The stellar mass - size relation for cluster galaxies at z=1 with high angular resolution from the Gemini/GeMS multi-conjugate adaptive optics system
Sarah M. Sweet, Robert Sharp, Karl Glazebrook, Francois Rigaut, Eleazar R. Carrasco, Mark Brodwin, Matthew Bayliss, Brian Stalder, Roberto Abraham, Peter McGregor
MMon. Not. R. Astron. Soc. , ?? – ?? (2016) Printed 12 October 2018 (MN L A TEX style file v2.2)
The stellar mass - size relation for cluster galaxies at z=1with high angular resolution from the Gemini/GeMSmulti-conjugate adaptive optics system.
Sarah M. Sweet (cid:63) , Robert Sharp , Karl Glazebrook , Francois Rigaut ,Eleazar R. Carrasco , Mark Brodwin , Matthew Bayliss , , Brian Stalder ,Roberto Abraham , Peter McGregor † Research School of Astronomy & Astrophysics, Australian National University, Canberra, ACT 2611, Australia Centre for Astrophysics & Supercomputing, Swinburne University of Technology, Mail H30 P.O. Box 218, Hawthorn, VIC 3122,Australia Gemini Observatory/AURA, Southern Operations Center, Casilla 603, La Serena, Chile Department of Physics & Astronomy, University of Missouri, 5110 Rockhill Road, Kansas City, MO 64110, USA Department of Physics & Astronomy, Colby College, 5800 Mayflower Hill, Waterville, Maine 04901, USA Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA Department of Astronomy and Astrophysics, University of Toronto, 50 St George Street, Toronto, ON M5S 3H8, Canada † Deceased
12 October 2018
ABSTRACT
We present the stellar mass - size relation for 49 galaxies within the z = 1.067 clusterSPT-CL J0546 − ∼ K s -band data from the Gemini multi-conjugate adaptive optics system (GeMS/GSAOI). This is the first such measurementin a cluster environment, performed at sub-kpc resolution at rest-frame wavelengthsdominated by the light of the underlying old stellar populations. The observed stellarmass - size relation is offset from the local relation by 0.21 dex, corresponding to asize evolution proportional to (1 + z ) − . , consistent with the literature. The slopeof the stellar mass - size relation β = 0.74 ± − HST /ACSimaging at wavelengths blueward of the Balmer break, similar to rest-frame UV re-lations at z = 1 in the literature. The stellar mass - size relation must be measuredat redder wavelengths, which are more sensitive to the old stellar population thatdominates the stellar mass of the galaxies. The slope is unchanged when GeMS K s -band imaging is degraded to the resolution of K -band HST/NICMOS resolution butdramatically affected when degraded to K s -band Magellan/FourStar resolution. Suchmeasurements must be made with AO in order to accurately characterise the sizes ofcompact, z = 1 galaxies. c (cid:13) a r X i v : . [ a s t r o - ph . GA ] S e p tellar mass - size relation at z=1 with GeMS/GSAOI astrometry Key words: galaxies: clusters – instrumentation – galaxies: morphology
In the local universe, most luminous galaxies belong to one oftwo dominant populations: early- or late-type galaxies. Theformer are typically passive, red, spheroids, further classi-fied into fast and slow rotators, while the latter are generallyblue, star-forming disks. These familiar Hubble-type classi-fications do not apply as readily to high-redshift galaxies,the most massive of which are compact and red (Szomoruet al. 2011; Talia et al. 2014). Few compact systems existat the present day (Trujillo et al. 2009; Taylor et al. 2010;Trujillo et al. 2012, 2014), so it is logical to suppose that themost massive high-redshift galaxies must undergo signifi-cant size evolution to become present-day passive ellipticalgalaxies. For example, z ∼ ∼ z = 0 (e.g. Daddi et al. 2005;van Dokkum et al. 2008; Damjanov et al. 2009), and thoseat z ∼ ∼ (cid:63) Corresponding author: [email protected] observed sufficient numbers of satellites around a z = 1.9compact galaxy to explain the predicted size growth, onceadditional star formation is taken into account. In the adia-batic expansion model proposed by Fan et al. (2008, 2010),galaxies experience a rapid mass loss event caused by AGNor supernova winds. After some time delay, expansion oc-curs in an amount proportional to the fraction of masslost (Ragone-Figueroa & Granato 2011). Recent analysis byWellons et al. (2016) of galaxies in the Illustris simulation(Genel et al. 2014; Vogelsberger et al. 2014a,b; Nelson et al.2015) suggests that adiabatic expansion is responsible forless size growth than mergers are. Adiabatic expansion as-sociated with the formation of new stellar populations (butnot due to AGN winds) during 2 > z > On onehand, sufficient resolution is required to measure effectiveradii and S´ersic (Sersic 1968) indices of the most compactgalaxies. On the other hand, and equally importantly, therest frame redwards of the 4000 ˚A spectral break is nec-essary for this measurement, as it is stellar mass that isthe main driver of galaxy properties such as colour, ageand specific star formation rate. Current efforts to mea-sure high-redshift galaxy morphologies at high resolution(e.g. Huertas-Company et al. 2013; Ryan et al. 2012; De-laye et al. 2014) are limited to optical HST imaging (e.g.FWHM 0.09 arcseconds in F814W ∼ I -band, Scoville et al.2007), but such filters are rest-frame UV at these redshifts.Consequently, they suffer from contamination of starburstevents rather than tracing the bulk of the stellar mass.Near infrared imaging has necessarily poorer resolution, e.g.HST/WFC3 ∼ H -band FWHM is 0.18 arcseconds (Guoet al. 2011), which is 1.48 kpc at z = 1 and thus may notprovide sufficient resolution for accurate profile fitting (e.g.Damjanov et al. 2009). Due to this tradeoff between reso-lution and wavelength, there is a wide variety of rest-framewavelengths at which the measurements are made, with cor-respondingly wide variety in the results. Carrasco et al.(2010) addressed this tradeoff with ground-based adaptiveoptics imaging, but were limited to just eight field galaxiesobserved one at a time due to the small effective field of viewof the Gemini NIRI camera when corrected by the Altairlaser guide star system. Consequently, the current literaturecannot be used to distinguish between major mergers, minormergers and adiabatic expansion. Limiting magnitude appears less critical than spatial resolutionfor morphological classification; (Povi´c et al. 2015). For clustergalaxies, sufficient spatial coverage of the cluster is also requiredin order to remove any environmental effect (e.g. Strazzullo et al.2010).c (cid:13) , ?? ––
In the local universe, most luminous galaxies belong to one oftwo dominant populations: early- or late-type galaxies. Theformer are typically passive, red, spheroids, further classi-fied into fast and slow rotators, while the latter are generallyblue, star-forming disks. These familiar Hubble-type classi-fications do not apply as readily to high-redshift galaxies,the most massive of which are compact and red (Szomoruet al. 2011; Talia et al. 2014). Few compact systems existat the present day (Trujillo et al. 2009; Taylor et al. 2010;Trujillo et al. 2012, 2014), so it is logical to suppose that themost massive high-redshift galaxies must undergo signifi-cant size evolution to become present-day passive ellipticalgalaxies. For example, z ∼ ∼ z = 0 (e.g. Daddi et al. 2005;van Dokkum et al. 2008; Damjanov et al. 2009), and thoseat z ∼ ∼ (cid:63) Corresponding author: [email protected] observed sufficient numbers of satellites around a z = 1.9compact galaxy to explain the predicted size growth, onceadditional star formation is taken into account. In the adia-batic expansion model proposed by Fan et al. (2008, 2010),galaxies experience a rapid mass loss event caused by AGNor supernova winds. After some time delay, expansion oc-curs in an amount proportional to the fraction of masslost (Ragone-Figueroa & Granato 2011). Recent analysis byWellons et al. (2016) of galaxies in the Illustris simulation(Genel et al. 2014; Vogelsberger et al. 2014a,b; Nelson et al.2015) suggests that adiabatic expansion is responsible forless size growth than mergers are. Adiabatic expansion as-sociated with the formation of new stellar populations (butnot due to AGN winds) during 2 > z > On onehand, sufficient resolution is required to measure effectiveradii and S´ersic (Sersic 1968) indices of the most compactgalaxies. On the other hand, and equally importantly, therest frame redwards of the 4000 ˚A spectral break is nec-essary for this measurement, as it is stellar mass that isthe main driver of galaxy properties such as colour, ageand specific star formation rate. Current efforts to mea-sure high-redshift galaxy morphologies at high resolution(e.g. Huertas-Company et al. 2013; Ryan et al. 2012; De-laye et al. 2014) are limited to optical HST imaging (e.g.FWHM 0.09 arcseconds in F814W ∼ I -band, Scoville et al.2007), but such filters are rest-frame UV at these redshifts.Consequently, they suffer from contamination of starburstevents rather than tracing the bulk of the stellar mass.Near infrared imaging has necessarily poorer resolution, e.g.HST/WFC3 ∼ H -band FWHM is 0.18 arcseconds (Guoet al. 2011), which is 1.48 kpc at z = 1 and thus may notprovide sufficient resolution for accurate profile fitting (e.g.Damjanov et al. 2009). Due to this tradeoff between reso-lution and wavelength, there is a wide variety of rest-framewavelengths at which the measurements are made, with cor-respondingly wide variety in the results. Carrasco et al.(2010) addressed this tradeoff with ground-based adaptiveoptics imaging, but were limited to just eight field galaxiesobserved one at a time due to the small effective field of viewof the Gemini NIRI camera when corrected by the Altairlaser guide star system. Consequently, the current literaturecannot be used to distinguish between major mergers, minormergers and adiabatic expansion. Limiting magnitude appears less critical than spatial resolutionfor morphological classification; (Povi´c et al. 2015). For clustergalaxies, sufficient spatial coverage of the cluster is also requiredin order to remove any environmental effect (e.g. Strazzullo et al.2010).c (cid:13) , ?? –– ?? S. Sweet et al.
In this paper we study the massive, evolved galaxy clusterSPT-CL J0546 − z = 1, and demonstrate the importance of measuringthe relation redward of the 4000 ˚A break by comparing withrest-frame UV stellar mass - size relations for the same sam-ple. In Section 2 we present our GeMS K s -band imagingand describe our observing and data processing strategies,including successful correction of the optical distortion andfaint source residual images. We also present our ancillarydata of GMOS spectroscopy and HST archival F606W andF814 band imaging. Section 3 contains the galaxy profilefitting and cluster membership. The stellar mass - size rela-tion is presented and discussed in Section 4. In Section 5 wesummarise our conclusions.Throughout this work we assume a concordance cosmologywith Ω M =0.264, Ω Λ =0.736 and H =71 km s − Mpc − , forconsistency with Brodwin et al. (2010). Magnitudes are pre-sented on the AB system. − The Gemini MCAO (multi-conjugate adaptive optics) sys-tem (GeMS; Rigaut et al. 2014; Neichel et al. 2014b)mounted on the 8.1-m Gemini South telescope uses fivelaser guide stars (d’Orgeville et al. 2012), and up to threenatural guide stars, to perform a multi-conjugate adaptiveoptics correction across the ∼ × (cid:48)(cid:48) field of view of theGemini South Adaptive Optics Imager (GSAOI, McGregoret al. 2004; Carrasco et al. 2012). The natural guide starsare required to correct for the tip-tilt atmospheric compo-nent, which is not sensed by the laser guide star system. Thenumber of high redshift galaxy clusters accessible to GeMS islimited by the magnitude restrictions ( R (cid:54) z = 1.067 structure SPT-CL J0546 − = 1 . +0 . − . x 10 M (cid:12) ;although it is massive for its redshift its existence is not inconflict with ΛCDM (Brodwin et al. 2010). At the redshiftof the cluster 1 (cid:48)(cid:48) = 8.2 kpc. The virial radius is r = 1.57Mpc = 191 (cid:48)(cid:48) (Brodwin et al. 2010).In the next subsection we present our GeMS K s -band imag-ing of this cluster. We also retrieve archival HST /ACSF606W and F814W imaging of the cluster of comparabledepth from program 12477 (PI: High); this is presented in § s and HST ACS F814W.) In § The GeMS near-infrared camera, GSAOI, is a 2 × ∼ (cid:48)(cid:48) . The nominal pixel scale of GSAOIis 19.7 mas, which samples the J -band Nyquist detectionlimit, and somewhat oversamples the K s -band PSF. Oper-ating at the diffraction limit of the 8.1-m Gemini telescope,GeMS/GSAOI achieves 2.25 times better angular resolution(in the H -band) than HST /WFC3 H -band, which has aPSF FWHM 0.18 ± (cid:48)(cid:48) sampled with 0.08 (cid:48)(cid:48) drizzled pixels(e.g. Law et al. 2012).Cluster SPT-CL J0546 − (cid:48)(cid:48) .6 to 1 (cid:48)(cid:48) .2.There are static distortions present in the GeMS/GSAOIsystem, caused by optical design and physical alignmentof the four arrays. We account for these via careful mea-surement of standard astrometric fields (with a high stardensity of tens per detector, and good relative astrometry)taken at the same position angle as our science data dur-ing the observing block. Previous work had warned of smallbut significant changes to the variable plate scale solutionwhen observing with large ( > (cid:48)(cid:48) ) relative offsets, due tothe design of the Canopus AO system wavefront sensor feedarrangement (Rigaut et al. 2014); however, our data showthis concern to be unfounded. To fill in the inter-chip gapsand provide a contiguous field of view in the final compositeimage, we conducted dithered observations offset by [4,4],[0,0], [-4,-4] (cid:48)(cid:48) relative to our base pointing. To maximise therejection of cosmetic defects on the detectors, and to min-imise correlated noise artefacts when generating sky frames,we also conducted nine micro-dithers with a pitch of ∼ . (cid:48)(cid:48) (cid:48) B (cid:48) C (cid:48) A (cid:48)(cid:48) B (cid:48)(cid:48) C (cid:48)(cid:48) ... .In this way, the frames at each large dither position (e.g.A) have two alternative large dither positions (B and C),whose micro-dithers ( (cid:48) , (cid:48)(cid:48) ,...) serve as sky frames. Such a se-quence of three large dither positions by nine micro-ditherobservations of 120 sec duration completes an on-source ex-posure sequence of 27 independent frames. The resulting Since observations are background-limited in modest dura-tion exposure with broadband filters, this oversampling has littlepenalty. c (cid:13) , ?? – ?? tellar mass - size relation at z=1 with GeMS/GSAOI astrometry
10" = 82 kpc
False−colour image:GeMS/GSAOI K s HST ACS F814WHST ACS F606W
1" = 8.2 kpcSPT z=1 cluster core
Figure 1.
