1 18:91± 0:01 19:19± 0:02 – 0:15719b foreground galaxy23FB6BConwlusionsTTUle 2.2- Lensing-amplification-corrected results from the model. The total aFIR for the z ∼ 2:9 galaxy group is (3:1±0:3)×1012L⊙, which gives aSFR of (450± 50) M⊙yr−1. The 95th percentile upper limits are given for galaxies not found to be contributing to the submm arc. Note that Galaxy9 is a foreground galaxy at z = 0:157 and is therefore not lensed.Gal id acIo SFR hNS0 h2R0 hPR0 hR00 h4R0 hUR0ID (K) (L⊙) (M⊙yr−N) (mJy) (mJy) (mJy) (mJy) (mJy) (mJy)1 − < 8:2× 109 < 1:3 − − − − − −2 44± 3 (6:7± 0:6)× 10NN 99± 9 0:94± 0:10 1:9± 0:2 1:9± 0:2 1:2± 0:2 1:4± 0:2 0:31± 0:063 − < 1:5× 10NN < 23 − − − − − −4 − < 3:3× 10NN < 50 − − − − − −5 − < 2:0× 10NN < 35 − − − − − −6 31± 4 (3:6± 0:9)× 10NN 53± 14 0:31± 0:12 0:7± 0:3 1:3± 0:4 1:5± 0:4 1:5± 0:4 0:7± 0:27 40± 3 (7:5± 1:0)× 10N0 11± 2 0:10± 0:02 0:22± 0:04 0:23± 0:06 0:16± 0:05 0:18± 0:04 0:04± 0:028 37± 2 (1:9± 0:3)× 10N2 290± 40 2:5± 0:4 5:6± 0:8 6:9± 1:0 5:1± 0:9 5:8± 1:0 1:5± 0:39 17± 9 (1:7± 0:5)× 109 0:25± 0:07 3:6± 1:0 2:5± 0:8 1:3± 0:5 0:5± 0:2 0:6± 0:2 0:08± 0:0424Chvpter 3Fitting spextrvl energ– yistriwutionsto sourxes in wlenyey imvging3CF IntroyuxtionWith the advent of single-dish submm observatories such as those using SCUBA-2 (Hollandet al., 2013) on the JCMT, BLAST (Pascale et al., 2008), and Hyrswhyl (Pilbratt et al., 2010a),we now have a window into the distant star-forming Universe (e.g. Smail et al., 1997; Bargeret al., 1999; Eales et al., 1999; Scott et al., 2002; Cowie et al., 2002; Borys et al., 2003; Coppinet al., 2006; Patanchon et al., 2009; Eales et al., 2010; Elbaz et al., 2011b; Oliver et al., 2012;Geach et al., 2013). However, due to the resolution of these observatories, instrumental noise isnot the limiting factor when determining the uncertainty in flux density of individual sources,when observed for sufficiently long period of time. Instead, we are limited by confusion noisecaused by the high density of sources relative to the resolution of imaging. Higher resolutionimaging can help with extracting the desired information from these confused images, but thecurrent methods of combining such data are lacking in statistical rigour.A common exercise in these wavebands is to determine the spectral energy distribution(SED) of a source. When the source is much brighter than the confusion limit, this task israther straight forward. However, if the source is near or below the confusion limit for anyparticular waveband, then determining the SED of a source becomes problematic. This hasbeen done with varying degrees of success using “de-blending” techniques (e.g. Makovoz andMarleau, 2005; Roseboom et al., 2010; Elbaz et al., 2011a; Swinbank et al., 2014), often usingpositional priors from other higher-resolution observations, to first extract fluxes, then sub-sequently fit SED models. This two-step process usually ignores the intricacies of confusionnoise (both spatial and between wavebands) and erases useful information regarding degenera-cies among SED model fits with nearby sources, and thus the attribution of uncertainties tofit parameters becomes problematic. We present here a method of combining high-resolutionimaging with confused imaging, which simultaneously fits SEDs and separates sources, thus de-blending SEDs instead of flux densities. We adapt the forward-modelling method of MacKenzieet al. (2014) (henceforth referred to as M14; see also Chapter 2) and generalise it to the caseof point source deblending of model SEDs. This new method forward-models each source SEDto recreate the image plane and uses an MCMC Metropolis-Hastings algorithm (Metropoliset al., 1953; Hastings, 1970) with Gibbs sampling (Geman and Geman, 1993) to determinethe uncertainties of the model parameters. We apply our method to the Atacama Large Mil-limeter/submillimeter Array (ALMA) Survey of Submillimeter Galaxies (ALESS, Hodge et al.,2013) in the Extended Chandra Deep Field South (ECDFS) to measure the far-IR propertiesof the LABOCA ECDFS Submm Survey selected sources (LESS, Weiß et al., 2009). This taskhas already been undertaken by Swinbank et al. (2014), allowing us to compare our results withthose of a more traditional method. Along with 870m ALMA data, this region of the skyhas also been imaged with the Hyrswhyl Spectral and Photometric Imaging Receiver (SPIRE,253BFB U frumywork for tting gEDs to vlynxyx sourwysGriffin et al., 2010) and Photoconductor Array Camera and Spectrometer (PACS, Poglitschet al., 2010), thus making it the ideal arena to test the effectiveness of our method. Through-out we employ a ΛCDM cosmology with Ω = 0:728, Ωm = 0:272, and H0 = 70:4 km s−NMpc−N(Komatsu et al., 2011).3C2 V frvmefiork for tting hEDs to wlenyey sourxes3C2CF boyel hED vny imvge rexonstruxtionWe adopt a modified blackbody SED with a power-law component for the shorter wavelengths,as in M14. Because we are not dealing with multiple images here (i.e. not strongly lensed), theimage planes are reconstructed as follows:bb(x) =∑ih¯b(id;iP ziP Xi)P,(x− ri) +Bb: (3.1)Here bb(x) is the reconstructed image for frequency channel b, x denotes the position withinthe image, h¯b is the source flux density of source i averaged over the channel b transmissionfilter, id;i is the dust temperature, zi is the redshift, Xi is a normalisation factor of source i,P,(x − ri) is the response function (i.e. the telescope beam), with ri denoting the position ofsource i, and Bb is the image background. The response functions for the Hyrswhyl channelsare approximated as Gaussians with FWHM values of 11.6, 18.1, 24.9 and 36.2 arcseconds at160, 250, 350 and 500m, respectively (Griffin et al., 2010).3C2C2 HerschelBheIgE sk– resiyuvlsIn M14, additional deep cosmological field imaging was used to estimate the covariance of thesky in the likelihood calculation. In this study, we are deblending the ALESS sources withthe catalogue of nearby MIPS 24m and JVLA sources provided in Swinbank et al. (2014),henceforth referred to as the NMJS catalogue. This catalogue accounts for the majority of theflux in the Hyrswhyl-SPIRE data and thus, using a cosmological field without subtracted sourcesto estimate the covariance for our likelihood calculations is not appropriate here. Instead, weuse the ECDFS SPIRE residuals, after subtracting our model SED, fit to every nearby sourceand ALESS source simultaneously.A maximum likelihood method is used to fit our model SEDs using a similar method to thatdescribed in Section 3.2.3, weighting each pixel equally within the SPIRE data and ignoringany covariance between pixels. No PACS or ALMA data are used in this step. We limit thisprocess to the region where the 250m instrumental noise is less than 1.2mJy, which includes4024 sources from both the ALESS and NMJS catalogues. Total flux densities from all sourcescombined of 37.2, 28.6 and 16.2 Jy are subtracted from the data at 250m, 350m and 500m,respectively. To test if we are over-subtracting flux from the maps, we stack the original mapson the positions of the catalogues, which produces total flux densities of 28.7±0.7, 23.4±0.6and 14.5±0.5mJy at 250m, 350m and 500m, respectively, with the errors estimated bybootstrapping. One might conclude that we are over-subtracting, but stacking on the modelsky (the images subtracted from the data to produce the residuals) produces total flux densitiesof 30.5, 24.0 and 14.0mJy at 250m, 350m and 500m, respectively. Both of these stackingresults significantly lower than the total flux densities of the subtracted sources, however weonly expect stacked results to equal the total flux densities of the sources if they are Poisson263BFB U frumywork for tting gEDs to vlynxyx sourwys9ighee 3.1- Left: SPIRE ECDFS field. Right: SPIRE ECDFS field, after source subtraction of 4024sources in the region of the sky where the 250m instrumental noise is less than 1.2mJy. The standarddeviations of the residuals in the region of the subtraction are 1.5, 1.6 and 1.4mJy at 250m, 350mand 500m, respectively. These residuals are larger than the instrumental noise and are presumablydominated by sources too faint to be included in the catalogue of sources subtracted. The scale at thebottom of the image is in Jy.273BFB U frumywork for tting gEDs to vlynxyx sourwysdistributed on the sky (Marsden et al., 2009). Because the stacking on the real and model skygive consistent results, we conclude that we are not significantly over-subtracting flux from ourmaps.The standard deviations of the residuals are 1.5, 1.6 and 1.4mJy at 250m, 350m and500m, respectively; significantly reduced from the confusion limits of 5.8, 6.3 and 6.8mJy,respectively (Nguyen et al., 2010). These residuals are greater than the instrumental noiselevels of 1.0, 1.1 and 1.2mJy in these regions; we are thus seeing the residual confusion noiseof the sources that are not bright enough to be included in the ALESS and NMJS catalogue ofsources we subtracted. These residuals will be used in Section 3.2.3 to estimate the covarianceof the sky. This method allows us to greatly reduce the effects of confusion noise; instead, weare left with degeneracies in SED fitting parameters among the many nearby sources in ourcatalogues.3C2C3 boyel ttingAs in M14, the model is fit to the data using an MCMC Metropolis-Hastings algorithm(Metropolis et al., 1953; Hastings, 1970) with Gibbs sampling (Geman and Geman, 1993).The log likelihood function for the Hyrswhyl-SPIRE data is− logapmIob = XpmIob + 12RTC−NRP (3.2)where R is a one-dimensional list of the residuals, and contains all three channels of SPIREdata (R = {D2R0(xk)−b2R0(xk)=c2R0P DPR0(xk)−bPR0(xk)=cPR0P DR00(xk)−bR00(xk)=cR00}),C−N is the inverse covariance matrix for the residuals, cb are the calibration factors of eachrespective band, and XpmIob is a constant. For each step in the MCMC chain, we are onlyinterested in the differences between log-likelihoods, thus any constants can be ignored.In M14 the area of the sky used was only a few arcminutes across, but the method describedhere must function on much larger areas of sky and the above calculation time scales with thesquare of the area used. Fortunately, the covariance between pixels is only significant for nearbypixels, and so we do not need the whole matrix. We can estimate the covariance for an imageof 10 × 10 pixels at each of the three SPIRE channels by selecting randomly chosen cutoutsfrom the residuals described in Section 3.2.2. The covariance matrix is inverted and the resultseparated into six lists, corresponding to inverse covariances between pixels within the samewaveband and between wavebands, which we then bin according to their angular separationon the sky. Where these bins are regular (due to the relative pixel sizes), we take the medianvalue of values in each bin to obtain a better estimate of the inverse covariance. For inversecovariances between 250m and 350m, and 350m and 500m, a high-order polynomial isfit to the data (the pixel sizes of 6, 8.3 and 12 arcseconds do not form simple repeating angularseparation bins between the wavelengths). Fig. 3.2 shows the inverse covariance as a function ofangular separation for the six lists. If we limit the log-likelihood calculation to only pixels withina fixed radius of the sources of interest and between pixels within a fixed angular distance, theresulting likelihood calculation only scales with the area of sky used.In practice, we could iterate on the process of making residual maps for use in estimatingthe residual sky covariance. Where we treated each pixel with equal weight in Section 3.2.2, wecould instead use the estimated covariance from the previous iteration. In practice however, thecomputational time of the likelihood calculation would become prohibitively large compared tothe simple approach we implemented. Fortunately, the residuals are likely dominated by sources283BFB U frumywork for tting gEDs to vlynxyx sourwys9ighee 3.2- Results of separating the inverted covariance matrix of the Hyrswhyl SPIRE residuals byangular separation and by wavelength. The inverse auto-covariances for 250m to 250m, 350m to350m, 500m to 500m at an angular separation of zero are 1.02×10+, 1.07×10+, and 7.9×10+ Jy−2,respectively, and are not shown on the graphs above for clarity.too faint to be included in our NMJS catalogue, and not by a poorly weighted fit, and thuslittle would be gained by iterating on the residuals.Flux calibration uncertainties, cb, are taken into account during the fitting procedure by set-ting priors on cb for each band. SPIRE waveband calibrations are correlated, with a covariancematrixCcal =0:001825 0:0016 0:00160:0016 0:001825 0:00160:0016 0:0016 0:001825 P (3.3)where the