Late-stage galaxy mergers in COSMOS to z~1
C. N. Lackner, J. D. Silverman, M. Salvato, P. Kampczyk, J. S. Kartaltepe, D. Sanders, P. Capak, F. Civano, O. Ilbert, K. Jahnke, A. M. Koekemoer, N. Lee, O. Le Fevre, C. T. Liu, N. Scoville, K. Sheth, S. Toft
aa r X i v : . [ a s t r o - ph . GA ] J un Draft version September 25, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
LATE-STAGE GALAXY MERGERS IN COSMOS TO Z ∼ C. N. Lackner , J. D. Silverman , M. Salvato , P. Kampczyk , J. S. Kartaltepe , D. Sanders , P. Capak ,F. Civano , O. Ilbert , K. Jahnke , A. M. Koekemoer , N. Lee , O. Le F`evre , C. T. Liu , N. Scoville ,K. Sheth , and S. Toft Draft version September 25, 2018
ABSTRACTThe role of major mergers in galaxy and black hole formation is not well constrained. To help addressthis, we develop an automated method to identify late-stage galaxy mergers before coalescence of thegalactic cores. The resulting sample of mergers is distinct from those obtained using pair-finding andmorphological indicators. Our method relies on median-filtering of high-resolution images in orderto distinguish two concentrated galaxy nuclei at small separations. This method does not rely onlow surface brightness features to identify mergers, and is therefore reliable to high redshift. Usingmock images, we derive statistical contamination and incompleteness corrections for the fraction oflate-stage mergers. The mock images show that our method returns an uncontaminated ( < . z ∼
1. We apply ournew method to a magnitude-limited ( m F W <
23) sample of 44164 galaxies from the COSMOS
HST /ACS catalog. Using a mass-complete sample with log M ∗ /M ⊙ > . . < z ≤ . ∼
5% of systems are late-stage mergers. Correcting for incompleteness and contamination,the fractional merger rate increases strongly with redshift as ℜ merge ∝ (1 + z ) . ± . , in agreementwith earlier studies and with dark matter halo merger rates. Separating the sample into star-formingand quiescent galaxies shows that the merger rate for star-forming galaxies increases strongly redshift,(1+ z ) . ± . , while the merger rate for quiescent galaxies is consistent with no evolution, (1+ z ) . ± . .The merger rate also becomes steeper with decreasing stellar mass. Limiting our sample to galaxieswith spectroscopic redshifts from zCOSMOS, we find that the star formation rates and X-ray selectedAGN activity in likely late-stage mergers are enhanced by factors of ∼ ±
5% of star formation and20 ±
8% of AGN activity is triggered by close encounters ( <
143 kpc) or mergers, once more suggestingthat major mergers are not the only channels for star formation and black hole growth.
Subject headings: galaxies: active – galaxies: formation – galaxies: interactions – techniques: imageprocessing INTRODUCTION
In a hierarchical universe, galaxies grow by accre-tion of gas and mergers. Dark matter simulationssuggest that the halo merger rate (in units per Gyr) [email protected] Kavli IPMU (WPI), The University of Tokyo, Kashiwa,Chiba 277-8583, Japan Max-Planck-Institut f¨ur extraterrestrische Physik, D-84571Garching, Germany Institute of Astronomy, Department of Physics, ETH Z¨urich,CH-8093 Z¨urich, Switzerland National Optical Astronomy Observatory, Tucson, AZ85719, USA Institute for Astronomy, University of Hawaii, Honolulu, HI96822 California Institute of Technology, Pasadena, CA 91125 Harvard-Smithsonian Center for Astrophysics, Cambridge,MA 02138 Department of Physics and Astronomy, Dartmouth College,Hanover, NH 03755 Aix Marseille Universit´e, CNRS, LAM (Laboratoire dAstro-physique de Marseille), 13388, Marseille, France Max-Planck-Institut f¨ur Astronomie, D-69117 Heidelberg,Germany Space Telescope Science Institute, Baltimore, MD 21218 Astrophysical Observatory, CUNY, College of Staten Is-land, NY 10314 USA National Radio Astronomy Observatory/NAASC, Char-lottesville, VA 22903 Dark Cosmology Centre, Niels Bohr Institute, University ofCopenhagen, Copenhagen, DK-2100 Denmark increases with redshift as (1 + z ) − (Lacey & Cole1993; Fakhouri et al. 2010). However, identifyingmerging galaxies and transforming those observationsinto a galaxy merger rate is not easy, as is evidencedby the large differences between different methods(see Patton & Atfield 2008; De Propris et al. 2007;Bell et al. 2006; Jogee et al. 2009; Lotz et al. 2011, andreferences therein). Many of the differences in mergerrates are due to differences in sample selection andmerger identification (see Lotz et al. 2011). Nonetheless,a precise determination of the merger rate of galaxiesis essential to the study of galaxy growth. In par-ticular, the galaxy merger rate is needed to comparethe growth of galaxies to the growth of dark matterhalos. Galaxy mergers may also play an important rolein shaping galaxy morphology (Toomre & Toomre1972; Sanders et al. 1988; Barnes & Hernquist1992; Hopkins et al. 2009), instigating star forma-tion (Mihos et al. 1992; Sanders & Mirabel 1996;Barton et al. 2000; Lambas et al. 2003; Ellison et al.2008; Patton et al. 2013), and inducing super-massiveblack hole growth (e.g., Hernquist 1989; Moore et al.1996; Hopkins et al. 2008; Di Matteo et al. 2008).There are two general classes of methods for findinggalaxy mergers. The first class of methods selects closepairs of galaxies, before the galaxies have merged (e.g.,L´opez-Sanjuan et al. 2013, 2011, 2012; Bundy et al. Lackner et al.2009; Lin et al. 2004, 2010; Patton & Atfield2008; Kartaltepe et al. 2007; de Ravel et al. 2009;Bell et al. 2006; Masjedi et al. 2008; Ellison et al. 2008;Williams et al. 2011; Robaina et al. 2010; Newman et al.2012; Ellison et al. 2013; Tasca et al. 2014). These meth-ods typically select galaxies with projected separationsless than 100 h − kpc. The line-of-sight separationdepends on the method used. Galaxy mergers selectedusing photometric redshifts include pairs that arewidely separated along the line-of-sight and will nevermerge (e.g., Kartaltepe et al. 2007; Bundy et al. 2009;L´opez-Sanjuan et al. 2011, 2012). Although these meth-ods cannot identify individual chance superpositions,superpositions can be easily accounted for statisti-cally in merger-rate calculations (e.g. Bundy et al.2009; L´opez-Sanjuan et al. 2011, 2012). In order tobetter distinguish chance superpositions from actualmergers, several studies utilize spectroscopic red-shifts and identify kinematic pairs of galaxies (e.g.,Lin et al. 2004; Patton & Atfield 2008; de Ravel et al.2009; de Ravel et al. 2011; Kampczyk et al. 2013;Ellison et al. 2013; L´opez-Sanjuan et al. 2013). Forspectroscopic samples, understanding the completenessof the spectroscopy as a function of galaxy separation isessential (Kampczyk et al. 2013; Patton & Atfield 2008;Lin et al. 2004). Although kinematic pairs eliminatemany chance superpositions from a sample of galaxymergers, spectroscopic samples contain far fewer galaxiesthan photometric samples and often miss close pairsdue to fiber collisions, leading to poorer statistics whenmeasuring galaxy merger rates.The second class of methods for finding galaxy mergerslooks for morphological signatures during or after amerger (e.g., double nuclei, tidal tails, outer shells). Mor-phological searches either involve visual inspection (e.g.,Kartaltepe et al. 2014, 2010; Kampczyk et al. 2007;Jogee et al. 2009; Bridge et al. 2010; Cisternas et al.2011), or quantitative, non-parametric measuresof galaxy morphology (e.g., Lotz et al. 2008a;Conselice et al. 2009; Scarlata et al. 2007; Shi et al.2009; De Propris et al. 2007; L´opez-Sanjuan et al.2009). Visual inspection involves searches for mergersignatures, some obvious, such as double nuclei,and some subtle, such as sharp breaks in the radiallight profile. Measurements, such as the the centralconcentration, asymmetry, and clumpiness (CAS)(Abraham et al. 1994; Conselice 2003), the secondmoment of the light profile ( M ) (Lotz et al. 2004), andthe Gini coefficient of the 2-dimensional flux distribution(Abraham et al. 2003; Lotz et al. 2004), seek to quantifythe morphological signatures of bulges, disks, and galaxymergers. By comparing visual classification with thesequantitative measures, Lotz et al. (2004) demonstratethat major mergers occupy a distinct part of the Gini- M -concentration-asymmetry space. However, neithervisual classification nor non-parametric morphologymethods directly measure the merger mass ratio and donot distinguish between major and minor mergers. Infact, morphology-based methods are sensitive to veryminor mergers and even close passages which causemorphological disturbances without leading to a merger(see Lotz et al. 2011).Both pair-finding methods and morphology-based methods are used to measure the galaxy merger frac-tion and its evolution. The methods are applied to manydata sets with various selection functions. The result-ing fractions of merging galaxies at z ∼ . −
20% and the evolution of the merger rate is eithervery steep, (1 + z ) , or non-existent, (1 + z ) . Severalworks address these differences (e.g., Patton & Atfield2008; Jogee et al. 2009; Lotz et al. 2011). Some of thedifferences may be due to the parent sample selectionwith redshift; samples selected at fixed number den-sity show a different merger rate evolution than thoseselected at fixed stellar mass (Lotz et al. 2011). Addi-tionally, the length of time each method is sensitive toa galaxy merger is highly uncertain and varies greatlyas a function of merger-finding method and as a func-tion of redshift and merger mass ratio. Both photo-metric pair-finding methods and morphological methodsmis-identify galaxy mergers and often select chance su-perpositions of galaxies that are widely separated alongthe line of sight. Spectroscopic pair studies greatly limitthe number of line-of-sight pairs, however. Morphology-based methods often select galaxies in which close pas-sages or very minor mergers caused dramatic morpholog-ical disturbances. While most studies correct for thesemis-identifications, the correction factor is difficult to ac-curately calculate. The typical assumed fraction of mis-identified mergers ranges from 0 to 60% (see Lotz et al.2011, and references therein).In this work, we present a new quantitative method foridentifying merging galaxies. Our method is in essencea high-pass filter which makes multiple peaks in galaxysurface brightness profiles easily distinguishable. Themethod is designed to select a sample of late-stage merg-ers in which two galaxy nuclei are still intact and onlyseparated by a few kpc. In particular, we select galaxieswhose nuclei are separated by 2 . − M , asymmetry) and our sample of late-stage mergers.This is likely due to the fact galaxies with two very close,equally-bright central peaks will not have abnormallylarge asymmetry or second moment measurements.In addition to the number of merging galaxies, theproperties of merging galaxies are also of much inter-est. Numerical simulations of merging galaxies demon-strate that major mergers can drive gas toward the cen-ter of galaxies leading to enhanced star formation, ef-ficient bulge creation, and AGN activity as some ofthe gas is deposited on the central black hole (e.g.,alaxy Mergers in COSMOS 3Hernquist 1989; Mihos et al. 1992; Barnes & Hernquist1992; Hopkins et al. 2008, 2006). Several observationalstudies have shown that merging galaxies typically haveenhanced star formation (e.g., Kartaltepe et al. 2012;Robaina et al. 2009; Xu et al. 2012; Kampczyk et al.2013; Hung et al. 2013). Indeed, almost all intenselystar-forming systems, such as luminous infrared galax-ies (LIRGS), in the local universe have morpholo-gies consistent with major mergers (Sanders & Mirabel1996; Wu et al. 1998; Cui et al. 2001; Kartaltepe et al.2010). Similarly, several studies between z ∼ z ∼ . HST images, Cisternas et al. (2011) find thatX-ray selected AGN are no more likely to be ongoingor recent major mergers than a control sample of inac-tive galaxies. Silverman et al. (2011) examine close kine-matic pairs with separations less than 75kpc and findthat 18% of X-ray selected AGN activity since z ∼ Hub-ble Space Telescope ( HST ) images taken as a part of theCOSMOS survey (Scoville et al. 2007; Koekemoer et al.2007). The galaxies are selected from the ACS galaxycatalog (Leauthaud et al. 2007). Photometric redshifts,stellar masses, and absolute magnitudes are taken fromthe most recent near infrared-selected COSMOS cata-log (Ilbert et al. 2013; McCracken et al. 2012). The dataand merger-finding method are described in detail in § §
3. The sample of 2047 late-stage mergers is pre-sented in Table 2. Thirty-two of these late-stage mergersare also detected in X-ray by either
Chandra or XMM .We test the robustness of our method using simu-lated images of mergers in § . ≤ z < . § H = 70 km s − Mpc − , Ω m = 0 .