False-colour image of SPT-CL J0546 − z = 1 . (cid:13) , ?? – ?? S. Sweet et al.
GeMS/GSAOI K s HST ACS F814W
Figure 2.
Zoom-in of cluster core. Left: Gemini GeMS/GSAOI K s ; Right: HST ACS F814W. The scale bar at lower left shows theangular and physical projected distances at the cluster redshift. N is up and E is left. on-source exposure time of 0.9 hours requires an elapsedtime of 1.5 hours, after accounting for telescope offsettingand near-infrared array readout time; that is, an efficiencyof 60%. Longer individual observations were considered tobe at risk from increased sky variability (although we findlimited evidence for this throughout the course of our runs)while shorter integrations would deliver a lower efficiency inthe duty cycle. This 27-exposure pattern was executed atsix different base positions for a total of approximately 5.5hours on source. The basic data reduction steps were conducted with theGemini IRAF GSAOI package , with data from individ-ual detectors stored as separate extensions within multi-extension fits files. Daytime calibration lamp-on and lamp-off dome flats were combined to generate a master domeflat. Variance and data quality extensions were populatedand non-linear or saturated pixels were flagged. The frameswere flat fielded using dome flats, as we found that thesegave lower residual structure compared to twilight or domemultiplied by twilight sky flats. The GeMS imaging system introduces a ∼
3% variation inthe plate scale across the field of view (Neichel et al. 2014a;Schirmer et al. 2015). The image distortion is largely static,with small, variable distortions that depend on instrumentflexure under gravity and the positions and relative magni-tudes of the guide stars. When there are many bright sourceswithin the field of view, this distortion may be corrected byreferencing to those sources. For example, Schirmer et al.(2015) report K s -band residuals of 10 mas (internal) and13 mas (with respect to external astrometry). Much of theerror for that correction arose from centroiding to galaxiesrather than stars. The resulting PSF in their stacked im-age was 70 < FWHM <
100 mas across the field, with the bestresolution being nearest the single natural guide star usedduring observations.When there are few bright sources within the field of view,as is generally the case for faint galaxy clusters at high red-shift, a separate astrometric field must be observed. Theastrometric field must have a deep reference catalogue withsimilar resolution to GSAOI. The chosen field should be ob-served during the same run as the science data, and have thesame position angle (PA) and, where possible, airmass. Ide-ally, the positions and relative magnitudes of the guide starsshould be matched to those in the science frames. An astro-metric distortion solution was derived for this work fromcontemporary observations of a field located within globu-lar cluster NGC 288 (catalogued in Anderson et al. 2008).Six 30-s exposures and five 30-s exposures offset by ∼ (cid:48) to serve as sky frames were taken at the same PA as ourscience observations, using two natural guide stars in a sim-ilar asterism and with similar relative magnitudes to those c (cid:13) , ?? – ?? tellar mass - size relation at z=1 with GeMS/GSAOI astrometry in the science field. Basic reduction was performed with theGSAOI IRAF package. We used the GAIA software pack-age (Draper et al. 2014) to perform a coarse, initial worldcoordinate solution (WCS) solution for each detector in theGSAOI mosaic. Following that we constructed a catalogueof sources in the astrometric field using SExtractor (Bertin& Arnouts 1996) and compared this to the HST catalogue(Anderson et al. 2008) with SCAMP (Bertin 2006). We ap-plied the resulting distortion correction to our science im-ages with SWarp (Bertin et al. 2002), which mosaicked theindividual detectors to a single image. We provide more de-tailed instructions at Appendix A. The mosaicked imageswere reregistered to a common reference by centroiding thesingle bright star common to our science images. The astro-metric rms is 5 mas internally and 8 mas with respect toHST ACS F814W imaging. The final combined image PSFFWHM varies across the field from 80 mas close to the cen-tre of the field to 130 mas at the edges of the field of view;measured from eight stars in the image (see Appendix C).The maximum Strehl ratio is 10% (median 8%), consistentwith the predictions of the Gemini Observing Tool, whichtakes into account the number, position and magnitude ofthe natural guide stars. The median 50% and 85% encircledenergy diameters are 0.22 (cid:48)(cid:48) and 0.50 (cid:48)(cid:48) respectively. The default median sky subtraction method results in sig-nificant subtraction residuals on the order of 1-2 times skyrms, coincident with the large dither pattern positions (seeSchirmer et al. 2015, and our Figure 3). This is a conse-quence of using a regular, semi-repeated dither pattern withoffset object frames used as sky frames and insufficient mask-ing of faint sources.A larger pseudo-random dither pitch may alleviate this prob-lem; however, early concern over differential distortions be-tween larger offset dithers, and the lack of a larger numberof independent restoration stars in our field, led to the ob-serving strategy described above.The faint sources causing the residual images are not de-tected in any individual 120-s image frames and thereforecannot be masked when the sky frames are constructed.When combining ∼
200 frames for the final stacked imagethe resulting residuals become significant at the level of thetypical rms sky noise. We overcame this issue by creatingan improved object mask from the stacked image. We calcu-lated the inverse distortion correction for each detector, anddistorted the object mask back to the observational referenceframe of each detector in each input observation. Detailedinstructions are provided at Appendix B. As demonstratedin Figure 3, the residuals are significantly reduced. The re-maining variation is accounted for in our Monte Carlo errorestimation ( § default sky sub improved sky sub Figure 3.
Example section of GeMS image showing white residu-als appearing in default sky subtraction (top) and reduced by thesky subtraction method outlined here (bottom). The scale bar atlower left shows the angular and physical projected distance atthe cluster redshift. then sky subtracted using a median scaling of the relevantsky frame. We then returned to the GSAOI IRAF pack-age at the sky subtraction step, performing the distortioncorrection as before.
We discarded the 15% of frames that have average PSFFWHM > c (cid:13) , ?? ––
We discarded the 15% of frames that have average PSFFWHM > c (cid:13) , ?? –– ?? S. Sweet et al. of 4 hours 42 min. Individual frames were median scaled tomultipliers computed from relative source fluxes, in orderto account for differences in airmass between the individualframes.The final combined image was flux calibrated by comparingmeasurements for the bright star in the field from GSAOIand 2MASS (Skrutskie et al. 2006). The 2MASS K s mea-surement for this star is 15.508 ± Ks (AB)= m Ks (Vega) + 1.86 mag .The limiting surface brightness rms per pixel at 3 σ abovesky level is µ K s = 16.22 ± . Archival high angular-resolution imaging data is availablefor SPT-CL J0546 − HST /ACS imaging in theF606W and F814W broad-band filters observed as partof program 12477 (PI: High). We obtained multi-drizzled
HST /ACS data from the Mikulski Archive for Space Tele-scopes . Exposure times were 1920 s for F606W and 1916 sfor F814W. Zero points were calculated in a similar mannerto § − HST /ACSF814W ( ∼ I -band) image is equivalent to that of the AO-assisted Gemini/GeMS K s image, as is highlighted by theclose-up of the cluster core region shown in Figure 2. In order to augment the number of known cluster mem-bers for SPT-CL J0546 − ii ] λ α emission-line, prominent in AGN or star-forming galaxies, lies at an observed frame wavelength of λ = 1.3565 µ m for sources at the cluster redshift of z = 1.067,placing the line within the region of strong atmospheric wa-ter absorption between the near-infrared J and H -bands.Consequently, near-infrared H α spectroscopy, which is valu-able as a tracer of ongoing star formation as well as a con-venient redshift indicator when present, is not practical atthis redshift with ground-based MOS facilities. http://archive.stsci.edu/ Due to the limited angular extent and high candidate sourcedensity of the compact cluster region, we performed theobservations in the nod-and-shuffle (N&S) observing mode(Glazebrook & Bland-Hawthorn 2001), using band shuffling (Abraham et al. 2004). This observation mode not only al-lows high-quality sky subtraction but also allows short slitssuch as the 1 (cid:48)(cid:48) apertures used in this work. In this way ahigh slit density can be achieved in the central third of the1-arcminute GMOS field, which corresponds roughly to the85 (cid:48)(cid:48) field size of the GeMS imaging. Two slit masks wereobserved, each for 3 × ±
100 ˚A) to fill in the wavelength gaps introduced inthe spectral range by the gaps in the CCD mosaic. This re-sulted in a total integration time on each mask of 4.5 hours.At the time of mask preparation neither the GeMS imag-ing ( § HST imaging ( § I -band preimage . Target galaxies were prioritised in the fol-lowing order:(i) likely cluster members within the proposed GeMSimaging field of view, particularly sources in the densely-populated region close to the assumed brightest clustergalaxy;(ii) similar sources within the GMOS mask field of viewbut outside the GeMS imaging footprint;(iii) repeat observation of known cluster members, to pro-vide a convenient cross-check of the new observations; and,(iv) filler targets including a tentatively detected grav-itational lens arc, potential faint PSF stars and probableforeground galaxies.The observations were processed using the standard Gem-ini IRAF packages. The 56 reduced spectra are uniformlydistributed across the GMOS field of view; 33 fall withinthe smaller GSAOI pointing. Redshifts for these were mea-sured manually using the runz template cross-correlationsoftware (developed originally by Will Sutherland for the 2-degree Field Galaxy Redshift survey (Colless 1999; Collesset al. 2001)). The resulting identifications of six new clus-ter members and two foreground galaxies are included inTable 3. We measured sources in the three imaging bands with SEx-tractor (Bertin & Arnouts 1996). We constructed a cata-logue of sources that are common to all three imaging bandsand have K s and F814W signal-to-noise ratio >
4, andsignal-to-noise ratio > . Wedefine cluster members as those galaxies that either are spec-troscopically confirmed to lie at the cluster redshift, or have The low signal-to-noise threshold in the F606W band does notadversely impact our work. Visual inspection of the model fitsshows that all but two of the galaxies (45 and 48) are well fit inF606W; those two are excluded from our analysis in that band.c (cid:13) , ?? – ?? tellar mass - size relation at z=1 with GeMS/GSAOI astrometry similar photometric properties, as per the following subsec-tions. Sources in the field are presented in Table 3, withcluster member properties given in Table 1. Seventeen sources in the observed field are known to be clus-ter members on the basis of ground-based spectroscopy. Ofthe 124 sources identified within the GeMS K s field, five arepreviously-confirmed cluster member galaxies with spectrapublished in Brodwin et al. (2010) and Ruel et al. (2014).One of these (our ID 50) has different redshifts given in thetwo catalogues; the rest have consistent redshifts in bothpapers. A further five spectra have redshifts 0.9 < z < z = 0.4 and 0.5.The cluster is being observed by the GOGREEN survey(PI: Michael Balogh), who have provided preliminary spec-troscopic redshifts for seven cluster members within ourGSAOI field of view. One of these is common to our GMOSspectroscopy (its GOGREEN redshift is within ∆ z = 0.03),while the remaining six are newly-identified cluster mem-bers, bringing the total to 17 spectroscopically-confirmedcluster members in our field. These have a median redshift z = 1.0669 ± z = 0.001 of,the previously published redshifts. A further 32 cluster members are identified by colour se-lection, for a total of 49 members. They were either nottargeted for spectroscopy (due to the limitations of slit gogreensurvey.ca packing with GMOS, even with the use of the nod-and-shuffle technique), or their GMOS spectra were of insuffi-cient signal-to-noise ratio to yield a redshift. In the left-hand panel of Figure 4 we show a colour-magnitude diagramfor all sources in the field of view. The spectroscopically-confirmed cluster members are plotted with red, filled cir-cles. The grey-scale density plot shows CANDELS sourcesat z = 1, with photometry from Guo et al. (2013) and pho-tometric redshifts from Hsu et al. (2014). We show the best-fitting line to the CANDELS red sequence, with the dot-ted lines showing the ± σ range. Sources within the 85 (cid:48)(cid:48) field that satisfy m F W − m K s (cid:54) . − . m K s and m F W − m K s (cid:62) . − . m K s are within that rangeand defined to be be photometrically-selected cluster mem-bers. There are 34 sources selected in this way, of which27 (55% of the total sample of 49 members) do not havespectroscopic redshifts. We add to that sample a further 5(10%) sources outside of that range with similar colour, size,morphology and location to the confirmed cluster members.Other sources red-ward of that range are likely z > z f = 3 .
