The SCUBA-2 Cosmology Legacy Survey: ALMA resolves the rest-frame far-infrared emission of sub-millimeter galaxies
J. M. Simpson, Ian Smail, A. M. Swinbank, O. Almaini, A. W. Blain, M. N. Bremer, S. C. Chapman, Chian-Chou Chen, C. Conselice, K. E. K. Coppin, A. L. R. Danielson, J. S. Dunlop, A. C. Edge, D. Farrah, J. E. Geach, W. G. Hartley, R. J. Ivison, A. Karim, C. Lani, C.-J. Ma, R. Meijerink, M. J. Michalowski, A. Mortlock, D. Scott, C. J. Simpson, M. Spaans, A. P. Thomson, E. van Kampen, P. P. van der Werf
aa r X i v : . [ a s t r o - ph . GA ] N ov Draft version October 13, 2018
Preprint typeset using L A TEX style emulateapj v. 04/17/13
THE SCUBA-2 COSMOLOGY LEGACY SURVEY: ALMA RESOLVES THE REST–FRAME FAR-INFRAREDEMISSION OF SUB-MILLIMETER GALAXIES
J. M. Simpson, Ian Smail, A. M. Swinbank, O. Almaini, A. W. Blain, M. N. Bremer, S. C. Chapman, Chian-Chou Chen, C. Conselice, K. E. K. Coppin, A. L. R. Danielson, J. S. Dunlop, A. C. Edge, D. Farrah, J. E. Geach, W. G. Hartley,
R. J. Ivison,
A. Karim, C. Lani, C. –J. Ma, R. Meijerink, M. J.Micha lowski, A. Mortlock,
D. Scott, C. J. Simpson, M. Spaans, A. P. Thomson, E. van Kampen, P. P.van der Werf Draft version October 13, 2018
ABSTRACTWe present high-resolution (0.3 ′′ ) ALMA 870 µ m imaging of 52 sub-millimeter galaxies (SMGs) inthe Ultra Deep Survey (UDS) field and investigate the size and morphology of the sub–millimeter (sub–mm) emission on 2–10 kpc scales. We derive a median intrinsic angular size of FWHM = 0 . ± . ′′ for the 23 SMGs in the sample detected at a signal-to-noise ratio (SNR) >
10. Using the photometricredshifts of the SMGs we show that this corresponds to a median physical half–light diameter of2 . ± . <
10 shows they have sizesconsistent with the 870 µ m–bright SMGs in the sample. We compare our results to the sizes of SMGsderived from other multi–wavelength studies, and show that the rest–frame ∼ µ m sizes of SMGsare consistent with studies of resolved CO ( J = 3–2 to 7–6) emission lines, but that sizes derivedfrom 1.4 GHz imaging appear to be approximately two times larger on average, which we attributeto cosmic ray diffusion. The rest–frame optical sizes of SMGs are around four times larger thanthe sub-millimeter sizes, indicating that the star formation in these galaxies is compact relative tothe pre-existing stellar distribution. The size of the starburst region in SMGs is consistent with themajority of the star formation occurring in a central region, a few kpc in extent, with a median starformation rate surface density of 90 ±
30 M ⊙ yr − kpc − , which may suggest that we are witnessingan intense period of bulge growth in these galaxies . Subject headings: galaxies: starburst, galaxies: high-redshift INTRODUCTION Institute for Computational Cosmology, Department ofPhysics, Durham University, South Road, Durham DH1 3LE,UK; email: [email protected] School of Physics and Astronomy, University of Nottingham,Nottingham NG7 2RD, UK Department of Physics & Astronomy, University of Leicester,University Road, Leicester LE1 7RH, UK School of Physics, HH Wills Physics Laboratory, TyndallAvenue, Bristol BS8 1TL, UK Department of Physics and Atmospheric Science, DalhousieUniversity Halifax, NS B3H 3J5, Canada Centre for Astrophysics Research, Science and TechnologyResearch Institute, University of Hertfordshire, Hatfield AL109AB, UK Institute for Astronomy, University of Edinburgh, RoyalObservatory, Blackford HIll, Edinburgh EH9 3HJ, UK Department of Physics, Virginia Tech, Blacksburg, VA24061, USA ETH Z¨urich, Institut f¨ur Astronomie, HIT J 11.3, Wolfgang-Pauli-Str. 27, CH-8093 Z¨urich, Switzerland European Southern Observatory, Karl SchwarzschildStrasse 2, Garching, Germany Argelander-Institute for Astronomy, Bonn University, Aufdem H¨ugel 71, D-53121 Bonn, Germany Leiden Observatory, Leiden University, P.O. Box 9513, NL-2300 RA Leiden, Netherlands Department of Physics & Astronomy, University of BritishColumbia, 6224 Agricultural Road, Vancouver, BC, V6T 1Z1,Canada Astrophysics Research Institute, Liverpool John MooresUniversity, Liverpool Science Park, 146 Brownlow Hill, LiverpoolL3 5RF, UK Kapteyn Astronomical Institute, University of Groningen,The Netherlands
Nearly twenty years after their discovery, there isstill debate about the nature of the population ofluminous, but highly dust-obscured sources detectedat high redshifts in sub-millimeter and millimetersurveys. The observational data suggest that the850 µ m–detected sub-millimeter galaxies (SMGs) lie ata median redshift z = 2 . ± ∼ M ⊙ and gas masses of ∼ × M ⊙ , e.g. Hainline et al.2011; Micha lowski et al. 2012; Bothwell et al. 2013) withspace densities of ∼ − Mpc − . A modest pro-portion of SMGs have been shown to host an ac-creting super-massive black hole (e.g. Alexander et al.2008; Pope et al. 2008; Wang et al. 2013) and manyappear disturbed or irregular in high-resolution rest–frame optical imaging from HST , albeit predomi-nantly with a low S´ersic index (e.g. Conselice et al.2003; Chapman et al. 2003; Swinbank et al. 2010a;Targett et al. 2013; Wiklind et al. 2014; Chen et al.2014). SMGs thus share some of the traits of local Ul-traluminous Infrared Galaxies (ULIRGs), although theyare ∼ times more abundant at a fixed far-infrared lu-minosity (e.g. Chapman et al. 2005; Lindner et al. 2011;Magnelli et al. 2012; Yun et al. 2012; Swinbank et al.2014) and appear to be more massive than these pro-posed analogs (e.g. Tacconi et al. 2002).In the past decade, near–infrared (NIR) spectroscopy S2CLS: Resolved ALMA imaging of sub–millimeter galaxieshas also identified a population of quiescent, red, galaxiesat z = 1.5–3, which have been proposed as the potentialdescendants of high redshift starbursts (SMGs). Thestellar populations in these high redshift quiescent galax-ies follow a fairly tight “red-sequence”, indicating thatthe stellar population was formed rapidly in an intensestarburst phase (e.g. Kriek et al. 2008). The high starformation rates of SMGs (300 M ⊙ yr − ; Magnelli et al.2012; Swinbank et al. 2014), combined with large molec-ular gas reservoirs, indicate that they have the potentialto form a stellar component of 10 –10 M ⊙ in 100 Myrs.Such rapid stellar mass growth, at high redshift, hasled to speculation that SMGs may be the progenitorsof both these high-redshift quiescent galaxies, and localelliptical galaxies (Lilly et al. 1999; Genzel et al. 2003;Blain et al. 2004; Swinbank et al. 2006; Tacconi et al.2008; Hainline et al. 2011; Hickox et al. 2012; Toft et al.2014; Simpson et al. 2014).Studies investigating this proposed evolutionary sce-nario typically compare properties such as the stel-lar mass, spatial clustering and space densities of thepopulation and the proposed descendants. However,each of these methods has significant associated un-certainties. In particular, the stellar masses of SMGshave been shown to be highly dependent on the as-sumed star formation history, with systematic uncer-tainties of a factor of around five on individual mea-surements (see Hainline et al. 2011; Micha lowski et al.2012). Studies of resolved H α and CO emission linesindicate SMGs have dynamical masses of (1–2) × M ⊙ (Swinbank et al. 2006; Alaghband-Zadeh et al. 2012;Bothwell et al. 2013), placing an upper limit on thestellar masses, but the number of SMGs with measureddynamical masses is small and the samples inhomoge-neous. The spatial clustering of single-dish detected sub-mm sources has been shown to match that expected forthe progenitors of local ellipticals (Hickox et al. 