calibration is normalised to unity (Bendo et al., 2013). This corresponds to a 4%correlated uncertainty between bands plus 1.5% uncorrelated uncertainty between bands.The log-likelihood for the ALMA fluxes for a given band is given by− logab = Xb +∑i122i;b(Di;b −bi;b=cb)2P (3.4)where Di;b is the measured flux density for source i, b¯i;b is the model flux density for source i,i;b is the uncertainty in the measurement of Di;b, cb is the calibration factor, Xb is a constant,and b denotes the band of the measurement. Unlike the Hyrswhyl SPIRE bandpass filters,the ALMA bandpass filter is narrow and b¯i;b is taken to be the flux density at the specified293B3B hysting with simulutyx sourwysfrequency. The data used in this study are 345GHz ALMA Band 7, although we also considerthe benefits of using additional 650GHz Band 9 data for constraining the far-IR properties ofthe ALESS sample in Section 3.3.1. Calibration uncertainties are 10% and 20% in Bands 7 and9, respectively (see Capabilities for ALMA Cycle 0).Because the 160m PACS data are dominated by instrumental noise, the log-likelihood forthese data is given by− logamACp = XNS0 +∑i12(xi)2(DNS0(xi)−bNS0(xi)=cNS0)2P (3.5)where DNS0(xi) are the data, bNS0(xi) is the sky model, (xi) is the instrumental error, XNS0is a constant, cNS0 is the calibration factor, and xi is the position of pixel i on the sky. The160m PACS calibration uncertainty is 5% (Mu¨ller et al., 2011).3C3 iesting fiith simulvtey sourxesWhile we do not require simulation of artificial sources in order to calibrate our method, wecan use it as a tool to verify the accuracy of the uncertainties reported. In particular, we cantest how redshift, uncertainty in redshift, dust temperature and far-IR luminosity affect ourability to constrain these same properties. We can also explore the effects of including nearbysources and the generated degeneracies. In addition, we can quantitatively assess the benefitsof adding further data, such as Band 9 ALMA measurements.3C3CF kerif–ing our methoyWe verify our method by injecting simulated sources into the residual Hyrswhyl SPIRE images,described in Section 3.2.2, along with simulated PACS data, and recording the resulting best-fit. The best-fit distribution of the injected sources should match the expected uncertaintiesfor such sources. Simulated ALMA 870m flux densities are given 0.5mJy Gaussian errors andthe PACS 160m data are simulated by generating a blank image with Gaussian random noiseequal to the instrumental noise. SPIRE calibration errors are randomly generated using thecovariance matrix given in Section 3.2.3 and calibration errors for the ALMA and PACS dataare also included. This is, in effect, a Monte Carlo verification of our method and allows usto verify the validity of our treatment of the Hyrswhyl SPIRE likelihood analysis. We adopt a“standard” source with a redshift of 2, a dust temperature of 30K, and a far-IR luminosity of10N2 L⊙, for the purpose of testing our method. This equates to flux densities of 4.5, 6.4, 7.6,5.6, and 1.8mJy at 160, 250, 350, 500, and 870m, respectively, with a peak flux density of7.7mJy at 323m. We inject a total of 441 fake sources for each case we test below. Injectinga single source at a time allows us to test our constraining power for a single isolated source(although this is a rare occurrence due to the density of sources on the sky). To see the effect ofsource confusion, we can injected multiple simulated sources in close proximity. Both of thesecases are discussed below.Because dust temperature and redshift are entirely degenerate, it would be possible toconstrain id=(1+z), instead of fixing the redshift and constraining dust temperature separately,as is done in most of the examples below. However, because we have redshift estimates for allthe ALESS sources, we think it is more beneficial to show constraints on dust temperaturesseparately. The effect of an uncertainty in redshift is also explored below, but separately (seeFig. 3.7).303B3B hysting with simulutyx sourwys9ighee 3.3- Results comparing the expected uncertainty in fitting a source given by our method (blackcontours), versus Monte Carlo simulated sources injected into the data. The blue points are the MonteCarlo simulated sources used to verify our method. In the right panel, we show our standard source witha redshift of 2, a dust temperature of 30K and a far-IR luminosity of 1012 L⊙. In the middle panel weshow the same standard source with half the luminosity, and in the left panel, the standard source witha quarter of the original luminosity. The black contours represent 68%, 95% and 99.7% credible regionsFig. 3.3 shows the verification of our method for our standard source, as well as the caseswhere we decrease its luminosity by a factor of two and by a factor of four. Good agreement isfound between our expected uncertainties and the Monte Carlo injected sources. It is interestingto see the drastic change in temperature uncertainty as the luminosity of the standard source isreduced. We could clearly provide good constraints on sources to well below the confusion limitof the SPIRE data, if only we had isolated sources on the sky. Of course this is just a tautology,since the sky is unfortunately a crowded place and our ability to constrain the properties ofsources is largely limited by nearby sources that generate degeneracies in the fit parameters.Fig. 3.4 shows the verification of our method for the case of two standard sources separatedby 5 arcseconds. This example demonstrates a typical case of submm multiplicity as seen formany of the ALESS sources (Hodge et al., 2013). Here, it is clear that the constraints on theproperties of a source are limited by the degeneracies with its neighbour and not the residualunresolved far-IR background. A linear degeneracy between the two far-IR luminosities isexpected, with the one-to-one degeneracy seen here the result of the two sources having thesame far-IR luminosity and redshift. The degeneracies seen between the other SED modelparameters, typically “banana-shaped,” depend on the values of the parameters themselves.It is these degeneracies that two-step SED fitting misses. Again, our Monte Carlo simulatedsources accurately reflect the expected uncertainties.Fitting large numbers of Monte Carlo simulated sources is a computationally expensive ex-ercise and thus we stop the verification of our method here. We have shown that the constraintsproduced by our method accurately reflect the results of Monte Carlo simulations, and thusour treatment of the SPIRE likelihood analysis is validated. For a standard source, Fig. 3.5shows the difference between our approach and an identical method where we only consider theinstrumental noise of the SPIRE data and ignore the correlations between neighbouring pixelsin angular separation as well as between wavelengths. Without our treatment of the SPIRElikelihoods, it is clear that we would be over-constraining the properties of sources within ourmodel.Assigning a realistic dust temperature is an issue that has been neglected in much of the313B3B hysting with simulutyx sourwys9ighee 3.4- Comparing the expected uncertainties for two standard sources separated by five arcsecondswith the Monte Carlo simulated results (blue points). The black contours represent 68%, 95% and 99.7%credible regions.323B3B hysting with simulutyx sourwys9ighee 3.5- Comparing the expected uncertainties for a standard source using our method (blackcontours show 68%, 95% and 99.7% credible regions) and an identical method with a naive approach ofthe Hyrswhyl SPIRE likelihood that considers only the instrumental noise in each pixel and ignores thecovariance with neighbouring pixels (red contours).333B3B hysting with simulutyx sourwys9ighee 3.6- Constraining power of our model as a function of redshift for our standard source whilekeeping peak flux density constant. We show 68%, 95% and 99.7% credible regions for redshifts of 1, 2,3, 4, 5 and 6 in black, red, blue, green yellow and purple, respectively.literature. Constraints on dust temperature are affected by several factors, such as the redshift ofthe source, the width of the telescope bandpass filters, the wavelength coverage of the telescopefilters, and the signal-to-noise of the source within the images. However, the dust temperatureuncertainty naturally falls out of the method employed here, and thus we perform a few testsas examples.Fig. 3.6 shows how our constraints change as we vary the redshift of our standard sourcewhile keeping the peak flux density constant and letting the far-IR luminosity change. Aninteresting effect is seen at high redshift, where a colder fit to the dust temperature starts toincrease the far-IR luminosity. This is because the peak of the SED shifts beyond the ALMA870m waveband. A similar effect is seen at low redshifts, when the peak of the SED shiftsto wavelengths shorter than 160m and the upper dust temperature bound starts to rise. Fora dust temperature of 30K, these effects do not become significant unless the redshift is lowerthan about 1 or greater than about 6, thus the wavelength coverage of the available data isideally suited for the sample of ALESS sources we are fitting in Section 3.4.Up to this point, we have assumed that the redshift of our standard source was well con-strained. Fig. 3.7 shows our model constraints for redshift uncertainties of 0, ±0.5, and ±1.How well we can constrain dust temperature and far-IR luminosity, along with degeneraciesamong nearby sources, strongly depends on the uncertainty in source redshift.3C3C2 ihe vyyition of v sexony VabV frequenx–ALMA follow-up of 870m sources selected from ALESS (Weiß et al., 2009; Hodge et al., 2013)have shown that a significant fraction of single-dish detected sources are in fact comprised ofmultiple galaxies. Since degeneracies with nearby sources are a dominating factor in determiningour ability to constrain their far-IR properties (see Fig. 3.4), such sources will have particularlypoor constraints on their far-IR properties. In Fig. 3.8 we explore the benefits of adding ALMABand 9 observations at 460m, with an rms of 1mJy, for the case of two standard sources343B3B hysting with simulutyx sourwys9ighee 3.7- Constraining power of our model for the case of varying redshift uncertainty. Here, 68%,95% and 99.7% credible regions are shown for redshift uncertainties of 0, ±0.5 and ±1, in black, red andblue contours, respectively. A large uncertainty in redshift is one of the main limitations for constrainingdust temperature,as well as far-IR luminosity.353B4B hhy propyrtiys of suvmm gulufiiys within thy ULEgg survyy9ighee 3.8- Constraining power of our model for the case of two standard sources separated by 5 arcsec-onds. The black contours denote 68%, 95% and 99.7% credible regions using 0.5mJy rms 870m ALMABand 7 observations, while the red contours are when 1mJy rms 460m ALMA Band 9 observationsare added along with 870m ALMA Band 7 observations.separated by 5 arcseconds on the sky. Since the peak of the SED for our standard sourceis at 323m, which is shorter than both the ALMA wavelengths considered, only moderateimprovement in constraining power is expected, and this is what is seen in the simulations.Specifically, the lower bound on the temperature is improved, which in turn improves theconstraint on far-IR luminosity. Much bigger improvements in constraining power are realisedwhen the peak of the SED is straddled by the two ALMA wavelengths, as would be the case ifour standard source were at a higher redshift or had a lower dust temperature. Fig. 3.9 showsthe improvement for the case of two standard sources separated by 5 arcseconds, where thestandard sources are moved to a redshift of 4 and their peak flux densities remain unchanged.In this case, degeneracies between the two sources are nearly eliminated when adding a secondALMA band.3CI ihe properties of suwmm gvlvxies fiithin the VaEhhsurve–When fitting our model to the data, we use the ALMA 870m fluxes and positions from Hodgeet al. (2013) and the photometric redshift estimates of Simpson et al. (2014), which were usedby Swinbank et al. (2014). The photometric redshift constraints are considered to be ±1363B4B hhy propyrtiys of suvmm gulufiiys within thy ULEgg survyy9ighee 3.9- Constraining power of our model for the case of two standard sources, moved to a redshiftof 4, while keeping the same peak flux density, and a separation of 5 arcseconds. The black contoursdenote 68%, 95% and 99.7% credible regions using 0.5mJy rms 870m ALMA Band 7 observations,while the red contours are when 1mJy rms 460m ALMA Band 9 observations are added along with870m ALMA Band 7 observations.373B4B