0, generated with EzGal (Man-cone & Gonzalez 2012) and normalised to the CANDELSred sequence.In the right-hand panel of Figure 4 we plot a colour-colourdiagram for stars in the GSAOI field. We use the stellarpopulation synthesis model of Robin et al. (2003) to sim-ulate Milky Way stars in the direction of our cluster, find-ing a median metallicity [Fe/H] ∼ − − In order to robustly estimate stellar masses we supple-ment our high resolution imaging with follow-up SPT surveyimaging presented in Song et al. (2012), namely riz
MosaicIIphotometry from the Blanco Cosmology Survey (Desai et al.2012; Bleem et al. 2015a) and 3.6 and 4.5 µ m Spitzer IRACphotometry (PI Brodwin; program ID 60099).We use the FAST (Fitting and assessment of synthetic tem-plates Kriek et al. 2009) code to fit Bruzual & Charlot (2003)models to the photometry, using a Chabrier (2003) IMF andCalzetti et al. (2000) dust law. Our grid of exponentiallydeclining star formation history models SF H ∼ exp( − t/τ )includes timescales 6.5 (cid:54) log( τ ) (cid:54)
11 in steps of 0.5, metal-licities z = 0.008, 0.02 (solar) and 0.05, and dust extinction0 (cid:54) A v (cid:54)
3. We limit ages to older than 10 Gyr and youngerthan the age of the Universe (that is, formation epochs priorto z = 2). model.obs-besancon.frc (cid:13) , ?? ––
3. We limit ages to older than 10 Gyr and youngerthan the age of the Universe (that is, formation epochs priorto z = 2). model.obs-besancon.frc (cid:13) , ?? –– ?? S. Sweet et al.
16 18 20 22 24m Ks [AB mag]−28 −26 −24 −22 −20M Ks [AB mag] at z=1−1012345 m F W − m K s [ AB m ag ] model starmodel galaxyCANDELS z=1other sourcestarspecz foregroundphotz memberspecz member −1 0 1 2 3m F606W −m F814W [AB mag]−1 0 1 2 3 −1012345 m F W − m K s [ AB m ag ] Figure 4.
Left:
Colour-magnitude diagram demonstrating photometric selection of additional cluster members. Red filled circles denotespectroscopically-confirmed cluster members. The grey density field depicts z = 1 galaxies in CANDELS (Guo et al. 2013), and thedashed line shows the line of best fit to the red sequence defined by that sample. Red open circles are photometric members eitherselected by eye as likely cluster members based on colour, size and morphology, or within ± σ (dotted lines) from the red sequence. Bluetriangles are spectroscopically-confirmed foreground galaxies. Magenta stars are known stars with obvious diffraction spikes in the HSTimaging or similar photometric properties. Black plus symbols show other sources in the field of view. Large, dark green diamonds depictmodel galaxies generated using a Bruzual & Charlot (2003) single burst model normalised to the CANDELS sample, with metallicitiesZ = 0.05, 0.02 (solar) and 0.008. Right:
Colour-colour diagram demonstrating validity of star colours. Green asterisk symbols are medianbinned model stars in the stellar libraries of Lejeune et al. (1997) with [M/H] = − > Resulting stellar masses are given in Table 1. We note thatFAST gives similar (0.2 dex lower at 10 M (cid:12) ) masses tothose obtained with a simple K -band mass-to-light ratioconversion at z = 1.1 derived by Drory et al. (2004) andgiven in Table 1 of that paper. We fit the cluster member galaxies using the IRAF interfaceto GALFIT (Peng et al. 2002, 2010). We use our interpolatedMoffat profile PSF described in detail in Appendix C forthe GeMS K s imaging. For the HST data we choose notto adopt the common methodology of creating a PSF usingthe Tiny Tim (Krist et al. 2011) software, which is idealwhen the PSF is under-sampled, but does not model thePSF of multi-drizzled data. In our case, the PSF is well-sampled due to the multi-drizzling process, and consistentacross the field of view, so we use an isolated star PSF forprofile fitting. Considering the modest signal-to-noise ratioand angular extent of the sources of interest in the SPT-CLJ0546 − r e = √ ab , where a and b are the effective semi-major and -minor axes fitted by GALFIT . We com-pare galaxy effective radii between the three bands in Fig-ure 6. Visually, measurements are not well matched betweenpairs of bands, a natural consequence of variation in the stel-lar populations probed at different wavelengths. We pointout that measured resolutions of the F606W and F814Wimages are similar to our mean K s -band image resolution(111, 132 and 112 mas respectively), so differences in reso-lution are not responsible for the differences in measured r e ;we have isolated the effect of rest-frame wavelength. We findthat there is a clear trend with a large amount of scatter ineach case, reflected in the moderate Spearman’s rank corre-lation values of 0.756 for F606W vs. F814, 0.834 for F814Wvs. K s and 0.712 for F606W vs. K s . The scatter largely re-sults from the HST imaging tracing the rest-frame UV, andthe size measurements are therefore biased by clumpy starformation regions. Indeed, for some single sources there aremultiple components fitted in the F606W imaging. This dis-crepancy demonstrates the need to perform such measure-ments in bands that trace the underlying old stellar popu-lation. We further discuss the impact of this on the stellarmass - size relation in Section 4 (see the upper right-handpanel of Figure 9). The measured source properties are givenin Table 1. The output of GALFIT contains a and q = b/a .c (cid:13) , ?? – ?? tellar mass - size relation at z=1 with GeMS/GSAOI astrometry Table 1.
Source properties in the cluster SPT-CL J0546 − K s log( r e /kpc) n log(M ∗ /M (cid:12) )[deg] [deg] [AB mag](1) (2) (3) (4) (5) (6) (7)15 86.64200 -53.76776 -22.31 ± ± . . ± ± . .
19 86.62950 -53.76595 -24.39 ± ± . . ± ± . .
20 86.66529 -53.76681 -22.46 ± ± . . ± ± . .
21 86.64479 -53.76673 -22.03 ± ± . . ± ± . .
25 86.64475 -53.76554 -25.33 ± ± . . ± ± . .
26 86.64337 -53.76559 -22.55 ± ± . . ± ± . .
32 86.65596 -53.76437 -21.63 ± ± . . ± ± . .
36 86.64292 -53.76368 -22.74 ± ± . . ± ± . .
37 86.64383 -53.76334 -23.36 ± ± . . ± ± . .
45 86.63371 -53.76251 -21.78 ± ± . . ± ± . .
48 86.63496 -53.76229 -22.46 ± ± . . ± ± . .
50 86.64887 -53.76176 -23.64 ± ± . . ± ± . .
51 86.63508 -53.76195 -22.75 ± ± . . ± ± . .
53 86.64000 -53.76137 -24.29 ± ± . . ± ± . .
54 86.65217 -53.76156 -22.45 ± ± . . ± ± . .
57 86.65371 -53.76140 -24.07 ± ± . . ± ± . .
58 86.65246 -53.76154 -21.31 ± ± . . ± ± . .
60 86.66146 -53.76012 -24.08 ± ± . . ± ± . .
61 86.64508 -53.75998 -23.12 ± ± . . ± ± . .
62 86.65804 -53.75987 -24.20 ± ± . . ± ± . .
65 86.65371 -53.75984 -22.01 ± ± . . ± ± . .
66 86.65054 -53.75965 -22.45 ± ± . . ± ± . .
67 86.65600 -53.75956 -22.09 ± ± . . ± ± . .
68 86.65879 -53.75959 -21.81 ± ± . . ± ± . .
69 86.65762 -53.75918 -23.48 ± ± . . ± ± . .
72 86.65746 -53.75890 -23.38 ± ± . . ± ± . .
75 86.65708 -53.75909 -22.69 ± ± . . ± ± . .
76 86.65333 -53.75912 -21.13 ± ± . . ± ± . .
77 86.65654 -53.75870 -24.90 ± ± . . ± ± . .
80 86.65696 -53.75884 -21.96 ± ± . . ± ± . .
81 86.63404 -53.75795 -24.03 ± ± . . ± ± . .
83 86.65275 -53.75854 -22.38 ± ± . . ± ± . .
85 86.65500 -53.75820 -22.79 ± ± . . ± ± . .
89 86.65483 -53.75834 -21.27 ± ± . . ± ± . .
90 86.65742 -53.75806 -21.23 ± ± . . ± ± . .
91 86.64396 -53.75743 -22.89 ± ± . . ± ± . .
92 86.65483 -53.75720 -24.25 ± ± . . ± ± . .
93 86.65162 -53.75729 -23.19 ± ± . . ± ± . .
97 86.65275 -53.75734 -22.64 ± ± . . ± ± . .
103 86.63679 -53.75676 -23.74 ± ± . . ± ± . .
104 86.62417 -53.75684 -22.28 ± ± . . ± ± . .
107 86.64717 -53.75568 -23.89 ± ± . . ± ± . .
109 86.64625 -53.75573 -21.58 ± ± . . ± ± . .
110 86.62558 -53.75568 -23.09 ± ± . . ± ± . .
111 86.65850 -53.75559 -22.03 ± ± . . ± ± . .
116 86.65275 -53.75434 -22.97 ± ± . . ± ± . .
117 86.65058 -53.75426 -22.45 ± ± . . ± ± . .
121 86.65237 -53.75315 -23.01 ± ± . . ± ± . .
126 86.64612 -53.75059 -24.70 ± ± . . ± ± . . Columns: (1) ID; (2) right ascension; (3) declination; (4) K s -band absolute magnitude; (5) K s -band effective radius; (6) K s -band S´ersicindex; (7) logarithm of stellar mass. Errors are Monte Carlo simulated: stellar mass within FAST and remaining properties with ourown simulations as described in the text. GALFIT uses a χ minimisation technique to fit profiles andestimate uncertainties under the assumption that an analyt-ical function (in this case, a single S´ersic profile) is an accu-rate description of the galaxy being fit, and thus that anyresidual difference between the model and observed galaxyis solely Poisson noise (Peng et al. 2010). However, this as- sumption is not valid in many cases, e.g. due to remainingsky structure and contamination by nearby galaxies, so theresiduals are not solely Poisson but also correlated (H¨aussleret al. 2007). This means that the true uncertainty is under-estimated by χ statistics.In our case we consider the dominant source of error to bestructure in the sky background, since GALFIT does a rea-sonable job of deblending neighbouring galaxies via simul- c (cid:13) , ?? ––
126 86.64612 -53.75059 -24.70 ± ± . . ± ± . . Columns: (1) ID; (2) right ascension; (3) declination; (4) K s -band absolute magnitude; (5) K s -band effective radius; (6) K s -band S´ersicindex; (7) logarithm of stellar mass. Errors are Monte Carlo simulated: stellar mass within FAST and remaining properties with ourown simulations as described in the text. GALFIT uses a χ minimisation technique to fit profiles andestimate uncertainties under the assumption that an analyt-ical function (in this case, a single S´ersic profile) is an accu-rate description of the galaxy being fit, and thus that anyresidual difference between the model and observed galaxyis solely Poisson noise (Peng et al. 2010). However, this as- sumption is not valid in many cases, e.g. due to remainingsky structure and contamination by nearby galaxies, so theresiduals are not solely Poisson but also correlated (H¨aussleret al. 2007). This means that the true uncertainty is under-estimated by χ statistics.In our case we consider the dominant source of error to bestructure in the sky background, since GALFIT does a rea-sonable job of deblending neighbouring galaxies via simul- c (cid:13) , ?? –– ?? S. Sweet et al. observed model residual Figure 5.