2012).However, these results are complicated by source blend-ing in the coarse (19 ′′ ) resolution single-dish sub-mmimaging (Hodge et al. 2013b), whereby the detected sub-mm source comprises of multiple individual SMGs. Fi-nally, while the space densities of SMGs and ellipticalsare in agreement, the analysis is highly dependent onthe assumed duty cycle of the SMG population (e.g.Simpson et al. 2014).The morphologies of SMGs provide an alternative,and potentially powerful, tool for testing any evolu-tionary connection, since the population of quiescentgalaxies at high redshift appear extremely compact inrest–frame optical imaging (half–light radius [ R e ] ∼ HST imaging of 48 SMGs,finding a median half-light radius of R e = 4.4 +1 . − . kpc,considerably larger than the quiescent population (seealso Targett et al. 2013; Wiklind et al. 2014). However,as discussed by Chen et al. (2014), the SMGs in theirsample are predominantly disturbed systems, with indi-cations that the intense star formation is triggered bymerger activity (see also Frayer et al. 1999; Greve et al.2005; Tacconi et al. 2006; Engel et al. 2010; Ivison et al. 2013). The sizes presented by Chen et al. (2014) are thuslikely to over-estimate the size of the system at post-coalescence. In addition, the high star formation ratesof SMGs, combined with large molecular gas reservoirs,means that they have the potential to at least doubletheir stellar mass during the starburst phase. As such,understanding the spatial distribution of the ongoingstar formation is crucial to understanding the stellardistribution of the post starburst galaxy.In the local Universe ULIRGs, the proposedanalogs of SMGs, appear to be compact (1–2 kpcdiameter) using resolved CO/dust/mid-infrared/radioemission (Condon et al. 1991; Downes & Solomon1998; Soifer et al. 1999; Sakamoto et al. 2008;Rujopakarn et al. 2011; Ueda et al. 2014). At thetypical redshift of SMGs ( z = 2.5) it has only beenpossible to resolve the dust emission in a small numberof the brightest sources. Younger et al. (2010) presentobservations of two bright SMGs ( S = 13 mJy &18 mJy) using the Sub-millimeter Array (SMA). Both ofthese SMGs appear resolved in the SMA data and havea FWHM of 0 . ± . ′′ ; at the typical redshifts of SMGsthis corresponds to a physical size of 4–5 kpc. Morerecently Hodge et al. (2013b) obtained interferometricfollow-up observations, with the Atacama LargeMillimeter Array (ALMA), of single-dish identifiedsub-mm sources. Hodge et al. (2013b) identified 99SMGs in the 1 . ′′ resolution ALMA maps, but foundthat only one SMG is resolved with a FWHM of 9 kpc.The remaining SMGs are unresolved, with sizes <
10 kpc(Hodge et al. 2013b).Limited studies in the radio and CO also hintthat SMGs have sizes of a few kpc in diameter(see Men´endez-Delmestre et al. (2009) for a discussion ofthe mid–infrared sizes of SMGs). However these studiessuffer from two limitations. In CO the resolutionachieved using facilities such as the Plateau de BureInterferometer (PdBI) or SMA is barely sufficient toresolve the emission to < ∼ CO observations are also typically carriedout in the higher- J transitions, which trace the denserand warmer gas, not necessarily reflecting the full extentof the gas reservoir, or star formation activity. Indeedthere is evidence from spatially-resolved CO ( J = 1–0)observations of a small sample of SMGs that the coolgas extents of these systems are considerably larger thanclaimed from high- J observations (e.g. Ivison et al. 2011;Riechers et al. 2011; Hodge et al. 2013a). In contrastto studies of CO emission, radio observations providethe resolution required to resolve SMGs at 1.4 GHz witheMERLIN (e.g. Biggs & Ivison 2008) or at higher fre-quencies with the Karl G. Jansky Very Large Array(VLA). However, such studies in the radio typically relyon the far–infrared radio correlation to identify the sub-mm sources. The identification procedure is inherentlyprobabilistic, and as shown by Hodge et al. (2013b) thereliability and completeness of the identifications is 80 %and 50 pc respectively . In addition, the form of thespatially–resolved far-infrared radio correlation is stilldebated in the local Universe, owing to the potentialdiffusion/leakage of the cosmic rays and the influence ofimpson et al. 3
Fig. 1.—
Grayscale K–band images of the 27 bright (SNR > σ ) ALMA-identified SMGs in our sample. The images are in order ofdecreasing 870 µ m flux density, except for the final four panels, which are classed as potentially lensed SMGs (images are separated by ablank panel). Each panel is 5 ′′ × ′′ and we contour the ALMA maps over the images of the galaxies. The green contours on each imagerepresent ALMA 870 µ m emission at 4, 8, 12, .... × σ , and a single red contour represents where the ALMA 870 µ m surface brightness is50 % of the peak value; for an ideal point source this contour should be identical to the size of the ALMA beam FWHM (bottom rightof each panel). We note that the red contour appears more extended than the beam, indicating that these SMGs are resolved in the 0.3 ′′ resolution ALMA data. Overall, 15 % of the SMGs are not detected in the K–band imaging (5 σ detection limit 25.0 mag). magnetic fields on the resulting emission (Bicay & Helou1990; Murphy et al. 2006, 2008). Hence translating radiosizes into star formation extents is uncertain, especiallywhen extrapolating the results of local studies to SMGsat z > ∼ µ m observations of 30 bright sub-millimeter sources.These SMGs are selected at 850- µ m from the SCUBA-2 (Holland et al. 2013) Cosmology Legacy Survey ofthe UKIDSS Ultra Deep Survey (UDS) field, and weremapped at an angular resolution of 0.3 ′′ FWHM usingALMA. In this work we focus on the sizes and mor-phologies of these SMGs; the catalogue and numbercounts will be presented in Simpson et al. (in prep). Wediscuss in § µ mobservations and their reduction. In § § §
5. Throughout the pa-per, we adopt a cosmology with Ω Λ = 0.73, Ω m = 0.27,and H = 71 km s − Mpc − , in which an angular size of1 ′′ corresponds to 8.5–7.5 kpc at z ∼ OBSERVATIONS AND ANALYSIS
The observations discussed here targeted 30 870 µ msources lying in the UKIDSS UDS field. These sourceswere selected from wide-field 850 µ m observations of theUDS field taken as part of the SCUBA–2 CosmologyLegacy Survey (S2CLS) program with the SCUBA-2camera on the James Clerk Maxwell Telescope (JCMT).The current SCUBA-2 observations reach a typical depthof σ = 1.2 mJy across a 0.8 × field, andhave an angular resolution of 14.8 ′′ FWHM. From anearly version of these observations, with σ = 2 mJy, weselected a sample of 30 of the brightest sub-millimetersources in the field, detected at > σ significance andhence having 850 µ m flux densities of 8 mJy–16 mJy. ALMA data
The data reduction and source extraction from ourALMA data is described in detail in Simpson et al.(in prep.). Here we give a brief description. TheALMA data were taken on 2013 November 1, as partof the Cycle-1 project 2012.1.00090.S. We observed all30 sub-millimeter sources with ALMA, using 7.5-GHz ofbandwidth centered at 344 GHz (870 µ m; Band 7); thesame frequency as the original SCUBA-2 observations.We used a “single continuum” correlator setup with fourbasebands of 128 dual-polarization channels each.The phase centers for the ALMA pointings are thecentroid position of the sub-millimeter source from theearly SCUBA-2 map. The ALMA primary beam at this S2CLS: Resolved ALMA imaging of sub–millimeter galaxies Fig. 2.—