25, Ω Λ = 0 .
75. Whenreferring to other studies, we use units of h − kpc where H = 100 km s − Mpc − . As in Ilbert et al. (2013),magnitudes are given on the AB system (Oke 1974) andstellar masses in units of M ⊙ with a Chabrier (2003) IMF. DATA
Finding late-stage galaxies mergers with two intact nu-clei out to z ∼ HST /ACS F814W ( I − band) images taken as part of theCOSMOS project (Koekemoer et al. 2007; Massey et al.2010). The pixel scale in these images in 0 . ′′ /pixel andthe point spread function has a FWHM of ∼ .
09 pixels,which corresponds to 0 . z = 1. Althoughour merger-finding method could be applied to ground-based data, it requires that stellar concentrations sepa-rated by a few kpc are resolved. In Sloan Digital SkySurvey (SDSS) images, the median seeing in 1 . ′′ , whichcorresponds to 2 . z = 0 .
1. Therefore, our methodcould only be applied to SDSS data at z < .
1. Forground-based data with better seeing, the redshift limitcould be increased to z ∼ .
3. However, in order to studythe evolution of the merger rate at significant redshift,
HST data is necessary.For each galaxy in the parent sample, we create an 8 ′′ × ′′ cutout from the ACS F814W image. These cutoutsare used for detection of late-stage mergers. For this workwe use two, overlapping samples of galaxies, both se-lected from the COSMOS ACS catalog (Leauthaud et al.2007). The first sample uses photometric redshifts andcontains ∼ ,
000 galaxies. The second sample includes ∼ ,
000 galaxies and uses spectroscopic redshifts fromthe zCOSMOS project (Lilly et al. 2007, 2009). Becauseof its greater size, we use the photometric sample tostudy the merger rate as a function of redshift. We usethe spectroscopic sample to study the star formation andAGN activity in late-stage mergers.
Photometric Redshift Sample
Our parent galaxy sample is selected from the COS-MOS ACS catalog (Leauthaud et al. 2007). We selectall objects classified as galaxies (
MU_CLASS = 1) with to-tal magnitudes brighter than I = 23. In the case of amerger, the total magnitude of the post-merger galaxywill be brighter than I = 23, while the individual com-ponents of the merging galaxy may be up to 5 timesfainter ( I ≈ . § K -bandselected sample of COSMOS galaxies with photomet-ric redshifts (McCracken et al. 2012; Ilbert et al. 2013).This catalog includes photometric redshifts and stellarmasses for 90% of the galaxies in our ACS-selected sam-ple. The missing galaxies are due to slight differences inthe area and the masking between the ACS and K − bandcatalogs. We exclude all galaxies masked in Ilbert et al.(2013), as these galaxies do not have reliable photomet-ric redshifts or stellar masses. Ilbert et al. (2013) reporta photometric redshift precision of σ ∆ z/ (1+ z ) = 0 .
008 for i + < .
5. The final sample contains 44164 galaxies. Lackner et al.In § XMM (Brusa et al. 2010) and
Chan-dra (Civano et al. 2012) detections. Depending on thetype of AGN, these photo-zs are computed using dif-ferent galaxy-AGN hybrid templates, different luminos-ity priors, and accounting for source variability. Notethat the
Chandra survey only covers ∼ / XMM counterpart, and 573 have a
Chandra counter-part, with 282 sources detected by both instruments.For X-ray sources, the photo-zs have a precision of σ ∆ z/ (1+ z ) = 0 .
015 (Salvato et al. 2011). For the sourcesidentified in
XMM , we use stellar masses computed byBongiorno et al. (2012). These masses and photo-zs aremost reliable for galaxies that are not AGN/quasar dom-inated (type I). For the analysis of the AGN fraction, wewill restrict our galaxy sample to systems that are notAGN-dominated, based on the photo-z templates used.This will eliminate galaxies with the least certain photo-zs and stellar masses.When matching the ACS catalog with the ground-based K -band selected catalog, 1% of sources (640sources) that are resolved into 2 galaxies in the HST data are not resolved in the ground-based data. Clearly,these galaxies are possible late-stage mergers with smallseparations, and, therefore, cannot simply be removedfrom the sample. For these cases, we ensure that thegalaxy is only included in the sample once, and we usethe sum of the I -band magnitudes for the total mag-nitude. Because our sample is selected from the ACScatalog, we may be missing resolved late-stage mergersin which both of the components are below the I − bandmagnitude limit. However, resolved galaxy pairs makeup less than 10% of our final late-stage merger sample,as most of the resolved pairs are more widely separatedthan the late-stage mergers selected below. From visualinspection, ∼
70% of these resolved galaxy pairs showclear signs of interaction, while the remaining pairs maybe chance superpositions. This fraction of chance super-positions agrees well with that obtained by other meth-ods (see § z ∼ .
7, suggesting that visualinspection cannot reliably distinguish real mergers fromchance superpositions. Because we use visual inspectionto ascertain the number of chance superpositions, we mayunderestimate the fraction of chance superpositions byalmost a factor of two.For chance superpositions in which two galaxies atdifferent redshifts are unresolved by ground-based ob-servations, the photometric redshifts are especially sus-pect (Bordoloi et al. 2010). Indeed, in comparing thephotometric redshifts to the available spectroscopic red-shifts (see § .
6% compared to1 .
0% for the entire sample of galaxies between 0 . 0. However, the catastrophic outlier rate forthe late stage merger candidates is still small, and the precision of the photometric redshifts remains unchanged( σ ∆ z/ (1+specz) = 0 . Spectroscopic redshift sample In § 5, we compare the AGN and star formation ratesin our sample of late-stage mergers to kinematically-selected pairs (Kampczyk et al. 2013; Silverman et al.2011) from the zCOSMOS survey (Lilly et al. 2007,2009). For the study of SFR ( § I < . ∼ § Chandra observations to identify AGN. Because the Chandra sur-vey (Elvis et al. 2009) only covers ∼ / Chandra footprint.Table 1 lists the various parent samples as well as thetheir properties. We have also included the cuts made tothese samples for the analysis in § § MERGING GALAXY SELECTION To separately detect each component in a merginggalaxy, we run the images through a high-pass filter,which makes multiple peaks in the flux distribution eas-ily distinguishable. Our procedure, illustrated in Figure1, is as follows: • We first convolve each postage stamp image witha median ring filter (Secker 1995). This smoothsthe image by replacing each pixel with the medianalaxy Mergers in COSMOS 5 Table 1 Parent sample propertiesParent sample m ( I ) limit z limits log M ∗ /M ⊙ limit N gal N merger pair sep. limits [kpc] sectionphoto-z < 23 – – 44164 2047 < § a photo-z < 23 – – 44164 1547 [2.2,8] § < 23 [0.25,1.0] > . § < . > . < § < . > . < § ba The full sample without any cuts in redshift, mass, or pair separation is very incomplete at high redshift. We do not use itfor any analysis. b The smaller spectroscopic sample overlaps with the Chandra survey (Elvis et al. 2009), which is used to select X-ray AGN. value in a ring surrounding that pixel, thus eras-ing structures on scales larger than the ring. Weset the inner ring radius to 9 pixels, which is ap-proximately 3 times the PSF width. This sets thesize of the smallest separation we can detect. At z ∼ . . . . 1) kpc.For comparison, in SDSS images at z ∼ . 1, a 9-pixel radius median ring filter could only detectpeaks separated by at least 6 kpc. In order to ap-ply this method to ground-based data, the size ofthe median ring filter (in pixels) would have to beadjusted for the seeing. • We then subtract the smoothed image from theoriginal image. Together, the first two steps cre-ate a high-pass filter. • In the difference image, we select all pixels 5 stan-dard deviations above the noise. Contiguous re-gions are considered a single peak. For a peakdetection to be significant, we require a region tocontain at least 8 pixels. These values ensure thatany detected peak is at least as large as the PSF.We demonstrate in § > z ∼ and to thegalaxy as a whole. We measure the flux in each compo-nent simply by summing the flux in the pixels associatedwith the peak. Because this only includes the flux in thecentral region of each merging component, this is an un-derestimate of the flux in each component of a merger.Based on merger selection in mock images (see § − 90% of the contamination from non-merging galax-ies and star-forming clumps, without greatly affectingthe completeness of our sample. In order to only studymajor mergers, we require that every detected peak is atleast 1 / ∼ ∼ 80% for mergersbetween bulge-dominated galaxies.Finally, there are some images that have more than 2detected peaks. We expect triple merging systems to beextremely rare, and visual inspection shows that mostimages with 3 or more peaks, after removing faint peaks,are edge-on disk galaxies, in which the bulge and the endsof the spiral arms or bar are detected. These galaxies canbe eliminated from the late-stage merger sample by re-quiring that multiple peaks do not lie along a single line,as is the case for edge-on galaxies. We implement thiscut by requiring that the absolute value of the Pearsoncorrelation coefficient for the peak centroids is less than0 . 5. After all the other cuts have been applied, this cuteliminates 7% of the detected late-stage mergers (145 of2047).With these restrictions, we find 2047 (1547 with sep-arations greater than 2 . Detected Peaks Figure 1. Demonstration of median filter and peak detection on an image of a merger. The (cyan) contours in the last panel outline thetwo detected peaks in the difference (original − median-filtered) image. The peaks are separated by 4.0 kpc and have a flux ratio of 1:1. Example Mergers Figure 2. Examples of merging galaxies in the photo-z sample after cuts in peak separation and peak flux. The × s show peaks found bythe median fing filter. The bottom center image may be an edge-on disk with asymmetric spiral arms instead of a merger. stage mergers in the zCOSMOS sample are also listedin Table 2. For each late-stage merger, we include theprojected separation between the two flux peaks as wellas the flux ratio of the peaks. In the photo-z sample,32 mergers are X-ray AGN detected in either Chandra or XMM . In the spectroscopic redshift sample, 10 late-stage mergers are matched with a Chandra source out of534 mergers that lie within the Chandra footprint.Although we are confident that the majority of late-stage mergers listed in Table 2 are physical late-stagemergers, not all the systems identified by our methodwill be real mergers. In addition to isolated galaxies withclumpy central structure, our sample contains line-of-sight superpositions. Below, we show these chance super-positions represent 30% of the late-stage merger sample. Without two spectroscopic redshifts for each member ofthe merger or detailed kinematic maps, it impossible todistinguish real late-stage mergers from widely-separatedchance superpositions or from isolated galaxies with com-plex structures. Indeed, by tuning the selection criteriato accept smaller peaks, our median-ring filter methodcould be used to find galaxies with several bright clumpsinstead of late-stage binary mergers.It is important to note that, other than the pair sepa-ration and flux ratio, all other measured properties (e.g.,color, redshift, stellar mass, X-ray flux) are properties ofthe merger, not the individual component galaxies. Ifwe divide galaxies by stellar mass, merging galaxies arecounted with galaxies more massive than either memberof the merger. In this way, late-stage mergers are treatedalaxy Mergers in COSMOS 7 Not selected as mergers Figure 3. Examples of galaxies with multiple peaks detected, but that are not considered mergers. The × s show peaks found by themedian ring filter. These galaxies are removed from the merger sample by the cuts explained in § 3. These galaxies fail because the detectedpeaks are too faint compared to the central peak (left), all but the central peak are too faint compared to the whole galaxy (middle), andthe two peaks have a projected separation larger than 8 kpc (right). more like post-merger galaxies than like pairs of galax-ies in the early stages of merging. This distinction isimportant to keep in mind when comparing to samplesof paired galaxies, in which properties for the individualgalaxies are reported.Figure 2 shows images of 6 late-stage mergers in thephoto-z sample. Although the galaxy in the lower middlepanel may be a spiral galaxy without any merging activ-ity, the remaining galaxies are clearly mergers at variousseparations. The typical peak separation is less than 1 ′′ ,demonstrating why our algorithm requires the high res-olution of space-based data. Figure 3 shows three exam-ples of galaxies which do not satisfy the cuts on peak fluxratio, peak separation, or peak Pearson correlation coeffi-cient. These galaxies are often spiral or barred galaxies.As noted above the median ring filter detects edge-ondisk galaxies, in which the bulge is bisected by dust inthe disk, as binaries mergers. However, these galaxiesrepresent a small contamination. At fixed star forma-tion rate, the fraction of late-stage mergers candidatesis independent of galaxy ellipticity (proxy for disk incli-nation), suggesting our detection algorithm is not biasedby galaxy inclination and dust obscuration. Simulated Merger Images We test our merger detection algorithm on a set of sim-ple mock images of merging galaxies. We create postagestamps of pairs of galaxies using the HST /ACS imagesfrom the photo-z sample. Each mock image contains 2random galaxies at the same photometric redshift. Wechoose galaxies at the same redshift in order to eliminateline-of-sight chance superpositions, which we address sta-tistically in § . 