Profile fitting of a selection of sources in K s -bandusing a GALFIT single S´ersic profile. Images are scaled to a com-mon inverse hyperbolic sin scaling to emphasise faint residualfeatures. Left to right: observed, S´ersic fit, residual. Top to bot-tom: isolated, blended, cluster core, foreground spiral galaxy. Thered spot in the lower left corner of the observed panels illustratesthe average PSF FHWM. The scale bar near cluster core showsthe angular and projected distance at the cluster redshift of z=1.N=up and E=left in each panel. taneous fitting. We consequently estimate uncertainties forboth GeMS and HST imaging with a Monte Carlo simula-tion as follows. We insert model galaxies matching the fittedparameters into random locations in a blank patch of sky,and measure the standard error in the recovered parameters.This traces the effect of the large-scale variation in the skybackground on the ability of GALFIT to provide a consis-tent solution. These uncertainties are given in Table 1 andas error bars in Figures 4 and 9.We show the distribution of recovered parameters of thebrightest cluster galaxy in Figure 7. There is an obvious co-variance between magnitude, effective radius and S´ersic in-dex, such that a smaller magnitude (resulting from a lowersky background and consequently higher flux attributedto the galaxy) corresponds to a higher S´ersic index andlarger effective radius. However, the recovered parametersare strongly clustered around the input model parameters;this is reflected in the low uncertainties in our simulation: σ m Ks = 0 . σ n = 0 . σ r e = 0 . −1.0 −0.5 0.0 0.5 1.0−1.0−0.50.00.51.0−1.0 −0.5 0.0 0.5 1.0F606W log(r e [kpc])−1.0−0.50.00.51.0 K s l og (r e [ k p c ] ) −1.0−0.50.00.51.01.5 F W l og (r e [ k p c ] ) −1.0 −0.5 0.0 0.5 1.0 1.5F814W log(r e [kpc]) Figure 6.
Cluster member effective radii measured in HSTF606W-band vs. HST F814W-band (top); K s -band vs. HSTF814W-band (bottom right); K s -band vs. HST F606W-band(bottom left). The dashed line in each panel is the 1:1 relation;the dotted line is the best fitting line. Spearman’s rank correlationcoefficients are 0.756, 0.834 and 0.712 respectively. We now investigate the stellar mass - size relation measuredat high angular resolution in the old stellar population lightfor SPT-CL J0546 − In Figure 8 we give the histogram of S´ersic indices for clustermembers and field galaxies. The median for the cluster is n = 3.8 ± ± c (cid:13) , ?? – ?? tellar mass - size relation at z=1 with GeMS/GSAOI astrometry Ks [AB mag]0.40.50.60.70.8 l og (r e [ k p c ] ) S e r s i c n Figure 7.
Covariance between recovered magnitude, effective ra-dius and S´ersic index of a Monte Carlo simulated brightest clustergalaxy. N Figure 8.
Histogram of S´ersic indices for entire sample (lightgrey) and cluster members (mid grey). The cluster member sam-ple consists of mostly early-type galaxies, with a median n = 3.8. z = 1 isoffset from that at z = 0. The size-mass distribution for the z = 1 SPT-CLJ0546 − r e ) = κ + β log(M ∗ ), are indicated in each panel of Fig-ure 9 as red circles and solid line, and given in Table 2. Inthe upper, left-hand plot we show that the z = 1 stellarmass - size relation is offset at log(M ∗ ) = 11 by 0.21 dexfrom the present-day SDSS relation (for early-type centralgalaxies in SDSS, Guo et al. 2009). We calculate the cor-responding redshift evolution γ ∝ (1 + z ) α of the medianmass-normalised size as γ = r e / ( M ∗ / M (cid:12) ), and find a slope of α = − z = 1 and z = 0. However, our measurement is not discrepant withthe literature, which exhibits a wide variation in redshiftevolution slope, e.g. α = − − − − α islikely driven by other differences in sample selection (includ-ing redshift and galaxy morphology), slopes (by which thesamples are mass-normalised) and rest-frame wavelengths(which we discuss below). For observations taken in the rest-frame UV, one would ex-pect that measured r e is affected by the clumpy star-formingregions that dominate the flux at those wavelengths. Thisshould be particularly the case for rest-frame U -band, whichfalls almost entirely blueward of the 4000˚A break, and B -band, which straddles it.At the cluster redshift of z = 1.067, our HST/ACS F606W,HST/ACS F814W and K s imaging correspond to rest-frame observations in approximately the U , B and Y bands(2930˚A, 3940˚A and 1.05 µ m). We investigate the effect ofrest-frame wavelength on the slope of the stellar mass - sizerelation by comparing the cluster member galaxies’ effec-tive radii in these three bands. The resulting stellar mass -size relations are illustrated in the upper, right-hand panelof Figure 9, and exhibit slopes of β = 0.44 ± ± ± U and B imaging yield significantly shallower slopesthan rest-frame Y , indicating that the bluer images are in-deed affected by clumpy star-formation events, particularlyin lower mass galaxies. However, there is no significant wave-length effect on the zero-point of the measured stellar mass- size relations, with an offset in log(r e ) at log(M ∗ ) = 11 ofjust − Y and B and +0.03 dex between Y and U bands. The rest-frame B and U relations have similarscatter to rest-frame Y . The fact that this analysis is basedon a consistent sample rules out any sample differences (suchas S´ersic index, mass, environment, redshift, star formationrate) as being responsible for the difference in slope. Themechanism for the shallower slopes from the two bluer im-ages is that in the case of some galaxies, star-forming clumpsat the edges of galaxies serve to overestimate their measured r e (preferentially for the smallest galaxies); while in othercases, multiple star-forming clumps within a galaxy are mea- c (cid:13) , ?? ––
Histogram of S´ersic indices for entire sample (lightgrey) and cluster members (mid grey). The cluster member sam-ple consists of mostly early-type galaxies, with a median n = 3.8. z = 1 isoffset from that at z = 0. The size-mass distribution for the z = 1 SPT-CLJ0546 − r e ) = κ + β log(M ∗ ), are indicated in each panel of Fig-ure 9 as red circles and solid line, and given in Table 2. Inthe upper, left-hand plot we show that the z = 1 stellarmass - size relation is offset at log(M ∗ ) = 11 by 0.21 dexfrom the present-day SDSS relation (for early-type centralgalaxies in SDSS, Guo et al. 2009). We calculate the cor-responding redshift evolution γ ∝ (1 + z ) α of the medianmass-normalised size as γ = r e / ( M ∗ / M (cid:12) ), and find a slope of α = − z = 1 and z = 0. However, our measurement is not discrepant withthe literature, which exhibits a wide variation in redshiftevolution slope, e.g. α = − − − − α islikely driven by other differences in sample selection (includ-ing redshift and galaxy morphology), slopes (by which thesamples are mass-normalised) and rest-frame wavelengths(which we discuss below). For observations taken in the rest-frame UV, one would ex-pect that measured r e is affected by the clumpy star-formingregions that dominate the flux at those wavelengths. Thisshould be particularly the case for rest-frame U -band, whichfalls almost entirely blueward of the 4000˚A break, and B -band, which straddles it.At the cluster redshift of z = 1.067, our HST/ACS F606W,HST/ACS F814W and K s imaging correspond to rest-frame observations in approximately the U , B and Y bands(2930˚A, 3940˚A and 1.05 µ m). We investigate the effect ofrest-frame wavelength on the slope of the stellar mass - sizerelation by comparing the cluster member galaxies’ effec-tive radii in these three bands. The resulting stellar mass -size relations are illustrated in the upper, right-hand panelof Figure 9, and exhibit slopes of β = 0.44 ± ± ± U and B imaging yield significantly shallower slopesthan rest-frame Y , indicating that the bluer images are in-deed affected by clumpy star-formation events, particularlyin lower mass galaxies. However, there is no significant wave-length effect on the zero-point of the measured stellar mass- size relations, with an offset in log(r e ) at log(M ∗ ) = 11 ofjust − Y and B and +0.03 dex between Y and U bands. The rest-frame B and U relations have similarscatter to rest-frame Y . The fact that this analysis is basedon a consistent sample rules out any sample differences (suchas S´ersic index, mass, environment, redshift, star formationrate) as being responsible for the difference in slope. Themechanism for the shallower slopes from the two bluer im-ages is that in the case of some galaxies, star-forming clumpsat the edges of galaxies serve to overestimate their measured r e (preferentially for the smallest galaxies); while in othercases, multiple star-forming clumps within a galaxy are mea- c (cid:13) , ?? –– ?? S. Sweet et al. O • ])-1012 l og (r e [ k p c ] ) GeMS (this work)Compilation (Damjanov et al. 2011)COSMOS (Huertas-Company et al. 2013)HCS (Delaye et al. 2014)CANDELS (van der Wel et al. 2014)GOODS-S (Newman et al. 2012)-1012 l og (r e [ k p c ] ) GeMS zspec (this work)GeMS zphot (this work)SDSS z=0.1 (Guo et al. 2009)9.5 10.0 10.5 11.0 11.5 12.0 9.5 10.0 10.5 11.0 11.5 12.0log(mass [M O • ])GeMS Ks (110 mas)NICMOS (220 mas)FourStar (510 mas) -1012KsF814WF606W9.5 10.0 10.5 11.0 11.5 12.0 -1012 Figure 9.
Stellar mass - size relation for the cluster SPT-CL J0546 − Top left: K s -band stellar mass - size relation at z = 1. The relation defined by ourcluster members has a slope of β = 0.74, consistent with but offset by 0.21 dex from the z = 0 relation shown as the dashed line. Bothrelations trace the underlying stellar population. The BCG (circled) and the next-largest galaxy appear as outliers above the stellar mass- size relation. Top right:
Stellar mass - size relation for the SPT cluster measured in GSAOI K s (red filled circles and black solid line),HST ACS F814W (rest-frame B-band shown as blue down triangles and dot-dashed line) and F606W (rest-frame U-band as magentasquares and dashed line) bands. Shorter wavelengths give a shallower slope with larger scatter in radius, being affected by UV-brightstar-forming knots. Bottom left:
Other z ∼ Bottom right:
The effect of resolution on the stellar mass - size relation.Filled red circles and solid line depict our GeMS K s -band imaging (FWHM ∼
110 mas). Blue down triangles and dot-dashed line showmeasurements from our imaging smoothed to the resolution of NICMOS (220 mas); magenta squares and dashed line are from smoothingto the resolution of FourStar (510 mas). The horizontal dotted lines indicate the physical size at z = 1 that corresponds to the resolutionof each instrument. sured as multiple galaxies with consequently underestimated r e (preferentially for the largest galaxies). We further illustrate the effect of rest-frame wavelength bycomparing with other z = 1 samples from the literature While many of the cluster members in this work are locatedon the red sequence, a significant proportion have bluer colourswith clumps or a frosting of star formation. It is these galaxiesin particular whose sizes can be under- or overestimated in thisway. in the lower, left-hand panel of Figure 9, where rest-frame B -band measurements are shown in blue and rest-frame V -band in green; these are also given in Table 2. The B -bandstellar mass - size relations measured in a compilation byDamjanov et al. (2011), in COSMOS by Huertas-Companyet al. (2013) and in HCS by Delaye et al. (2014) ( β = 0.51 ± ± ± U -band and B -band slopes. Onthe other hand, the rest-frame V -band stellar mass - sizerelations measured in 3D-HST+CANDELS by van der Welet al. (2014) and GOODS-S by Newman et al. (2012) ( β = c (cid:13) , ?? – ?? tellar mass - size relation at z=1 with GeMS/GSAOI astrometry Table 2.