Components of the complex visibility versus uv -distance for the phase (Ph) and bandpass (BP) calibrators from bothmeasurement sets (top), and an example eight SMGs from our sample (lower panels). The real components of the complex visibilitiesare plotted as data points, while the 1- σ range of the imaginary components is shown as a grey shaded region. Both the real and imaginarycomponents are plotted on the same scale on the left axis. The amplitudes of both sets of calibrators are relatively flat with uv -distance,indicating that they are unresolved point sources, although we note a marginal drop in the flux of the phase calibrator, which suggests it isweakly resolved. In contrast the amplitudes for seven of the SMGs decline strongly with uv -distance, confirming our conclusion that thesesources are resolved in the sub–mm imaging at 0.3 ′′ resolution. We plot on each SMG a dashed line representing the best-fitting Gaussianto the amplitudes. We note that our measurements of the size and flux density of these SMGs in the image plane are consistent with theGaussian fits to the amplitudes (the median ratio in size is FWHM uv / FWHM image = 0.9 ± frequency is 17 . ′′ FWHM, larger than the 14.8 ′′ FWHMof the SCUBA-2 beam and so is sufficient to recover all ofthe SMGs contributing to the single-dish sub-millimeteremission. The array configuration for our observationswas such that the 26 ALMA 12–m antennae employedhad a maximum baseline of 1250 m, and a median base-line of 200 m. This is in fact more extended than ourrequested compact C32–1 configuration and as a resultyields a synthesized beam of 0.35 ′′ × ′′ using Briggsweighting (robust parameter = 0.5). The maximumangular scale that our observations are sensitive to is5 ′′ , which as we show in § Common Astron-omy Software Application ( casa version 4.2.1). Asdetailed in Simpson et al. (in prep) the uv -data wereFourier transformed to create a “dirty” image. We thenimpson et al. 5 Fig. 3.—
Examples showing 2 ′′ × ′′ images of our high resolution 870 µ m maps (0.3 ′′ ; left) alongside the residuals from fitting a pointsource model (PS; middle of each set of three panels) and an elliptical Gaussian model (resolved; right) for 12 example SMGs in oursample. The green contours represent 870 µ m emission at 4, 8, 12, .... × σ , and the color–scale in each image is clipped at ± σ . The ALMAbeam is shown in the bottom left of the left–hand column. The SMGs presented here are chosen such that they span the full range indetection significance for the sample, and are a fair representation of the data quality of our ALMA maps. In eleven of these images thereare significant residuals when fitting a point source model to the 870 µ m emission, indicating that these sources are resolved in our ALMAmaps. In contrast we highlight UDS392.0, which is well–described by a point source model and is classed as unresolved in our analysis. Forthe full sample of 23 SMGs the median difference in χ between the best-fit extended and point-source model is ∆ χ = 20 ±
2. We findthat 22 / 23 SMGs are resolved in our 0.3 ′′ resolution imaging, and derive a median angular size for the sample of 0.30 ± ′′ (deconvolvedFWHM of the major axis). applied the same procedure adopted by Hodge et al.(2013): a tight clean box was placed around all > σ emission in each map and these were cleaned down toa depth of 1.5 σ . The final cleaned maps have a medianangular resolution of 0.35 ′′ × ′′ (P.A. ∼
55 deg), usingBriggs weighting (robust parameter = 0.5), and a medianrms of σ = 0.21 mJy beam − (with a range from 0.19–0.24 mJy beam − ). We inspect our maps and find thatwe do not detect any sources at sufficiently high SNR to reliably self–calibrate.To construct the master catalog, and ensure that theextended flux from the SMGs is recovered, we repeatedthe imaging procedure described above, but using nat-ural weighting, and applying a Gaussian taper to thedata in the uv -plane. Applying a Gaussian taper meansthat a lower weighting is given to visibilities at largedistances in the uv -plane, producing a map with a largersynthesized beam, hence with less emission resolved out, S2CLS: Resolved ALMA imaging of sub–millimeter galaxiesat the expense of higher noise. The resulting maps havea median angular resolution of 0.8 ′′ × ′′ , and medianrms of σ = 0.26 mJy beam − . Hence two sets of mapswere created; “detection” maps with a synthesised beamof ∼ ′′ FWHM and “high-resolution” maps at ∼ ′′ FWHM.To construct our catalog, we identify sources withinthe ALMA primary beam FWHM that are detected at > σ in the 0.8 ′′ FWHM “detection” maps, and extractboth the peak flux density and the total flux density in a0.8 ′′ radius aperture for each SMG. We search for sourcesoutside the ALMA primary beam FWHM, but do notfind any statistically significant detections (see Simpsonet al. in prep). In total we identify 52 SMGs above4 σ in the 30 ALMA maps, at 0.8 ′′ FWHM resolution.These SMGs have a range of 870 µ m flux density of 1–14 mJy and we recover the single–dish SCUBA-2 witha median ratio of S SCUBA2 / S ALMA = 1.04 ± ≥
10 ( S > ∼ ′′ resolution, whichreduces our sample to 27 SMGs. In order to checkthe measured fluxes of these sources we also used the imfit routine in casa to model each SMG and findgood agreement between the model and aperture derivedflux densities ( S Model / S Aperture = 1.02 ± S < ∼ > ∼ . Indeed, we identify four ex-amples of potential gravitationally-lensed sources in ourbright SMG sample: UDS 109.0, UDS 160.0, UDS 269.0,and UDS 286.0. All of these sources appear to be closeto, but spatially offset from, galaxies at z < ∼ > σ Robustness of imaging Lensing models predict that our sample contains 1–2SMGs that are lensed with an amplification factor > As we show in § ′′ resolution ALMA maps. However,we now perform two tests to ensure that an error in thecalibration of the raw data does not drive our conclusionthat the sources are resolved.The observing strategy for our targets was such thateach SMG was observed five separate times throughthe observing block, with phase calibration observationsbetween each repeat observation. First, we test forvariations in the source size as a function of time, asmight be expected if the phase solution applied to thedata does not correctly model fluctuations. To do so, weseparately image each repeat observation of UDS 204.0,the brightest SMG in our sample (the integration time issufficient to detect the source at 8–10 σ in an individualscan). The SMG appears resolved in all five images, withan intrinsic source size in the range 0 . ′′ –0 . ′′ , and allsizes consistent within the associated 1– σ uncertainties( ∼ ′′ ).Secondly, we re-classify an observation of the phasecalibrator as a science target observation in the observingsequence and repeat the calibration of the data set.If an error in the calibration of the raw data, due tophase variations, are causing the SMGs in our sample toappear resolved then the phase calibrator will also appearresolved in this scan. We image this phase calibratorscan in the same manner as the SMG observations andmodel the emission using the imfit routine. In theindividual scan the phase calibrator has an intrinsic sizeof FWHM = 0.06 ± ′′ , which is marginally higher thatthe intrinsic size measured in an image combining allscans (FWHM = 0.03 ± ′′ ). However, by removing aphase calibrator scan we have introduced a ten minutegap in our calibration observations, which is double thatused throughout the observations. Hence any differencein the size of the phase calibrator should be classed asan upper limit on the