5, 1 . 5, 2 . 0, 2 . . 0, 5 . 0, 7 . 0, and 10 . § ∼ 10 pixels, or the sizeof the median ring filter (see Figure 18). This moti-vates using a lower bound of 2.2 kpc (9 pixels at z ∼ ∼ 40% of the mock mergers with separation larger than2.2 kpc to z = 1. This completeness depends stronglyon galaxy morphology. Because the median ring fil-ter smooths away diffuse structures, our merger-findingmethod is biased toward mergers between concentrated,early-type galaxies . For these mergers, our methodis 80% complete, while for mixed mergers (late+early)and mergers between late-type galaxies, the median ringfilter only selects 40% of mock mergers. After remov-ing contamination, the completeness of our selection ofearly-type mergers is independent of redshift. For late-type galaxies, the completeness drops slightly at higherredshifts (see Figure 17, right panel). For all morpholo-gies together, the completeness drops between z ≈ . z ≈ . 5, as the fraction of early-type galaxies alsodecreases toward higher redshift.In addition to using the mock mergers to study com-pleteness, we can use them to study the contaminationfrom non-merging, clumpy galaxies and minor mergers(see Figure 20). We find that, unlike the complete-ness, the contamination is essentially independent of red-shift. This may reflect the fact that our merger-findingmethod is less sensitive to all structures at lower signal-to-noise, and, therefore, higher redshift. Using artifi-cially redshifted mergers, Kampczyk et al. (2007) findthat mergers identified in low-z data will not appear asmergers at higher redshift due to lower resolution andsignal-to-noise, which may explain the incompleteness We use the ZEST parameter (Scarlata et al. 2007) to ascertainthe morphologies of the galaxies in a mock merger. See § Lackner et al. Table 2 Late-stage mergers in photo-z + spec-z samplesRA (J2000) a Dec (J2000) a photo-z b spec-z c m I d log M ∗ /M ⊙ e separation [ ′′ ] flux ratio Chand. log L X f XMM log L X f . . . 49 – 22 . 21 9.57 0 . 35 0 . 50 – –149 . . . 66 0.70 22 . 48 9.50 0 . 78 0 . 61 – –149 . . . 73 0.73 21 . 25 10.95 0 . 62 0 . 31 42.6 –150 . . . 11 – 22 . 76 10.80 0 . 31 0 . 88 43.8 43.9150 . . . 96 21 . 71 10.57 0 . 44 0 . 96 43.1 –150 . . . 37 – 22 . 71 8.81 0 . 36 0 . 34 – – Note . — Table 2 is published in its entirety in the electronic edition. A portion is shown here for guidance regarding its formand content. a From Ilbert et al. (2013). b From Ilbert et al. (2013), except for x-ray sources, which are from Salvato et al. (2011). c spectroscopic redshift from zCOSMOS (Lilly et al. 2007, 2009) d HST /ACS FW814 AB magnitude from Leauthaud et al. (2007). e Stellar masses for XMM sources from Bongiorno et al. (2012); for sources without a photo-z, from Bolzonella et al. (2010) andPozzetti et al. (2010); otherwise, from Ilbert et al. (2013). f log L X is the X-ray luminosity in the band 0 . − 10 keV in units of erg s − . XMM data from Brusa et al. (2010), Chandra datafrom Civano et al. (2012). of our merger selection at high redshift. However, un-like Kampczyk et al. (2007), our merger identificationdoes not take into account morphological k-corrections.Because galaxies are less smooth at bluer wavelengthsand have a larger fraction of their flux concentratedin smaller regions, our peak-finding method may detectmore non-merging, star forming galaxies at bluer restframe wavelengths, increasing the contamination. Evenif morphological k-corrections are taken into account,galaxies at high redshift are expected to be clumpier(e.g. Bournaud et al. 2007; Genzel et al. 2011) and havehigher star formation rates, thus again increasing thecontamination from non-merging, clumpy star-forminggalaxies. The lack of redshift dependence in the contam-ination suggests our method is not particularly sensitiveto clumpy star-formation at high redshift, possibly be-cause these clumps are too small and faint. A better un-derstanding of the effects of morphological k-correctionswill require further study using multi-wavelength data,in particular near-infrared data at z ∼ > > ∼ § Caveats Although our simulations demonstrate the effective-ness of our merger-finding, there are several failure modesof the algorithm. First, the method does not distin-guish between merging galaxies and chance superposi-tions. Since we are looking at extremely small separa-tions, we expect the number of chance superpositions tobe small. Although we correct the merger rates in § § Comparison with other selection techniques There are many established methods for selectingmerging galaxies. The simplest methods select galaxiesbased on angular separation (e.g., Carlberg et al. 1994;Zepf & Koo 1989). These methods typically look at sep-arations of 5 − h − kpc, and need to be correctedfor chance superpositions and galaxies that are physi-cally close, but will not merge within a Hubble time.alaxy Mergers in COSMOS 9The number of superpositions can be limited by re-quiring the galaxies have similar photometric redshifts(e.g., Kartaltepe et al. 2007; Bundy et al. 2009). Sim-ilarly, spectroscopic redshifts are also useful in elimi-nating chance superpositions (e.g., Patton et al. 2002;Patton & Atfield 2008; Kampczyk et al. 2013; Lin et al.2004, 2008; Le F`evre et al. 2000; de Ravel et al. 2009;de Ravel et al. 2011; Ellison et al. 2008). However, spec-troscopic samples are limited in size and depth. Fur-thermore, the late-stage mergers reported here typicallyhave sub-arcsecond separations. Systems with such smallseparations will not be resolved in ground-based spec-troscopic studies, even when including pairs that areobserved in the same slit (e.g. Kampczyk et al. 2013).Comparing our results to the spectroscopically-selectedpair sample in Kampczyk et al. (2013), we find only 20%of late-stage mergers are also considered kinematic pairsand most of these mergers have separations larger than2 ′′ .Pair samples look for galaxies in the early stages ofmerging. Morphological studies, on the other hand,look for evidence of mergers at all stages, including late-stage mergers and post-merger galaxies. Merger studiesbased on morphology rely on visual classification (e.g.,Kampczyk et al. 2007; Bridge et al. 2010; Darg et al.2010a; Kartaltepe et al. 2010), or quantitative morphol-ogy indicators. Indicators used to distinguish merg-ers include the Gini coefficient and the second mo-ment of the brightest pixels, M (e.g., Abraham et al.2003; Lotz et al. 2004, 2008a); the galaxy asymmetryand concentration (e.g., Conselice et al. 2009; Shi et al.2009; L´opez-Sanjuan et al. 2009); and combinations ofthe above as well as parametric fits to galaxy luminosityprofiles (e.g., Scarlata et al. 2007; Cassata et al. 2005).In particular, Scarlata et al. (2007) use principle com-ponent analysis to reduce the space spanned by Gini, M , concentration, asymmetry, clumpiness, and galaxyS´ersic index to three dimensions. Regions in this spaceare then assigned a ZEST (Zurich Estimator of Struc-tural Types) type. This estimator has been applied tothe COSMOS ACS images, making comparisons to ourlate-stage merger sample possible.Figures 4 and 5 show the ZEST classifications ofour sample. All morphological values are taken fromScarlata et al. (2007). As described in Scarlata et al.(2007), the ZEST types are computed based on ‘clean’ACS images, in which close companions, if found, aremasked. Therefore, we expect that for some mergers,one member of the pair will be masked, decreasing themeasured asymmetry and M . However, inspection ofthe COSMOS ‘clean’ images shows that the majority oflate stage mergers are considered a single system (seeCisternas et al. 2011). We limit the sample to galax-ies with stellar masses above 2 . × M ⊙ and I − bandmagnitudes brighter than 23 . 5. The mass-restricted par- The Gini coefficient measures relative distribution of fluxin pixels associated with a galaxy. It is given by G =1 / (cid:0) fn ( n + 1) (cid:1) Σ ni =1 Σ nj =1 | f i − f j | , where f i is the flux in a pixel, n is the number of pixels, and ¯ f is the mean flux per pixel(Abraham et al. 2003) M is the second moment of the flux around a galaxy’s center(Σ ni =1 f i ( x i + y i )), only counting the brightest pixels which total20% of the galaxy’s flux. This is then normalized by the galaxy’stotal second moment, summing over all pixels (Lotz et al. 2004). G i n i mergersZEST=1ZEST=2ZEST=3 G−M Mergers −3.0−2.5−2.0−1.5−1.0−0.50.0 M f r a c t i o n allmergers Figure 4. Top : Gini coefficient and M values for late-stagemergers (black points). The contours show the parent sample color-coded by ZEST galaxy type (Scarlata et al. 2007). The sample islimited to galaxies with stellar masses greater than 2 . × M ⊙ .ZEST=1,2,3 are ellipticals, spirals (with bulges), and irregulars,respectively. The inner(outer) contours contain 30%(80%) of thegalaxies of each ZEST type. The dashed magenta line is the crite-rion for merging galaxies from Lotz et al. (2004). Most late-stagemergers lie below this line and would not be detected using the G − M method. Bottom: Distribution of M for our sample ofmergers (solid lines) and the parent sample (dashed lines). Colorsindicate ZEST type as in the top panel. ent sample is shown by colored contours, while the late-stage mergers are denoted by black points. In these fig-ures, it is clear that most mergers are either ZEST type 2(bulge+disk galaxies) or ZEST type 3 (irregular). Out of212 late-stage mergers, 28, 112, and 72 are of types 1, 2,and 3, respectively. If the late-stage merger sample hadthe same distribution as the parent sample, the expectednumber of each type would be 50, 152, and 10. Thesedifferences in ZEST type distribution are shown in thehistograms in Figures 4 and 5.These histograms show the distributions of M andconcentration for late-stage mergers compared to normalgalaxies for each ZEST type. For late-stage mergers clas-sified as spirals, the distribution of M is shifted towardlarger values (blue lines), closer to the distribution forirregular galaxies (green line). This demonstrates that,while the ZEST categorization does not clearly separatelate-stage mergers from spiral galaxies, the morphologiesof late-stage mergers are measurably different from thoseof regular spiral galaxies. Nonetheless, most mergers areclassified as spirals, in agreement with Kampczyk et al.(2007). Furthermore, most irregular galaxies are notclassified as mergers by our method. This is to be ex-pected, since our merger selection only finds major merg-ers which still have two nuclei, ignoring other merger sig-natures.In Figure 4, the magenta dashed line shows the crite-rion for merging galaxies from Lotz et al. (2004). Thiscriterion is designed for observations in the rest frame0 Lackner et al. A s y mm e t r y mergersZEST=1ZEST=2ZEST=3 Concentration f r a c t i o n allmergers Figure 5. Top: Petrosian concentration and asymmetry (about180 ◦ rotation). Symbols and contours are as in Figure 4. Half ofthe late-stage mergers are of ZEST type 2 (spirals). A late-stagemerger is 7 times more likely to be an irregular galaxy (ZEST=3)than a galaxy from the parent sample. Bottom: Distributionof concentration for mergers (solid lines) and the parent sample(dashed lines). Colors indicate ZEST type as in the top panel. Onaverage, late-stage mergers of ZEST type 2 (blue lines) are lessconcentrated than typical ZEST=2 galaxies. B − band and is therefore appropriate for the portion ofour sample above z ≈ . 