Table of properties of samples presented in Figure 9, where log( r e ) = κ + β log(M ∗ ).Sample z rest-frame β κ ReferenceGeMS Ks 1.067 Y 0.74 ± ± z ± ± ± ± ± ± < z < ± ± < z < ± ± < z < ± ± ± ± < z < ± ± ± ± ± ± ± ± Y -band β . From this agreement we draw theconclusion that observations made in the rest-frame V -band,which falls entirely redward of the 4000˚A break, are notgreatly affected by star-forming clumps. When measuring the sizes of galaxies, one requires suffi-cient resolution that the sources are resolved in the imag-ing. Given that high-redshift galaxies are very compact,one would expect that resolution is particularly importantwhen measuring the stellar mass - size relation at high red-shift.We investigate the impact of substituting our ∼
110 mas res-olution K s -band GeMS imaging with the effective resolutionof imaging from alternative instruments at similar wave-lengths: HST/NICMOS , with diffraction-limited FWHM= 220 mas in the F222M filter ( ∼ K -band) (Scoville et al.2000), and Magellan/FourStar, with seeing-limited FWHM= 510 mas in K s -band (Lee et al. 2012). We smooth our K s -band image with a Gaussian filter to simulate the resolutionof two such data-sets. The resulting stellar mass - size rela-tions are given in the lower, right-hand panel of Figure 9,and in Table 2. The slope of the NICMOS-resolution stellarmass - size relation is not significantly different from GeMSat β = 0.84 ± e ) at log(M ∗ ) = 11. This broad agreement suggeststhat the resolution delivered by current space-based instru-ments may be sufficient for accurate measurement of thehigh-redshift stellar mass - size relation in the rest-framelight of the old stellar population, even though the sizesof the smallest galaxies are below the resolution limit. Wepoint out that the narrow field of view of NICMOS (19 (cid:48)(cid:48) .5x 19 (cid:48)(cid:48) .5) makes this measurement observationally expensivefor large sample sizes. Similarly, there is agreement betweenthe slopes measured at 180 mas in the observed H -bandof 3D-HST+CANDELS and GOODS-S (green best fittinglines in lower, left-hand panel of Figure 9) and that of ourhigher resolution GeMS relation. However, while this impliesthat HST/ACS H -band observations are adequate for this We do not compare to WFC3 as that instrument does not havea ∼ K -band filter. type of measurement at z = 1, they would not suffice forsignificantly higher redshifts, at which this filter straddlesthe 4000˚A break.In contrast to the space-based resolutions presented above,the stellar mass - size relation measured at seeing-limitedground-based resolution (FourStar) is significantly steeperthan our GeMS stellar mass - size relation, indicating thatthe relation cannot be accurately measured from the groundwithout the use of adaptive optics. This is as expected, sincethe true r e falls well below the FourStar resolution for allbut the largest galaxies in our sample. z = 1 is consistent with that at z = 0. Major mergers have been proposed as a mechanism for theobserved evolution in the stellar mass - size relation. Theseare known to cause massive galaxies to grow more quicklythan less massive ones (Khochfar & Silk 2006). Thus if ma-jor mergers were a dominant source of the evolution in thestellar mass - size relation, then the most massive galaxieswould experience the most rapid growth, so that the slopeof the stellar mass - size relation would be steeper at thepresent day than at z = 1. However, our z = 1 slope of β = 0.74 ± z = 0.1 slope of β =0.70 measured by Guo et al. (2009) (upper, left-hand panelof Figure 9). The two samples have very similar wavelengthranges (rest-frame Y -band and z -band), which both tracethe old stellar population; thus this comparison is not af-fected by clumpy star formation, but instead demonstratesthat the slope of the stellar mass - size relation is constantfrom z = 1 to today. Consequently, massive galaxies typi-cally grow at the same rate as smaller galaxies, so that majormergers are not responsible for the evolution in the stellarmass - size relation between z = 1 and today . Interestingly, our BCG (and the second-largest galaxy) has asomewhat enhanced size above the stellar mass - size relation,suggesting that it may have had an increased history of majormergers by virtue of its location at the bottom of the potentialwell. Also note that our analysis applies to the most massiveevolved clusters at z = 1, and not to galaxies in more typicalclusters at that redshift, in which there is strong evidence formajor mergers driving galaxy assembly. The timing of the growthc (cid:13) , ?? ––
110 mas res-olution K s -band GeMS imaging with the effective resolutionof imaging from alternative instruments at similar wave-lengths: HST/NICMOS , with diffraction-limited FWHM= 220 mas in the F222M filter ( ∼ K -band) (Scoville et al.2000), and Magellan/FourStar, with seeing-limited FWHM= 510 mas in K s -band (Lee et al. 2012). We smooth our K s -band image with a Gaussian filter to simulate the resolutionof two such data-sets. The resulting stellar mass - size rela-tions are given in the lower, right-hand panel of Figure 9,and in Table 2. The slope of the NICMOS-resolution stellarmass - size relation is not significantly different from GeMSat β = 0.84 ± e ) at log(M ∗ ) = 11. This broad agreement suggeststhat the resolution delivered by current space-based instru-ments may be sufficient for accurate measurement of thehigh-redshift stellar mass - size relation in the rest-framelight of the old stellar population, even though the sizesof the smallest galaxies are below the resolution limit. Wepoint out that the narrow field of view of NICMOS (19 (cid:48)(cid:48) .5x 19 (cid:48)(cid:48) .5) makes this measurement observationally expensivefor large sample sizes. Similarly, there is agreement betweenthe slopes measured at 180 mas in the observed H -bandof 3D-HST+CANDELS and GOODS-S (green best fittinglines in lower, left-hand panel of Figure 9) and that of ourhigher resolution GeMS relation. However, while this impliesthat HST/ACS H -band observations are adequate for this We do not compare to WFC3 as that instrument does not havea ∼ K -band filter. type of measurement at z = 1, they would not suffice forsignificantly higher redshifts, at which this filter straddlesthe 4000˚A break.In contrast to the space-based resolutions presented above,the stellar mass - size relation measured at seeing-limitedground-based resolution (FourStar) is significantly steeperthan our GeMS stellar mass - size relation, indicating thatthe relation cannot be accurately measured from the groundwithout the use of adaptive optics. This is as expected, sincethe true r e falls well below the FourStar resolution for allbut the largest galaxies in our sample. z = 1 is consistent with that at z = 0. Major mergers have been proposed as a mechanism for theobserved evolution in the stellar mass - size relation. Theseare known to cause massive galaxies to grow more quicklythan less massive ones (Khochfar & Silk 2006). Thus if ma-jor mergers were a dominant source of the evolution in thestellar mass - size relation, then the most massive galaxieswould experience the most rapid growth, so that the slopeof the stellar mass - size relation would be steeper at thepresent day than at z = 1. However, our z = 1 slope of β = 0.74 ± z = 0.1 slope of β =0.70 measured by Guo et al. (2009) (upper, left-hand panelof Figure 9). The two samples have very similar wavelengthranges (rest-frame Y -band and z -band), which both tracethe old stellar population; thus this comparison is not af-fected by clumpy star formation, but instead demonstratesthat the slope of the stellar mass - size relation is constantfrom z = 1 to today. Consequently, massive galaxies typi-cally grow at the same rate as smaller galaxies, so that majormergers are not responsible for the evolution in the stellarmass - size relation between z = 1 and today . Interestingly, our BCG (and the second-largest galaxy) has asomewhat enhanced size above the stellar mass - size relation,suggesting that it may have had an increased history of majormergers by virtue of its location at the bottom of the potentialwell. Also note that our analysis applies to the most massiveevolved clusters at z = 1, and not to galaxies in more typicalclusters at that redshift, in which there is strong evidence formajor mergers driving galaxy assembly. The timing of the growthc (cid:13) , ?? –– ?? S. Sweet et al.
Our conclusion corresponds with other authors’ findingsspanning this redshift range. The general understandingbuilt by the literature is that the majority of structures werein place by z = 1 (Papovich et al. 2005), and that majormergers at all galaxy masses are rare since then (see alsoBundy et al. 2009; Lotz et al. 2011). At lower redshifts thisis evidenced by a constant size-mass slope at lower redshifts,e.g. Delaye et al. (2014) found the slope to be constant up to z ∼ < z < n > r e than low-mass ones, due to a greaternumber of major mergers for high-mass galaxies, e.g. Ryanet al. (2012). Brodwin et al. (2013) also found significant ma-jor merger rates in clusters above z ∼ z > < z < < z < V band in both cases. Damjanov et al. (2011) also observeda consistent slope over 0.2 < z < U -band imaging, though if we were to (incorrectly) compareour rest-frame U -band relation with the rest-frame z -bandone at z = 0 we would in fact detect an evolving slope andattribute the growth to major mergers. The consistent slopeabove z > z ∼ α = d log r e /d log M ∗ . The dependence of growthefficiency on mass ratio µ is given by α = 2 − log(1 + µ − β )log(1 + µ ) , (1)where β is the slope of the stellar mass - size relation (New-man et al. 2012). For major mergers of equal-sized galaxies, µ = 1 so that the minimum α = 1. For minor mergers theliterature contains a wide range in growth efficiency, for ex-ample α = 1.3 (Nipoti et al. 2009), α = 1.6 (Newman et al.2012) and α (cid:38) β = 0.74 ± α = 1.43 ± may also be different in the field, since the cluster environmentaccelerates galaxy evolution. the same minor merger mass ratio µ =0.1. This is a some-what lower growth efficiency than Newman et al. (2012) dueto the steeper slope we measure, but more efficient than theNipoti et al. (2009) result for minor mergers. It may be suf-ficiently efficient to explain the amount of observed growthfrom z = 1 to today (though not from z = 2 to 1) (Newmanet al. 2012). With regards to the requirement to match theobserved constancy of slope, we note that the mass ratio µ was shown to be independent of stellar mass of the largergalaxy in the low-redshift GAMA survey (Robotham et al.2014), so the growth efficiency is also independent of stel-lar mass. Size growth by minor mergers therefore appearsto be consistent with the slope of the size-mass remainingunchanged with redshift.Next we consider the case where adiabatic expansion dueto rapid mass loss is responsible for the size growth. In thiscase, expansion scales in proportion to mass lost (Ragone-Figueroa & Granato 2011), so for a constant size-mass slopeeach galaxy must experience the same amount of mass lossper unit host galaxy mass. Mass loss driven by AGN windsis consistent with this case, as it is known that outflow en-ergy scales with luminosity of the black hole (Bˆırzan et al.2004; King et al. 2013; Heckman & Best 2014), and thereforewith the host galaxy mass (Ferrarese & Merritt 2000; Geb-hardt et al. 2000). However, it does not hold for mass lossdriven by supernovae, since the specific supernova rate isnot constant with stellar mass (smaller galaxies have highersupernova rates, Li et al. 2011). Further to this, Hopkinset al. (2010) note that adiabatic expansion caused by stel-lar winds is only sufficient to cause a size increase of 20%,much less than the observed size increase. Damjanov et al.(2009) also concluded that adiabatic expansion due to stel-lar winds was unlikely. This suggests that adiabatic expan-sion due to supernova-driven mass loss cannot be responsiblefor the redshift evolution of the stellar mass - size relation,though adiabatic expansion due to AGN-driven mass lossmay. We present the first high angular-resolution measurementof the rest-frame Y -band stellar mass - size relation forthe galaxy cluster SPT-CL J0546 − z = 1.067. Wedemonstrate our strategies for addressing the data process-ing challenges associated with these complex imaging datain order to achieve a final stacked image with a mean PSFFWHM ∼
110 mas (corresponding to a radius of 450 pcat the cluster redshift), with a uniform sky subtraction freefrom strong residual images that echo faint field sources. Thespatial variation of the PSF is modelled as a two-dimensionalMoffat profile fit to known stars across the field and inter-polated at the location of each measured galaxy.Forty-nine cluster member galaxies are detected, with me-dian S´ersic index n = 3.8 ± z ∼ z ∼ γ ∝ (1 + z ) − . , whichis consistent with previous results for minor mergers (Nipotiet al. 2009).The stellar mass - size relation exhibits a slope of β = 0.74 c (cid:13) , ?? – ?? tellar mass - size relation at z=1 with GeMS/GSAOI astrometry ± β = 0.70 ± − z ∼
1, has ceased itsearly, rapid growth dominated by major mergers, leavingthe galaxies to increase in size via minor mergers and/oradiabatic expansion due to AGN mass loss winds.The stellar mass - size relation for the cluster members isalso measured in the rest-frame B and U bands from archival HST /ACS F814W and F606W imaging. We show that thosemeasurements are contaminated by knots of star formationthat affect the light profiles. Galaxy effective radii are pref-erentially overestimated for low-mass systems and preferen-tially underestimated for high-mass systems when measuredin the rest-frame UV wavelengths that are blueward of orstraddle the λ = 4000˚A break, with a stronger bias at shorterwavelengths. The effect of this is that the slope of the stel-lar mass - size relation is severely affected by the rest-framewavelength range at which it is measured, although the zero-point is not affected such that a 10 M (cid:12) galaxy has aneffective radius of 2.45 kpc, consistent with the literature.This is a vivid illustration of the necessity of performingsize measurements in the rest-frame underlying old stellarpopulation in order to avoid bias by clumpy regions of starformation.We measure the stellar mass - size relation after Gaus-sian smoothing to typical imaging resolutions obtainedwith diffraction-limited HST/NICMOS K -band and seeing-limited Magellan/FourStar K s -band. The NICMOS resolu-tion gives a result consistent with our GSAOI imaging, butthe seeing-limited FourStar resolution gives a significantlysteeper slope. Hence the stellar mass - size relation cannotbe accurately measured at z (cid:38) < z < ACKNOWLEDGEMENTS
Based in part on observations obtained at the Gemini Obser-vatory, which is operated by the Association of Universitiesfor Research in Astronomy, Inc., under a cooperative agree-ment with the NSF on behalf of the Gemini partnership: theNational Science Foundation (United States), the NationalResearch Council (Canada), CONICYT (Chile), the Aus-tralian Research Council (Australia), Minist´erio da Ciˆencia,Tecnologia e Inoval¸˜ao (Brazil) and Ministerio de Ciencia,Tecnolog´ıa e Innovaci´on Productiva (Argentina).Elements of the data presented in this paper were obtainedfrom the Mikulski Archive for Space Telescopes (MAST).STScI is operated by the Association of Universities forResearch in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08Gand by other grants and contracts.This publication makes use of data products from the TwoMicron All Sky Survey, which is a joint project of the Uni-versity of Massachusetts and the Infrared Processing andAnalysis Center/California Institute of Technology, fundedby the National Aeronautics and Space Administration andthe National Science Foundation.This research has made use of NASA’s Astrophysics DataSystem.This research has made use of the VizieR catalogue accesstool, CDS, Strasbourg, France. The original description ofthe VizieR service was published in A&AS 143, 23.This research was conducted with the support of AustralianResearch Council DP130101667. We thank the InternationalTelescope Support Office and Gemini Observatory for con-tributing travel funding. c (cid:13) , ?? ––
Based in part on observations obtained at the Gemini Obser-vatory, which is operated by the Association of Universitiesfor Research in Astronomy, Inc., under a cooperative agree-ment with the NSF on behalf of the Gemini partnership: theNational Science Foundation (United States), the NationalResearch Council (Canada), CONICYT (Chile), the Aus-tralian Research Council (Australia), Minist´erio da Ciˆencia,Tecnologia e Inoval¸˜ao (Brazil) and Ministerio de Ciencia,Tecnolog´ıa e Innovaci´on Productiva (Argentina).Elements of the data presented in this paper were obtainedfrom the Mikulski Archive for Space Telescopes (MAST).STScI is operated by the Association of Universities forResearch in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08Gand by other grants and contracts.This publication makes use of data products from the TwoMicron All Sky Survey, which is a joint project of the Uni-versity of Massachusetts and the Infrared Processing andAnalysis Center/California Institute of Technology, fundedby the National Aeronautics and Space Administration andthe National Science Foundation.This research has made use of NASA’s Astrophysics DataSystem.This research has made use of the VizieR catalogue accesstool, CDS, Strasbourg, France. The original description ofthe VizieR service was published in A&AS 143, 23.This research was conducted with the support of AustralianResearch Council DP130101667. We thank the InternationalTelescope Support Office and Gemini Observatory for con-tributing travel funding. c (cid:13) , ?? –– ?? S. Sweet et al.