uncertainty due to errors in thephase calibration of the data. Taken together these testsindicate that the SMGs in our sample do not appearresolved due to errors in the calibration of the raw data.In our analysis in § imfit routine in casa to fit an elliptical Gaussian model (convolved withthe synthesised beam) for the 870 µ m emission from eachSMG. However, before applying this approach to thebright SMGs in our sample, we now test the reliabilityof the fits as a function of SNR using simple simulatedgalaxies. To do so, we create 20,000 elliptical Gaussianmodel sources with a uniform distribution of peak SNRfrom 4 to 30 (covering the range of SMGs in our fullsample) and a major-axis size distribution that is uniformfrom 0 to 1 ′′ . The model sources are distributed uni-formly in SNR at 0.8 ′′ resolution, reflecting the selectionfunction of our full SMG catalog. In order to use realisticnoise maps we add these models to a randomly chosenposition in one of the residual (source-subtracted) ALMAmaps.We use casa to fit an elliptical Gaussian to eachinjected model source and derive the best-fit size foreach. We note that the imfit routine can return apoint source solution if this is the best model. Foreach model parameter we calculate the fractional off-set between the input model value and the recoveredvalue. As expected we find that the precision of therecovered parameters is a function of SNR. To en-impson et al. 7sure that the sizes we derive for the SMGs are reli-able we define a selection limit that the 1- σ spread in( FWHM Model − FWHM
True ) / FWHM
True < ≥
10, which is thejustification for our use of this limit to define the brightSMG sample analysed in this paper.These simulations also indicate a small bias in therecovered size for sources with SNR between 10 to 30 σ of( FWHM Model − FWHM
True ) / FWHM
True = 0.018 ± σ spread of ± . imfit routine returns a point source best-fit solution.For SMGs with SNR = 10–30 we find that 90% of themodel sources that are best fit by point source modelsusing imfit actually have a “true” size ≤ ′′ (i.e.smaller than half the size of the beam major axis).Hence, we can be confident that any SMGs that havea point source best-fit model have a size ≤ ′′ , andwe adopt this as an upper limit for the size of theunresolved SMGs. Multi–wavelength properties
During our analysis we use archival multi–wavelengthinformation on this well-studied field. An extensiveanalysis of the multi–wavelength properties of the SMGsample will be presented in Ma et al. (in prep), but for thepurposes of this paper we use two pieces of informationfrom that work: constraints on the likely redshifts of theSMGs using photometric redshifts; and estimates of theirfar-infrared luminosities.First, we use the photometric redshift catalog of thisfield produced by the UKIDSS UDS team, which isbased on a K -band selected sample of sources. Tobriefly summarise, photometric redshifts are determinedfor each field source by fitting template spectral energydistributions (SEDs) to the observed U BV Ri ′ z ′ JHK and IRAC 3.6 and 4.5 µ m photometry, using the publicSED fitting code eazy (Brammer et al. 2008). Excellentagreement is found between the photometric and spec-troscopic redshifts for 2146 sources in the field, with amedian dispersion of ( z phot − z spec ) / (1 + z spec ) = 0 . ′′ of the 23 brightSMGs, which leaves four of the SMGs without redshiftinformation. We also searched for IRAC counterpartsfor the four SMGs without photometric redshifts and findthat three have detections in the IRAC imaging; however,the limited number of photometric bands available for allof these sources mean it is impossible to derive precisephotometric redshifts. Simpson et al. (2014) argue thatthese NIR–faint SMGs typically lie at higher redshiftsthan the optical/NIR–brighter SMGs, and so we adopttheir approach and assign these sources a redshift of z = 4 ± Herschel
SPIRE imaging (Pilbratt et al. 2010;Griffin et al. 2010) of the field at 250, 350 and 500 µ m,along with the precise position of the ALMA source todeblend and extract flux densities for the SMGs. Fol- lowing the approach of Swinbank et al. (2014), they usea prior catalog of sources detected at 24 µ m or 1.4 GHz,along with the ALMA source positions, to model thesources contributing to the map flux in the vicinity ofeach SMG. Having extracted flux densities or limits inthe three SPIRE bands, along with the ALMA 870 µ mflux density, they fit a library of model spectral en-ergy distribution (SED) templates (see Swinbank et al.2014), to the FIR-photometry and determine the best-fit template. We integrate the best-fit SED from 8 to1000 µ m to derive the total far-infrared luminosity ofeach SMG. If an SMG is undetected in the Herschel µ m imaging then the far-infrared lu-minosity is treated as an upper limit. We measurea median far-infrared luminosity for the 23 SMGs inour sample of L FIR = (5.7 ± × L ⊙ , and a me-dian dust temperature of T d = 32 ± σ andSNR = 4–5 σ , respectively, are undetected in the Herschel µ m imaging. We stack the Herschel
SPIRE maps for these subsets and derive an average L FIR = 3 . +0 . − . × L ⊙ and L FIR = 2 . +1 . − . × L ⊙ for the SNR = 5–10 σ and SNR = 4–5 σ subsets, respec-tively. RESULTS
Resolved dust emission
We show the ALMA maps with a 0.3 ′′ FWHM res-olution synthesized beam for the 27 SNR ≥
10 SMGsin Figure 1. These are presented as contours overlaidon K –band grayscale images, to allow the reader tomake a qualitative comparison of the size and shapeof the contour corresponding to the half-peak-flux leveland the corresponding size for the synthesized beam.We see evidence in a majority of the SMGs that thesub-millimeter emission appears to be more extendedthan would be expected for an unresolved source withthe same peak flux, with several examples also showingstructure on smaller scales (e.g. UDS 74.0, UDS 216.0,UDS 218.0, UDS 361.0, UDS 408.0).To quantitatively test if the SMGs are resolved inour data we initially perform two non-parametric tests.First we compare the peak flux of each source in the0.8 ′′ FWHM observations to the higher resolution 0.3 ′′ FWHM imaging (note that the maps are calibratedin Jy beam − ). The peak flux of the SMGs is lowerin the 0.3 ′′ resolution maps, with a median ratio of S . / S . = 0.65 ± σ range of ± ′′ and 0.8 ′′ resolution imaging corresponds to anintrinsic source size of ∼ ′′ .As a second test we compare the total flux density inan aperture for each source to the peak flux density atboth 0.3 ′′ and 0.8 ′′ FWHM resolution. We convert eachmap into units of Jy pixel − and measure the “total”flux density in an 0.8 ′′ radius aperture. The ratio of thepeak-to-total flux density is 0.50 ± ′′ FWHMresolution, compared to 0.83 ± ′′ FWHM. Thissupports the conclusion that the bulk of the bright SMGsare resolved by ALMA at 870 µ m with a 0.3 ′′ FWHM S2CLS: Resolved ALMA imaging of sub–millimeter galaxies
Fig. 4.—
Top:
Angular size distribution of the 870 µ m emission from SMGs as a function of their 870- µ m flux density. A dashed linerepresents our surface brightness selection limit. The 23 SMGs detected at ≥ σ , have a median intrinsic size of 0.30 ± ′′ (deconvolvedFWHM of the major axis). We stack the 870 µ m emission from SMGs detected at 5–10 σ and 4–5 σ , and show the size derived from eachstack. We find that these 870 µ m–faint SMGs have sizes that are on average consistent with the brighter SMG distribution. We highlightfour SMGs that are potentially lensed sources, but note that these are not included in our analysis. For comparison we show the sizes oftwo bright SMGs measured from observations with the SMA (Younger et al. 2010). Bottom left:
Physical size of SMGs as function ofredshift. Four SMGs in our sample do not have a photometric redshift, and we fix the redshift of these sources at z = 4 ± . ± . σ of 2 . ± . µ m–brighter SMGs. We alsoshow the results of stacking the 14 SMGs detected at SNR = 4–5 σ , but note that 8/14 sources in the stack do not have a photometricredshift. Bottom right:
Physical size of the SMGs in our sample as a function of FIR-luminosity. The 23 SMGs shown have a medianFIR luminosity of L FIR = (5.7 ± × L ⊙ , and a median physical size of FWHM = 2 . ± . L FIR and the physical size of the SMGs. For comparison we also show the sizes of local “merger–remnants” measured from interferometricobservations of the CO ( J = 1–0 / 2–1 / 3–2) molecular emission line. These local galaxies have a median size of 1 . ± . J CO typically exceeds the size of the star forming region, the starformation in SMGs appears to be considerably more extended than in local U/LIRGs. synthesised beam, and suggests that the average angularsize of the population is 0.3–0.4 ′′ . We note that theaperture fluxes of the SMGs measured in the 0.3 ′′ and0.8 ′′ imaging are in good agreement, with a median ratioof S . / S . = 1.02 ± uv -plane, rather than in the image plane, com-pared to the calibrator sources used for our observations(which are expected to be unresolved). For each sourcewe align the phase centre of the map to the positionof the SMG or calibrator source, and extract the am-plitudes for each source as a function of uv -distance.The amplitudes represent the observed flux of the sourceon different angular scales in the image plane, with thelongest baseline providing information on the smallest angular scales that our observations are sensitive to. Foran ideal point source the amplitudes should be constantwith uv -distance. As Figure 2 demonstrates we do indeedrecover an effectively flat distribution for both the phaseand bandpass calibrators.In Figure 2 the amplitudes as a function of uv -distancefor the eight SMGs which are the sole sources detectedin their respective ALMA maps (restricting the samplein this way removes any complications due to modellingand subtracting other sources in the primary beam).The amplitudes of seven of the SMGs clearly decreasewith increasing uv -distance. A single SMG, UDS 392.0,appears to be only marginally resolved on the longestbaselines (our analysis in the image plane identifies thisSMG as unresolved, see Fig 2 and 3). We fit the ampli-tudes for each SMG with a single Gaussian componentimpson et al. 9 Fig. 5.—
Comparison of the 870 µ m sizes of the SMGs in oursample, to the sizes of SMGs measured in 1.4 GHz / VLA imag-ing (Biggs & Ivison 2008) and H –band/ HST imaging (Chen et al.2014). To allow a fair comparison between the samples we presentall of the sizes in terms of an effective radius. The median size ofthe 12 SMGs identified in the 1.4 GHz imaging is R e = 2 . ± . µ m size of SMGs, R e =1 . ± . µ m emission with a kernel ofscale length 1–2 kpc, which is appropriate for modelling cosmic raydiffusion in star-forming galaxies at low redshift (Murphy et al.2008), increases the median size of the SMGs to 3 . . R e = 4.4 +1 . − . kpc fromrest–frame optical HST imaging of 17 interferometrically–identifiedSMGs at z = 1–3. The H -band sizes of these SMGs are on average3 times larger than the 870 µ m sizes presented here, indicating thatthe obscured star-forming region in SMGs is compact relative tothe stellar emission. and determine the equivalent size in the uv -plane. Themodel fits in the uv and image planes are consistent, andderive a median size ratio between the image- and uv -derived sizes of FWHM uv / FWHM image = 0.9 ± S image / S uv = 1.1 ± > ∼
600 k λ , indicating that there is unresolvedflux in these sources on an angular scale of < ∼ ′′ , butthis unresolved component comprises < ∼
10 % of the totalflux density.Given that our non-parametric tests indicate that theSMGs are resolved in our 0.3 ′′ imaging, we now choseto fit a more complex model to the sources. Usingthe imfit routine we determine the best-fit ellipticalGaussian model for the 23 SMGs in our bright sample(SNR > σ ). The free parameters of the model areposition; peak flux density; major and minor axis; andposition angle. The median intrinsic size of the 23 SMGsis 0.30 ± ′′ (deconvolved FWHM of the major axis),and one SMG is modelled as a point source; as theintrinsic sizes of the sources are comparable to the beamwe choose to focus our analysis on the FWHM of themajor axis. The median χ for the elliptical Gaussian fitis 38.3 ± χ between the best-fitextended and point-source model is ∆ χ = 20 ± . We also determined the best-fit Gaussian model for the SMGsin the 0.8 ′′ imaging but find that 65 % are unresolved, consistent The top panel of Figure 4 shows the sizes of theSMGs as a function of their 870 µ m flux density. Thedispersion of the 870 µ m sizes is small and there is noclear trend in the size of the dust emission region with870 µ m flux density. We note however that the twoSMG with S ∼
12 mJy in the sample are aroundtwo times larger than the median of the sample. Whilethis may be interpreted as a weak trend in the size ofSMGs with 870– µ m flux density we caution against astrong conclusion, given the limited sample size at thesefluxes. We also show the sizes of two bright SMGs( S = 13 mJy and 18 mJy) presented by Younger et al.(2010). These SMGs were observed with the SMA andboth appear marginally resolved in the uv –plane, withsizes of 0 . ± . ′′ (deconvolved FWHM). While the sizemeasurements for these sources have large associateduncertainties, they are consistent with the sizes presentedhere.To search for trends in our sample over a larger dynam-ical range we have also used the fainter SMGs detectedin our ALMA maps. While the individual sizes measuredfor these galaxies have significant uncertainties, we canattempt to derive a typical size for samples of faintSMGs via stacking (this is reasonable as the synthesisedbeam does not vary significantly between observations;the beam major and minor axes vary by at most 0.03 ′′ and 0.02 ′′ , respectively across the full sample). Wesplit the fainter 25 SMGs into roughly equal sub-samplesdetected at SNR = 5–10 σ (median S = 3.1 ± σ (median S = 2.6 ± ′′ FWHM maps of these sub-samples and use imfit tomeasure the size of the stacked profile. We derive sizesof 0.30 ± ′′ and 0.35 +0 . − . ′′ for the two sub-samplesrespectively. The errors on the measured size of eachsubset are derived by bootstrapping the maps includedin the stacks and repeating the analysis. These resultsindicate that at least on average the 1–4 mJy SMGs inour full sample have the same size distribution as thosewith observed 870 µ m flux densities of 4–15 mJy sources(see Figure 4). DISCUSSION
Physical size of SMGs
The 23 SMGs detected at > σ in our sample have amedian angular FWHM of 0.30 ± ′′ . For each SMGwe use the photometric redshift to convert the measuredangular diameter into an intrinsic physical scale, andderive that the median physical size of the SMGs is2 . ± . . ± . . +1 . − . kpc, at a median redshift of z = 2 . ± . z = 4 ±
1, for the SNR = 5–10 σ andSNR = 4–5 σ subsets, respectively, indicating no trend in with our results from the higher resolution (0.3 ′′ ) imaging. The re-solved sources in the 0.8 ′′ imaging have a median FWHM ratio be-tween the two sets of imaging of FWHM . / FWHM . = 1.2 ± z > ∼ .