hhy propyrtiys of suvmm gulufiiys within thy ULEgg survyyGaussian priors in our model. As in Swinbank et al. (2014), we treat any source in the NMJScatalogue as a duplicate if it is within 1.5 arcseconds of an ALESS or another NMJS source.We found that our data have almost no constraining power on the dust emissivity, , whenit is allowed to range over 1.0−2.5, and thus we simply fix it to a nominal value of 1.5 so thatwe may easily compare the ALESS sample with the sample of Symeonidis et al. (2013). We seta hard prior on the dust temperature such that it must be above 10K, since no colder galaxieshave been found in any similar surveys (e.g. Dale et al., 2012; Amblard et al., 2010; Symeonidiset al., 2013). This hard prior is useful for when the peak of the SED is shifted close to, orbeyond, the ALMA 870m wavelength, which occurs at high-redshifts when the source is cold(see Fig.3.6); thus this prior keeps the model from entering an unphysical region of parameterspace. We also use a hard prior to keep the dust temperature from going beyond 100K, sinceno source in the ALESS sample was found to be this warm by Swinbank et al. (2014).We report the median values of our MCMC chains and report 68% credible intervals through-out. Far-IR luminosities are calculated by integrating the model SED from 8 to 1000m. Wheneither the dust temperature or far-IR luminosity lower credible interval are consistent with ei-ther zero far-IR luminosity or 10K for dust temperature, we report the upper 84% credibleinterval as an upper limit. Note that because of our prior on dust temperature, upper limits fordust temperature are somewhat subjective in that the upper limit would move if we changedthe dust temperature prior. While we may only have upper limits in one of these parameters,this does not necessarily translate into an upper limit on the other. In fact, for only one casedo we have an upper limit on both far-IR luminosity and dust temperature. The resultingfar-IR luminosity and dust temperature constraints are given in Table A.1. Note that we donot report any constraints for ALESS083.4, since the redshift of the source puts the peak ofthe SED shorter than the available data and thus no constraints on dust temperature or far-IRluminosity are possible.3CICF Compvrison fiith hfiinwvnk et vlC =2EFI)The benefit of applying our method to this sample of ALESS sources is that we can compareour results with those of Swinbank et al. (2014), who employed a modern competing method ofdeblending and SED fitting. To facilitate the comparison, we have used much of the same data,although there are also key differences that make a detailed comparison less than straightfor-ward. To facilitate the comparison, we have used the same ALESS catalogue of positions andflux densities (Hodge et al., 2013), the same NMJS catalogue, the same Hyrswhyl-SPIRE andPACS 160m data, and the same redshift estimates (Simpson et al., 2014). Aside from themethod used to deblend the Hyrswhyl data, important differences include the use of an SEDlibrary and the inclusion of both shorter and longer wavelength data when fitting SEDs (seeSwinbank et al., 2014).Fig. 3.11 compares the results of our two methods to assess their level of agreement. Theblack dashed line in both plots shows the locus representing complete agreement, and theSwinbank et al. (2014) dust temperatures used in the comparison are those that were derivedfrom fitting a modified blackbody to the Hyrswhyl photometry. We use a fixed dust emissivityindex of 1.5, primarily so that we may also compare our results with those of Symeonidis et al.(2013). An apparent systematic shift towards hotter dust temperatures is seen for our resultsof around 4K; however, comparing dust temperatures requires knowledge the SED used to fitthe data and any priors on the dust emissivity. We found that using a dust emissivity of ∼ 1:9would eliminate this systematic, however Swinbank et al. (2014) allowed the dust emissivity tovary between 1.5 and 2.2 and found an average best fit value of 1.8, thus this dust temperature383B4B hhy propyrtiys of suvmm gulufiiys within thy ULEgg survyydiscrepancy is mostly due to a difference in dust emissivity. When we allow the dust emissivityto vary freely between 1 and 2.5, we found that the data had almost no constraining power onthe dust emissivity.When comparing the far-IR luminosities, a clear correlation can bee seen between the twomethods with a slight tendency for our method to fit higher far-IR luminosities for more lu-minous objects and and lower far-IR luminosities for less luminous objects. Again, the choiceof specific SED model will affect results here, primarily the lack of a shorter wavelength hotcomponent to our SED model, as well as the use of shorter and longer wavelength data usedby Swinbank et al. (2014). Such a comparison would require us to develop a more complicatedSED model that would allow us to incorporate these other wavelengths.Overall, we believe our method to be an improvement over what has been used in manyprevious studies of submm galaxies and its effectiveness has been shown in Section 3.3.1. Itforgoes the need to deblend confused imaging prior to fitting SEDs; Our method fits SEDs anddeblends the images simultaneously and harnesses prior knowledge of the expected source SEDshape.3CIC2 Dust tempervtures vny selextion effexts for VaEhh sourxesThe top panel of Fig. 3.10 plots the dust temperature versus far-IR luminosity for the ALESSsample. Many previous studies showed a correlation between dust temperature and far-IRluminosity (the a–id relation, e.g. Chapman et al. (2005); Magnelli et al. (2012); Casey (2012);Symeonidis et al. (2013)), although some authors have noted that many of these studies arebiased by selection effects (e.g. Chapin et al., 2009, 2011; Swinbank et al., 2014). Over-plottedon the top panel of Fig. 3.10, using a solid black line, is the a–id relation as found by Symeonidiset al. (2013). The sample of sources used to find this relation were specifically chosen with theaim of minimising selection effects and are likely the most accurate representation of the a–idrelation in the literature. A major result of Symeonidis et al. (2013) is that sources at z < 0:1are on average a few Kelvin warmer than those with redshifts ranging from 0.1 to 2. For ourstudy, we have specifically chosen a value of the dust emissivity that allows us to compareour results directly to those of Symeonidis et al. (2013), to test if dust temperature evolvesfurther at higher redshifts. Upon first inspection, it would appear that the ALESS sourcesare indeed cooler, however, we must consider the selection effects of our sample. In the toppanel of Fig. 3.10, the red and purple, dot and dashed lines, denote representative ALMA 3.5detection limits for redshifts of 1, 3, 5, and 7. In the region where our two samples overlap, itis clear that these detection limits bias our sample to cooler temperatures.To test whether or not our sample is indeed cooler, we devise a method of applying theALESS sample selection effects to the Symeonidis et al. (2013) sample. We obtained thecatalogue of sources used to create the estimate of the a–id relation of Symeonidis et al.(2013) (solid black line in Fig. 15), including source far-IR luminosities and dust temperatures.We randomly draw n objects from this source list, where n is the number of sources in thelist, with replacement. We randomly assign to these sources, redshifts from the ALESS sourcecatalogue, such that they will have the same redshift distribution. We retain those sources thathave a predicted flux density greater than the 3.5 ALMA flux limit at 870m and calculate themean dust temperature of this sample of sources. We perform this procedure many times, thusbootstrapping the sample, and restrict our test to sources with luminosities between 10N2 and10NP L⊙ (where the two samples overlap). We find a mean dust temperature of (35.6±0.8)K.Using a similar procedure, we find a mean dust temperature of (33.9±2.4)K for the ALESSsample. Since these values are completely consistent, we cannot conclude that we detect any393B4B hhy propyrtiys of suvmm gulufiiys within thy ULEgg survyy1e+11 1e+12 1e+13 1e+14Far-IR luminosity [Solar Lum]20406080Du st  te mp er at ur e [ K]ALESSALESS: upper far-IR lumALESS: upper dust tempz = 1 ALMA 1.75 mJyz = 3 ALMA 1.75 mJy z = 5 ALMA 1.75 mJyz = 7 ALMA 1.75 mJySymeonidis et al. (2013)0 2 4 6Redshift1e+111e+121e+131e+14F ar -I R l umi no si t y [ So l ar  Lu m]ALESSALESS: upper far-IR lumTz = 32 K, 250 microns, 1.4 mJyTz = 32 K, 350 microns, 1.6 mJyTd = 32 K, 500 microns, 1.5 mJyTd = 32 K, 870 microns, 0.5 mJy9ighee 3.10- hop: Dust temperature vs far-IR luminosity for the ALESS sample. Black points areALESS sources with constraints on both the far-IR luminosity and dust temperature. Red points areALESS sources with 1 upper limits on far-IR luminosity. Green points are ALESS sources with 1upper limits on dust temperature. Dot and dashed lines are representative 3.5 detection limits ofthe ALMA data for redshifts between 1 and 7. The solid black line is the far-IR luminosity to dusttemperature relation found by Symeonidis et al. (2013). It is clear from the detection limits that oursample is biased towards colder dust temperatures. Vottom: Far-IR luminosity vs redshift for the ALESSsample. The colour of the points denote the same objects as above. Representative 1 detection limitsare drawn for a id=33K source for 250, 350, 500 and 870m in black, red, green, and blue, respectively.ALESS sources with upper limits on dust temperature can be found in the region between the ALMAand Hyrswhyl SPIRE detection limits, implying a detection by ALMA, but little or no flux seen byHyrswhyl SPIRE.403B4B hhy propyrtiys of suvmm gulufiiys within thy ULEgg survyy10 20 30 40 50 60Swinbank et al. (2014) Dust Temperature [K]1020304050607080Du st  Te mp er at ur e [ K]ALESSALESS: upper dust tempAgreement1e+12 1e+13Swinbank et al. (2014) Far-IR luminosity [Solar Lum]1e+111e+121e+13F ar -I R l umi no si t y [ So l ar  Lu m]ALESSALESS: upper far-IR lumAgreement9ighee 3.11- A comparison of our results with those found by Swinbank et al. (2014). hop: comparisonof dust temperatures between the two methods. Vottom: Comparison of far-IR luminosities. Black pointsare ALESS sources with constraints on both the far-IR luminosity and dust temperature. Red pointsare ALESS sources with 84% upper limits on far-IR luminosity. Green points are ALESS sources with84% upper limits on dust temperature. The dashed black line shows the expected relation if the twomethods were in agreement. While our results show a clear correlation with those found by Swinbanket al. (2014), there is disagreement for many of the ALESS sources. One prominent feature appears tobe roughly a 4K offset in temperature between the two methods. This discrepancy is explained by adifference in dust emissivity used.413B4B hhy propyrtiys of suvmm gulufiiys within thy ULEgg survyy1e+11 1e+12 1e+13Far-IR Luminosity (Solar Lum)204060Du st  Te mp er at ur e ( K)Hezaveh (2013)Mackenzie (2013)Sklias (2013)9ighee 3.12- Dust temperature versus far-IR luminosity for a sample of lensed submm galaxies(MacKenzie et al., 2014; Sklias et al., 2014; Hezaveh et al., 2013). The black line denotes the av-erage dust temperature of the ALESS sample with the ±8K standard deviation shown as the blackdashed lines. Red and purple dot and dashed lines are representative 3.5 detection limits of the ALMAdata for redshifts of 1, 3, 5, and 7.evolution in dust temperature with redshift in the ALESS sources when compared to those ofSymeonidis et al. (2013). The selection effects of the ALESS sample unfortunately precludeany attempt at performing this same test for those sources with z < 0:1.Instead of going deeper, a useful way to probe the a–id relation for fainter sources athigh redshift is to use strong gravitational lensing. The particular striking case of a stronglylensed galaxy group at z = 2:9 was presented in Chapter 2 and is another example of sourcemultiplicity. Along with the lensed sources of Sklias et al. (2014), we have examples of sevenhigh redshift sources in the region of the a–id plane excluded by the ALMA selection effects,five of which have dust temperatures warmer than the average of the ALESS sample. Fig. 3.12shows these sources along with sources from Hezaveh et al. (2013), which although fainter,would be bright enough to be included in the ALESS catalogue. The solid and dashed linesdenote the 34.6K average temperature and 8K standard deviation of the ALESS sample. Thissupports our conclusion that selection effects drive the a–id to apparently lower temperatures.3CIC3 Contriwution to the xoBmoving stvr formvtion rvte yensit– of theUniverseFig. 