7. Objects above this line areconsidered mergers, However, only a small fraction oflate-stage mergers are also mergers based on the G- M criterion (see also Kartaltepe et al. 2010; Jogee et al.2009; Lotz et al. 2011). Similarly, in Figure 5, majormergers are expected to be highly asymmetric (asymme-try & . M , or asymmetry values.Some differences may be due to the fact that the Gini, M and asymmetry values reported by Cassata et al.(2005) are based on deblended images, which will splittwo concentrated nearby galaxies into separated sources.This will eliminate late-stage mergers from the G − M and asymmetry-selected samples. Furthermore, the highcentral concentrations of late-stage mergers selected herebiases the asymmetry upward, making it less likely theyare selected as mergers based on asymmetry. In lookingat mergers selected by Gini- M and asymmetry but not by our method, we find that the asymmetry and Gini- M methods are more sensitive to minor mergers andsmall perturbations in the galaxy flux distribution thanour methods. Together, these reasons help explain thepoor overlap between our sample of late-stage mergersand those derived using other morphology methods. MERGER RATES In section § l og M ∗ / M (cid:2) m(I F814W ) Figure 6. The mass completeness of our photometric sample( I < 23) as a function of I apparent magnitude in three red-shift bins. Quescient(star-forming) (see § z = 0 . 7, the sample is complete for both popu-lations. Beyond z = 0 . 7, the completeness drops to ∼ z = 0 . correcting for these effects, we can compute the majormerger rate as a function of redshift to z = 1. To calcu-late merger rates, we use the photo-z parent sample, witha few additional restrictions. We restrict our parent sam-ple to the approximately volume-limited sample between0 . ≤ z < . M ∗ / M ⊙ > . 6. The stellar masslimit is derived by comparing the completeness of our I − band selected catalog to that of the deeper K − bandselected catalog (Ilbert et al. 2013). Up to z = 1, 93%of the galaxies from the deeper K − band selected catalogare included in our sample. Figure 6 shows the measuredstellar masses as a function of apparent magnitude in 3redshift bins. While the sample is mass-complete for thelower redshift bins, the completeness drops to 82% for z > . 9. For the merger rate analysis, we also removeall sources with X-ray detections because the colors andphotometric redshifts for these sources are less certain.This eliminates 3% of the sample. The final sample forthe merger rate analysis contains 5894 galaxies, of which136 are late-stage mergers. Line-of-sight pairs correction Before computing the merger rate, we need to correctthe observed number of late-stage mergers for chance su-perpositions. For each galaxy in the sample, we computethe expected number of projected neighbors by summingthe average sky density of possible neighbors over thearea of the search annulus between 2 . / / . . 4. In other words,alaxy Mergers in COSMOS 1130% of the 136 late-stage mergers are likely to be chancesuperpositions. Because the angular diameter distance,and, therefore, the size of the annulus searched for closepairs, changes slowly with redshift beyond z ∼ . 5, thefraction of chance superpositions does not change signifi-cantly with increasing redshift. Therefore, we correct thefraction of late-stage mergers by a factor of C l . o . s . = 0 . C l . o . s . given above agrees well with thefraction of chance superpositions found by visually in-specting a fraction of the merger images in § C l . o . s . based on numerical simulations where C l . o . s . ≈ . − . C l . o . s . ∼ C l . o . s . re-mains highly uncertain and contributes significantly tothe uncertainty in the merger rates calculated below. Contamination and completeness Using the mock merger images from § ± ∼ 20% from minormergers and ∼ 10% from non-merging, clumpy galaxies.The contamination does not depend strongly on redshift,although it does depend on the flux ratio of the merger.For the merger rate calculation, we correct the numberof late-stage mergers for contamination by multiplyingby 0 . ± . ∼ 20% to ∼ 40% asa function of redshift. Based on the mock mergers, wecompute the completeness in the three redshift bins usedbelow. The correction factor for incompleteness is sim-ply the inverse of the completeness fraction. In additionto redshift, the completeness of our late-stage merger se-lection depends strongly on galaxy morphology. In § C l . o . s . ,the contamination (0 . ± . / completeness fraction. Together, we denote these cor-rections as C merge . The values of C merge are given inTable 3 along with the corrected merger fraction f merge .The errors on C merge are the bootstrap-derived errors onthe completeness and contamination fractions (see Ap-pendix A) and do not include the uncertainty in C l . o . s . .The redshift dependence of C merge is due entirely to theincompleteness correction. In § Evolution of the merger rate In order to calculate the merger rate, we simply countthe number of pairs in three redshift bins, chosen suchthat each redshift bin spans the same amount of time.Our results are unchanged if the bins are chosen suchthat they contain the same number of galaxies. The rawmerger fractions are corrected for chance superpositions,contamination, and incompleteness using the correctionfactor, C merge , given in Table 3. The corrected mergerfraction for our total sample is C merge × / . ± . C merge = 2 . ± . 1, and the com-pleteness fraction is 0 . ± . 01. This is comparable tothe typical pair fraction found in studies of more widelyseparated pairs (Lin et al. 2004; Kartaltepe et al. 2007;de Ravel et al. 2009; Bundy et al. 2009; Robaina et al.2010). and the fraction of morphologically disruptedsystems (De Propris et al. 2007; Conselice et al. 2009;Lotz et al. 2008a). As noted in § ℜ merge = f merge h T obs i , (1)where T obs is the duration of time a merger will beobservable. Because T obs is highly dependent on themerger/pair selection, using the correct value for T obs is essential when comparing merger rates based on dif-ferent techniques (see Lotz et al. 2011). For the late-stage mergers studied here, T obs is sensitive to many pa-rameters such as the galaxy masses, gas fractions, or-bital parameters, and observational angle. Many pairstudies use the dynamical friction timescale for T obs (Lin et al. 2004; Bell et al. 2006; Patton & Atfield 2008;Masjedi et al. 2008). Another way to determine T obs isusing hydrodynamical simulations of galaxy mergers anddirectly measuring how long close pairs or morpholog-ical signatures are observable (e.g., Patton et al. 2000;Conselice 2006; Kitzbichler & White 2008; Lotz et al.2008b, 2010a,b, 2011). For close pairs separated by5 − h − kpc, Lotz et al. (2011) find h T obs i ≈ . 33 Gyr,2 Lackner et al. Table 3 Pair fractions and merger rates z N gal N mgr C merge f merge ℜ [Gyr − ][0 . , . 45) 867 15 1 . ± . . ± . 5% 5 . ± . . , . 70) 1644 39 1 . ± . . ± . 8% 12 . ± . . , . 00) 3383 82 2 . ± . . ± . 8% 20 . ± . . < log M/ M ⊙ < . 9) sample[0 . , . 45) 399 9 1 . ± . . ± . 9% 7 . ± . . , . 70) 782 23 1 . ± . . ± . 2% 15 . ± . . , . 00) 1766 42 2 . ± . . ± . 1% 19 . ± . M/ M ⊙ ≥ . 9) sample[0 . , . 45) 468 6 1 . ± . . ± . 6% 4 . ± . . , . 70) 862 16 1 . ± . . ± . 9% 9 . ± . . , . 00) 1617 40 2 . ± . . ± . 1% 20 . ± . . , . 45) 413 8 1 . ± . . ± . 1% 8 . ± . . , . 70) 763 21 2 . ± . . ± . 4% 16 . ± . . , . 00) 1131 36 3 . ± . . ± . 0% 32 . ± . . , . 45) 454 7 0 . ± . . ± . 3% 2 . ± . . , . 70) 881 18 0 . ± . . ± . 3% 3 . ± . . , . 00) 2252 46 0 . ± . . ± . 2% 3 . ± . . < log M/ M ⊙ < . 9) sample[0 . , . 45) 225 4 1 . ± . . ± . 3% 7 . ± . . , . 70) 469 10 2 . ± . . ± . 5% 13 . ± . . , . 00) 660 22 3 . ± . . ± . 6% 33 . ± . . < log M/ M ⊙ < . 9) sample[0 . , . 45) 243 2 0 . ± . . ± . 3% 1 . ± . . , . 70) 393 6 0 . ± . . ± . 4% 2 . ± . . , . 00) 957 18 0 . ± . . ± . 3% 3 . ± . M/ M ⊙ ≥ . 9) sample[0 . , . 45) 188 4 1 . ± . . ± . 6% 9 . ± . . , . 70) 294 11 2 . ± . . ± . 5% 23 . ± . . , . 00) 471 14 3 . ± . . ± . 8% 30 . ± . M/ M ⊙ ≥ . 9) sample[0 . , . 45) 211 5 0 . ± . . ± . 6% 4 . ± . . , . 70) 488 12 0 . ± . . ± . 4% 4 . ± . . , . 00) 1295 28 0 . ± . . ± . 3% 4 . ± . Note . — The fraction of mergers is corrected by a factor of C merge for line-of-sight superpositions, contamination from mi-nor mergers/non-mergers, and incompleteness. The fractionalmerger rate is calculated using h T obs i = 0 . 33 (Lotz et al. 2011). and that h T obs i is essentially independent of galaxy gasfraction, and, therefore, redshift. Therefore, T obs only af-fects the normalization of the merger rate, not the slopeas a function of redshift. Below, we use the mergerobservation timescale computed by Lotz et al. (2011), h T obs i = 0 . 33 Gyr. This is roughly 2 × longer than the minimum expected T obs , namely the orbital timescale.For mergers with masses near the Milky Way mass, sep-arated by 8 kpc, the orbital timescale is ∼ . Gyr .Nonetheless, the value of T obs introduces significant un-certainty in the normalization of the merger rate. Using h T obs i = 0 . 33, the computed values for ℜ merge are re-ported in the last column in Table 3.Based on the corrected fraction of late-stage mergers, redshift ℜ m e r g e [ G y r − ] this workde Ravel 09Lopez-Sanjuan 09 Bundy 09Conselice 09 Figure 7. The fractional merger rate as a function of redshift de-rived from our sample of late-stage mergers (black, filled circles),compared to other stellar mass-selected studies of merging galax-ies. Bundy et al. (2009) and de Ravel et al. (2009) identify merg-ing galaxies as photometric pairs. L´opez-Sanjuan et al. (2009);Conselice et al. (2009) identify mergers based on galaxy asymme-try. All data is from Lotz et al. (2011) in which the timescales forobservation of mergers are calibrated to facilitate easy comparison.Our merger rates are corrected from line-of-sight superpositions,contamination and incompleteness. The error bars on our points(black) are the statistical error bars only, but include the uncer-tainties in the correction for contamination and incompleteness. we find ℜ merge ∝ (1 + z ) . ± . , consistent with, al-beit slightly steeper than, results of other studies thatfind significant evolution in the merger rate with red-shift (de Ravel et al. 2009; Lin et al. 2008; Robaina et al.2010, but see Bundy et al. 2009; Lotz et al. 2011). Themerger rate is also consistent with the expected mergerrate for dark matter halos, which grow as (1 + z ) − (e.g., Fakhouri et al. 2010, but see Berrier et al. 2006;Guo & White 2008). This suggests that, at late times,massive galaxy growth traces halo growth. Figure 7shows the fractional merger rate for late-stage mergerscompared to other merger rate studies, including stud-ies using close pairs (de Ravel et al. 2009; Bundy et al.2009) and galaxy asymmetry (L´opez-Sanjuan et al. 2009;Conselice et al. 2009). The values plotted are fromLotz et al. (2011) and take into account differences in T obs for different merger-finding methods.Because the measured merger rate evolution dependson galaxy selection (Lotz et al. 2011), we limit the com-parison to other mass-selected samples. All four studiesin Figure 7 use mass-selected samples, with mass limitsnear log M ∗ / M ⊙ & 10, lower than our mass limit. Addi-tionally, for the pair studies, the mass refers to the massof the individual merging galaxies, n ot the final mergedgalaxy, as is the case in our study. Therefore, care mustbe taken when comparing these results. Nonetheless, theagreement between the different methods suggests thatabove log M ∗ / M ⊙ ∼ 10, the merger rate does not dependstrongly on galaxy mass. However, the errors on ℜ merge are statistical errors only and do not include uncertain-ties in T obs . A smaller value for T obs will increase themeasured ℜ merge , and lessen the agreement between ourstudy and previous results.alaxy Mergers in COSMOS 13 M(r + )−M(J) M ( NUV ) − M ( r + ) Figure 8. Color-color diagram for selecting queiscent and star-forming galaxies. The cuts are from Ilbert et al. (2013, 2010).Queiscent galaxies are in the upper left. The data shown is in theredshift range 0 . < z < . > M ⊙ .The contours show the distribution of the full photo-z sample, withcontours at the 30 th , 50 th , and 90 th percentiles. The points showthe late-stage mergers. Mergers