Table 3: Source identifications in the field of SPT-CL J0546 − z GMOS z B10 z R14 spec phot m K s m F814 W m F606 W (b/a) (PA)[deg] [deg] [AB mag] [AB mag] [AB mag] [deg](1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)3 86.63450 -53.77259 - - - 0 0 22.03 23.32 23.51 0.74 -4.224 86.63946 -53.77115 - - - 0 0 22.05 25.28 25.28 0.67 71.805 86.62975 -53.77023 - - - 0 0 22.98 23.70 23.51 0.77 88.356 86.64387 -53.76906 - - - 0 0 20.30 23.92 24.48 0.80 -29.737 86.63387 -53.76948 - - - 0 0 23.12 25.99 25.17 0.99 9.328 86.65075 -53.76931 - - - 0 0 22.64 25.25 24.97 0.54 52.169 86.66058 -53.76859 0.0000 - - 0 0 18.67 19.66 21.46 0.04 -54.4210 86.65396 -53.76834 - - - 0 0 21.40 25.29 25.53 0.74 64.7111 86.64921 -53.76823 - - - 0 0 21.62 23.07 23.53 0.57 -71.5012 86.66296 -53.76823 - - - 0 0 22.23 - 24.48 0.85 19.3113 86.65008 -53.76790 - - - 0 0 21.69 24.65 25.46 0.33 -47.3514 86.65562 -53.76770 - - - 0 0 21.57 23.46 23.93 0.91 -44.8115 86.64200 -53.76776 - - - 0 0 21.98 24.31 24.97 0.83 -59.6416 86.65179 -53.76768 - - - 0 0 21.22 - 25.80 0.23 -83.5417 86.64246 -53.76756 0.5083 - - 0 0 22.10 23.09 23.73 0.37 -75.1118 86.63133 -53.76740 - - - 0 1 23.14 24.72 25.93 0.50 -69.2319 86.62950 -53.76595 - - - 0 0 19.90 22.59 23.54 0.24 12.3920 86.66529 -53.76681 - - - 1 0 21.84 23.67 24.04 0.92 37.3421 86.64479 -53.76673 - - - 0 0 22.27 24.52 24.88 0.77 68.2222 86.66071 -53.76615 0.0000 - - 0 0 20.82 21.80 24.31 0.45 75.9323 86.65296 -53.76576 - - - 0 0 21.46 24.51 25.63 0.75 -1.2824 86.63625 -53.76579 - - - 0 0 22.18 24.73 25.91 0.34 30.6925 86.64475 -53.76554 - 1.0567 1.0567 1 1 18.97 22.62 23.96 0.66 61.4026 86.64337 -53.76559 - - - 0 1 21.75 24.13 24.76 1.00 -47.9327 86.65246 -53.76490 - - - 0 0 21.04 22.66 24.47 0.76 54.9428 86.63808 -53.76498 - - - 0 0 21.45 25.12 27.25 0.42 -19.1729 86.64354 -53.76468 - - - 0 0 20.70 24.44 26.17 0.44 75.8730 86.63475 -53.76409 - - - 0 0 20.53 21.09 22.82 0.66 53.3131 86.65746 -53.76412 - - - 0 1 20.43 23.32 25.20 0.88 -71.7032 86.65596 -53.76437 - - - 1 0 22.66 24.21 25.61 0.80 -87.7733 86.65979 -53.76429 - - - 0 0 22.28 25.36 25.37 0.66 -2.7634 86.64917 -53.76434 - - - 0 0 23.62 26.05 25.65 1.00 10.4335 86.66371 -53.76415 - - - 0 0 22.97 40.02 26.84 0.25 29.7036 86.64292 -53.76368 - - - 0 1 21.56 23.93 25.30 0.53 -29.2537 86.64383 -53.76334 - - - 0 1 20.93 23.25 24.60 0.91 -49.5538 86.63292 -53.76362 - - - 0 0 23.57 - 26.22 0.74 44.6039 86.65192 -53.76351 - - - 0 0 21.84 24.75 27.09 0.68 -24.7141 86.64442 -53.76290 - - - 0 0 20.75 23.60 24.15 0.77 72.5442 86.65925 -53.76309 - - - 0 0 22.54 25.30 26.43 0.99 3.0843 86.64862 -53.76270 - - - 0 0 20.23 23.65 24.10 0.86 -56.7544 86.65725 -53.76229 - - - 0 0 21.28 22.79 24.28 0.45 -48.1145 86.63371 -53.76251 - - - 0 1 22.52 24.55 23.51 0.54 44.3646 86.63575 -53.76256 - - - 0 1 23.96 25.23 25.45 0.60 -83.3148 86.63496 -53.76229 - - - 0 1 21.84 24.11 23.74 0.37 75.8349 86.63675 -53.76223 - - - 0 0 21.92 - 23.41 0.53 -58.4450 86.64887 -53.76176 - 1.0710 1.0042 1 1 20.66 23.09 24.13 0.60 5.9051 86.63508 -53.76195 - - - 0 0 21.55 24.15 24.93 0.56 38.9152 86.63887 -53.76151 - - - 0 0 20.77 23.00 23.93 0.51 58.2553 86.64000 -53.76137 - 1.0775 1.0775 1 1 20.01 22.23 23.53 0.71 -46.0154 86.65217 -53.76156 - - - 1 1 21.85 24.54 25.85 0.75 85.0755 86.64687 -53.76159 - - - 0 0 21.17 - - 0.43 88.3456 86.63533 -53.76159 - - - 0 0 22.71 25.10 24.97 0.79 -38.1157 86.65371 -53.76140 - - - 0 1 20.23 24.12 24.71 0.53 -65.9058 86.65246 -53.76154 - - - 0 0 22.99 25.24 26.25 0.91 19.4159 86.62962 -53.76109 - - - 0 0 21.57 24.18 25.21 0.74 -50.4160 86.66146 -53.76012 1.0693 - - 1 1 20.22 23.11 24.70 0.88 -72.32Continued on next page c (cid:13) , ?? – ?? tellar mass - size relation at z=1 with GeMS/GSAOI astrometry Table 3: Source identifications in the field of SPT-CL J0546 − z GMOS z B10 z R14 spec phot m K s m F814 W m F606 W (b/a) (PA)[deg] [deg] [AB mag] [AB mag] [AB mag] [deg](1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)61 86.64508 -53.75998 0.9331 - - 1 0 21.18 - 23.62 0.65 11.1062 86.65804 -53.75987 - - - 1 1 20.10 23.02 24.56 0.92 -87.3063 86.66200 -53.76004 - - - 0 1 23.46 24.71 25.60 0.90 -81.4364 86.63596 -53.75962 - - - 0 0 20.68 23.62 23.98 0.55 -34.7465 86.65371 -53.75984 - - - 0 1 22.29 24.37 25.63 0.99 -31.5266 86.65054 -53.75965 - - - 0 0 21.84 24.23 25.43 0.70 19.5567 86.65600 -53.75956 - - - 0 1 22.21 23.97 26.41 0.94 24.8268 86.65879 -53.75959 - - - 0 0 22.48 24.65 25.71 0.04 22.0269 86.65762 -53.75918 0.9954 - - 1 1 20.81 23.15 - 0.46 40.9570 86.63875 -53.75868 0.0000 - - 0 0 18.06 20.20 22.21 0.63 -13.6471 86.65158 -53.75943 - - - 0 0 22.11 24.96 26.72 0.78 -17.8872 86.65746 -53.75890 0.9954 - - 1 1 20.92 23.32 - 0.82 39.7673 86.63637 -53.75920 - - - 0 0 22.95 25.39 25.94 0.90 -73.3874 86.64667 -53.75915 - - - 0 0 22.18 - 24.73 0.35 75.8975 86.65708 -53.75909 - - - 0 1 21.61 24.05 - 0.50 -52.4876 86.65333 -53.75912 - - - 0 0 23.16 25.23 26.21 0.96 -1.8277 86.65654 -53.75870 - - - 0 1 19.40 22.79 - 0.90 -89.5578 86.63575 -53.75845 0.0000 - - 0 0 19.95 21.23 23.73 0.69 -1.6679 86.63387 -53.75881 - - - 0 0 22.33 24.91 25.17 0.29 -62.9280 86.65696 -53.75884 - - - 0 1 22.34 24.42 - 0.86 50.6881 86.63404 -53.75795 - - - 0 0 20.26 22.73 - 0.53 -32.3482 86.64087 -53.75818 0.0000 - - 0 0 20.14 21.48 24.05 0.75 73.8583 86.65275 -53.75854 - - - 0 1 21.91 24.12 24.86 0.79 -57.2284 86.65521 -53.75851 - - - 0 0 22.65 25.05 - 0.57 10.2285 86.65500 -53.75820 1.0592 - - 1 1 21.51 23.65 26.28 0.34 39.1686 86.65408 -53.75843 - - - 0 1 22.61 24.19 26.39 0.78 44.2388 86.63317 -53.75823 0.3916 - - 0 0 22.32 22.98 23.08 0.53 -26.2889 86.65483 -53.75834 - - - 0 1 23.02 24.76 27.02 0.27 49.4190 86.65742 -53.75806 - - - 0 1 23.07 25.00 28.00 0.85 36.5991 86.64396 -53.75743 - - - 0 0 21.40 23.96 24.30 0.66 -7.6092 86.65483 -53.75720 - 1.0647 1.0647 1 1 20.05 22.97 24.53 0.94 -31.4893 86.65162 -53.75729 - - - 0 1 21.10 23.53 24.08 0.43 10.2194 86.65746 -53.75743 - - - 0 0 20.98 - 25.13 0.68 61.6395 86.62533 -53.75709 - - - 0 0 20.39 22.66 23.40 0.54 -87.9596 86.62700 -53.75754 - - - 0 0 22.09 23.72 23.47 0.69 0.0897 86.65275 -53.75734 - - - 0 1 21.65 24.17 25.24 0.86 -31.9498 86.65125 -53.75745 - - - 0 0 23.63 26.75 27.06 0.41 30.1599 86.64542 -53.75729 - - - 0 0 22.14 24.74 24.75 0.67 24.64100 86.65067 -53.75723 - - - 0 0 22.60 - 26.18 0.61 13.73101 86.64158 -53.75720 - - - 0 0 21.52 24.88 25.42 0.81 -72.49102 86.63850 -53.75676 - - - 0 0 21.09 23.09 - 0.43 44.05103 86.63679 -53.75676 1.0783 - - 1 1 20.56 23.34 23.66 0.84 43.05104 86.62417 -53.75684 - - - 0 1 22.02 24.29 24.27 0.94 46.87105 86.65300 -53.75679 - - - 0 0 22.05 - - 0.57 59.04106 86.65150 -53.75604 0.0000 - - 0 0 20.61 22.21 23.31 0.13 40.47107 86.64717 -53.75568 - - - 0 1 20.41 22.92 23.66 0.44 34.16108 86.63804 -53.75543 0.0000 - - 0 0 18.24 19.87 20.59 0.61 19.57109 86.64625 -53.75573 - - - 0 0 22.72 24.78 25.23 0.58 13.47110 86.62558 -53.75568 - - - 0 1 21.21 23.66 22.57 0.66 20.81111 86.65850 -53.75559 - - - 1 1 22.26 24.35 24.88 0.66 -70.51112 86.65750 -53.75556 - - - 0 0 22.05 26.16 35.59 0.69 35.61113 86.64729 -53.75515 0.0000 - - 0 0 21.54 22.59 - 0.13 35.15114 86.63567 -53.75509 - - - 0 0 23.12 - 24.10 0.81 19.55115 86.64733 -53.75340 0.0000 - - 0 0 16.45 19.52 20.64 0.87 21.88116 86.65275 -53.75434 - - - 0 1 21.33 24.15 25.15 0.39 81.14117 86.65058 -53.75426 - - - 1 1 21.84 24.35 25.43 0.83 33.76Continued on next page c (cid:13) , ?? ––