3.13 shows the co-moving SFR density for the ALESS sources with flux densities greaterthan 4.2mJy, using a conversion factor of 1:08 × 10−N0M⊙yr−NL−N⊙ for a Chabrier IMF, as inSwinbank et al. (2014). The vertical error bars on our results are 68% confidence intervalsfor the co-moving SFR density after bootstrapping the MCMC chains and the horizontal errorbars are the 16th and 84th percentile of the redshift distribution used to generate each datapoint, with the data point being plotted at the 50th percentile of the redshift distribution usedwithin that bin. For comparison, the points plotted from Swinbank et al. (2014) are divided423B4B hhy propyrtiys of suvmm gulufiiys within thy ULEgg survyy0 2 4 6Redshift0.0010.010.1C o- Mo vi ng  S FR  De ns i ty  ( Ms olyr- 1Mp c-3 ) S870 > 4.2 mJy, Swinbank (2013)S870 > 4.2 mJy, this work9ighee 3.13- Contribution of the ALESS sources with flux densities greater than 4.2mJy to the co-moving star formation history of the Universe. The vertical error bars on our results are 68% confidenceintervals for the co-moving SFR density after bootstrapping the MCMC chains and the horizontal errorbars are the 16th and 84th percentile of the redshift distribution used to generate each data point, withthe data point being plotted at the 50th percentile of the redshift distribution used within that bin. Forcomparison, we include the data points from Swinbank et al. (2014), divided by a factor of 2, which theyuse to correct their estimate, as the region is though to be under dense (Casey et al., 2009).433BIB Conwlusionsby a factor of 2, which they use to correct their estimate, as the region is though to be underdense (Casey et al., 2009). Although our competing methods may produce significantly differentfar-IR constraints for individual sources, this particular measurement agrees rather well withthose of (Swinbank et al., 2014). As such, we refer the reader to Swinbank et al. (2014) forinterpretations and extrapolations for this particular metric of the data.3C5 ConxlusionsAfter generalising our method from Chapter 2 for the case of deblending SEDs of confused pointsources, we were able to show that our method gives realistic estimates of far-IR properties andtheir uncertainties and accurately captures the degeneracies among SED parameters of nearbysources caused by confusion. When applied to the ALESS catalogue, we were able to giveconstraints on dust temperatures and far-IR luminosities and show that our results correlatewith those of Swinbank et al. (2014), although our derived far-IR properties differ significantlywhen comparing individual sources. Hyrswhyl SPIRE currently provides the best view of the250, 350 and 500m extragalactic sky in terms of depth and sky coverage. The majority ofthese data are confusion limited, yet many of the methods being used . Using the sample ofSymeonidis et al. (2013) and applying the same selection function as the ALESS sample, wewere able to show that any evolution of the a–id relation to cooler dust temperatures at highredshifts, are indistinguishable from selection effects.With the large quantities of confusion limited imaging now available, such as that fromHyrswhyl, applications of our method are many. One possibility is obvious: the co-movingSFR density of the Universe as seen within the Hubble Ultra Deep Field (HUDF). Confusionlimited Hyrswhyl-SPIRE imaging for this field are already available, and in Section 3.3.2 weshowed how ALMA observations at more than one frequency can greatly aid in deblendingSEDs. Combining these observations with the spectroscopic and photometric catalogues thatcurrently exist would yield worthwhile results.44Chvpter IhCUBV{2 follofiBup of xvnyiyvteelvnxk protoBxlustersICF IntroyuxtionNew submm observatories, such as the JCMT (Holland et al., 1999), BLAST(Pascale et al.,2008) and Hyrswhyl (Pilbratt et al., 2010a), have allowed us to view larger and larger portionsof the submm sky to greater and greater depths, continually improving the statistics on thisrelatively new population of sources. Of particular interest is the role of these sources in theircontribution to global star formation rates (SFR) and the driving force behind their intense starformation. While some may be triggered by mergers(e.g. Sanders and Mirabel, 1996), othersmay simply be at the bright end of what have been named the “main sequence” of galaxies(Noeske et al., 2007; Daddi et al., 2007; Elbaz et al., 2011b). While most wide-field cosmologysurveys try to characterise this population as a whole, it is important to consider the effects ofgalaxy environment on star formation. Due to detection techniques, most known clusters are atredshifts below that of the peak of star formation, and their star formation has been quenchedthrough various physical processes, although galaxies falling into their gravitational potentialwells for the first time may still experience an increase in star formation (Verdugo et al., 2008;Braglia et al., 2009, 2011). Those clusters detected through the Sunyaev-Zeldovich effect,while redshift independent above z ∼ 0:25, require the presence of hot intra-cluster plasma(Zeldovich and Sunyaev, 1969; Sunyaev and Zeldovich, 1970). This technique has been usedto detect hundreds of clusters out to z ∼ 1:5 (e.g. Planck Collaboration VIII, 2011; Hasselfieldet al., 2013; Planck Collaboration XXIX, 2014; Planck Collaboration XX, 2014; Bleem et al.,2015).A complementary high-z cluster detection technique is to look for regions of exceptionalstar formation. Due to the density of such objects on the sky, large areas must be probed inorder to find a significant sample, thus all-sky surveys are needed. dlunwk (with its 5 arcminutebeam that closely matches the expected size of a forming galaxy cluster at z ∼ 2–4), along withits all-sky coverage, makes it a good observatory for finding such objects. Thus, the searchwas performed and the first results can be found in Planck Collaboration XXVII (2015) andCan˜ameras et al. (2015).Two methods were used to generate a list of potential high-z targets to follow-up withHyrswhyl (see Planck Collaboration XXVII 2015 and Planck Collaboration XXXIX 2015 fordetails). The first uses CMB and Galactic-cirrus cleaned dlunwk maps at 353, 545 and 857GHz,using only 26% of the sky which is the least contaminated by Galactic sources. S/N S 5 sourcesare identified in a 545GHz excess map, defined to be the 545GHz map with a linear interpolationbetween the 353 and 857GHz maps subtracted. On top of this, S/N S 3 detections are requiredat 353, 545 and 857GHz. To remove cold Galactic cores and extragalactic radio sources, onlysources with hR4R=hURT S 0:5 and hPRP=hR4R < 0:9 are retained. The second method usedThe Planck Catalogue of Compact Sources (PCCS, Planck Collaboration XXVIII, 2014) and454BEB Introxuwtiona selection method based on the work of Negrello et al. (2010b). Here, 52% of the sky is usedbased on the 857GHz Galactic mask, and sources with S/N S 4 at 545GHz are selected fromthe catalogue. From this list, sources are only retained with hURT=hR4R < 1:5 and h2NT=hPRP < 1,and which are not identified as a local galaxy, a bright radio source or Galactic cirrus in eitherthe NASA/IPAC Extragalactic Database (NED), ALADIN, or IRAS maps. The result is alist of over 2000 high-z candidate sources, selected to have apparent redshifted flux densitiespeaking between 353 and 857GHz. Included in this is a combination of strongly lensed sources,proto-clusters undergoing massive starbursts, chance overdensities of star forming galaxies, andperhaps a few Galactic interlopers. The fraction of objects in the various categories is currentlyunknown, which is why follow-up observations are critical.A total of 228 of these candidates were observed by Hyrswhyl using the Spectral and Pho-tometric Imaging Receiver Griffin et al. (SPIRE, 2010). This instrument, with a beamsize16 times smaller than dlunwk’s, has the ability to resolve the dlunwk candidates into eithersingle bright point-sources or overdensities within the dlunwk beam. The former were shownto be among the brightest strongly lensed sources on the sky by Can˜ameras et al. (2015);11 out of 15 of these bright sources were followed-up (two were previously known (Fu et al.,2012; Combes et al., 2012) and two are in the far south) with a host of instruments, includingSCUBA-2 at 850m, spectroscopic observations using the wide-band heterodyne receiver EightMIxer Receiver (EMIR) at the Institut de Radioastronomie Millime´trique telescope (IRAM)and SMA 850m interferometry to confirm their lensed nature. Their redshifts range from 2.2to 3.6, with peak flux densities ranging from 0.35 to 1.14 Jy, and they have apparent far-IRluminosities up to 3× 10N4 L⊙. Due to their extra-ordinary flux densities and far-IR luminosi-ties, these sources have been aptly named “dlunwk’s dusty GEMS” (Gravitationally EnhancedsubMillimetre Sources).The first results covering the overdensity fields are presented in Planck Collaboration XXVII(2015). They find significant enhancements in the surface density of sources at 350 and 500m,with the majority of sources peaking at 350m. Assuming an average dust temperature of 35K,they find a typical redshift of 2 for the overdensity fields with average far-IR luminosities ofaround 4× 10N2 L⊙ per SPIRE source. These overdensities may be high redshift proto-clustersundergoing rapid starformation, although they may also be chance line-of-sight alignments.Without spectroscopic redshift estimates of the objects within these overdensities, it is impos-sible to distinguish between these two possibilities.The analysis here focuses on the SCUBA-2 observations, based on 61 of the 228 Hyrswhylfields that have been followed up with 850m observations at the JCMT. 11 of these fieldsare observations of dlunwk’s dusty GEMS and are detailed in Can˜ameras et al. (2015). The51 overdensity fields are discussed here. The more favourable “k-correction” (A method ofcorrecting the measured flux density of an object for the effects of redshift, given that weare observing an intrinsically brighter region of the SED; Franceschini et al., 1991; Blain andLongair, 1993) at 850m means that we have a significantly less biased view on the redshiftdistribution of the overdensity fields than Hyrswhyl and a greater sensitivity for sources atredshifts ≳ 3. We use the method adapted from Chapter 2, as described in more detail inChapter 3, to fit modified blackbody SEDs to the SCUBA-2-detected sources. To do this, weuse the SCUBA-2 positions and fluxes, as well as the Hyrswhyl-SPIRE imaging. We use a prioron dust temperature to break its degeneracy with redshift, giving us useful constraints on bothredshift and far-IR luminosities. Throughout we employ a ΛCDM cosmology with Ω = 0:728,Ωm = 0:272, and H0 = 70:4 km s−NMpc−N (Komatsu et al., 2011).464BFB hhy dlunwk wunxixutys followAupIC2 ihe elvnxk xvnyiyvtes follofiBupIC2CF hCUBVB2 follofiBup51 overdensity fields observed with Hyrswhyl have been followed-up with SCUBA-2 850mobservations at the JCMT (project codes:M12AC19, M13AC22, M13BC05, M13BU09, andM14AC02) with approximately 10 arcminute diameter Lissajous scans. The observations werereduced using fmhef (Chapin et al., 2013) called from the oeac-de pipeline (Gibb and Jenness,2010) using the standard blank-field map-making recipe optimised for finding point-sources.Readings from the JCMT water-vapour monitor (WVM, Dempsey and Friberg 2008) and thescaling relations found by Dempsey (Dempsey et al., 2010) were used to correct for atmosphericextinction.To facilitate finding and extracting of point-sources, we use the standard “matched-filter”provided by oeac-de. This procedure subtracts a 30 arcsecond smoothed map from a mapconvolved with the PSF of the telescope and applying a scaling factor such that point sourcesreturn the correct flux density. The purpose of the filter is to remove any large scale structuresfrom the map and facilitate the identification of point like sources. The minimum rms depths ofeach field range from 1.5 to 3mJy, with a median of 1.9mJy for point sources in the matched-filtered images. We extract peak flux densities and positions from these maps to generate acatalogue of 172 SCUBA-2-detected sources with a S/NS4 in 1.20 deg2 of sky for the 51 dlunwkoverdensity fields. We also require a flux density uncertainty of less than 4mJy for every sourcesince higher noise regions near the edges of the maps are more likely to be artifacts of the map-making procedure. Of the 1.2 deg2, 0.69 deg2 was within the dlunwk beam, which we define tobe the area in the dlunwk 353GHz map