5. Four SMGs do nothave a photometric redshift and it is likely that thesesources lie at z ∼ z = 4these SMGs have a distribution of physical FWHM from < z = 6, then the range of FWHM is < z < z > . unlensed SMGs presented here, we do not find anyevolution in the sizes of the 870 µ m emitting region at z < Comparison of the multi-wavelength sizes of SMGs
We now compare the 870 µ m sizes presented hereto the sizes of SMGs measured from observations atdifferent wavelengths. First, we compare our resultsto a sample of 12 SMGs (median S = 6.8 ± . ′′ resolution1.4 GHz/ VLA imaging (Biggs & Ivison 2008). In theiranalysis Biggs & Ivison (2008) fit an elliptical Gaussianmodel to the 1.4 GHz emission from each SMG, derivinga median angular size of FWHM = 0 . ± . ′′ . At theredshifts of these SMGs this angular size corresponds toa median physical size of FWHM = 5 . ± . z = 2; con-sistent with the radio–detected SMGs in Simpson et al.2014). Hence the 1.4 GHz sizes for the SMGs presentedby Biggs & Ivison (2008) are about two times larger thanthe 870 µ m sizes presented here.It is important to initially note that the radiocounterparts to the sub-mm emission presented inBiggs & Ivison (2008) were identified via a probabilisticapproach using the far-infrared radio correlation. Asshown by Hodge et al. (2013b) these identifications are80 % reliable, and so we might expect that 2–or–3 of theradio sources presented in Biggs & Ivison (2008) are notthe true counterpart to the sub-mm emission. However,we do not know if such mis–identifications are likely tobe biased towards galaxies with larger, or smaller, sizesat 1.4 GHz.Another possible explanation for the discrepancy be-tween the radio and far–infrared sizes of SMGs is that thediffusion length of cosmic rays ( ∼ ∼
100 pc), due to magnetic fields efficiently transportingcosmic rays through the host galaxy. Murphy et al.(2008) present a study of 18 local star-forming galaxieswith resolved imaging at 70 µ m and 1.4 GHz. Theyshow that the radio emission from these galaxies can bemodelled as the convolution of the far-infrared emissionwith an exponentially declining kernel, with an e -foldinglength of the kernel of 1–2 kpc (see also Bicay & Helou1990; Murphy et al. 2006). We convolve the median 870 µ m size of the SMGs with this exponential kerneland find that the FWHM of the convolved profile is 3 . . µ m sizes.The galaxies presented by Murphy et al. (2008) are“normal” star-forming galaxies, with star formation ratesthree orders of magnitude lower than the SMGs pre-sented here. The e -folding length of the kernel hasbeen shown to depend on both star formation ratedensity and morphology, with high star formation ratedensities and irregular galaxies having lower e -foldinglengths (Murphy et al. 2008). In both of these situationsordered magnetic fields are disrupted, allowing cosmicray electrons to stream more freely out of the galaxy,resulting in a shorter scale length. As such, we cautionthat a scale length of 1–2 kpc might be an over-estimateof the appropriate scale length for the radio emissionfrom SMGs.Next we compare the 870 µ m sizes of SMGs to thesizes of SMGs measured from CO emission lines.Engel et al. (2010) present a compilation (including newobservations) of the sizes of SMGs measured from re-solved CO ( J = 3–2 / 4–3 / 6–5 / 7–6) emission lines(see also Tacconi et al. 2006, 2008). Deriving a mediansize for the sample is challenging, as the upper limitson the size of unresolved SMGs are typically similar tothe sizes of the resolved sources. Treating the unresolvedsources as point sources, the median size of the sampleis FWHM = 2.3 ± . ± . CO-emissionlines are often either unresolved, or marginally resolved,with sizes constrained at only 1–2 σ . The sizes arealso measured from CO emission lines across a rangeof rotational transitions, from J = 2–1 to 7–6, and wenote that there is ongoing debate over whether emissionfrom different transitions traces the same molecular gas(Weiß et al. 2007; Panuzzo et al. 2010; Bothwell et al.2013; Narayanan & Krumholz 2014). Due to these issueswe simply note that the sizes derived from moderate – J transitions of CO are broadly consistent with themedian 870 µ m size of the SMGs in our sample.Finally, we compare our results to the sizes ofSMGs derived from high-resolution, HST , near–infraredimaging. Chen et al. (2014) recently presented H –band/ HST imaging (rest–frame optical imaging) of 48SMGs. These SMGs were drawn from the ALESS sample(Hodge et al. 2013b), and have precise < ∼ . ′′ identifi-cations from ALMA 870 µ m observations. Chen et al.(2014) fit a S´ersic profile to the H –band emission, de-riving a median half–light radius of R e = 4.4 +1 . − . kpc(see also Targett et al. 2013; Wiklind et al. 2014). Asrecommended by Chen et al. (2014), we have restrictedtheir sample to the 17 SMGs with an apparent H –bandmagnitude <
24 mag and a photometric redshift between z phot = 1–3, which ensures that the size distributionis complete (median S = 4.0 ± Fig. 6.—
Star formation rate surface density of the SMGsin our sample as a function of redshift. The dashed line repre-sents luminosity evolution L IR ∝ (1 + z ) . A dotted line showsthe 90 th percentile luminosity surface density for a sample ofultraviolet–selected sources (Meurer et al. 1997). The SMGs havea median star formation rate density of 90 ±
30 M ⊙ yr − kpc − ,and we note that no SMGs exceed the Eddington limit for aradiation pressure supported starburst ( ∼ ⊙ yr − kpc − ;Andrews & Thompson 2011) profile with S´ersic index n = 0 .
5. If we convert our870 µ m sizes to a half–light radius we find that the SMGshave a median R e = 1 . ± . § µ m emission fromthe SMGs is consistent with the median size from theelliptical Gaussian fit. The optical sizes of the SMGs areabout four times larger than the 870 µ m dust emittingregion, and as can be seen in Figure 5 the distributionof near–infrared sizes has considerably more dispersionthan the 870 µ m sizes. The compact nature of the starformation means that it is plausible we are observingbulge growth in the form of obscured star formation.However, to test this hypothesis requires high-resolutiondust and optical imaging of the same sample of SMGsto pinpoint the location of the star formation within thehost galaxy. Comparison to local U/LIRGs
We now compare the sizes of the SMGs in our sam-ple to the sizes of local infrared–bright galaxies. Re-cently Ueda et al. (2014) presented a compilation of < CO ( J = 1–0; 2–1; 3–2) emission from 30local star-forming galaxies classified as “merger rem-nants”. We select galaxies from their sample with far-infrared luminosities > × L ⊙ (SFR > ∼ ⊙ yr − ),resulting in a sample of 24 galaxies with a median L FIR =(1 . ± . × L ⊙ . The sample contains one ULIRG( L FIR > L ⊙ ) and 12 LIRGs ( L FIR > L ⊙ ).Ueda et al. (2014) measure the size of each galaxy as theradius containing 80 % ( R ) of the total CO flux. Toensure a fair comparison with the results presented here,we derive the correction between FWHM and R , andapply this correction to the sizes presented by Ueda et al.(2014). The sample of 24 local galaxies has a mediandiameter of 1 . ± . σ dispersion of 1 . low – J transitions of CO: 12 sources are observed in CO ( J = 1–0) emis-sion, ten in CO ( J = 2–1), and two in CO ( J = 3–2).The lowest J transitions trace cold molecular gas, andare expected to reflect the size of the total gas reservoir,rather than the star-forming region. Indeed, studies ofArp 220, the closest ULIRG, find that the size of therest–frame 860 µ m emission is 50–80 pc, which is approx-imately two to four times smaller than the extent ofthe CO ( J = 1–0) emission (Downes & Solomon 1998;Sakamoto et al. 2008).The sizes of local U/LIRGs measured from low – J transitions of CO appear marginally smaller than the870 µ m sizes of the SMGs presented here, although thetwo samples are consistent within the associated uncer-tainties. However, as we have discussed, sizes measuredfrom the J = 1–0 transition of CO are likely to be anupper limit on size of the star-forming region. In theabsence of a sample of local ULIRGs with sizes measuredat approximately the same wavelength as the SMGs inthis paper, we simply note that the star-forming regionsin SMGs may be significantly larger than local U/LIRGs.