as a function of color and stellar mass Because our sample of late-stage mergers is relativelylarge, we can explore the evolution of the merger rateas a function of color and stellar mass. We divide theparent sample into two mass bins, choosing the medianstellar mass, log M/ M ⊙ = 10 . − r + and r + − J col-ors, where NUV corresponds to the GALEX filter at0 . µ m, and r + refers to the Subaru r − band. Col-ors are computed from the best-fit SED templates inIlbert et al. (2013). The color cuts for quiescent galaxiesare: (NUV − r + ) > r + − J ) + 1 and (NUV − r + ) > . T obs for all sub-samples of galaxies, even though T obs will likely to depend on the galaxy masses and color.Within a single sub-population, however, T obs does notdepend strongly on redshift, and, therefore, does not af-fect the evolution of the merger rate, only the normaliza-tion. The pair fractions reported in Table 3 are correctedfor incompleteness and contamination. In addition to adependence on redshift, C merge is different for quiescentand star-forming galaxies because the completeness ofour merger selection depends on galaxy morphology, and,therefore, color. For quiescent galaxies, we use the com-pleteness fraction for early-type galaxies, while for star-forming galaxies, we assume the completeness of late-type mergers. For quiescent galaxies, C merge is indepen-dent of redshift, while, for star-forming galaxies, C merge increases by a factor of ∼ z ≈ . z ≈ . § ℜ merge ∼ (1 + z ) . ± . , while for red galax-ies ℜ merge is consistent with no evolution, ℜ merge ∼ (1 + z ) . ± . . This suggests that the evolution in themerger rate for all galaxies is driven by the evolutionin the merger rate for blue galaxies and the increasingcontribution of blue galaxies to the galaxy population athigh redshift.For massive (log M/ M ⊙ > . ℜ merge ∼ (1 + z ) . ± . , consistent with no evolu-tion. The lack of evolution in the merger rate for mas-sive, red galaxies agrees with results from pair stud-ies (de Ravel et al. 2009; de Ravel et al. 2011; Lin et al.2008; Bundy et al. 2009; L´opez-Sanjuan et al. 2011,2012) and simulations (Kitzbichler & White 2008). As inLin et al. (2008), de Ravel et al. (2009) and Darg et al.(2010b), we find that most mergers are star-forming, andthat the fraction of star-forming mergers increases signifi-cantly with redshift. Figure 10 shows that dry, quiescentmergers mergers make up ∼ 20% of all mergers in oursample, once the merger fractions are corrected for in-completeness and contamination.It is interesting to note that Figure 9 shows a weakincrease in the fractional merger rate for low mass, qui-escent galaxies ( ℜ merge ∝ (1 + z ) . ± . ). However, low-mass quiescent galaxies suffer the most from incomplete-ness in this I − band selected sample. If the average stel-lar mass for low mass quiescent galaxies increases as afunction of redshift, then it is not surprising that thefractional merger rate in the highest redshift bin matchesthat of the high-mass quiescent galaxies. This suggeststhe evolution the low mass quiescent galaxy merger ratemay be a selection effect.The fractional merger rate for star-forming galaxiesgrows significantly with increasing redshift, ℜ merge ∝ (1 + z ) . ± . for high mass galaxies, and ℜ merge ∝ (1 + z ) . ± . for low mass galaxies. This demonstrates theincreasing importance of wet major mergers at high red-shift, in agreement with previous studies (Li et al. 2008;Bundy et al. 2009; L´opez-Sanjuan et al. 2012, 2011).The strongly increasing fraction of star-forming mergersalso agrees with the increase in bright infrared sources asa function of redshift (Le Floc’h et al. 2005). This is ex-pected as these sources are often associated with mergers(Sanders & Mirabel 1996; Kartaltepe et al. 2010).As with quiescent galaxies, the merger rate evolutionfor low mass galaxies is steeper than for high mass galax-ies. Although this may be driven by incompleteness,the steepness of the merger rate for lower mass galax-ies suggests a dependence of the merger rate on halomass. Note, however, that the range of masses understudy is small (10 . ≤ log M/ M ⊙ . ℜ merge for samples of star-forming, quiescent,low mass and high mass galaxies help explain the differ-ences in merger rates found using different parent sam-ples, especially the differences in ℜ merge between mass-limited and luminosity-limited samples (e.g., Lotz et al.2011; Lin et al. 2004).4 Lackner et al. redshift f m e r g e r [ % ] star−forming galaxies logM ∗ ≥10.9logM ∗ <10.9 0.3 0.4 0.5 0.6 0.7 0.8 0.9 redshift quiescent galaxies logM ∗ ≥10.9logM ∗ <10.9 Figure 9. The fraction of mergers for different types of galaxies, corrected for chance line-of-sight superpositions, contamination, andincompleteness, as a function of redshift. The left panel shows star-forming galaxies while the right panel shows queiscent galaxies, separatedby the color cuts in Figure 8. The solid (empty) symbols show high (low) mass galaxies. Small horizontal offsets are added for visibility. redshift m e r g e r s / t o t a l[ % ] SF, logM ∗ ≥10.9quies., logM ∗ ≥10.9 logM ∗ <10.9logM ∗ <10.9 Figure 10. The fraction of pairs split by galaxy color and mass,corrected for line-of-sight superpositions, incompleteness and con-tamination. With these corrections, mergers between star-forminggalaxies dominant at all redshifts, and the number of star-formingmergers increases significantly with redshift. Without incompleteness/contamination corrections The results in Figures 7 through 10 use late-stagemerger fractions corrected for incompleteness and con-tamination. While these correction factors are based onsimulations well-matched to the observed data, the cor-rections are still uncertain. Therefore, we perform thesame analysis, excluding the completeness and contam-ination corrections, setting C merge = 0 . redshift m e r g e r s / t o t a l[ % ] SF, logM ∗ ≥10.9quies., logM ∗ ≥10.9 logM ∗ <10.9logM ∗ <10.9 Figure 11. As in Figure 10, but the fractions are not correctedfor incompleteness or contamination. Without the incompletenesscorrections, there is no statistically significant increase in mergeractivity at high redshifts. Because the correction factor is small forearly-type galaxies, the fraction of queiscent mergers is nearly thesame as in Figure 10. and contamination corrections, and the measured mergerrates are certainly invalid without any corrections. With-out the incompleteness corrections, the overall late-stagemerger fraction drops by a factor of ∼ 2. Furthermore,the measured evolution in the merger rate disappearsif we do not include an evolving correction for incom-pleteness. Figure 11 demonstrates that the fraction oflate-stage mergers only evolves slightly with redshift, f merge ∝ (1 + z ) . ± . This is in contrast to Figure 10,which shows a large increase in the corrected merger frac-alaxy Mergers in COSMOS 15tion with redshift.Comparing Figures 10 and 11 also shows that the frac-tion of quiescent mergers is unchanged by the correc-tion factor for contamination and incompleteness. Thisis unsurprising since our merger sample is complete forearly-type galaxies out to z ∼ 1. The completeness cor-rection mainly affects star-forming galaxies, particularlyat high redshift. Without corrections for contaminationand incompleteness, the merger rates for quiescent andstar-forming galaxies grow as ℜ merge ∝ (1 + z ) . ± . and ℜ merge ∝ (1 + z ) . ± . , respectively. While themerger rate evolution for quiescent galaxies is unchanged,the merger rate for star-forming galaxies is significantlylower, and only marginally inconsistent with a flat mergerrate. These results suggest that the non-evolving mergerrate for quiescent galaxies is robust. For star-forminggalaxies, the uncorrected merger rates represent a lowerlimit. Even if the exact values of the incompleteness wemeasure using mock merger images are inaccurate, oursample of late-stage mergers is demonstrably incompleteat high redshift, particularly for late-type, star-forminggalaxies. Therefore, the merger rate for star-forminggalaxies will evolve at least as quickly as (1 + z ) . ± . .In the above analysis, we use a contamination correc-tion that is independent of redshift and galaxy type (qui-escent or star-forming). However, there are several con-tamination effects which are likely larger for star-forminggalaxies than for quiescent galaxies. These contami-nants may artificially boost the late-stage merger frac-tion at high redshift. Correcting for these effects willlower the merger rate evolution rate. The star-forminggalaxy merger rate is particular sensitive to morphologi-cal k-corrections and the overall increase in the fractionof clumpy, star-forming galaxies at high redshift. Thisincrease in the contamination will lead to an artificialincrease in the merger rate for star-forming galaxies athigh redshift. However, as demonstrated in § ∼ ∼ PROPERTIES OF LATE-STAGE MERGERS To study the internal properties of late-stage mergers,we limit our parent sample to galaxies from the spectro-scopic zCOSMOS survey (Lilly et al. 2007, 2009). The‘bright’ zCOSMOS sample contains spectra for ∼ , I < . K -band selected sample fromIlbert et al. (2013) described above, but differences inmasking mean that some zCOSMOS galaxies are missingfrom the photo-z sample. To ensure no galaxies are miss-ing, we rerun our merger selection algorithm on postagestamps generated from the zCOSMOS parent sample.The final sample is selected in the same way as that usedin Kampczyk et al. (2013) and Silverman et al. (2011) tostudy the SFRs and AGN properties of kinematic pairs.Below, we compare the properties of late-stage mergersboth to the parent zCOSMOS sample and to more widelyseparated kinematic pairs from the same parent sample.Because these galaxies are observed in zCOSMOS, we use the spectroscopic redshifts, and stellar masses fromPozzetti et al. (2010) and Bolzonella et al. (2010). Thesestellar masses use the spectroscopic redshifts and arein good agreement with those measured in Ilbert et al.(2013) using photometric redshifts. For the analysis be-low, we examine galaxies with M ∗ > . × M ⊙ in theredshift range 0 . ≤ z < . 05, the same mass and red-shift range used in kinematic pair studies in zCOSMOS(Silverman et al. 2011; Kampczyk et al. 2013). For theanalysis of the SFR ( § Chandra or XMM detection. This leaves a sample of 4586galaxies of which 154 are classified as late-stage merg-ers. We use the non-merging galaxies from the parentzCOSMOS sample as a control sample. However, wefirst check that the control sample is well-matched to themerger sample in stellar mass and redshift. Since AGNactivity, SFR and, in this sample of galaxies, sSFR (seeMaier et al. 2009), are strong functions of M ∗ and z , itis important that the late-stage merger sample is not bi-ased relative to the control sample. Kolmogorov-Smirnov(K-S) tests show that both the mass and redshift distri-butions for late-stage mergers and the control sample areindistinguishable. Star formation in late-stage mergers Simulations show that galaxy mergers lead to enhancedstar formation (e.g., Hernquist 1989; Di Matteo et al.2007; Mihos & Hernquist 1996; Barnes & Hernquist1991; Springel et al. 2005; Hopkins et al. 2006). Thereis also much observational evidence to support thisconclusion. Galaxies identified as mergers are oftenbluer (e.g., Kampczyk et al. 2007; Darg et al. 2010a) andshow enhanced UV and IR SFR (e.g., Jogee et al. 2009;Robaina et al. 2009). Spectroscopy confirms that galax-ies in close pairs have higher star formation rates thanisolated galaxies (e.g., Barton et al. 2000; Lambas et al.2003; Kampczyk et al. 2013; Ellison et al. 2013). Stud-ies of far-infrared selected galaxies show that galaxieswith very high star formation rates are much more likelyto be disturbed morphologically than galaxies with typ-ical star formation rates (e.g., Sanders & Mirabel 1996;Kartaltepe et al. 2010). In this section, we compare theSFR in late-stage mergers to that of isolated galaxies.Our control sample of isolated galaxies is simply the setof zCOSMOS galaxies that are not identified as late-stagemerger candidates.Figure 12 shows the narrow 4000-Angstrom break(Balogh et al. 1999) for late stage mergers and the con-trol sample. As expected, at fixed stellar mass, the late-stage mergers have a lower median D n (4000) than thecontrol sample. This is indicative of recent, within thelast Gyr, star formation in the late stage mergers. A K-S test shows that the distributions of D n (4000) for thelate-stage mergers and the control sample are distinct.Indeed, at masses below log M/ M ⊙ = 10 . 