with flux density greater than half the peak flux densityof the dlunwk source, as in Planck Collaboration XXVII (2015). Of the 172 SCUBA-2-detectedsources, 138 are located within the dlunwk beam. Table A.2 list the source positions and fluxdensities, as well as constraints on their far-IR luminosities and redshifts.In order to assess the number of spurious sources within our catalogue, we perform thesame source extraction procedure for negative sources within our maps and find 28 negativepeaks satisfying our selection criteria. This is higher than expected given the area observed,possibly caused by map-making/bolometer artifacts. For this process, we avoid negative sourcesassociated with “negative bowls” surrounding bright positive sources caused by the matched-filter. More details pertaining to the possibility of spurious sources are given below. Since thenumber counts in these regions will differ from those in cosmological fields, and hence it is hardto estimate the effects of confusion(see e.g. Coppin et al., 2006; Scott et al., 2010), we refrainfrom deboosting the flux densities of our catalogue.IC2C2 Herschel heIgE yvtvAll our observed fields have accompanying Hyrswhyl-SPIRE observations at 250, 350 and 500m.These observations have been reduced using hice 10 (Ott, 2010), with the details given in PlanckCollaboration XXVII (2015). The images have instrumental noise levels of 7.7, 6.3 and 7.6mJyper pixel using the standard pixel sizes of 6, 10 and 14 arcseconds at 250, 350 and 500m,respectively. Thus, the noise level in the images are near the confusion limit of Hyrswhyl-SPIRE(Nguyen et al., 2010).474B3B gED moxyl unx ttingIC3 hED moyel vny ttingWe use the same modified blackbody SED and fitting method as described in Section 3.2.1,with a few key differences. First, since we do not have a catalogue of nearby sources to usefor deblending, we instead use blank sky to estimate the sky covariance matrix. Specifically,we turn to the GOODS-North HerMES field used in MacKenzie et al. (2014), with Gaussianrandom noise added in quadrature to the instrumental noise, so that the images contain thesame noise properties as the overdensity fields. We treat the SCUBA-2-detected sources inthe same way as the ALMA resolved LESS sources in Section 3.2.1, using the source positionsand flux density estimates at 850m (although source positions are not as well constrained, ofcourse). To account for this, we allow source positions to vary, with a 3 arcsecond positionalprior, applied to the radial offset, up to a maximum of 10 arcseconds. Such positional errorsare typical for 5 SCUBA-2 850m sources (Simpson et al., 2015). In addition to allowing forsource position uncertainties, we allow the telescope pointing to vary with a 1.5 arcsecond prior.The former positional prior accounts for source position uncertainty due to instrumental noiseand applies to sources individually, while the later accounts for telescope pointing uncertaintyand affects all sources within a field the same way. As well as that, a 5% calibration uncertaintyis used for the SCUBA-2 flux estimates (Dempsey et al., 2013).While the ALESS sample had independent photometric redshift estimates (Simpson et al.,2014), our catalogue does not. Instead, we apply a prior on dust temperature in order to gener-ate estimates for both redshifts and far-IR luminosities of our sample. Of course, the adoptionof a dust temperature prior means that our redshift estimates would change if we imposed adifferent prior; however, we make sure to choose a prior distribution with a realistic width, andto the extent that the dust temperature does not change dramatically with redshift, our far-IRluminosity estimates should be good in a relative sense. Using sources above the 4.2mJy fluxlimit of LESS for the ALESS follow-up in Chapter 3, we found a dust temperature distributionof 33HNP−9 K using 68% confidence intervals, and we use this as our dust temperature prior. Notethat this represents the distribution and not the error on the mean of the distribution. Thiscentral dust temperature and range is consistent with previous estimates for sources selectedat 850m (e.g. Chapman et al., 2005; Swinbank et al., 2014).In addition to fitting SEDs to the SCUBA-2-selected sources in the dlunwk overdensity fields,we also apply the same method to SCUBA-2-selected sources from the Cosmology Legacy Survey(CLS, Simpson et al., 2015) within the Ultra Deep Survey (UDS) field (Lawrence et al., 2007).This field also has accompanying Hyrswhyl-SPIRE observations from HerMES (Oliver et al.,2012). By performing an identical treatment to the sources that are detected in this field, weare able to perform a direct comparison with the dlunwk overdensity fields. In addition to theavailability of both SCUBA-2 and Hyrswhyl-SPIRE observations, this field was chosen since thedata are deeper and the area of the sky surveyed is almost identical to that covered by thedlunwk overdensity fields. Before fitting SEDs to these sources, we add Gaussian random noisein quadrature to the instrumental noise of the HerMES SPIRE images to give it the same noiseproperties as the dlunwk overdensity fields, while accounting for the difference in pixel sizes.This catalogue contains 619 SCUBA-2-detected sources within 1.05 deg2 of sky, with an averagesource flux density uncertainty of 1.2mJy. Similarly, we find 26 negative sources within theUDS field.484B4B gED tting rysultsICI hED tting resultsThe results of the SED fitting are shown in Fig. 4.1 and listed in Table A.2 along with 68%percent confidence intervals. Due to the wavelength coverage of the data, we are not able toconstrain redshifts for sources with redshifts greater than 6.5, and for those sources we report84% confidence lower limits. For high redshift sources, these limits are affected by a hard priorthat sources cannot have a redshift greater than 10. Using our temperature prior of 33HNP−9 K, weachieve a photometric redshift uncertainty of z=(1 + z) ≈ 0:28, with 68% confidence intervalsskewed to higher redshifts due to the asymmetric prior. In addition to fitting SEDs to the 172SCUBA-2-detected sources, we fit SEDs to the 28 negative sources in the map above the 4cutoff (treating the negative flux densities at 850m as positive). Since there should be noHyrswhyl counterparts, the majority of these sources are constrained to the high redshift regionof Fig. 4.1, with 19 of the 28 negative sources falling into this category. Of the 172 positivesources in our catalogue, 32 sources have median redshifts greater than 6.5. Thus, the majorityof sources with a redshift greater than 6.5 should be considered suspect. Only 9 negative sourcescoincidentally have Hyrswhyl counterparts and redshift estimates lower than 6.5, therefore thosesources with lower redshifts should be considered reliable (∼ 6% contamination).IC5 DisxussionIn Fig. 4.1, the majority of well constrained sources have far-IR luminosity estimates of around10NPL⊙, corresponding to SFRs of roughly 1000M⊙ yr−N. On average, these sources are moreluminous than those found by Planck Collaboration XXVII (2015), which have an averageof 4 × 10N2L⊙ (assuming a dust temperature of 35K), although this is easily explained whenconsidering the selection effects. A representative 2mJy 1 detection limit for a 33K source isplotted in Fig. 4.1 with a solid blue line along with Hyrswhyl-SPIRE confusion limits for a sourceof the same dust temperature and dust emissivity. From these detection limits, it is clear thatSCUBA-2 is significantly less biased toward low redshift sources than Hyrswhyl-SPIRE and ismore sensitive for sources at redshifts of ≳3. While Planck Collaboration XXVII (2015) foundthat only 3.5% of Hyrswhyl-SPIRE 350m-detected sources peak in the 500m waveband, wefind that 33% of the SCUBA-2-detected sources have SED models with predicted a 500m to350m flux density ratio greater than 1.Fig. 4.2 shows the estimated redshift distribution of the SCUBA-2 catalogues within thedlunwk beam for the dlunwk overdensities, with 68% confidence intervals. Also plotted is theexpected CLS UDS redshift distribution, given the same survey area and selection function.This plot is generated by bootstrapping the MCMC chains and is corrected for contributionsfrom spurious sources by subtracting the redshift distribution of the negative SCUBA-2 sources.The majority of these sources have redshifts greater than 6 due to the absence of associatedHyrswhyl-SPIRE detections and their subtraction should correct the estimated redshift distri-bution for contribution from spurious positive SCUBA-2 detections. In order to give the CLSsources a similar selection function and flux density boosting as the overdensity fields, we addGaussian random noise to the CLS SCUBA-2 fluxes, such that the distribution of flux densityuncertainties matches the distribution of randomly selected points within the dlunwk overden-sity fields with a flux density uncertainty < 4mJy and that are within the dlunwk beam. It isimportant to note that this estimated redshift distribution is actually a convolution betweenthe true redshift distribution and the redshift error distribution, and because of this, the plot-ted points are not independent. For the majority of sources in the z = 1 - 7 range, this error494BIB Diswussion1e+12 1e+13 1e+14Far-IR Luminosity (Solar Lum)02468Re ds hi f t250 microns: 6.8 mJy350 microns: 6.3 mJy500 microns: 6.8 mJy850 microns: 2.0 mJyDetection limitLower redshift limitsPlanck sources9ighee 4.1- Constraints on far-IR luminosities and photometric redshifts for the sample of SCUBA-2-detected sources within the Planck overdensity fields. We report the median values from the MCMCchain points and plot 68% confidence intervals for both far-IR luminosities and photometric redshifts.Photometric redshifts for sources with redshifts less than 1 or greater than 7 are not possible due to thepeak of the SED being located outside wavelength coverage; these sources are shown with red pointsand 84% upper/lower confidence intervals are plotted. Solid lines denote 2.0, 6.8, 6.3, and 5.8mJylimits at 850, 500, 350, and 250m, respectively, for a 33K dust temperature and 1.5 dust emissivitymodified blackbody (the former is a representative 850m point source flux density uncertainty andthe later are the Hyrswhyl-SPIRE confusion limits, Nguyen et al., 2010). The black dashed line denotesa representative 4 sigma detection limit for our 850m selected sample. Note that our source list isexpected to have a rather high number of spurious sources (∼ 28). When fitted, many of these sourcesget constrained to redshifts greater than 6.5 since the SPIRE images contain no sources in their proximity.For redshifts less than 6.5, we only expect ∼ 9 spurious source, based on searching for negative peaks.504BIB Diswussiondistribution function is z=(1 + z) ≈ 0:28. This distribution peaks at a higher redshift thanfound by Planck Collaboration XXVII (2015) and due to the favourable selection effects ofobserving at 850m, this redshift distribution may more accurately reflect the true redshiftdistribution of the dlunwk overdensities. If most of the dlunwk overdensities are in fact physi-cally associated structures, those sources found by Planck Collaboration XXVII (2015) wouldbe at higher redshifts and have warmer dust temperatures than assumed. Conversely, we maybe detecting colder components of these structures. However, the redshift distribution of theSCUBA-2-selected dlunwk overdensity sources is not significantly different than those within theCLS UDS field, other than a factor of ∼ 4 increase in the number of sources. This may suggestthat most of these structures are line-of-sight enhancements rather than physically associated.Using sources within the dlunwk beam and the CLS UDS, we can assess what fraction of thedlunwk 353GHz flux density we recover at 850m with SCUBA-2. To do this, we must firstquantify the expected total flux density recovered from the CLS UDS so that we may subtractthe expected blank field contribution from the total within the dlunwk beam. Applying thesame selection function to the CLS UDS source list as the dlunwk overdensity fields, as describedabove, we recover a total flux density of 0.39 Jy within the 1.05 deg2, of the dlunwk beam. Fromthe Cosmic Background Explorer (COBE) satellite, the total flux density of this area shouldbe 46 Jy (although admittedly with a ∼30% uncertainty, Fixsen et al., 1998), thus we onlyrecover about 1% of the far-IR background. dlunwk measured an average 850m flux densityof 470mJy per field, totalling 23.6 Jy, and with SCUBA-2, we have recovered 1.53 Jy of thisflux. Subtracting off the expected blank-field contribution