Table 3: Source identifications in the field of SPT-CL J0546 − z GMOS z B10 z R14 spec phot m K s m F814 W m F606 W (b/a) (PA)[deg] [deg] [AB mag] [AB mag] [AB mag] [deg](1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)3 86.63450 -53.77259 - - - 0 0 22.03 23.32 23.51 0.74 -4.224 86.63946 -53.77115 - - - 0 0 22.05 25.28 25.28 0.67 71.805 86.62975 -53.77023 - - - 0 0 22.98 23.70 23.51 0.77 88.356 86.64387 -53.76906 - - - 0 0 20.30 23.92 24.48 0.80 -29.737 86.63387 -53.76948 - - - 0 0 23.12 25.99 25.17 0.99 9.328 86.65075 -53.76931 - - - 0 0 22.64 25.25 24.97 0.54 52.169 86.66058 -53.76859 0.0000 - - 0 0 18.67 19.66 21.46 0.04 -54.4210 86.65396 -53.76834 - - - 0 0 21.40 25.29 25.53 0.74 64.7111 86.64921 -53.76823 - - - 0 0 21.62 23.07 23.53 0.57 -71.5012 86.66296 -53.76823 - - - 0 0 22.23 - 24.48 0.85 19.3113 86.65008 -53.76790 - - - 0 0 21.69 24.65 25.46 0.33 -47.3514 86.65562 -53.76770 - - - 0 0 21.57 23.46 23.93 0.91 -44.8115 86.64200 -53.76776 - - - 0 0 21.98 24.31 24.97 0.83 -59.6416 86.65179 -53.76768 - - - 0 0 21.22 - 25.80 0.23 -83.5417 86.64246 -53.76756 0.5083 - - 0 0 22.10 23.09 23.73 0.37 -75.1118 86.63133 -53.76740 - - - 0 1 23.14 24.72 25.93 0.50 -69.2319 86.62950 -53.76595 - - - 0 0 19.90 22.59 23.54 0.24 12.3920 86.66529 -53.76681 - - - 1 0 21.84 23.67 24.04 0.92 37.3421 86.64479 -53.76673 - - - 0 0 22.27 24.52 24.88 0.77 68.2222 86.66071 -53.76615 0.0000 - - 0 0 20.82 21.80 24.31 0.45 75.9323 86.65296 -53.76576 - - - 0 0 21.46 24.51 25.63 0.75 -1.2824 86.63625 -53.76579 - - - 0 0 22.18 24.73 25.91 0.34 30.6925 86.64475 -53.76554 - 1.0567 1.0567 1 1 18.97 22.62 23.96 0.66 61.4026 86.64337 -53.76559 - - - 0 1 21.75 24.13 24.76 1.00 -47.9327 86.65246 -53.76490 - - - 0 0 21.04 22.66 24.47 0.76 54.9428 86.63808 -53.76498 - - - 0 0 21.45 25.12 27.25 0.42 -19.1729 86.64354 -53.76468 - - - 0 0 20.70 24.44 26.17 0.44 75.8730 86.63475 -53.76409 - - - 0 0 20.53 21.09 22.82 0.66 53.3131 86.65746 -53.76412 - - - 0 1 20.43 23.32 25.20 0.88 -71.7032 86.65596 -53.76437 - - - 1 0 22.66 24.21 25.61 0.80 -87.7733 86.65979 -53.76429 - - - 0 0 22.28 25.36 25.37 0.66 -2.7634 86.64917 -53.76434 - - - 0 0 23.62 26.05 25.65 1.00 10.4335 86.66371 -53.76415 - - - 0 0 22.97 40.02 26.84 0.25 29.7036 86.64292 -53.76368 - - - 0 1 21.56 23.93 25.30 0.53 -29.2537 86.64383 -53.76334 - - - 0 1 20.93 23.25 24.60 0.91 -49.5538 86.63292 -53.76362 - - - 0 0 23.57 - 26.22 0.74 44.6039 86.65192 -53.76351 - - - 0 0 21.84 24.75 27.09 0.68 -24.7141 86.64442 -53.76290 - - - 0 0 20.75 23.60 24.15 0.77 72.5442 86.65925 -53.76309 - - - 0 0 22.54 25.30 26.43 0.99 3.0843 86.64862 -53.76270 - - - 0 0 20.23 23.65 24.10 0.86 -56.7544 86.65725 -53.76229 - - - 0 0 21.28 22.79 24.28 0.45 -48.1145 86.63371 -53.76251 - - - 0 1 22.52 24.55 23.51 0.54 44.3646 86.63575 -53.76256 - - - 0 1 23.96 25.23 25.45 0.60 -83.3148 86.63496 -53.76229 - - - 0 1 21.84 24.11 23.74 0.37 75.8349 86.63675 -53.76223 - - - 0 0 21.92 - 23.41 0.53 -58.4450 86.64887 -53.76176 - 1.0710 1.0042 1 1 20.66 23.09 24.13 0.60 5.9051 86.63508 -53.76195 - - - 0 0 21.55 24.15 24.93 0.56 38.9152 86.63887 -53.76151 - - - 0 0 20.77 23.00 23.93 0.51 58.2553 86.64000 -53.76137 - 1.0775 1.0775 1 1 20.01 22.23 23.53 0.71 -46.0154 86.65217 -53.76156 - - - 1 1 21.85 24.54 25.85 0.75 85.0755 86.64687 -53.76159 - - - 0 0 21.17 - - 0.43 88.3456 86.63533 -53.76159 - - - 0 0 22.71 25.10 24.97 0.79 -38.1157 86.65371 -53.76140 - - - 0 1 20.23 24.12 24.71 0.53 -65.9058 86.65246 -53.76154 - - - 0 0 22.99 25.24 26.25 0.91 19.4159 86.62962 -53.76109 - - - 0 0 21.57 24.18 25.21 0.74 -50.4160 86.66146 -53.76012 1.0693 - - 1 1 20.22 23.11 24.70 0.88 -72.32Continued on next page c (cid:13) , ?? – ?? tellar mass - size relation at z=1 with GeMS/GSAOI astrometry Table 3: Source identifications in the field of SPT-CL J0546 − z GMOS z B10 z R14 spec phot m K s m F814 W m F606 W (b/a) (PA)[deg] [deg] [AB mag] [AB mag] [AB mag] [deg](1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)61 86.64508 -53.75998 0.9331 - - 1 0 21.18 - 23.62 0.65 11.1062 86.65804 -53.75987 - - - 1 1 20.10 23.02 24.56 0.92 -87.3063 86.66200 -53.76004 - - - 0 1 23.46 24.71 25.60 0.90 -81.4364 86.63596 -53.75962 - - - 0 0 20.68 23.62 23.98 0.55 -34.7465 86.65371 -53.75984 - - - 0 1 22.29 24.37 25.63 0.99 -31.5266 86.65054 -53.75965 - - - 0 0 21.84 24.23 25.43 0.70 19.5567 86.65600 -53.75956 - - - 0 1 22.21 23.97 26.41 0.94 24.8268 86.65879 -53.75959 - - - 0 0 22.48 24.65 25.71 0.04 22.0269 86.65762 -53.75918 0.9954 - - 1 1 20.81 23.15 - 0.46 40.9570 86.63875 -53.75868 0.0000 - - 0 0 18.06 20.20 22.21 0.63 -13.6471 86.65158 -53.75943 - - - 0 0 22.11 24.96 26.72 0.78 -17.8872 86.65746 -53.75890 0.9954 - - 1 1 20.92 23.32 - 0.82 39.7673 86.63637 -53.75920 - - - 0 0 22.95 25.39 25.94 0.90 -73.3874 86.64667 -53.75915 - - - 0 0 22.18 - 24.73 0.35 75.8975 86.65708 -53.75909 - - - 0 1 21.61 24.05 - 0.50 -52.4876 86.65333 -53.75912 - - - 0 0 23.16 25.23 26.21 0.96 -1.8277 86.65654 -53.75870 - - - 0 1 19.40 22.79 - 0.90 -89.5578 86.63575 -53.75845 0.0000 - - 0 0 19.95 21.23 23.73 0.69 -1.6679 86.63387 -53.75881 - - - 0 0 22.33 24.91 25.17 0.29 -62.9280 86.65696 -53.75884 - - - 0 1 22.34 24.42 - 0.86 50.6881 86.63404 -53.75795 - - - 0 0 20.26 22.73 - 0.53 -32.3482 86.64087 -53.75818 0.0000 - - 0 0 20.14 21.48 24.05 0.75 73.8583 86.65275 -53.75854 - - - 0 1 21.91 24.12 24.86 0.79 -57.2284 86.65521 -53.75851 - - - 0 0 22.65 25.05 - 0.57 10.2285 86.65500 -53.75820 1.0592 - - 1 1 21.51 23.65 26.28 0.34 39.1686 86.65408 -53.75843 - - - 0 1 22.61 24.19 26.39 0.78 44.2388 86.63317 -53.75823 0.3916 - - 0 0 22.32 22.98 23.08 0.53 -26.2889 86.65483 -53.75834 - - - 0 1 23.02 24.76 27.02 0.27 49.4190 86.65742 -53.75806 - - - 0 1 23.07 25.00 28.00 0.85 36.5991 86.64396 -53.75743 - - - 0 0 21.40 23.96 24.30 0.66 -7.6092 86.65483 -53.75720 - 1.0647 1.0647 1 1 20.05 22.97 24.53 0.94 -31.4893 86.65162 -53.75729 - - - 0 1 21.10 23.53 24.08 0.43 10.2194 86.65746 -53.75743 - - - 0 0 20.98 - 25.13 0.68 61.6395 86.62533 -53.75709 - - - 0 0 20.39 22.66 23.40 0.54 -87.9596 86.62700 -53.75754 - - - 0 0 22.09 23.72 23.47 0.69 0.0897 86.65275 -53.75734 - - - 0 1 21.65 24.17 25.24 0.86 -31.9498 86.65125 -53.75745 - - - 0 0 23.63 26.75 27.06 0.41 30.1599 86.64542 -53.75729 - - - 0 0 22.14 24.74 24.75 0.67 24.64100 86.65067 -53.75723 - - - 0 0 22.60 - 26.18 0.61 13.73101 86.64158 -53.75720 - - - 0 0 21.52 24.88 25.42 0.81 -72.49102 86.63850 -53.75676 - - - 0 0 21.09 23.09 - 0.43 44.05103 86.63679 -53.75676 1.0783 - - 1 1 20.56 23.34 23.66 0.84 43.05104 86.62417 -53.75684 - - - 0 1 22.02 24.29 24.27 0.94 46.87105 86.65300 -53.75679 - - - 0 0 22.05 - - 0.57 59.04106 86.65150 -53.75604 0.0000 - - 0 0 20.61 22.21 23.31 0.13 40.47107 86.64717 -53.75568 - - - 0 1 20.41 22.92 23.66 0.44 34.16108 86.63804 -53.75543 0.0000 - - 0 0 18.24 19.87 20.59 0.61 19.57109 86.64625 -53.75573 - - - 0 0 22.72 24.78 25.23 0.58 13.47110 86.62558 -53.75568 - - - 0 1 21.21 23.66 22.57 0.66 20.81111 86.65850 -53.75559 - - - 1 1 22.26 24.35 24.88 0.66 -70.51112 86.65750 -53.75556 - - - 0 0 22.05 26.16 35.59 0.69 35.61113 86.64729 -53.75515 0.0000 - - 0 0 21.54 22.59 - 0.13 35.15114 86.63567 -53.75509 - - - 0 0 23.12 - 24.10 0.81 19.55115 86.64733 -53.75340 0.0000 - - 0 0 16.45 19.52 20.64 0.87 21.88116 86.65275 -53.75434 - - - 0 1 21.33 24.15 25.15 0.39 81.14117 86.65058 -53.75426 - - - 1 1 21.84 24.35 25.43 0.83 33.76Continued on next page c (cid:13) , ?? –– ?? S. Sweet et al.