7, there are al-most no quiescent late-stage mergers. This indicates thata significant fraction of star formation may be associatedwith mergers.We use the SFR computed from the 24 µ m fluxas measured by Spitzer/MIPS (Sanders et al. 2007;Le Floc’h et al. 2009). The total infrared luminosity, L IR is computed using the spectral energy distribution mod-els from Dale & Helou (2002) and the photometric red-shifts from Ilbert et al. (2009) and Salvato et al. (2009)6 Lackner et al. P ( D n ( )) ∗ /M ⊙ <10.92 fieldmergers1.00 1.25 1.50 1.75 2.00 D n (4000) P ( D n ( )) ∗ /M ⊙ <11.66 Figure 12. The distribution of the narrow 4000 ˚A-break for late-stage mergers (red) and the parent sample (black) from zCOSMOS.The galaxies are divided into two mass bins. In the upper(lower)panel there are 1582(2375) control galaxies and 69(67) merginggalaxies. The corresponding vertical lines show the medians ofeach distribution. The median D n (4000) for late-stage mergers issmaller in both mass bins, indicating most late-stage mergers haveundergone recent star formation. for X-ray sources. Below z ∼ 1, the 24 µ m flux is anaccurate measure of the total infrared luminosity (e.g.,Elbaz et al. 2010). From the infrared luminosity, the to-tal SFR is given by Kennicutt (1998):SFR [M ⊙ yr − ] = 4 . × − L IR /L ⊙ . (2)We only utilize sources with a 24 µ m-detection and a mea-sured SFR. This limits our sample to 2318 galaxies, ofwhich 111 are late-stage mergers. Among galaxies withnon-zero 24 µ m-based SFRs, the fraction of late-stagemergers is 4 . ± . . ± . µ m-based SFR and the stellarmass from Pozzetti et al. (2010). The measured stellarmass is increased by a factor 1 . −2 −1 0 1 log[sSFR Gyr −1 ] c u m u l a t i v e f r a c t i o n fieldmergers Figure 13. The cumulative distribution of sSFR for late-stagemergers and non-interacting galaxies from the zCOSMOS sample.The sSFR is derived from the Spitzer /MIPS 24 µ m flux. The me-dian sSFR in late-stage mergers is a factor of 2 . ± . enhanced by a factor of 2 . ± . µ m-derived sSFR in late-stagemergers.As with the merger rate, the association of late-stagemergers with star forming galaxies may be affected bycontamination from clumpy, star-forming galaxies, par-ticularly at high redshift. Our peak-finding method mayidentify clumpy, star-forming galaxies as late-stage merg-ers, which would enhance the typical sSFR in late-stagemergers. However, we show in § ∼ ii ] λ h − kpc is en-hanced by factors of 2 − ii ] λ . ± . µ m- and [O ii ]-derived sSFRs sug-gests that the extinction in late-stage mergers is not sig-nificantly different from that in field galaxies. Howeverthe mean sSFR computed using [O ii ] emission is a factorof ∼ µ m-derived sSFR.We can add our sample of late-stage mergers to themore widely separated pairs in Kampczyk et al. (2013)to obtain the fraction of star formation between 0 . 05 due to merging galaxies separated by less than30 h − kpc. Kampczyk et al. (2013) report that 6 ± h − kpc. The sSFR in these galaxies isenhanced by a factor of 1 . ± . 6. In the same sample, wefind 3 . ± . 3% of galaxies are late-stage mergers, whichhave sSFRs 2 . ± . ± 5% of star forma-tion is associated with mergers, but only 8 ± 5% of allstar formation can be considered “excess” star forma-tion triggered by mergers. This modest enhancement inthe star formation due to major mergers is in agreementwith other studies of visually classified mergers and closepairs (Robaina et al. 2009; Jogee et al. 2009). In addi-tion, these results also agree with semi-analytic models(Somerville et al. 2008), which report that only 7% ofstar formation is directly associated with major mergers.Since the enhancement in sSFR for late-stage merg-ers is small, it is important to note that these sys-tems are not starburst galaxies. The small shift in theSFR for late-stage mergers is in agreement analysis bySargent et al. (2012). They suggest that the sSFRs forstarburst galaxies and main sequence star-forming galax-ies form a double Gaussian, in which the means are offsetby only a factor of ∼ 4. This is in contrast to other def-initions of starburst galaxies, requiring SFRs an orderof magnitude larger than predicted by the star-formingmain sequence. While the majority of starburst galax-ies are major mergers (e.g., Sanders & Mirabel 1996;Kartaltepe et al. 2010; Wu et al. 1998; Cui et al. 2001),the majority of late-stage mergers in our study are notstarburst galaxies. AGN fraction In addition to triggering star formation, major merg-ers may drive black hole growth through AGN activity.Mergers can induce disk instabilities in coalescing galax-ies that drive gas to the center of galaxies. This gas isused up both in star formation and in growing the blackhole (e.g., Mihos & Hernquist 1996). Many simulationsshow that the periods of most intense star formation andblack hole growth occur in late-stage mergers near coa-lescence (Mihos & Hernquist 1996; Springel et al. 2005;Di Matteo et al. 2007; Johansson et al. 2009). Whilesimulations suggest that luminous accretion (i.e. QSOs)is dominated by major mergers, more than half of low-luminosity (log L bol . /L ⊙ . 11) AGN activity can befueled by stochastic, non-major merger processes (e.g.,Hopkins & Hernquist 2006; Hopkins et al. 2013). Thisis in agreement with studies of AGN host galaxiesthat demonstrate most AGN activity occurs in galax-ies with undisturbed (non-merging) morphologies (e.g.,Cisternas et al. 2011; Kauffmann et al. 2004; Liu et al.2012; Kocevski et al. 2012). Nonetheless, there aremany observations that show some enhancement innuclear activity in galaxy pairs (Alonso et al. 2007;Silverman et al. 2011; Ellison et al. 2011; Koss et al.2012; Ellison et al. 2013; Woods & Geller 2007, but seeDarg et al. 2010a; Li et al. 2008; Barton et al. 2000). Us-ing spectroscopic pairs out to z ∼ 1, Silverman et al.(2011) show the fraction of X-ray selected AGN with10 < L . − < erg s − increases from 3 . +0 . − . %for isolated galaxies to 9 . +2 . − . % for galaxies in pairs witha maximum projected separation of 75 kpc and a line-of-sight velocity separation less than 500 km s − . Despite this enhancement, only ∼ 25% of AGN activity occursin galaxy pairs, and an even smaller fraction, ∼ 18% ofAGN activity is triggered by close interactions.We can improve the estimate of the fraction of AGNsdue to merging by including late-stage mergers with thekinematic galaxy pairs in Silverman et al. (2011). In or-der to simplify the comparison, we use a parent sam-ple identical to that of Silverman et al. (2011), and de-scribed above (log M ∗ / M ⊙ > . . ≤ z < . Chandra (Elvis et al. 2009). Due to the limited areaof the Chandra survey, the zCOSMOS parent sampleused here only contains 3474 galaxies of which 92 arelate-stage mergers. The X-ray sources are matched tooptical/IR sources as described in Civano et al. (2012).As in Silverman et al. (2011), we only consider X-raysources with total fluxes (0 . − 10 keV) greater than1 × − erg cm − s − and luminosities larger than2 × erg s − . The latter requirement eliminates galax-ies in which the contribution from star formation to theX-ray flux is not negligible. Ninety-five percent of the X-ray sources have luminosities L . − < erg s − .This ensures that most of the AGN hosts we examineare not AGN-dominated in the optical/NIR, and thatthe derived properties, especially stellar masses are re-liable (Bongiorno et al. 2012; Salvato et al. 2011). Thefinal sample contains 164 Chandra X-ray sources, whichare certain to be AGN-dominated. Figure 14 shows the6 late-stage mergers which are also X-ray selected AGN.The left panel of Figure 15 shows the AGN fractionas a function of pair separation for our sample of late-stage mergers(filled square) and for more widely sepa-rated kinematic pairs (Silverman et al. 2011) drawn fromthe same parent sample. We define the AGN fraction asthe fraction of late-stage mergers (close pairs) with anassociated X-ray source. We compute the AGN fractionas in Silverman et al. (2011), equation 1. This formuladown-weights compulsory zCOSMOS targets, which areX-ray selected, and likely to be AGN (Lilly et al. 2007).It also accounts for the spatially varying Chandra sensi-tivity by weighting each AGN by the fraction of galaxiesin which the measured X-ray flux is below the sensitivity,i.e., the fraction of galaxies which could host each AGN.The values for the kinematic pairs in the left panel ofFigure 15 are taken from the Bayesian likelihood analy-sis in Silverman et al. (2011). This method takes into ac-count contamination of the control sample with galaxiesin kinematic pairs in which only one member is observedspectroscopically. Since late-stage mergers fall into a sin-gle slit, this more sophisticated approach for calculatingthe AGN fraction is unnecessary. We find 6 late-stagemergers that are also X-ray selected AGN. Although thestatistics are poor, the AGN fraction among late-stagemergers is 6 . ± . . +0 . − . % (Silverman et al.2011). At 95% confidence, we find that the AGN fractionin late-stage mergers is enhanced by less than a factor of3 . 0, with a mean value of 1 . ± . 7, in agreement with(although less stringent than) Cisternas et al. (2011).Given the upper limit on the enhancement of AGNactivity associated with late-stage mergers, we can com-pute an upper limit for the AGN activity triggered bymergers. Following the same procedure as § Figure 14. Images of the six late-stage mergers that are also X-ray selected AGN. The (blue) contours show the total (0 . − . Chandra (Elvis et al. 2009). The (cyan) crosses show the position of the two peaks found by our merger-finding method. The galaxyin the lower middle panel may be a spiral galaxy. proj. separation [kpc] A G N F r a c t i o n [ % ] redshift Figure 15. Left: The fraction of AGN in galaxy pairs at variousprojected separations. The 3 right points are from Silverman et al.(2011) (see their Figure 5). The empty symbol is the field value,corrected for unidentified kinematic pairs. The square shows theAGN fraction in late-stage mergers (6 mergers). The points areplotted at the median separation in each bin, and the horizontalerror bars denote the interquartile range (25% − Right: The AGN fraction in pairs in two redshift bins.The squares denote late-stage mergers. There are no late-stagemergers in the low redshift bin and the error bar denotes the 1 σ upper limit. The filled and empty circles are the AGN fractionin pairs separated by < ∼ . − 1% lower. stage merger fraction in this sample is 3 . ± . 3% and theenhancement in the AGN fraction is at most a factor of 3above the control sample. Therefore, the fraction of AGNactivity associated with late stage-mergers is < . ± . triggered by late-stagemergers is at most 6 . ± . . ± . ± / . +8 . − . % of AGN can be directlycontributed to the pair interaction. Combining the kine-matic pairs with our late-stage mergers gives a total frac-tion of AGN activity triggered by mergers of ∼ ± . ≥ z < . . ≥ z < . 05. Among late-stage mergers, all 6X-ray selected AGN occur above z = 0 . 65. This booststhe AGN fraction at high redshift to 11 . ± . ∼ . − z ∼ . 65, none of our late-stage merg-ers are also X-ray AGN. The error bar in Figure 15 showsthe 1 σ upper limit for the AGN fraction, which is consis-alaxy Mergers in COSMOS 19tent with the AGN fraction in the field, albeit with largeuncertainty. Although our results rule out a decrease inthe merger rate at close separations, and suggest someenhancement in the AGN fraction at z & . 