estimated from the CLS UDS field,we conclude that we recover around 5% of the dlunwk flux density within these fields. Thismeans that the 850m number counts are enhanced by a larger amount at high flux densitiescompared to fainter sources. One must also consider that the dlunwk flux densities likely havea significant flux boosting, due to their low signal-to-noise and the large area used to find theseoverdensities.We can also try to estimate the contribution of these sources to the cosmic star-formationhistory. Fig. 4.3 shows the co-moving SFR density for SCUBA-2-detected dlunwk overdensitysources within the dlunwk beam and CLS UDS fields with flux densities greater than 8mJy(and flux density uncertainty < 2mJy) assuming a dust temperature prior of 33HNP−9 K and aconversion factor of 1:08 × 10−N0M⊙yr−NL−N⊙ for a Chabrier IMF (Swinbank et al., 2014). Wesee up to an order of magnitude increase in the dlunwk overdensity fields in comparison with theCLS UDS field, across a broad range of redshifts. Again, this plot is a convolution of the true co-moving SFR density with the redshift error function. This plot is generated by bootstrappingthe MCMC chains and is corrected for contributions from spurious sources by subtractingnegative SCUBA-2 sources (although with our chosen flux cut, we only have 1 negative sourceto subtract from the dlunwk overdensity fields and no correction is applied to the CLS UDSfield). We add noise to the CLS SCUBA-2 flux densities in order to simulate the dlunwkoverdensity selection function, similar to above, but here we match the flux density uncertaintydistribution of regions with uncertainty below 2mJy. With this more strict flux density cut-off, only 0.11 deg2 and 45 sources of the dlunwk overdensity fields remain. In comparison, anaverage of 70 CLS UDS sources and the majority of the original survey area are still used.This translates to uncorrected number counts of 409 and 67 sources per square degree brighterthan 8mJy for the dlunwk overdensity and CLS UDS fields, respectively, i.e. the dlunwk fieldscontain approximately 6 times higher surface density of 850m sources than random parts ofthe sky.514BIB Diswussion0 2 4 6Redshift05101520253035Nu mb er  of  So ur ce sCLS UDSPlanck over-densities9ighee 4.2- Redshift distribution of SCUBA-2-selected sources, assuming a dust temperature priorof 33+13−9 K, for the dlunwk overdensity sample within the dlunwk beam. Also plotted is the expecteddistribution of CLS UDS sources given the same sky coverage and similar selection and flux boostingeffects. Error bars are 68% confidence intervals derived from bootstrapping the sample and have beencorrected for estimated contributions from spurious sources. The dlunwk overdensity fields contain afactor of about 4 more sources than the CLS UDS field, when given a similar selection function and skycoverage.524BIB Diswussion0 2 4 6 8Redshift0.0010.010.1C o- Mo vi ng  S FR  De ns i ty  ( Ms ol yr- 1 Mp c-3 ) Planck over-densities: S850 > 8 mJyCLS UDS:                   S850 > 8 mJy9ighee 4.3- Co-moving SFR density vs redshift for SCUBA-2-detected sources with flux densitiesgreater than 8mJy assuming a dust temperature prior of 33+13−9 K. For comparison, we include resultsfrom fitting to sources within the CLS UDS field using the same technique, given a similar selectionand flux boosing effects. An order of magnitude increase in star formation rate density is seen acrossall redshifts. The grey points are measurements of the global co-moving star formation density from anassortment of sources, as compiled by Madau and Dickinson (2014). This sample is only expected tohave ∼ 1 contributing spurious SCUBA-2 source.534B6B ConwlusionsIC6 ConxlusionsWe have followed up 61 dlunwk high-z candidates using SCUBA-2 on the JCMT. Of these, 10are strong gravitational lenses discussed in Can˜ameras et al. (2015). The other 51 of the fieldsare dlunwk overdensities and possible proto-cluster candidates. We have used the same methodas in Chapter 3 and the available SCUBA-2 and Hyrswhyl-SPIRE observations to constrain theredshifts and far-IR luminosity of 172 SCUBA-2-detected sources, assuming a dust temperatureprior of 33HNP−9 K, as found in Chapter 3. A redshift uncertainty of z=(1+ z) ≈ 0:28 is achievedfor the majority of sources.We show that these overdensity fields have a factor of roughly 6 more sources greater than8mJy than blank field surveys, peaking between a redshift of 2 and 4. These sources appear tofollow approximately the same redshift distribution as those found in blank field surveys. Weresolve around 5% of the total dlunwk flux density. Given the same selection function, blank fieldsurveys only recover about 1% of the extragalactic far-IR background, and thus we concludethat the number counts in these fields are more enhanced at high flux densities (S 8mJy) thanat lower flux densities. We show that the SFR density in these fields are approximately anorder of magnitude higher for sources S 8mJy for redshifts out to z ∼ 6. Determining if thesestructures are in fact physically associated will require spectroscopic redshifts at either opticalor submm wavelengths. Several such projects and proposals are currently underway.54Chvpter 5Conxlusions5CF hummvr– of xonxlusionsWe have developed a new method of deblending SEDs using confused imaging and a forward-modelling technique that preserves important degeneracies that arise when nearby sources arepresent. To fit the model to the data, we use the inverse of the estimated sky covariance (withor without a catalogue of nearby sources subtracted), where residuals are primarily unresolvedfaint sources, rather than instrumental noise. We adapted and applied our method to variousdata sets to show both its flexibility and improvements when compared to traditional methods.First, in Chapter 2, we discovered several new multiply imaged galaxies behind the massiveMS0451.6−0305 cluster at z = 0:55. Using an updated lensing model, we were able to concludethat at least 7 of these multiply imaged galaxies are at a redshift of about 2.9, and possiblyconstitute an interacting galaxy group. With our new method, we were able to disentanglewhich of these galaxies were contributing to the “massive submm arc” in the same region ofthe sky, constraining their dust temperatures, far-IR luminosities, and SFRs. Our methodcapitalises on the unique fact that the multiple images have unique positions and magnificationfactors. We also highlight the improbable nature of finding such a lensed interacting galaxygroup.Going forward, the methods developed here give valuable lessons for approaching otherstrongly lensed submm systems. While several lensed systems appear to be comprised of morethan one lensed source (e.g. Can˜ameras et al., 2015), singly lensed sources can also benefit fromour approach. A single galaxy is not a uniform object that looks the same in every waveband,especially so when considering strongly lensed starburst galaxies being found by current large-area submm surveys (Negrello et al., 2010b; Weiß et al., 2013; Can˜ameras et al., 2015). Suchgalaxies often have disturbed morphologies and when lensed, different regions of the galaxyare magnified by different amounts. When analysing observations that do not fully resolvethe lens, it is critical to employ a forward-modelling approach similar to that which we havedeveloped here. Fu et al. (2012) give a good example of this where they model their sourceas separate components at multiple wavelengths (optical, submm, and radio), which are thenforward-modelled through the lensing potential to recreate the image plane at each wavelength.Using their method, they were able to show that the gas and dust is offset from the stellar massand that the gas component is significantly more extended than the dust. MS 0451.6−0305 canbe seen as a more extreme example of this, where each galaxy in the high-z group has a differentSED, and the lens model therefore gives a morphology that varies with wavelength in the imageplane. Improving on our method would mean adopting the approach of Fu et al. (2012) forforward modelling sources through the lensing model, as opposed to using point sources at thelocation of the multiple images, as we have done.In Chapter 3, we adapted our method for the case of confused point sources and usedit to deblend the SEDs of the ALESS sample (Hodge et al., 2013; Swinbank et al., 2014).Through simulations, we were able to show that our method gives realistic estimates of far-IR properties and their uncertainties, and accurately captures the degeneracies among SED55IBEB gummury of wonwlusionsparameters of nearby sources, caused by confusion. When compared, our results are similarto those of Swinbank et al. (2014), although significant disagreement is seen when comparingsources individually. Using the sample of Symeonidis et al. (2013) and applying the sameselection function as for the ALESS sample, we were able to show that any evolution of thea–id relation to cooler dust temperatures at high redshifts, are indistinguishable from selectioneffects.Implications of this work for the extragalactic submm field are widespread, since confusionlimited Hyrswhyl-SPIRE imaging is currently the highest-impact data available at these wave-lengths. Studies of submm populations through large area surveys, such as HerMES (Oliveret al., 2012) and Hyrswhyl-ATLAS (Eales et al., 2010), are currently being analysed throughdistorted lens of the two-step SED fitting methods. One current method in use, XID (Rose-boom et al., 2010), cannot give independent flux density uncertainty estimates, but relies onassigning flux density uncertainties for populations of sources as a whole. In reality, the flux den-sity uncertainty of an individual source will depend partially on the density of nearby sources.However, XID does make interesting use of a statistic, the AIC (Akaike, 1974), as a tool todetermine which sources from their catalogues they use to deblend the Hyrswhyl-SPIRE images.Such an approach could be used to refine our method. Moving forward, a fraction of the deepestfields within these surveys, such as the Hubble Ultra Deep Field (HUDF), will inevitably befollowed-up using ALMA, and thus our methods can be applied directly to the combined datasets.In Chapter 4, we have followed up 51 dlunwk overdensity fields using SCUBA-2 on theJCMT. We used the same method as in Chapter 3 and the available SCUBA-2 and HyrswhylSPIRE observations to constrain the redshifts and far-IR luminosities of 172 SCUBA-2-detectedsources by assuming a dust temperature prior of 33HNP−9 K, as found in Chapter 3. A redshiftuncertainty of z=(1+ z) ≈ 0:28 is achieved for the majority of sources. We show that these so-called “dlunwk overdensity fields” have a factor of roughly 6 more sources brighter than 8mJythan blank field surveys, with up to an order of magnitude increase in SFR density, whichpeaks between a redshift of 2 and 4. We resolve around 5% of the total dlunwk flux densityinto individual SCUBA-2 sources, and when compared to blank field surveys where only about1% of the extragalactic far-IR background is recovered, we conclude that the number counts inthese fields are more enhanced at high flux densities (S 8mJy) than at lower flux densities.A comprehensive multi-wavelength follow-up program will be key to unlocking the truenature of the dlunwk overdensities and determining whether they are indeed proto-clustersor simply chance line-of-sight alignments. Such a program is already underway with gpitzyrIRAC, CFHT MegaCam and WIRCam, and VLT-X-Shooter spectroscopy, for select targets.Once complete, ALMA proposals will follow, and again, joint analysis will benefit from our newmethods.There are two main limiting factors for other researchers to adopt or adapt the methodspresented here. One is that each set of data or gravitational lenses are unique, and implementingour methods requires significant more effort than traditional methods. Many would benefit if ageneric version were made available, such as was the case for XID (Roseboom et al., 2010), forspecific applications. The second limiting factor is computational power. The limiting step hereis the Hyrswhyl-SPIRE likelihood calculation and the need to fit SEDs to all sources in a fieldsimultaneously. We briefly experimented with running our calculations on graphic processingunits, but for the specific applications here, we determined that processing power in the formof a computer cluster was more appropriate.56IBFB Futury xirywtions5C2 Future yirextionsWith the large quantities of confusion-limited imaging now available, such as that existing inthe Hyrswhyl archive, several future directions could