Table 3: Source identifications in the field of SPT-CL J0546 − z GMOS z B10 z R14 spec phot m K s m F814 W m F606 W (b/a) (PA)[deg] [deg] [AB mag] [AB mag] [AB mag] [deg](1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)118 86.64479 -53.75404 - - - 0 0 22.35 - 25.51 0.43 75.26119 86.62475 -53.75384 0.0000 - - 0 0 21.34 22.39 22.52 0.27 -28.27120 86.63892 -53.75379 - - - 0 1 23.10 24.83 25.19 0.79 40.62121 86.65237 -53.75315 - - - 0 1 21.28 23.78 25.40 0.40 54.29122 86.65162 -53.75268 - - - 0 0 20.43 24.21 23.75 0.27 67.01123 86.64612 -53.75168 - - - 0 0 21.01 24.04 25.03 0.51 -26.23124 86.64087 -53.75168 - - - 0 0 21.03 - 22.88 0.47 -85.32125 86.62729 -53.75156 - - - 0 1 21.79 23.87 24.54 0.67 -12.88126 86.64612 -53.75059 - 1.0676 1.0676 1 1 19.60 22.75 24.04 0.70 20.71127 86.64408 -53.74954 - - - 0 0 21.95 25.46 25.20 0.64 20.03128 86.65237 -53.74687 0.0000 - - 0 0 19.70 21.06 22.90 0.70 30.80129 86.65250 -53.74687 0.0000 - - 0 0 19.93 21.30 22.51 0.49 10.16Columns: (1) Source ID; (2) right ascension; (3) declination; (4) redshift from GMOS spectroscopy (this work); (5) redshiftfrom Brodwin et al. 2010; (6) redshift from Ruel et al. 2014; (7) 1 denotes spectroscopically-confirmed cluster member; (8)1 denotes photometrically-classified cluster member; (9) K s -band apparent magnitude; (10) F814W apparent magnitude;(11) F606W apparent magnitude; (12) K s -band ratio of semi-major to semi-minor axis; (13) K s -band position angle. Notes:Sources 69 & 72 and 85 & 89 are blended in our GMOS spectroscopy; see text for details. c (cid:13) , ?? – ?? tellar mass - size relation at z=1 with GeMS/GSAOI astrometry REFERENCES
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APPENDIX A: DISTORTIONCORRECTION ∼ pdraper/gaia/gaia.htmland THELI (Erben et al. 2005; Schirmer 2013) fromhttps://astro.uni-bonn.de/ ∼ theli/.(i) Observe a set of high signal-to-noise pointings of a starfield, for which an excellent astrometry catalogue is avail-able. We suggest the LMC or NGC288 depending on whichis observable during your run. Use the same photometricband, position angle and similar airmass as science image,with similar guide star locations and relative magnitudes asfar as possible. Resolution of the catalogue should be simi-lar to observations, and magnitude range overlapping so thatsufficient ( > tens of) stars are available per CCD. Formatconversion can be done with THELI if necessary.(ii) Calculate coarse correction to astrometric field head-ers using GAIA. This allows interactive input to the grossdistortion calculation, and is particularly necessary whenthe image headers are significantly translated with respectto the true right ascension and declination.(iii) Use the GAIA correction (header keywords CRVALi,CRPIXi, CDi j) to make an input .ahead file for SCAMP.(iv) Calculate fine correction using SCAMP.(v) Apply SCAMP correction (except CRVAL) usingSWarp. SWarp must be run on each frame separately, asthe telescope pointing information is not sufficient.(vi) Coadd science frames based on the relative locationof a bright star in the image. c (cid:13) , ?? – ?? tellar mass - size relation at z=1 with GeMS/GSAOI astrometry APPENDIX B: SKY SUBTRACTIONRESIDUAL CORRECTION
When observing faint sources it is often desirable to use off-set object frames as sky frames, in order to maximise the to-tal time on source. However, faint sources are not detectedin individual images so are not masked out from the off-set frames, leading to residuals after sky subtraction. Herewe outline our method for creating improved masks. Thisis particularly beneficial for observing with a semi-regulardither pattern, which may be desirable for extended sourcesor ensuring adequate coverage of the chip gaps.(i) Calculate the inverse correction on the astrometricfield for each CCD, firstly with GAIA to make a coarse cor-rection, then with SCAMP to calculate the fine correction.(ii) Rotate the final stacked image and flip to the observedN is up, E is right reference frame. SCAMP and SWarp knowabout the true WCS, so cannot deal with this in the inversecorrection.(iii) Offset the stacked image by recalculating the refer-ence pixels (CRPIXi) for each CCD in each observed image.(iv) Apply the inverse correction with SWarp.(v) Cut out the region of the corrected image thatmatches the each observed CCD region.(vi) Create a mask for each cutout.(vii) Combine the masks with the data quality (DQ) ex-tensions of the observed images, and proceed to the GeminiIRAF sky creation routine gasky.
APPENDIX C: PSFCHARACTERISATION
Conventional AO imaging, which uses a single natural orlaser guide star, results in a PSF that is composed of adiffraction-limited core profile plus a seeing-limited (typi-cally Gaussian) uncorrected halo term, with minor smooth-ing due to tip-tilt jitter. The relative contribution of eachterm to the composite observed PSF is characterised by theStrehl ratio achieved during observation.The nature of the MCAO imaging data presented in thiswork results in a PSF that is complex and varying. First,the laser asterism allows estimation of the high-order wave-front aberrations across GeMS, with the degree of correctiondegrading away from the field centre as error terms in the at-mospheric reconstruction model grow. Next, due to the pas-sage of the lasers’ light up through the atmosphere prior togeneration of the laser asterism in the sodium layer, naturalguide stars are required to make the low-order (e.g., tip-tilt)correction. GeMS is equipped with three natural guide starprobes, designed to observe a widely-separated three-star as-terism spanning the GSAOI field. When three stars are notavailable, MCAO observations are still possible using twostars or even a single natural guide star, with the caveat thatthe quality of AO correction degrades with angular distancefrom the region nearest the star/s as the unprobed isokinetic error grows (Rigaut et al. 2010). Finally, an additional modi-fication to the classic narrow-field AO core+halo PSF modelis also appropriate due to the long composite exposure forour wide-field image. The total exposure time for our finalstacked image is 4 hours 42 min, spread over three nights ofobservation at a range of airmasses and with variable natu-ral seeing and laser guide star return power. The effect of thevariable conditions over this extended observation period isto somewhat blur the diffraction-limited image core. The re-sulting PSF is illustrated in Figure C1. It is clear that thetraditional AO profile does not fit the MCAO observationswell.The corollary of these observational necessities is that thePSF unavoidably varies across the GSAOI field of view. Fordense star fields this poses little problem, since a high stardensity allows for excellent PSF modelling as a function ofimage location. For an extragalactic survey field (locatedat high Galactic latitude, with consequently few stars) itis much more challenging to quantify the variation in thePSF. For instance, we detect only eleven unsaturated starsin our imaging (including a close visual binary pair withseparation of order the PSF). These were detected using aby-eye classification: eight brighter stars ( m F W <
22 ABmag) have obvious diffraction spikes in the HST imaging,and a further three rather faint stars ( m F W ∼ . HST
PSFs. However, such an endeavour is not possible withoutaccess to sufficient reference data .We chose the pragmatic compromise of fitting a low orderparametric model to the eight brighter unsaturated starsin the GSAOI field. The stellar images are shown in theleft-hand column of Figure C2. Visual inspection indicatesthat a 2D PSF model of moderate ellipticity is required tofit these, with rotation of the major axis across the field.We show the residuals of a 2D elliptical Gaussian profile inthe centre column of Figure C2. Unsurprisingly, the Gaus-sian profile is inadequate as it has insufficient independentcomponents to trace the complex modified MCAO profile A basic Fourier analysis of the imaging indicates that the resid-ual wavefront error varies coherently, with the principal variationacross the field being a trefoil aberration. However, due to thelimited number of stars in the cluster field, and the associatedsignal-to-noise ratio of each star such an analysis was deemed un-likely to deliver significant improvement over the model adoptedin this work.c (cid:13) , ?? ––
PSFs. However, such an endeavour is not possible withoutaccess to sufficient reference data .We chose the pragmatic compromise of fitting a low orderparametric model to the eight brighter unsaturated starsin the GSAOI field. The stellar images are shown in theleft-hand column of Figure C2. Visual inspection indicatesthat a 2D PSF model of moderate ellipticity is required tofit these, with rotation of the major axis across the field.We show the residuals of a 2D elliptical Gaussian profile inthe centre column of Figure C2. Unsurprisingly, the Gaus-sian profile is inadequate as it has insufficient independentcomponents to trace the complex modified MCAO profile A basic Fourier analysis of the imaging indicates that the resid-ual wavefront error varies coherently, with the principal variationacross the field being a trefoil aberration. However, due to thelimited number of stars in the cluster field, and the associatedsignal-to-noise ratio of each star such an analysis was deemed un-likely to deliver significant improvement over the model adoptedin this work.c (cid:13) , ?? –– ?? S. Sweet et al. I n t en s i t y datacore+haloGaussianMoffat0.00 0.05 0.10 0.15 0.20 0.25 0.300.00 0.05 0.10 0.15 0.20 0.25 0.30Radius [arcsec]−0.050.000.05 R e s i dua l Figure C1.
Top:
1D star profile, fit with Airy core + Gaussianhalo (magenta, dash-dot line), Gaussian (blue, dotted line) andMoffat (red, dashed line) profiles. Discontinuities in the data andfits are illustrative of the pixel sampling.
Bottom:
Residual profile.The observed profile is not well fit by the traditional AO-style core+ halo shape, for the reasons explained in the text; the Moffatprofile best represents the data. described above. Ultimately, we adopt a 2D Moffat (1969)profile as the simplest profile model capable of adequatelyrepresenting the stellar PSF structure without introducingsignificant instability to the fitting procedure. Fitting resid-uals for the identified stars with the Moffat PSF are shownin the right-hand column of Figure C2. These are foundto be at a level of ∼
10% of the stellar profiles. Neverthe-less, in Figure C3 we demonstrate that effective radii mea-sured with a modelled Moffat profile PSF are essentially thesame as those measured with an empirical stellar PSF. Weillustrate the variation in PSF parameters across the fieldin Figure C4. This variation motivates us to construct amodel PSF at the location of every source to be measured,rather than using an empirical profile measured from oneor more of the stars within the field. The spatial variationis modelled by interpolating the best-fitting Moffat profilemodel parameters for each known star using an inverse dis-tance interpolation. Note that this choice of a Moffat pro-file for the PSF is vindicated by Neichel et al. (2014b), whofound that the best functional form fitting the GeMS PSF is(1+ αr . ) − , which is close to a Moffat profile with β = 1 . Normalised intensity Gaussian residual Moffat residual
Figure C2.
Profile fitting to known stars in the final GSAOI im-age, one star per row. Columns (left to right) show observed star,and Gaussian and Moffat residuals. Stars are normalised to thesame intensity. The red scale bar is one arcsecond in length. Thestar in the bottom row is a binary, fitted by two function profileswith identical parameters except for amplitude and position.c (cid:13) , ?? – ?? tellar mass - size relation at z=1 with GeMS/GSAOI astrometry −1.0 −0.5 0.0 0.5 1.0 1.5−1.0−0.50.00.51.01.5−1.0 −0.5 0.0 0.5 1.0 1.5log(r e [kpc]) (Moffat PSF)−1.0−0.50.00.51.01.5 l og (r e [ k p c ] ) ( s t e ll a r PS F ) Figure C3.
Cluster member galaxy effective radii measured withtwo different PSFs: the x axis is constructed from an interpolatedMoffat profile as used in this work; the y axis an empirical PSFof the nearest star to each galaxy. The dashed line shows the 1:1relation, while the dotted line is the best fitting line. a r cs e c ond s a l ong a x i s Figure C4.
Variation of PSF FWHM and ellipticity across finalstacked image, after discarding frames with mean FWHM > (cid:13) , ?? ––