7, a largersample is required to determine if any enhancement inthe AGN rate for late-stage mergers is statistically sig-nificant.From the X-ray and optical images alone, it is unclear ifany of the late-stage mergers with AGN are dual AGNs.The possible dual AGN, CID-42 (Comerford et al. 2009;Civano et al. 2010), is excluded from the sample abovesince the measured stellar mass of the system is below2 . × M ⊙ , however our method does select CID-42as a late-stage merger. We have examined the spectrafor the 6 mergers with AGN and find no evidence for ve-locity offsets, suggesting that only one of the black holesin the system is actively accreting. Nonetheless, sincethe late-stage mergers are selected to have two, concen-trated central cores, this sample would be well-suited tosearches for galaxies with dual AGN. AGN in the photo-z sample We can check the fraction of mergers with AGN usingthe photo-z sample. For the photo-z sample, we use thesame stellar mass and redshift cuts as the spectroscopicsample. However, we exclude X-ray sources that arebest-fit by a Type I AGN/QSO template (Salvato et al.2011).Since we identify late-stage mergers based on theflux ratio of two central peaks, our method is poorly-suited to selecting companions of bright Type I AGN,in which the optical flux is dominated by a single pointsource. This means that the AGN fraction reported hereis for lower luminosity, obscured AGN, not bright TypeI AGN.Using the photo-z sample, we find 8 late-stagemergers that are Chandra -detected X-ray AGN with L [0 . − 10 keV] > × erg s − , 4 of which are also iden-tified in the spectroscopic sample. The missing 2 galax-ies are excluded because of differences in the maskingin the K − band and I − band selected catalogs, used forthe photo-z and spec-z samples (see Ilbert et al. 2013;Lilly et al. 2007). These 8 late-stage mergers yield anAGN fraction of 5 ± Chandra will improve the statistics of these resultsby a factor ∼ in prep ).As with the star formation rates, we find that, al-though AGN activity may be slightly enhanced in late-stage mergers, mergers do not drive the majority of AGNactivity, and, hence, black hole growth. Including late-stage mergers along with more widely separated pairs,only ∼ 20% of AGN activity is triggered by mergers,and late-stage mergers are responsible for at most 6% ofAGN activity. The small increase in AGN activity as-sociated with close pairs is in agreement with previousstudies (Ellison et al. 2013; Alonso et al. 2007) and sug-gests minor mergers or secular processes within galaxiesdrive the majority of low-luminosity AGN activity. Sim-ilarly, while the star formation rate in late-stage mergers is typically enhanced compared to a control sample, theenhancement is less than a factor of 2 and only 8 ± h − kpc until shortly before coalescence. Further-more, the 0 . − − 20, suggesting the AGN in late-stagemergers are highly obscured. Nonetheless, the low en-hancement in X-ray selected AGN and star formationactivity in late-stage mergers and kinematic pairs recon-firms the results that galaxy and black hole growth arenot solely driven by major mergers. SUMMARY Although mergers of dark matter halos underpin theo-ries of structure and galaxy formation, the actual role ofgalaxy mergers is less clear. In this work, we seek to ex-pand the study of merging galaxies to galaxy pairs withsmall separations. By including late-stage mergers withsamples of more widely separated (as yet not merging)pairs, we can obtain a better understanding of the role ofmergers in galaxy evolution since z ≈ 1. To that end, wedevelop a method to identify late-stage galaxy mergersusing HST images.We utilize a high-pass filter which easily detects thebright, concentrated, central cores of both member galax-ies of a merger before coalescence. By implementinglimits on the flux ratio and brightness of the measuredpeaks, we are able to produce a clean sample of 2055galaxy mergers from COSMOS ACS I − band images ofgalaxies brighter than I = 23. These late-stage merg-ers have two intact galaxy nuclei that are separated byless than 8 kpc. If we restrict the parent sample to amass-complete (log M ∗ /M ⊙ > . 6) sample of galaxies inthe redshift range 0 . < z < . 0, with pair separationsbetween 2 . . ± . 2% of the massive galaxy pop-ulation, or 4 . ± . 5% when corrected for contaminationand incompleteness. The sample of late-stage mergersidentified here is distinct from other samples of merginggalaxies, such as kinematic pairs, and morphologicallydisrupted galaxies identified by CAS or Gini/M20.We create mock images of mergers by placing tworeal galaxies in one postage stamp and use these to testthe completeness and contamination in our sample. Al-0 Lackner et al.though the sample suffers little from contamination (10%from clumpy, non-merging galaxies and 20% from minormergers), we only successfully select ∼ 20% of all ma-jor mergers, and the selection efficiency decreases withincreasing redshift. Our method is most successful formergers between concentrated early-type galaxies, select-ing 80% of all simulated mergers, independent of red-shift.Using the sample of late-stage mergers we study boththe evolution of the merger rate and the properties ofmerging galaxies. Our results can be summarized as fol-lows: • For galaxies with stellar masses above log M/ M ⊙ > . 6, we find that the fraction of mergers evolves as f merge ∝ (1 + z ) . ± . when corrected for incom-pleteness, and contamination from minor mergers,non-mergers and line-of-sight superpositions. De-spite uncertainties in the sample completeness, andthe merger timescale, T obs , the normalization of thefractional merger rate, ℜ merge , agrees well with thatfound in previous studies. The measured evolutionin the merger rate becomes significantly flatter ifwe remove the redshift-dependent correction for in-completeness of the sample, ℜ merge ∝ (1+ z ) . ± . . • Dividing the sample into quiescent, star-forming,low mass, and high mass galaxies, we find that themerger rate for star-forming galaxies is a strongfunction of redshift, ℜ merge ∝ (1 + z ) . ± . , whilethat for quiescent galaxies is a mild function of red-shift, consistent with no evolution, (1 + z ) . ± . .Therefore, among massive galaxies, the increase inthe total merger rate is driven by the increase inthe merger rate for star-forming galaxies and by theincreasing fraction of massive star-forming galaxiesat high redshift. Lower mass (10 . < log M/ M ⊙ < . 9) galaxies also exhibit a steeper merger rateevolution than higher mass (log M/ M ⊙ > . z ) . ± . compared to (1 + z ) . ± . .These results use different corrections for complete-ness for star-forming (late-type) mergers and qui-escent (early-type) mergers. Although the mergerrate slopes are not as steep without the correc-tions for incompleteness, the merger rate for star-forming (low-mass) galaxies still evolves more thanthat of quiescent (high-mass) galaxies. This showsthat the differences in the merger rates as a func-tion of stellar mass and SFR are robust. Further-more, these differences suggest that measurementsof the merger rate as a function of redshift are verysensitive to the sample of galaxies. • Examining the properties of late-stage mergers,we find that the SFR in late-stage mergers withlog M ∗ / M ⊙ > . . ± . ± 5% of star for-mation between z = 0 . 25 and z = 1 . 05 is associatedwith late-stage mergers or pairs separated by lessthan 30 h − kpc. However, the excess star forma-tion that can be attributed to major mergers is onlyhalf of that. • The AGN fraction in late-stage mergers at z > . . ± . . < z < . . < z < . 05 is enhanced by a factor of 3 above the activ-ity in field galaxies. Together with more widelyseparated pairs, 20 ± 8% of AGN activity is in-duced by mergers at separations less than 143 kpc.The fraction of AGN triggered by late-stage merg-ers and kinematic pairs is similar to the fraction ofSFR activity triggered by the same class of merg-ers. This suggests that the processes responsi-ble for star formation and AGN activity in ma-jor mergers are coupled, indicating a co-evolutionscheme (Jahnke et al. 2009; Cisternas et al. 2011;Schramm & Silverman 2013).The measurement of the blue galaxy merger rate is par-ticularly sensitive to morphological k-corrections and theincreasing fraction of blue, star-forming, clumpy galax-ies at high redshift. Because galaxies appear clumpier atblue rest frame wavelengths and the entire galaxy pop-ulation contains more clumpy, star-forming galaxies athigh redshift, we expect our peak-finding method to de-tect more late-stage merger candidates at high redshift.We plan to address this by applying our peak-findingmethod near-infrared data WFC3 HST data from theCANDELS survey (Koekemoer et al. 2011; Grogin et al.2011). Performing this study at longer wavelengths mayalso help increase the completeness of our merger sam-ple. Galaxies appear more bulge-dominated and con-centrated at longer wavelengths and our merger-findingmethod is significantly more sensitive to mergers betweenconcentrated, early-type galaxies than mergers betweenlate-type galaxies.Although we have examined the SFRs and X-ray emis-sion of late-stage mergers, resolved properties of themergers require additional data. For instance, we have asample of ∼ 20 late-stage mergers with significant X-raydetections and 2 concentrated central cores. Althoughthe X-ray detection cannot resolve the merging galaxies,these sources provide an excellent parent sample for spec-troscopic searches for dual AGN (e.g., Comerford et al.2009; Liu et al. 2010; Civano et al. 2010). By focus-ing only on X-ray AGN, we are only studying a sub-set of AGN. There are many AGN selected in IRAC (Donley et al. 2012), radio (Smolˇci´c et al. 2008), and op-tical/infrared (Fiore et al. 2008; Dey et al. 2008). In-creasing the sample size of AGN will increase the numberof AGN in late-stage mergers. Further work is needed todetermine if the fraction of AGN activity associated withlate-stage mergers will also increase using AGN selectedin the optical, infrared, or radio.Obtaining a sample of late-stage mergers between 1 . z . z ∼ k − corrections, asalaxy Mergers in COSMOS 21there is evidence that galaxies typically have more struc-ture at shorter wavelengths (e.g., Kuchinski et al. 2000).Near-infrared WFC3 HST data from the CANDELS sur-vey (Grogin et al. 2011; Koekemoer et al. 2011) could beused for such a study. Additionally, since the star forma-tion and AGN activity also continue to grow with red-shift, expanding the sample of mergers to higher redshiftwill increase the statistical significance of the sample oflate-stage mergers with ongoing star formation and AGNactivity. This will help determine the role of major merg-ers in the growth of galaxies and super-massive blackholes at their peak epoch of formation.We thank the referee for their insightful comments which greatly improved this work. We also thankRichard Massey and Kevin Bundy for helpful commentson a draft. This work was supported by World Pre-mier International Research Center Initiative (WPI Ini-tiative), MEXT, Japan. ST acknowledges support fromthe Lundbeck Foundation. The Dark Cosmology Cen-tre is funded by the Danish National Research Founda-tion. This research has made use of the NASA/IPACInfrared Science Archive, which is operated by the JetPropulsion Laboratory, California Institute of Technol-ogy, under contract with the National Aeronautics andSpace Administration. This research made use of APLpy,an open-source plotting package for Python hosted athttp://aplpy.github.com APPENDIX APPENDIX A: SIMULATED MERGER IMAGES In order to test our merger-finding algorithms, we create a sample of mock mergers by coadding real galaxy imagesfrom our original sample to create new postage stamps. These fake merger images have the same properties as the realgalaxy images and allow us to test both the completeness and contamination of our merger selection. In particular, themock mergers will have the same redshifts, magnitudes, morphologies, and merger ratios as the real galaxy population.Because the fraction of real mergers is small, they represent a small contamination in our sample of mock mergers.While these simulations are realistic in many ways, they do not include any structural changes wrought by the mergerin the images. However, since our method is sensitive to only the brightest features in merging galaxies, this omissionis likely unimportant. Below, we focus on mergers in which the total mass is larger than 4 × M ⊙ and the redshiftis between 0 . < z < . 