Are SMGs Eddington Limited Starbursts?
The high star formation rates of SMGs means thatthey could host regions with an extreme star forma-tion density, which could result in very different starformation conditions to other galaxy populations. Inan isolated star-forming region the radiation pressurefrom massive stars may provide sufficient feedback toregulate the further collapse of the giant molecularcloud. Andrews & Thompson (2011) show via the bal-ance of radiation pressure from star formation withself-gravitation, that the maximum star formation ratesurface density, assuming optically thick dust emission( τ > , and in the absence of nuclear heating via anactive galactic nucleus (AGN), isSFR max > ∼ f − . f − M ⊙ yr − kpc − , (2)where f gas is the gas fraction in the star-forming region,and f dg is the dust-to-gas ratio (see also Murray et al.2005; Thompson et al. 2005; Murray et al. 2010). Weadopt a dust–to–gas ratio of f dg = 1 /
90 (Magnelli et al.2012; Swinbank et al. 2014), but note that f dg =1 /
50 has also been suggested for star-forming galax-ies (Kov´acs et al. 2006). Estimates of the dynamicalmasses (Swinbank et al. 2006; Alaghband-Zadeh et al.2012), stellar masses (Hainline et al. 2011; Simpson et al.2014) and gas masses (Bothwell et al. 2013) indicate that Andrews & Thompson (2011) state that a starburst shouldbe treated as optically thick if the gas is above a critical surfacedensity, Σ g > ∼ ⊙ kpc − . (1)Here we have adopted a Rosseland mean dust opacity of5 cm − g − and a dust-to-gas ratio of f dg = 90 (seeAndrews & Thompson 2011; Swinbank et al. 2014). Assuming thetypical gas mass of SMGs, 4 × M ⊙ (Swinbank et al. 2014),then the typical gas density of SMGs is Σ g = 4000 M ⊙ kpc − . ∼
40 %; however,this is a global property of the galaxy. As the sizeof the rest–frame optical emitting region in SMGs isaround four times larger than the size of the star–formingregion (Figure 5), it is likely that the gas fraction isconsiderably higher in the star-forming region. In ouranalysis we adopt a gas fraction of unity, i.e. gas isthe dominant component, as this sets a lower limit onthe maximum star formation rate surface density. If weadopt a gas fraction of 40 % then the maximum star for-mation rate surface density would rise by 60 %. Adoptingthese values the maximum star formation rate surfacedensity predicted by Andrews & Thompson (2011) is ∼ ⊙ yr − kpc − .The 23 SMGs in our sample have a median far-infraredluminosity of (5.7 ± × L ⊙ , which corresponds toa median SFR = 990 ±
120 M ⊙ yr − (for a Salpeter IMF).To derive the star formation rate surface density forour sample we initially divide the SFR of each SMGby a factor of two (the measured size of each SMGcorresponds to the half-light radius of the profile). Weshow our sample in Figure 6, and assuming a uniformdisc profile for the gas and cool dust distribution themedian star formation rate surface density of the SMGsis 90 ±
30 M ⊙ yr − kpc − . Only two SMGs have a starformation rate surface density above 500 M ⊙ yr − kpc − ,and no SMGs exceed the maximum value predicted byAndrews & Thompson (2011).The SMGs in our sample are forming stars at surfacerate densities an order of magnitude lower than theestimated Eddington limit. However, we stress thatthese surface rate densities are integrated across the star-forming region (see Meurer et al. 1997). In the well–studied lensed SMG SMM J2135-0102 (Swinbank et al.2010b) it has been shown that the star formation isin four distinct “clumps” (FWHM = 100–300 pc), lo-cated within a gas disc with a half light radius ∼ z = 0–3) have a 90 th percentile globalluminosity surface density of 2 × L ⊙ kpc − (with anassociated uncertainty of a factor of three), which theyinterpret as an upper limit on the global luminositysurface density of a starburst. The SMGs presentedhere have a median global luminosity surface densityof ( 5.2 ± × L ⊙ kpc − , a factor of three timeshigher than the value found by Meurer et al. (1997) (seeFigure 6). A possible explanation for this discrepancyis that Meurer et al. (1997) measure half–light radii forthe galaxies in their sample from ultraviolet imaging,and assume that dust attenuation is uniform across thegalaxy. As discussed in § µ m dust half–light radius. Thediscrepancy in the optical sizes and dust sizes of SMGsindicates that their is significant differential reddeningin these sources. If the ultraviolet–selected sources in(Meurer et al. 1997) suffer from similar differential red-dening then the half–light radii measured in the ultra– Fig. 7.—
Comparison of the FWHM of the rest–frame FIR emis-sion in SMGs to z ∼ HST imaging,with a median half light size of R e = 1 . ± .
2, (van Dokkum 2008;Krogager et al. 2013). violet are likely to overestimate the true extent of thestar formation.
Are SMGs the progenitors of compact quiescentgalaxies at z ∼ ? It has been suggested that an evolutionary sequenceexists whereby SMGs transition into local ellipticalgalaxies via a quiescent galaxy phase at redshift z ∼ z = 1–3 is that they are extremely com-pact, with half-light sizes of ∼ (e.g. Daddi et al.2005; Zirm et al. 2007; Toft et al. 2007; Buitrago et al.2008; van Dokkum et al. 2008; Newman et al. 2012;Patel et al. 2013; Krogager et al. 2013). A morphologicalanalysis of SMGs thus provides an alternative route toinvestigating the proposed evolutionary sequence.We construct a sample of spectroscopically confirmedquiescent galaxies at z ∼
2, to compare to SMGs, bycombining the samples presented by van Dokkum (2008) We note that mass selected samples ( M ⋆ > × M ⊙ )containing both star–forming and quiescent galaxies at z = 1–3,have an half–light radius (4 kpc) that is higher than, and a S´ersicindex (1.5) which is lower than, our sample of quiescent galaxies(see Patel et al. 2013; Buitrago et al. 2013) impson et al. 13and Krogager et al. (2013). The galaxies in these sam-ples have spectroscopically confirmed 4000˚A / Balmerbreaks, indicative of an old ( > ∼ Galfit to fit a S´ersic profile tothe H –band emission from each galaxy. The combinedsample of 24 quiescent galaxies has a median half–lightradius of R e = 1.5 ± n = 3.3 ± > ∼ M ⊙ and the median redshiftof the sample is z = 2.2 ± z = 2.5–3 consistentwith the redshift distribution of SMGs (Toft et al. 2014;Simpson et al. 2014). We note that the half–light radiiof the spectroscopically confirmed quiescent galaxies inour comparison sample are consistent with the sizesmeasured for a large sample of color–selected quiescentgalaxies at a similar redshift ( z = 1.5–2.5) (Patel et al.2013).As discussed in § R e = 4.4 +1 . − . kpc and S´ersic indexof n = 1.2 ± .