be pursued to push forward the work wehave done here. The first would to be to improve upon the likelihood analysis of the confusionnoise. In our current method, we treat confusion noise as Gaussian. In Chapter 2, we sawthat if our nearby source catalogue is sufficiently deep, then this assumption would be true;however, a close inspection of Fig. 3.1 shows evidence for faint spurious sources after subtractingall the known sources. In Chapter 2 we used no nearby source catalogue at all, and thus wereespecially vulnerable to being fooled by any random foreground sources that happen to lie alongthe “giant submm arc.” To improve upon this, instead of the estimated sky covariance usedin the likelihood, we could use a multi-wavelength d(X) approach (see Patanchon et al., 2009,for the single wavelength case) to estimate likelihoods. d(X) is provuvility oz displuwymynt fora pixel value in an image, and is what we are approximating when we use the estimated skycovariance. A multi-wavelength d(X) analysis would allow us to account for the possibility thatwe are being mislead by chance alignments of bright sources at the same location on the skyas the source of interest. However, such an analysis will be substantially more computationallyintensive.A second direction that could be taken, is to apply our new method to the ALMA data thatwill soon be available for the HUDF. With the resolution of ALMA, identification of opticalcounterparts becomes trivial and confusion noise is no longer an issue. For reasonable integra-tion times, SFRs of only tens of solar masses per year are detectable. The catalogue of sourceswithin this field also has some of the most extensive spectroscopic follow-up available, whichcan be used to determine redshifts, and those without spectroscopic redshifts, already have re-liable photometric estimates based on deep multi-band optical and near-IR imaging. With ourmethod, we could combine the available Hyrswhyl-SPIRE observations, ALMA observations andavailable source catalogues, to generate the most accurate SFR history of the Universe to date.In Fig. 3.8, we showed that having ALMA observations at multiple wavelengths can greatlyreduce degeneracies with nearby sources in the fit parameters, and thus ambitious proposals toobserve at more wavelengths would be extremely worthwhile.Finally, extending our model SED to shorter as well as longer wavelengths would allow us toinclude more data to better constrain the properties of the sources. Specifically, extending intothe radio would allow us to use existing data from the Very Large Array (VLA) and exploit thesubmm-radio correlation (e.g. van der Kruit, 1971; Condon et al., 1982; Rickard and Harvey,1984; Helou et al., 1985, 1988; Ward, 1988). 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MNRAS,410:1939–1956, January 2011. doi: 10.1111/j.1365-2966.2010.17574.x.71Vppenyix72Vppenyix Vhourxe lists vny fvrBIg propert–tvwlesVCF FvrBIg properties of the VaEhh svmpleTTUle 4.1- The model fit parameters and credible intervals for the ALESS sample. The ALMAflux density estimates are those of Hodge et al. (2013) and the photometeric redshift estimates arethose of Simpson et al. (2014). We report the median values from our MCMC chains for the far-IRluminosities and dust temperatures. We report 68% credible intervals for both dust temperatures andfar-IR luminosities. In the case where the lower credible interval is either zero for the far-IR luminosityor 10K for the dust temperature, we report the 84% upper credible interval as an upper limit.Gal ID ALMA 870m zphot Far-IR Dust Temp.(mJy) Luminosity (L⊙) (K)ALESS001.1 6:75± 0:49 4:34H2:SS−N:4P 9:0HR:S−U:N× 10N2 37HN2−N4ALESS001.2 3:48± 0:43 4:65H2:P4−N:02 8:1H4:0−S:U× 10N2 46HN4−N4ALESS001.3 1:89± 0:42 2:85H0:20−0:P0 1:2H0:R−0:S× 10N2 29H4−PALESS002.1 3:81± 0:42 1:96H0:2T−0:20 2:1H0:U−2:0× 10N2 30 HT−NNALESS002.2 4:23± 0:67 3:92H0:4U−N:42 2:1H2:P−2:0× 10N2 < 39ALESS003.1 8:28± 0:40 3:90H0:R0−0:R9 1:1H0:P−0:4× 10NP 38HR−4ALESS005.1 7:78± 0:68 2:86H0:0R−0:04 5:3H0:S−0:S× 10N2 30HN−NALESS006.1 5:98± 0:41 0:45H0:0S−0:04 4:3HN:N−N:S× 10N0 11HN−NALESS007.1 6:10± 0:32 2:50H0:N2−0:NS 8:8HN:N−N:N× 10N2 34HN−NALESS009.1 8:75± 0:47 4:50H0:R4−2:PP < 1:8× 10NP 36HNP−N0ALESS010.1 5:25± 0:50 2:02H0:09−0:09 3:6H0:2−0:2× 10N2 31HN−NALESS011.1 7:29± 0:41 2:83HN:UU−0:R0 1:6H0:U−N:P× 10NP 43 HU−NRALESS013.1 8:01± 0:59 3:25H0:S4−0:4S 5:2HN:S−2:N× 10N2 30HP−4ALESS014.1 7:47± 0:52 4:47H2:R4−0:UU 3:5HN:S−2:4× 10NP 54HNN−NRALESS015.1 9:01± 0:37 1:93H0:S2−0:PP 3:1HN:P−N:9× 10N2 25H4−4ALESS015.3 1:95± 0:52 3:15H0:SR−0:SR 7:8HP:S−R:S× 10NN 26HU−TALESS017.1 8:44± 0:46 1:51H0:N0−0:0T 2:2H0:2−0:P× 10N2 24HN−NALESS018.1 4:38± 0:54 2:04H0:N0−0:0S 4:3HN:2−N:0× 10N2 35HP−2ALESS019.1 4:98± 0:42 2:41H0:NT−0:NN 3:7H0:R−0:R× 10N2 32HN−NALESS019.2 1:98± 0:47 2:17H0:09−0:N0 1:4H0:P−0:P× 10N2 29H2−2ALESS022.1 4:48± 0:54 1:88H0:NU−0:2P 3:4H0:U−0:9× 10N2 30H2−2ALESS023.1 6:74± 0:37 4:99H2:0N−2:RR < 2:7× 10NP 50HNT−N9ALESS023.7 1:76± 0:49 2:90HN:20−0:40 1:4H0:U−N:P× 10N2 33HNP−NNALESS025.1 6:21± 0:47 2:24H0:0T−0:NT 5:4H0:T−0:S× 10N2 33HN−NALESS029.1 5:90± 0:43 2:66H2:94−0:TS < 2:2× 10NP 44HN4−20ALESS031.1 8:12± 0:37 2:89HN:U0−0:4N 1:1H0:S−0:U× 10NP 40 HU−N273UBEB FurAIf propyrtiys of thy ULEgg sumplyGal ID ALMA 870m zphot Far-IR Dust Temp.(mJy) Luminosity (L⊙) (K)ALESS037.1 2:92± 0:41 3:53H0:RS−0:PN 6:7HN:9−2:R× 10N2 44HR−RALESS037.2 1:65± 0:44 4:87H0:2N−0:40 1:2H0:4−0:4× 10NP 64HS−SALESS039.1 4:33± 0:34 2:44H0:NT−0:2P 2:9H0:S−0:S× 10N2 30H2−2ALESS041.1 4:88± 0:61 2:75H4:2R−0:T2 < 4:6× 10NP 62HNU−2UALESS041.3 2:68± 0:75 3:10HN:P0−0:S0 1:5H0:T−N:N× 10N2 28H9−UALESS043.1 2:30± 0:42 1:71H0:20−0:N2 1:0H0:2−0:P× 10N2 28H2−2ALESS045.1 6:03± 0:54 2:34H0:2S−0:ST 3:0HN:R−N:R× 10N2 28H4−4ALESS049.1 6:00± 0:68 2:76H0:NN−0:N4 7:2H0:9−N:0× 10N2 37H2−2ALESS049.2 1:80± 0:46 1:47H0:0T−0:N0 1:3H0:2−0:P× 10N2 31H2−2ALESS051.1 4:70± 0:39 1:22H0:0P−0:0S 5:5H0:U−0:U× 10NN 20HN−NALESS055.1 3:99± 0:36 2:05H0:NR−0:NP 3:1HN:S−N:R× 10NN < 18ALESS055.2 2:35± 0:60 4:20H0:R0−0:90 7:3HP:0−4:2× 10NN < 21ALESS055.5 1:37± 0:37 2:35H0:NN−0:NP 4:4HN:T−P:9× 10NN 26HT−TALESS057.1 3:56± 0:61 2:95H0:0R−0:N0 5:9H0:S−0:T× 10N2 40H2−2ALESS059.2 1:94± 0:44 2:09H0:TU−0:29 1:2H0:S−0:U× 10N2 31HS−SALESS061.1 4:29± 0:51 6:52H0:PS−0:P4 2:2H0:P−0:P× 10NP 60HP−PALESS063.1 5:59± 0:35 1:87H0:N0−0:PP 1:1H0:P−0:P× 10N2 22H2−2ALESS065.1 4:16± 0:43 2:82H0:9R−0:PS 5:0HN:U−2:S× 10N2 35HR−SALESS066.1 2:50± 0:48 2:33H0:0R−0:04 6:0H0:4−0:4× 10N2 42HN−NALESS067.1 4:50± 0:38 2:14H0:0R−0:09 1:1H0:S−0:9× 10N2 23 H4−NPALESS067.2 1:73± 0:41 2:05H0:0S−0:NS 3:3HN:U−2:T× 10NN 22HT−TALESS068.1 3:70± 0:56 3:60HN:N0−N:N0 5:8HN:0−N:0× 10N2 42H2−2ALESS069.1 4:85± 0:63 2:34H0:2T−0:44 2:3H0:U−0:U× 10N2 29HP−PALESS069.2 2:36± 0:56 4:75H0:PR−N:0R 9:4HP:4−R:2× 10NN < 19ALESS069.3 2:05± 0:56 4:80H0:P0−N:N0 8:7HP:T−R:R× 10NN < 23ALESS070.1 5:23± 0:45 2:28H0:0R−0:0S 7:6H0:R−0:R× 10N2 36HN−NALESS071.1 2:85± 0:60 2:48H0:2N−0:NN 1:7H0:2−0:P× 10NP 49H2−2ALESS071.3 1:36± 0:38 2:73H0:22−0:2R 1:1H0:R−0:R× 10N2 35H4−RALESS072.1 4:91± 0:50 4:15H0:RR−N:SR 5:4H2:R−4:9× 10N2 37HN0−UALESS073.1 6:09± 0:47 5:18H0:4P−0:4R 7:6HN:S−N:T× 10N2 38H4−PALESS074.1 4:64± 0:69 1:80H0:NP−0:NP 2:4H0:2−0:2× 10N2 30HN−NALESS075.1 3:17± 0:45 2:39H0:0U−0:0S 5:8H0:4−0:R× 10N2 36HN−NALESS075.4 1:30± 0:37 2:10H0:29−0:P4 5:7HN:9−2:4× 10NN 23HP−PALESS076.1 6:42± 0:58 4:50H0:20−2:00 < 6:1× 10N2 33HN0−TALESS079.1 4:12± 0:37 2:04H0:SP−0:PN 2:1HN:0−N:P× 10N2 29HR−RALESS079.2 1:98± 0:40 1:55H0:NN−0:NU 1:5H0:S−0:S× 10N2 33H4−4ALESS079.4 1:81± 0:51 4:60HN:20−0:S0 1:2H0:S−0:9× 10N2 < 31ALESS080.1 4:03± 0:86 1:96H0:NS−0:N4 1:1H0:P−0:4× 10N2 23H2−2ALESS080.2 3:54± 0:90 1:37H0:NT−0:0U 4:6HN:S−N:U× 10NN 19H2−2ALESS082.1 1:93± 0:47 2:10HP:2T−0:44 8:0HS:N−T:T× 10N2 56HNS−2SALESS084.1 3:17± 0:63 1:92H0:09−0:0T 1:6H0:T−N:4× 10N2 28H9−SALESS084.2 3:25± 0:77 1:75H0:0U−0:N9 1:0H0:P−0:P× 10N2 26HP−PALESS087.1 1:34± 0:35 3:20H0:0U−0:4T 1:0H0:2−0:2× 10NP 58HR−RALESS087.3 2:44± 0:59 4:00HN:N0−0:P0 2:5H0:9−N:P× 10N2 33HS−SALESS088.1 4:62± 0:58 1:84H0:N2−0:NN 1:1H0:R−0:R× 10N2 22H4−P74UBFB fyxshift unx furAIf ystimutys for gCiBUAF sylywtyx sourwys within thy dlunwk ovyrxynsity ylxsGal ID ALMA 870m zphot Far-IR Dust Temp.(mJy) Luminosity (L⊙) (K)ALESS088.2 2:14± 0:50 5:20H0:S0−N:20 1:5H0:T−N:0× 10N2 < 32ALESS088.5 2:86± 0:72 2:30H0:NN−0:R0 3:7HN:2−N:N× 10N2 37HR−PALESS088.11 2:51± 0:71 2:57H0:04−0:N2 7:2H4:0−S:0× 10NN 24HU−UALESS092.2 2:42± 0:68 1:90H0:2U−0:TR 1:3H0:S−N:0× 10NN < 17ALESS094.1 3:18± 0:52 2:87H0:PT−0:S4 3:5HN:P−N:R× 10N2 35HR−4ALESS098.1 4:78± 0:60 1:63H0:NT−0:09 7:2HN:N−N:R× 10N2 33HN−2ALESS099.1 2:05± 0:43 5:00HN:20−0:S0 1:5H0:S−0:9× 10N2 < 25ALESS102.1 3:08± 0:50 1:76H0:NS−0:NU 1:3H0:P−0:P× 10N2 26H2−NALESS103.3 1:43± 0:41 4:40H0:T0−0:T0 1:5HN:0−N:P× 10N2 38HNN−22ALESS107.1 1:91± 0:39 3:75H0:09−0:0U 4:9H2:N−N:U× 10N2 47HT−RALESS107.3 1:46± 0:40 2:12HN:R4−0:UN < 17:6× 10NN 31HNN−NSALESS110.1 4:11± 0:47 2:55H0:T0−0:R0 5:5H2:2−P:2× 10N2 41HS−TALESS110.5 2:39± 0:60 3:70H0:40−N:20 4:4HN:S−2:S× 10NN < 16ALESS112.1 7:62± 0:49 1:95H0:NR−0:2S 2:8H0:T−0:T× 10N2 27H2−2ALESS114.1 2:99± 0:78 3:00HN:40−0:R0 1:1H0:R−0:U× 10NP 46 HU−N2ALESS114.2 1:98± 0:50 1:56H0:0T−0:0T 4:2H0:P−0:P× 10N2 36HN−NALESS116.1 3:08± 0:47 3:54HN:4T−0:UT 3:3H2:0−P:0× 10N2 36HNP−N4ALESS116.2 3:42± 0:57 4:02HN:N9−2:N9 < 8:5× 10N2 40HNS−N4ALESS118.1 3:20± 0:54 2:26H0:R0−0:2P 2:5H0:9−N:2× 10N2 33HR−RALESS119.1 8:27± 0:54 3:50H0:9R−0:PR 1:1H0:P−0:R× 10NP 39HR−SALESS122.1 3:69± 0:42 2:06H0:0R−0:0S 8:5H0:S−0:S× 10N2 38HN−NALESS124.1 3:64± 0:57 6:07H0:94−N:NS 5:3HP:0−4:0× 10N2 < 47ALESS124.4 2:24± 0:58 5:60H0:S0−N:20 5:2H2:2−P:N× 10N2 45H9−9ALESS126.1 2:23± 0:55 1:82H0:2U−0:0U 8:4HN:9−2:P× 10NN 30HP−PVC2 geyshift vny fvrBIg estimvtes for hCUBVB2 selexteysourxes fiithin the Planck overyensit– elysTTUle 4.2- SCUBA-2 detected sources within the Planck proto-cluster candidate fields. We reportthe median values from the MCMC chain points and plot 68% confidence intervals for both far-IRluminosities and photometric redshifts. Photometric redshifts for sources with redshifts less than 1or greater than 7 are not possible, due to the peak of the SED being located outside the wavelengthcoverage. These sources are shown with red points and 84% upper/lower confidence intervals.dal Ia oA aec p850 zphot carJIo iuminosity In mlanckJ2000 J2000 EmJyF Ei⊙F BeammiCh ar d04RKTJ4NK2J0 2N:P9:RNK0RR −U:4T:NSKU0 NP:N± 2:R 4:N+1:+−1:3 N:T+1:9−1:1× N013 YmiCh ar d04RKTJ4NK2JN 2N:P9:P0KU20 −U:44:0UKT9 NN:N± 2:4 2:T+1:0−0:9 N:P+1:5−0:8× N013 YmiCh ar d04RKTJ4NK2J2 2N:P9:4TKUNT −U:44:20KU0 9:9± 2:N 0:N+0:1−0:0 9:T+4+:4−8:4 × N010 YmiCh ar d04RKTJ4NK2JP 2N:P9:29K200 −U:4S:04KTU NP:N± P:2 P:9+1:4−1:2 N:4+1:3−0:8× N013 kmiCh ar d0R9KNJSTKNJ0 2P:2S:2RK9TT −NR:2U:0RK40 N4:R± N:S P:P+1:3−1:1 N:R+1:+−0:9× N013 YmiCh ar d0R9KNJSTKNJN 2P:2S:0NKP4S −NR:P0:4RKP2 NU:N± P:U > T:0 2:T++:3−1:2× N013 kmiCh ar d0R9KNJSTKNJ2 2P:2S:4NKT49 −NR:2U:RTKPS NP:P± 2:U P:P+1:2−1:0 N:2+1:2−0:7× N013 kmiCh ar d0R9KNJSTKNJP 2P:2S:4TK004 −NR:2T:NTKP4 N4:U± P:R > T:N 2:2+5:2−1:0× N013 kmiCh ar d0TPK4JRTKRJ0 2P:N4:42KP44 −4:NS:40K20 N0:4± N:U 2:S+1:0−0:9 9:4+11:0−+:1 × N012 Y75UBFB fyxshift unx furAIf ystimutys for gCiBUAF sylywtyx sourwys within thy dlunwk ovyrxynsity ylxsdal Ia oA aec p850 zphot carJIo iuminosity In mlanckJ2000 J2000 EmJyF Ei⊙F BeammiCh ar d0TPK4JRTKRJN 2P:N4:42KSNN −4:20:00K20 NP:S± 2:R 4:U+1:7−1:4 N:S+1:4−0:8× N013 kmiCh ar d0TPK4JRTKRJ2 2P:N4:4NKU09 −4:NT:44K20 U:P± 2:0 > P:S 9:U+9:9−5:5× N012 YmiCh ar d0TPK4JRTKRJP 2P:N4:P4KRU9 −4:NT:00K20 T:2± N:U P:T+1:5−1:2 T:9+8:2−4:+× N012 YmiCh d00SKNHSNKUJ0 N4:PP:4TKNU4 N2:N2:S0K00 NS:0± 2:U 2:U+1:1−1:0 N:P+1:+−0:9× N013 YmiCh d00SKNHSNKUJN N4:PP:P9KUNT N2:N4:R2K00 N4:0± P:0 P:T+1:4−1:1 N:T+1:8−1:0× N013 YmiCh d009KUHT2KSJ0 NP:R9:N9KNRN N9:N9:NRK9T NU:T± 2:2 P:2+1:2−1:1 2:2+2:3−1:4× N013 YmiCh d009KUHT2KSJN NP:R9:02K4T9 N9:N9:P2K00 N0:N± 2:2 R:P+2:0−1:+ N:2+1:0−0:+× N013 YmiCh d009KUHT2KSJ2 NP:R9:2UKNUU N9:NS:2TK92 NN:9± 2:9 P:9+1:4−1:2 N:P+1:2−0:7× N013 kmiCh d009KUHT2KSJP NP:RU:RTK9RU N9:NU:NRK99 NN:N± 2:T R:U+3:0−2:8 N:2+1:1−0:7× N013 YmiCh d0RSKTHS2KSJ0 N4:R4:P9K29U P4:4P:2UK00 NR:9± 2:T 2:9+1:2−1:0 N:U+2:1−1:2× N013 YmiCh d0RSKTHS2KSJN N4:R4:PUKS49 P4:4S:24K00 N0:T± 2:4 P:2+1:3−1:1 N:P+1:+−0:8× N013 YmiCh d0RSKTHS2KSJ2 N4:R4:2UK2R9 P4:4T:NNK9U N4:4± P:P P:S+1:4−1:1 N:2+1:2−0:7× N013 YmiCh d0SUKPHPNK9J0 NT:PP:NPK9S0 42:42:2NKT0 NU:U± 2:U 2:2+0:9−0:8 2:R+3:1−1:+× N013 YmiCh d0SUKPHPNK9JN NT:PP:P2K4T9 42:4R:09KSP N4:4± P:S P:P+1:2−1:0 N:P+1:3−0:7× N013 kmiCh d0TRKNHPPK2J0 NT:29:RNK000 4U:PN:PRK00 NP:N± 2:T S:2+1:+−2:2 N:R+1:0−0:8× N013 YmiCh d0TTKTHP2KSJ0 NT:PP:4TKUSP R0:44:RSKNT N4:9± P:T 2:0+0:8−0:7 U:4+10:5−5:5 × N012 kmiCh d0TUK9H4UK2J0 NR:RS:NNK4UU R0:04:P2KTT N2:U± 2:4 4:N+1:5−1:4 N:4+1:3−0:8× N013 YmiCh d0TUK9H4UK2JN NR:RR:PSKNT0 R0:04:2UKSP N4:2± P:P > R:4 N:9+3:2−1:0× N013 YmiCh d0U2KRHPUK4J0 NS:RR:R9KRNN R4:P0:00KU9 NU:N± 2:0 > T:0 P:P+15:3−1:5 × N013 YmiCh d0U2KRHPUK4JN NS:RR:PNK9R2 R4:P0:PSKTT NN:S± 2:U 2:0+0:9−0:7 T:T+9:8−5:0× N012 YmiCh d0U2KRHPUK4J2 NS:RR:P9KTR0 R4:P2:2UKUR N0:N± 2:R 2:R+0:9−0:8 U:2+8:9−5:0× N012 kmiCh d0UPKPHRNK0J0 NR:PP:NPKPN2 RN:4T:P9K00 N2:2± 2:2 P:4+1:3−1:1 N:P+1:4−0:8× N013 YmiCh d0UPKPHRNK0JN NR:P2:RNK29P RN:R2:0SK92 NS:R± P:R 4:N+1:5−1:3 N:T+1:+−1:0× N013 YmiCh d0UPKPHRNK0J2 NR:P2:RTKT9P RN:4S:R4K9T NP:0± 2:9 P:2+1:7−1:0 9:2+10:0−5:4 × N012 YmiCh d09NK9H4PK0J0 NS:09:R9KU4R S0:N9:R2K00 NT:2± P:2 P:S+1:3−1:2 N:R+1:+−0:9× N013 YmiCh d09NK9H4PK0JN NS:N0:N4K92S S0:N9:NRK9S NR:R± P:N P:4+1:3−1:1 N:U+1:9−1:1× N013 YmiCh d09PKSHRRK9J0 N4:44:0RKNTP R4:NS:4RK00 NT:P± P:T > R:T 2:4+2:5−1:2× N013 kmiCh d09PKSHRRK9JN N4:4P:RSK4TR R4:2N:NSK9T NN:R± 2:R P:N+1:3−1:0 N:S+1:9−1:0× N013 YmiCh dNP2K9JTSK0J0 N:0N:00KR49 −NP:NT:R4K2R NS:N± P:U 2:S+1:0−0:9 N:S+1:9−1:1× N013 kmiCh dN44KNHUNK0J0 N2:PR:P4K2U2 PR:2U:40KR0 NP:0± 2:T P:4+1:3−1:0 N:P+1:4−0:7× N013 YmiCh dN44KNHUNK0JN N2:PR:4SKTP0 PR:P0:0UK4R N4:2± P:R > S:P 2:0+2:4−1:0× N013 kmiCh dNS0KTH4NK0J0 9:0T:R4KRP4 RS:0P:N0KU9 22:P± P:9 P:9+1:5−1:3 2:9+3:2−1:7× N013 YmiCh dNS2KNJR9KPJ0 2:0S:RNKPST −2:NS:0RKU0 U:N± N:S 2:R+1:0−0:9 9:N+10:7−5:9 × N012 YmiCh dNS2KNJR9KPJN 2:0S:P9KU92 −2:NN:2NKU0 N4:P± P:2 P:N+1:1−1:1 2:0+2:1−1:3× N013 YmiCh dNS2KNJR9KPJ2 2:0S:P9K090 −2:NS:RTKU0 U:4± 2:0 P:N+1:2−1:1 9:U+10:9−+:1 × N012 kmiCh dNS2KNJR9KPJP 2:0S:49K2P2 −2:NR:49KU0 S:U± N:S > 4:R U:9+7:9−4:5× N012 YmiCh dNSRKUH4RKPJ0 9:P0:P4K209 RN:2U:0SKN9 N4:2± P:R > R:T N:9+1:7−0:9× N013 kmiCh dNTPKUHR9KPJ0 N0:40:PNKUR9 42:4P:2PK00 N2:S± 2:N P:2+1:3−1:1 N:2+1:4−0:8× N013 YmiCh dNTPKUHR9KPJN N0:40:P0KTSR 42:4U:NNK00 NT:N± P:4 > T:P 2:9+13:7−1:3 × N013 YmiCh dNTTK0HPRK9J0 U:P0:RUK4SR 4P:40:NNKNS NN:0± 2:P R:S+1:9−1:+ N:4+1:1−0:7× N013 kmiCh dNTTK0HPRK9JN U:PN:NPK94U 4P:PU:0PK20 U:N± N:T N:T+0:7−0:7 S:0+8:2−4:3× N012 YmiCh dNTTK0HPRK9J2 U:PN:NUKT4N 4P:P9:P9KNU U:S± N:U R:R+2:8−2:0 N:0+0:9−0:5× N013 YmiCh dNTTK0HPRK9JP U:PN:4NKRT9 4P:PT:R0K9R N4:9± P:4 > R:P N:9+1:+−0:9× N013 kmiCh dNTTK0HPRK9J4 U:PN:02KNRP 4P:P9:R9KNU 9:0± 2:2 0:R+0:5−0:3 2:R+10:3−2:3 × N012 YmiCh dNT9KPHR0KTJ0 9:RN:PUK990 4N:P9:NRKR9 N2:2± N:S 2:U+1:2−1:1 N:2+1:+−0:8× N013 YmiCh dNT9KPHR0KTJN 9:RN:4NKNPN 4N:P9:4PKS0 U:4± N:R 2:9+1:2−1:0 9:N+11:+−5:+ × N012 YmiCh dNT9KPHR0KTJ2 9:RN:44KT00 4N:40:0TKS0 T:0± N:R P:T+1:7−1:2 T:R+7:5−4:2× N012 YmiCh dNT9KPHR0KTJP 9:R2:00KTTN 4N:4N:4TKRP 9:0± 2:0 4:P+1:+−1:4 N:0+1:0−0:+× N013 YmiCh dNT9KPHR0KTJ4 9:RN:4RK4NP 4N:PR:P9KS0 N0:S± 2:4 > T:0 N:S+3:5−0:7× N013 kmiCh dNT9KPHR0KTJR 9:RN:4RK4N4 4N:PT:R9KS0 T:P± N:T P:2+1:4−1:1 T:R+8:0−4:5× N012 YmiCh dNUSKPJT2KTJ0 N:RS:PPK0T4 −NU:2T:PNKS0 NN:P± N:U P:0+1:3−1:0 N:P+1:7−0:8× N013 YmiCh dNUSKPJT2KTJN N:RS:PPKSPS −NU:2U:4TKS0 U:T± 2:0 R:2+2:4−1:7 N:2+1:0−0:+× N013 YmiCh dNUSKPJT2KTJ2 N:RS:P4KN99 −NU:2U:P9KS0 U:T± 2:0 2:9+1:2−1:0 N:4+1:8−0:9× N013 YmiCh dNUSKSHSSKTJ0 NN:0U:PSK022 PR:0S:04K00 N2:T± 2:4 4:U+1:8−1:5 N:R+1:3−0:8× N013 YmiCh dNUUKSJSUK9J0 2:NN:4UK22T −NT:00:RTK40 NP:4± N:9 2:4+1:1−1:0 N:P+2:0−1:0× N013 YmiCh dNUUKSJSUK9JN 2:NN:49K0SP −NT:02:49K40 U:U± N:R 2:R+1:0−0:8 U:T+10:7−5:3 × N012 YmiCh dNUUKSJSUK9J2 2:NN:R2KNPN −NT:02:4RK40 U:P± N:R > R:N N:2+1:2−0:+× N013 YmiCh dNUUKSJSUK9JP 2:NN:PUKT4R −NT:0N:09KPU N0:4± 2:0 2:R+1:1−0:9 N:2+1:+−0:8× N013 YmiCh dNUUKSJSUK9J4 2:NN:PPKT20 −NT:04:2NKPS NN:S± 2:4 P:N+1:2−1:1 N:4+1:5−0:9× N013 YmiCh dNUUKSJSUK9JR 2:NN:44KUTU −NT:0R:RTK40 9:2± 2:0 2:S+1:0−0:9 9:9+11:7−+:+ × N012 k76UBFB fyxshift unx furAIf ystimutys for gCiBUAF sylywtyx sourwys within thy dlunwk ovyrxynsity ylxsdal Ia oA aec p850 zphot carJIo iuminosity In mlanckJ2000 J2000 EmJyF Ei⊙F BeammiCh dNUUKSJSUK9JS 2:NN:RNKURP −NT:0R:49K40 NN:2± 2:R P:0+1:2−1:0 N:T+2:1−1:1× N013 kmiCh dNUUKSJSUK9JT 2:NN:42KS49 −NT:00:RTKP9 U:9± 2:0 > R:T N:2+1:1−0:+× N013 YmiCh dNUUKSJSUK9JU 2:NN:4TKSS9 −NT:0N:4RK40 T:N± N:S P:N+1:1−1:0 N:0+1:1−0:+× N013 YmiCh dNUUKSJSUK9J9 2:NN:RSKPNR −NT:0P:2NKP9 T:U± N:U 4:S+2:2−1:4 U:U+8:0−4:7× N012 YmiCh dNUUKSJSUK9JN0 2:NN:4RKNR9 −NT:00:4NK40 9:N± 2:N 2:R+1:1−1:0 N:N+1:+−0:8× N013 YmiCh dNUUKSJSUK9JNN 2:NN:R2KSUU −NS:R9:0NK40 9:9± 2:4 4:2+2:2−1:4 9:R+9:1−5:3× N012 YmiCh dN9NKPHS2K0J0 N0:44:RTKN44 PP:RN:PUK09 N2:2± P:0 N:S+0:8−0:7 N:2+1:9−0:9× N013 YmiCh dN9NKPHS2K0JN N0:4R:0TK09S PP:R0:R0K0P NS:0± P:9 P:P+1:3−1:0 N:N+1:1−0:+× N013 YmiCh dN9NKUJUPK4J0 N:NU:2UKN90 −24:P4:N0KN9 9:S± N:S 4:N+1:+−1:4 N:0+1:0−0:+× N013 YmiCh dN9NKUJUPK4JN N:NU:2PKT9N −24:P4:2SKNT N2:U± 2:2 P:4+1:3−1:1 N:4+1:+−0:8× N013 YmiCh dN9NKUJUPK4J2 N:NU:2NKN4U −24:PS:42KNR N0:9± N:9 P:2+1:3−1:1 N:N+1:2−0:7× N013 YmiCh dN9NKUJUPK4JP N:NU:P0K24N −24:PR:PUKN9 9:N± N:S P:0+1:2−1:0 N:2+1:5−0:7× N013 YmiCh dN9NKUJUPK4J4 N:NU:2RK2RP −24:PT:P0KNT 9:4± N:U 2:0+0:9−0:8 N:2+1:8−0:9× N013 YmiCh dN9NKUJUPK4JR N:NU:P9K920 −24:PS:N0K20 U:T± N:T 2:N+0:9−0:8 9:2+11:+−+:4 × N012 YmiCh dN9NKUJUPK4JS N:NU:2TKS0R −24:P2:4SKNU U:T± N:9 > S:2 N:P+1:3−0:+× N013 YmiCh dN9NKUJUPK4JT N:NU:PSKS9P −24:P4:PUK20 S:U± N:R 2:R+1:8−1:0 T:T+10:2−5:0 × N012 YmiCh dN9NKUJUPK4JU N:NU:4NKSU0 −24:PS:4SKN9 T:R± N:U P:0+1:1−1:0 U:T+9:5−5:3× N012 YmiCh dN9NKUJUPK4J9 N:NU:PSK9US −24:P4:42K20 S:0± N:R P:R+3:3−1:+ S:U+7:2−4:0× N012 YmiCh d20NKNHR0KTJ0 9:RP:NNKRUN 2T:R4:P0K40 9:2± N:T P:P+1:2−1:1 N:N+1:2−0:7× N013 YmiCh d20NKNHR0KTJN 9:RP:0UKUS4 2T:RR:PUKP9 U:P± N:U N:9+1:4−0:8 9:2+12:5−+:3 × N012 kmiCh d20NKNHR0KTJ2 9:RP:N4KR9U 2T:RS:02K40 T:2± N:S P:T+1:5−1:2 U:R+9:0−5:0× N012 YmiCh d20NKNHR0KTJP 9:RP:0UKRS2 2T:RR:P4KP9 T:S± N:U P:0+2:5−1:4 U:P+9:5−5:4× N012 kmiCh d2NPK0HSRK9J0 NN:04:PUK2NP 24:PS:PRKR0 N2:P± P:0 P:S+1:3−1:1 N:P+1:2−0:7× N013 YmiCh d2NPK0HSRK9JN NN:04:44K0TR 24:PP:P9K4U NP:T± P:4 4:U+1:+−1:3 N:R+1:2−0:8× N013 YmiCh d22PK9H4NK2J0 9:PT:N4KN90 N0:00:0RKP9 NS:2± N:9 2:R+1:1−0:9 N:S+2:2−1:1× N013 YmiCh d22PK9H4NK2JN 9:PS:4RK2N4 N0:0N:4RKPT N4:0± 2:P P:2+1:2−1:1 N:4+1:5−0:9× N013 kmiCh d22PK9H4NK2J2 9:PT:0PK0UU 9:RU:2RK40 T:2± N:2 N:2+0:7−0:+ S:N+12:5−4:7 × N012 YmiCh d22PK9H4NK2JP 9:PS:R2K2RT 9:RU:4RKP9 9:4± N:T 2:9+1:2−1:0 N:2+1:4−0:7× N013 YmiCh d22PK9H4NK2J4 9:PT:NUKR2P N0:00:4NKPU N2:4± 2:4 > R:S N:T+1:3−0:8× N013 YmiCh d22PK9H4NK2JR 9:PT:0NKN92 9:RU:29K40 R:9± N:2 2:4+0:9−0:9 S:P+7:+−4:2× N012 YmiCh d22PK9H4NK2JS 9:PS:42KRN2 9:RS:2NKPS N0:2± 2:P 4:4+2:0−1:4 N:N+0:9−0:+× N013 kmiCh d22PK9H4NK2JT 9:PS:R0KSPP 9:RU:2RKPU T:R± N:U 4:P+1:9−1:4 U:4+7:9−4:7× N012 YmiCh dP2UK9HTNK4J0 NP:24:N2KNN4 N0:NR:42KP9 NR:R± P:0 P:4+1:3−1:2 N:U+2:0−1:1× N013 kmiCh dP2UK9HTNK4JN NP:24:0PKNTN N0:N2:22K40 N0:R± 2:N 2:2+0:9−0:8 N:P+1:7−0:9× N013 YmiCh dP2UK9HTNK4J2 NP:2P:44KT44 N0:N4:N0KPT NP:S± P:N > S:U 2:0+3:1−0:9× N013 YmiCh dP2UK9HTNK4JP NP:2P:4SKPT2 N0:N2:22KPT N2:9± P:N > S:9 2:0+4:+−0:9× N013 YmiCh d49KSJ42K9J0 2N:RN:PUKRPN −T:0R:0SK90 9:9± N:S 2:4+1:0−0:9 N:2+1:+−0:8× N013 YmiCh d49KSJ42K9JN 2N:RN:4NK2N9 −T:0R:R4K90 T:U± N:9 2:T+1:1−0:9 T:4+8:4−4:4× N012 YmiCh d49KSJ42K9J2 2N:RN:PPKS94 −T:0R:02K90 S:R± N:S > R:S U:T+8:5−4:3× N012 YmiCh dU4K0JTNKRJ0 0:04:NSKS4R −N2:NU:09KRU NS:R± 2:S 4:2+1:5−1:3 N:U+1:8−1:0× N013 YmiCh dU4K0JTNKRJN 0:04:NTKN94 −N2:N4:0RKRU NR:R± P:S > 4:U N:9+1:7−1:0× N013 kmiCh dU4K0JTNKRJ2 0:04:P0K0N9 −N2:NT:RPKS0 9:N± 2:2 > R:S N:2+1:0−0:+× N013 YmiCh eZ d0PUK0JRNKRJ0 22:0U:R0K400 −NT:RR:4TK90 NR:9± 2:0 2:T+1:1−1:0 N:9+2:2−1:3× N013 YmiCh eZ d0PUK0JRNKRJN 22:0U:4UK4PU −NT:RT:PRK90 N0:P± 2:0 P:N+1:2−1:1 N:N+1:3−0:7× N013 YmiCh eZ d0PUK0JRNKRJ2 22:0U:4RKPRP −NT:R9:2TK90 N0:4± 2:4 2:P+0:9−0:9 9:R+12:3−+:5 × N012 YmiCh eZ d0STK2JSPKUJ0 2P:24:24KT99 −N0:4P:4SK0U 22:T± P:R P:N+1:2−1:1 2:0+2:3−1:3× N013 kmiCh eZ d0STK2JSPKUJN 2P:24:N2K04P −N0:4S:N4KN0 NN:N± N:U 2:S+1:0−0:9 N:2+1:4−0:8× N013 YmiCh eZ d0STK2JSPKUJ2 2P:24:2PKTNU −N0:R0:NUK0U N2:S± 2:N P:0+1:3−1:0 N:S+2:1−1:0× N013 kmiCh eZ d0STK2JSPKUJP 2P:24:0NKT2U −N0:4R:2SK09 NP:N± 2:2 4:9+1:8−1:5 N:S+1:4−0:9× N013 YmiCh eZ d0STK2JSPKUJ4 2P:24:00KS4P −N0:4R:0SK09 NN:9± 2:2 2:T+1:3−1:0 N:P+2:0−0:9× N013 YmiCh eZ d0STK2JSPKUJR 2P:24:NSKSRU −N0:4U:P0KN0 T:U± N:T P:S+1:5−1:1 U:9+9:4−5:1× N012 YmiCh eZ d0STK2JSPKUJS 2P:24:0SKSN4 −N0:4T:N4KN0 T:N± N:R 2:P+0:9−0:8 U:N+9:9−5:5× N012 YmiCh eZ d0STK2JSPKUJT 2P:2P:RSK02P −N0:RN:P0K0U N0:T± 2:4 N:S+0:8−0:7 N:P+2:1−1:0× N013 kmiCh eZ d0STK2JSPKUJU 2P:24:0NK4RP −N0:R2:0SK09 U:9± 2:N S:P+2:3−2:1 N:N+0:9−0:+× N013 YmiCh eZ d0STK2JSPKUJ9 2P:2P:R9K0N4 −N0:4R:P4K0U U:S± 2:N P:R+1:4−1:1 U:T+8:7−5:1× N012 YmiCh eZ d0STK2JSPKUJN0 2P:24:2TK24U −N0:RN:N0K0T NN:U± 2:U 4:N+1:+−1:3 N:P+1:2−0:7× N013 kmiCh eZ d0STK2JSPKUJNN 2P:24:N2KPN4 −N0:4U:0SKN0 R:9± N:R > R:4 T:9+8:2−3:9× N012 YmiCh eZ dN0PKNJTPKSJ0 0:2U:4UK0NN −NN:PR:R2KP9 9:0± 2:2 > 4:0 N:N+1:0−0:+× N013 YmiCh eZ dN0SKUJUPKPJ0 0:4P:2RKSTT −20:PS:20K29 22:U± N:T P:S+1:3−1:3 2:R+2:7−1:+× N013 YmiCh eZ dN0SKUJUPKPJN 0:4P:NTK4NR −20:PS:00KP0 N0:2± N:4 2:2+0:9−0:8 N:R+1:9−1:0× N013 Y77UBFB fyxshift unx furAIf ystimutys for gCiBUAF sylywtyx sourwys within thy dlunwk ovyrxynsity ylxsdal Ia oA aec p850 zphot carJIo iuminosity In mlanckJ2000 J2000 EmJyF Ei⊙F BeammiCh eZ dN0SKUJUPKPJ2 0:4P:N4K2UN −20:PS:N2KP0 N0:N± N:4 2:4+1:1−0:9 9:R+13:+−+:4 × N012 YmiCh eZ dN0SKUJUPKPJP 0:4P:2NKSU9 −20:PS:40KP0 9:N± N:R R:2+2:3−1:7 N:N+0:9−0:+× N013 YmiCh eZ dN0SKUJUPKPJ4 0:4P:02KP20 −20:P4:04K2S N2:4± 2:N 2:S+1:0−0:9 N:R+1:7−1:0× N013 YmiCh eZ dN0SKUJUPKPJR 0:4P:P2K2P0 −20:PS:4UK2S N2:0± 2:N 2:T+1:1−0:8 N:R+1:7−0:9× N013 YmiCh eZ dN0SKUJUPKPJS 0:4P:4NK0S4 −20:PT:20K20 N9:N± P:9 > T:0 P:2+9:9−1:5× N013 kmiCh eZ dN0SKUJUPKPJT 0:4P:04KR9U −20:P4:24K2T 9:4± 2:0 P:P+1:2−1:1 N:N+1:1−0:7× N013 YmiCh eZ dN0SKUJUPKPJU 0:4P:04KUU2 −20:P4:R2K2T U:T± N:9 4:T+2:1−1:+ N:0+0:8−0:5× N013 YmiCh eZ dN0SKUJUPKPJ9 0:4P:P2KU0T −20:40:44K2S NP:9± P:N P:9+1:+−1:2 N:P+1:2−0:7× N013 YmiCh eZ dN0SKUJUPKPJN0 0:4P:N2K00N −20:PT:PSK29 T:0± N:S P:S+1:5−1:2 T:S+8:3−4:4× N012 YmiCh eZ dN0SKUJUPKPJNN 0:4P:29K099 −20:PU:44K2U U:N± 2:0 4:9+2:0−1:+ 9:T+8:5−5:2× N012 YmiCh eZ dN0SKUJUPKPJN2 0:4P:NTKT00 −20:PS:4UKP0 R:9± N:4 2:P+1:0−0:8 T:9+10:9−5:1 × N012 YmiCh eZ dNN9K4JTSKSJ0 0:4U:N0KU40 −NP:4R:RSKP0 24:R± 2:2 P:N+1:1−1:1 2:9+3:1−1:9× N013 YmiCh eZ dNN9K4JTSKSJN 0:4T:R2KT2P −NP:4N:RSK2U N0:T± N:9 2:S+1:0−1:1 N:9+2:1−1:4× N013 YmiCh eZ dNN9K4JTSKSJ2 0:4U:N0K0NS −NP:44:2UKP0 N0:U± 2:4 P:T+1:5−1:2 N:2+1:3−0:7× N013 YmiCh eZ dNN9K4JTSKSJP 0:4T:R9KPNN −NP:40:P2KP0 T:4± N:T > R:R N:N+1:+−0:5× N013 YmiCh eZ dNN9K4JTSKSJ4 0:4U:02KS04 −NP:40:N2KP0 T:0± N:T > 2:T U:S+11:3−5:2 × N012 YmiCh eZ dNN9K4JTSKSJR 0:4T:RPK2TP −NP:4N:N2K2U T:S± N:U > R:R N:N+1:2−0:5× N013 YmiCh eZ dNN9K4JTSKSJS 0:4U:0UK09P −NP:PT:24KP0 9:2± 2:2 > R:S N:2+1:1−0:+× N013 kmiCh eZ dNN9K4JTSKSJT 0:4T:4RKUS4 −NP:P9:PSK2S N0:0± 2:R 2:P+0:9−0:8 9:S+12:1−+:4 × N012 kmiCh eZ dNN9K4JTSKSJU 0:4U:NPKRU4 −NP:4P:N2K29 U:N± 2:0 > S:9 N:N+1:2−0:5× N013 YmiCh eZ dNP2KSJUNKNJ0 0:RT:4UKU9R −NU:N9:2PKR0 NP:P± 2:N P:P+1:4−1:2 N:R+1:8−1:0× N013 YmiCh eZ dNP2KSJUNKNJN 0:RT:R2K2SR −NU:N9:0PK49 U:S± 2:N > 4:U N:N+1:0−0:+× N013 YmiCh eZ dNTNKNJTUKTJ0 N:2T:0NK92S −N9:N9:4NKS0 N4:S± 2:N P:N+1:1−1:1 N:S+1:7−1:0× N013 YmiCh eZ dNTNKNJTUKTJN N:2S:R0KPP9 −N9:20:NPKRS NR:4± P:S R:4+2:4−1:7 N:T+1:5−0:9× N013 YmiCh eZ dNTNKNJTUKTJ2 N:2T:0UKT0U −N9:NU:RTKS0 9:0± 2:N 4:9+2:4−1:7 N:N+1:0−0:+× N013 YmiCh eZ dNTNKNJTUKTJP N:2T:0UKT0U −N9:N9:0NKS0 U:T± 2:N 4:0+2:0−1:3 N:N+1:0−0:+× N013 YmiCh eZ dNTPK9HRTK0J0 N0:2U:PUKN24 4P:2R:PTKS9 U:R± N:9 P:T+1:+−1:2 9:R+9:9−5:+× N012 YmiCh eZ dNTPK9HRTK0JN N0:2U:4UKTTN 4P:24:RPKT0 U:T± 2:0 2:4+1:0−0:9 N:N+1:5−0:8× N013 YmiCh eZ dNTSKSHR9K0J0 N0:PS:RSKRRS 4N:2T:22K40 NR:U± 2:S P:P+1:2−1:2 N:9+1:9−1:2× N013 YmiCh eZ dNTSKSHR9K0JN N0:PT:0RK4RN 4N:2T:P0KPU N2:R± P:0 2:N+1:0−0:8 N:4+2:2−1:0× N013 YmiCh eZ d2N4KNH4UKPJ0 9:R2:P4K2SU N9:0U:NUKS9 NR:T± P:N S:4+2:2−2:0 N:U+1:4−0:9× N013 YmiCh eZ d2N4KNH4UKPJN 9:R2:P9KP49 N9:0U:P0KST N4:9± P:2 > S:9 2:2+5:1−1:0× N013 YmiCh eZ d2N4KNH4UKPJ2 9:R2:09KTN4 N9:0S:2SKSS NR:2± P:S R:S+2:1−1:+ N:T+1:3−0:8× N013 kmlanckNUpN94J0 U:P0:4SK4RR N9:PS:4TKN9 N9:S± N:9 P:P+1:4−1:1 2:2+2:7−1:4× N013 YmlanckNUpN94JN U:P0:R4KPU2 N9:PT:PNK20 N4:9± N:T P:P+1:4−1:2 N:U+2:2−1:1× N013 YmlanckNUpN94J2 U:P0:RNKRRN N9:PT:RRK20 N0:T± N:S R:P+2:1−1:7 N:P+1:1−0:7× N013 YmlanckNUpN94JP U:P0:4NK0TP N9:P9:4PKNU NP:T± 2:R 4:9+1:7−1:5 N:S+1:5−0:9× N013 YmlanckNUpN94J4 U:PN:04K2UT N9:P4:2PKNU NP:T± P:N P:4+1:3−1:1 N:R+1:5−0:9× N013 kmlanckNUpN94JR U:P0:40K22U N9:PS:NRKNT U:R± 2:0 > S:T N:P+2:3−0:+× N013 YmlanckNUpN94JS U:P0:RNK2SU N9:PT:PNK20 S:U± N:T P:2+1:2−1:0 U:9+9:7−5:4× N012 YmlanckNUpN94JT U:P0:4UKTN9 N9:PT:RRK20 S:R± N:S 4:0+1:5−1:2 U:N+7:8−4:+× N012 YmlanckNUpTPRJ0 N:RU:4UK0UR −T:R2:4PKR0 U:R± 2:0 2:U+1:2−1:0 N:P+1:7−0:9× N013 Ymlanck24pN94J0 U:40:40KRUU 22:N2:PTKS0 U:P± N:S 2:U+1:1−0:9 N:2+1:4−0:8× N013 Y78


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