3. In contrast, the quiescent galaxies inour comparison sample have a median half–light radiusof R e = 1.5 ± H –band/ HST imaging (82 ±
9) % of SMGs havesignatures of interactions and/or irregular morphologies(Chen et al. 2014), and the low S´ersic index n measuredfor the population is consistent with merging systems(Kartaltepe et al. 2012); dynamical studies of resolvedH α emission from SMGs find strong evidence of kine-matically distinct multiple components (Swinbank et al.2006; Alaghband-Zadeh et al. 2012); and a study ofmolecular line emission from SMGs finds that 75 % ofsources are ongoing mergers, with the remaining 25 %classed as either disc or late stage mergers (Engel et al.2010).It is well established that mergers can induce torquesthat are effective at removing angular momentum fromthe gas in the system, allowing the gas to fall intothe inner regions and potentially resulting in a kpc–scale nuclear starburst (e.g. Barnes & Hernquist 1991;Mihos & Hernquist 1994). Recently, Hopkins et al.(2013) presented numerical simulations of two gas richdisc galaxies undergoing a major merger at high-redshift.Hopkins et al. (2013) show that the major merger trig-gers an intense central starburst, with 50% of the starformation activity concentrated within a diameter of ∼ n = 4) profile. S´ersic index
We now investigate whether there is evidence that thestar formation in SMGs is more highly concentrated thanthe stellar component. First, we test whether our datahave sufficiently high SNR to recover a more complexS´ersic profile . We create 4000 model sources with ahalf-light size fixed at the median size of the SMGs,a range of S´ersic index from n = 0.5–4 and an SNRdistribution that is uniform from 10–30 σ . To simulaterealistic noise we add these models to a randomly chosenposition in one of the residual (source-subtracted) ALMAmaps.We fit a S´ersic profile to each model source usingthe code galfit (Peng et al. 2010), and find that thehalf-light size of the model sources is recovered ac-curately at all values of SNR and S´ersic index ( R rece / R inpute = 0.99 ± σ dispersion ± n rec / n input = 0.97 ± σ dispersion of 0.4–2.2, indicating that measurementsfor individual sources are highly uncertain . Crucially,we find that the dispersion in the recovered S´ersic indexis dependent on the SNR of the injected source; forSNR > σ the 1– σ dispersion is 0.6–1.8. As such wedo not attempt to fit a S´ersic profile on a source-by-source basis, but instead stack the 870 µ m emission fromthe 23 SMGs detected at > σ and use galfit to fit aS´ersic model to the stacked profile. The best-fit modelto the stacked profile has a S´ersic index of n = 2.5 ± R e = 0.17 ± ′′ , where theerrors are derived by bootstrapping the maps used inthe stacking.The median S´ersic index of the 870 µ m emission fromthe SMGs is higher than the S´ersic index of the un-obscured rest–frame optical light in SMGs (Chen et al.2014, but see also Targett et al. 2013), indicating thatthe ongoing star formation is more centrally concen-trated. As we show in Figure 7, the half–light radius ofthe star formation in SMGs, median R e = 1.2 ± R e = 1.5 ± ∼ z ∼ ±
9) % of SMGs have The test we perform is to investigate the required SNR, anddoes not test the effects of spatial filtering on our ALMA maps,due to the configuration of the array. However, we note that themaximum angular scale that our maps are sensitive to is 5 ′′ , whichis an order of magnitude larger than the FWHM of the SMGs inour sample. If we re–fit our model sources, but force the S´ersic in-dex to n = 0.5 the median recovered half–light size is R rece / R inpute = 0.99 ± σ dispersion ± z ∼ CONCLUSIONS
In this paper we have presented high-resolution (0 . ′′ )ALMA imaging of 52 SMGs in the UDS field. The mainconclusions from our work are: • We fit an elliptical Gaussian model to the 870 µ memission from 23 SMGs detected at SNR > σ .The median diameter, deconvolved from the beam,of these 23 SMGs is FWHM = 0 . ± . ′′ , andthe distribution has a narrow interquartile rangeof 0.26–0.42 ′′ . Two SMGs in our sample (10 %)are best fit by a point source model, and have anupper limit on their size of < . ′′ . We stack the870 µ m emission from SMGs detected at SNR = 4–5 σ and SNR = 5–10 σ , measuring an average sizeof 0.35 +0 . − . ′′ and 0 . ± . ′′ for each subset,respectively, consistent with the brighter examples. • Using photometric redshifts we convert the angulardiameter of each SMG to a physical scale. Themedian physical FWHM of the 23 SMGs detectedat SNR > σ is 2 . ± . µ m flux density. • We compare the 870 µ m sizes of the SMG presentedin this work to the sizes of SMGs measured at1.4 GHz. The median FWHM of these SMGs is5 . ± . µ m size presented here. Weconvolve the median 870 µ m profile of the SMGswith an exponentially declining kernel, with ascale length of 1–2 kpc, appropriate for modellingthe radio and far–infrared emission in local star-forming galaxies (Murphy et al. 2008). The con-volved profile has a FWHM = 3.8–5.2 kpc, showingthat the radio sizes may be consistent with oursub–millimeter sizes. However, we caution that asstated by Murphy et al. (2008) the scale length ofthe convolution kernel may be sensitive to the starformation rate and morphology of the galaxy. • We also compare the sizes we derive for the 870 µ memission region in SMGs to the sizes of SMGs mea-sured from observations of resolved “moderate”– J CO emission lines. Treating the upper limitsin the CO studies as point sources, the median FWHM for the sample is 2 . ± . . ± . µ m sizes measured here. • The pre–existing stellar population in SMGs has ahalf–light radius of 4.4 +1 . − . kpc, as measured fromrest–frame optical HST imaging (Chen et al. 2014),which is about four times larger than the extent ofthe ongoing star formation. The high dust contentof SMGs means that the starburst component islikely to be missed in rest–frame optical imaging,while their prodigious star formation rates meanthey have the potential to transform their stellarmass distribution. Hence, we expect the post–starburst galaxy to be compact, with a smallerhalf–light radius than the pre-existing stellar pop-ulation. • SMGs are slightly larger than local far–infraredbright galaxies (U/LIRGs), with low– J moleculargas sizes for the latter, median FWHM = 1 . ± . • The 23 SMGs in our sample have a median starformation rate of SFR = 1170 ±
160 M ⊙ yr − (fora Salpeter IMF), and a median star formationdensity of 90 ±
30 M ⊙ yr − kpc − . The Eddingtonlimit for a radiation pressure regulated starburstis ∼ ⊙ yr − kpc − (Andrews & Thompson2011). Hence, the SMGs in our sample haveintegrated star formation rate densities that areon average an order of magnitude lower than theEddington limit. We suggest that this is due to thestar formation occurring in “clumps”, which maybe Eddington limited, but appear sub–Eddingtonwhen integrated across the whole star formationregion. • The half-light radius of the ongoing star formationin SMGs is similar to the size of z = 2 . ± R e = 1.5 ± ACKNOWLEDGMENTS
We thank Adam Avison and the Manchester ALMAARC node for their assistance verifying the calibra-tion and imaging of our ALMA data. JMS andALRD acknowledge the support of STFC studentships(ST/J501013/1 and ST/F007299/1, respectively). AMSacknowledges financial support from an STFC AdvancedFellowship (ST/H005234/1). IRS acknowledges supportfrom the ERC Advanced Investigator program DUSTY-GAL 321334, an RS/Wolfson Merit Award and STFC(ST/I001573/1). JSD acknowledges the support of theEuropean Research Council via the award of an Ad-vanced Grant, and the contribution of the EC FP7impson et al. 15SPACE project ASTRODEEP (312725). JEG acknowl-edges support from the Royal Society. RJI acknowledgessupport from the European Research Council (ERC) inthe form of Advanced Grant, COSMICISM.This paper makes use of the following ALMA data:ADS/JAO.ALMA
Spitzer and
Herschel archives.
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