0. These are the cuts in § late-late mergerz=0.69 8 kpc late-late mergerz=0.85 8 kpcearly-late mergerz=0.34 8 kpc early-early mergerz=1.04 8 kpc Figure 16. Example mock merger images. The circles show the position of the coadded galaxies, while the crosses show the positionsof the detected peaks. Both galaxy mergers on the right are sucessfully detected and pass the cuts implemented to remove contaminants.For the merger in the upper left, both galaxies are late-type and too diffuse to be detected. For the merger in the lower left, the flux ratiobetween the two galaxies is too large to be detected. To create a mock merger postage stamps, we randomly select 2400 galaxies from our photo-z sample. For eachselected galaxy, we select at random a second galaxy at approximately the same photometric redshift (∆ z < . § HST /ACS postage stamp images of these galaxies. Foreach galaxy pair, we make 8 postage stamps with different separations between the galaxy centers, spanning from0 . √ 22 Lackner et al. redshift c o m p l e t e n e ss f r a c t i o n early-earlyearly-late late-laterandom redshift c o m p l e t e n e ss f r a c t i o n early-earlyearly-late late-laterandom Figure 17. The completeness of the late-stage major mergers in simulated images as a function of redshift, before applying cuts in fluxratio for contamination (left) and after applying cuts (right). The thick black line shows the completeness for a random sample of galaxies,with a representative morphological mix. While the other lines show the completeness for mock mergers in which the merging galaxies areboth early types (red, solid), both late types (blue, dotted), and mixed (magenta, dashed). The morphologies are determined by the ZESTparameter. The error are derived by bootstrap resampling. The completeness is a stronger function of morphology than redshift. nosier than the original images. However, because we are creating merger images by coadding images from our sample,the mock mergers are up to a factor of 2 brighter than the real galaxies in the sample. These effects approximatelycancel out and we neglect the differences in signal-to-noise between the mock mergers and the real galaxy images.Figure 16 also demonstrates that our method does not detect all mock mergers (blue × s in Figure 16). Our selectionis particularly incomplete for mergers among late-type galaxies, in which neither galaxy has a dominant bulge. Theleft panel of Figure 17 indicates our completeness as a function of redshift (black solid line). In this figure, we examinethe completeness for major mergers ( > . . z ∼ . 5, our method only detects20% of the mock late-stage mergers. Dividing the sample by the ZEST morphology of the merging galaxies showsthat the completeness is a strong function of morphology. The median ring filter selects 80% of early-type mergers,but only ∼ 40% of late-type mergers. This is expected, since our method requires a strong central bulge in order todetect a peak. However, in comparing the merger rates of early and late type galaxies, it is important to note theirvery different completeness fractions. Furthermore, the decrease in the completeness up to z ∼ . 5, suggests that ourmerger rate evolution may be underestimated, as we are missing ∼ × as many galaxies at high redshift than at lowredshift.Figure 18 shows the completeness as a function of pair separation, similarly divided by galaxy morphology. For allmorphologies, the completeness is independent of pair separation beyond ∼ − . z = 1). The lower panel shows the fractional error in our measurement of the pairseparation. For large separations, the separation is well-measured. However, for small real separations, the measuredseparation is typically too large. By cutting off the pair separations at 2 . ∼ detected peaks at ∼ . 5% does not significantly affect our results. Before applying ourmethod to different imaging data, similar simulations should be conducted in order to determine the threshold value.In addition to contamination from star-forming clumps and galactic substructure, our merger finding method issomewhat sensitive to minor mergers. Since we are only interested in studying late-stage major mergers, it is importantto understand the contamination from minor mergers. To create a mock merger sample with a realistic fraction ofminor mergers, we build a sample of 2400 mock mergers in which one member of the pair is brighter than I = 20 . c o m p l e t e n e ss f r a c t i o n early-earlyearly-late late-laterandom0 1 2 3 4 5 6 7 8 separation [kpc] −10123 f r a c t i o n a l e rr o r Figure 18. Top : The completeness of the mock mergers as a function of pair separation. Note that each galaxy pair was simulated at adiscreet set of separations. The completeness drops sharply for separations comparable to the median ring filter size. The different linesshow the completeness for different morphologies for the members of the merger, as in Figure 17. The vertical line shows the cut madein separation at 2 . Bottom: The fractional error in the measured peak separation compared to the real separation for the ‘random’sample of morphologies only. The separation is reasonably well measured beyond a few kpc. However, small separations are typicallyoverestimated which will lead to contamination of our sample by mergers with separations < . -4 -3 -2 -1 peak flux/total galaxy flux nu m b e r real galaxiesother peaks Figure 19. Distribution of the detected peak flux ratios. The thick line histogram shows the distribution of peak to total flux for detectedgalaxy sources in the mock merger images. The thin line shows the distribution of extraneous peaks detected. By putting a cutoff at 3%,the contamination from extraneous peaks is 10%. This ensures that, from a sample of galaxies with I < 23, we include a realistic spectrum of merger ratios down to1 : 10. Note that our algorithm only measures the flux ratio of the merger, not the underlying mass ratio, whichrequires color information about the separate galaxies. However, in our mock merger images, we find that the real flux ratio of a merger is well-correlated with the mass ratio, and that the flux ratio of 0 . 25 corresponds approximatelyto a mass ratio of 0 . . 25. Overall, 70% of the detected late-stagemergers are real major mergers, and only 10% of mergers are false positives, as expected from the peak flux to totalflux cut explained above. The total fraction of minor mergers is 20%, and the contamination is worse at lower flux4 Lackner et al. meas. flux ratio f r a c . o f d e t ec t e dp a i r s detected mergersnon mergersminor mergers real flux ratio −1012 f r a c t i o n a l e rr o r Figure 20. Top: The fraction of detected mergers which are major mergers (solid line), minor mergers (dashed line) and contaminants(dotted lines). The major (minor) mergers consist of two galaxies with a flux ratio larger (smaller) than 0 . 25. The contaminants aredetected late-stage mergers which do not match the mock galaxies placed in each image. These include detections of galactic substructure. Bottom: The fractional error in the measured flux ratio as a function of real flux ratio. For small real flux ratios, our method typicallyoverestimates small flux ratios, which leads to a contaimination from minor mergers. ratios. The lower panel in Figure 20 shows the fractional error in the measured flux ratio. While the measured fluxratio correlates with the real flux ratio, the errors are extremely large, particularly at small real flux ratios. Bettermeasurements of the flux ratio could be obtained by fitting a late-stage merger with two realistic galaxy profilescentered on each detected peak. However, in this work, we only use the measured flux ratio to discriminate betweenmajor and minor mergers. By only selecting mergers with a flux ratio larger than 0 . 25, we only eliminate 15% of thedetected major mergers and 30% of minor mergers. Note, that the median ring filter is less sensitive to minor mergersthan major mergers, and that many minor mergers are eliminated by the peak flux to total flux cut of 3%. Both ofthese effects further help to limit contamination from minor mergers.Taken together, our cuts in peak to total flux ratio, and peak to peak flux ratio, do affect the overall completeness,particularly the late-type galaxy merger completeness. After implementing the flux ratio cuts, the overall completenessdrops to 20 − 25% (see the right panel of Figure 17), with most of the decrease coming from late-type mergers.However, these cuts are important since they significantly decrease the contamination from star forming clumps andminor mergers. Using the results of Figure 17 and 20, we can correct the measured late-stage merger fractions forincompleteness and contamination and use the corrected fractions to determine the merger rate evolution. In studyingthe internal properties of late-stage mergers, we cannot include a correction for incompleteness. However, in this case,it is more important to have a minimally contaminated sample of late-stage mergers, as significant contamination willmask any differences between the field population and the merger population. APPENDIX B: COMPARISON TO CAS AND GINI- M In order to better understand the poor overlap between our sample of late-stage mergers and mergers selected basedon their Gini (G), M and asymmetry (A) values, we examine a small random set of galaxy images. A galaxy isconsidered a merger by the Gini- M method if G > − . M + 0 . 38 (Lotz et al. 2008a). A galaxy is considered amerger based on its asymmetry if A > . 35 (Conselice 2003). The morphology measurements G, M , and asymmetry( A ) values are taken from Cassata et al. (2005). Note that the deblending done by Cassata et al. (2005) leads todifferent values for the morphology metrics than those derived directly from the images shown here. However, becausewe are looking for merging, deblending close pairs may not always be desirable, and we include differences in thedeblending as part of our comparison.The Gini- M and asymmetry merger selections were designed to work in the rest frame B − band at low redshift(e.g. Conselice 2003; Lotz et al. 2008a). In order to compare the results to higher redshifts, morphological k-correctionsneed to be taken into account. By using galaxies at redshifts above z ∼ . 6, the observed I − band images are closeto the rest frame B − band images and corrections to the measured G, M , and A can be neglected. We do include acorrection of δA = 0 . 05 for the effect of surface brightness dimming at high redshift (see Conselice et al. 2009; Conselice2003; Conselice et al. 2003).Figure 21 shows late-stage mergers selected by our method that are not selected by the Gini- M criterion. Panels b , c , d , g , and h show galaxies with Gini and M values close to the division line. In panel a , the detected peaks arealaxy Mergers in COSMOS 25 =−1.09A =0.13G =0.41a)10:01:07.8 +1:55:55.5 8 kpcz=0.61 M =−1.17A =0.11G =0.44b)10:02:48.1 +2:33:57.6 8 kpcz=0.84 M =−1.70A =0.13G =0.54c)09:58:31.7 +2:17:46.7 8 kpcz=0.93 M =−1.70A =0.21G =0.50d)10:01:49.2 +2:10:36.18 kpcz=1.00 M =−2.39A =0.04G =0.55e)09:59:48.6 +2:20:30.6 8 kpcz=0.66 M =−1.92A =0.34G =0.55f)10:01:43.2 +2:05:12.7 8 kpcz=0.95 M =−1.53A =0.24G =0.51g)10:01:53.7 +2:02:23.1 8 kpcz=0.80 M =−1.73A =0.17G =0.51h)10:01:38.6 +1:39:00.2 Figure 21. Examples of galaxies which are late-stage mergers but are not detected as mergers by the Gini- M method (Lotz et al.2008a). We only examine galaxies with z > . B − band.Crosses show all detected peaks, before any cuts on projected separation or flux ratio. The images are shown with an arcsinh stretch andwith the same scaling. =−1.69A =0.20G =0.49a)10:02:51.8 +2:40:26.1 8 kpcz=0.69 M =−1.65A =0.19G =0.44b)10:00:36.0 +2:28:30.6 8 kpcz=1.00 M =−1.98A =0.19G =0.61c)10:01:17.7 +2:00:14.1 8 kpcz=0.97 M =−2.33A =0.04G =0.54d)10:02:42.7 +2:44:26.38 kpcz=0.99 M =−1.80A =0.21G =0.57e)09:59:13.2 +1:52:39.6 8 kpcz=0.78 M =−1.26A =0.19G =0.43f)09:58:47.4 +1:53:44.1 8 kpcz=0.78 M =−1.13A =0.17G =0.45g)10:01:11.2 +2:29:02.1 8 kpcz=0.94 M =−0.88A =0.26G =0.45h)10:00:25.3 +2:17:51.4 Figure 22. Examples of galaxies which are late-stage mergers but are not selected as mergers based on their asymmetry around a 180 ◦ rotation ( A > . 35, (see Conselice 2003)). We use the asymmetry measurements from Cassata et al. (2005) and include a correction of 0 . z > . 6, which limits the morphological k-correctionswhen comparing to the rest frame B -band. The images have the same stretch and scaling as those in Figure 21. well-separated from the main galaxy and are likely a separate system. In panels e and f , the central peaks are wellenough separated to be deblended before measuring the morphology. This will lower the M coefficient in particular.In general, the galaxies our merger method selects are highly concentrated, which leads to lower M values than forother mergers.Figure 22 shows late-stage mergers with A < . 35 that are not considered mergers based on their asymmetry.Galaxies in panels c , d , g , and h likely have low asymmetry values due to differences in deblending. However, it isworth noting that an equal mass merger between two similar galaxies will be symmetric about an 180 ◦ rotation, whichmay contribute to the low A values in the case of galaxies in panels d and g . As with the galaxies in Figure 21, thegalaxies shown here are highly concentrated, which also tends to lower the asymmetry value.6 Lackner et al. =−1.34A =0.25G =0.55a)10:01:54.9 +2:24:16.5 8 kpcz=0.90 M =−1.81A =0.14G =0.60b)10:02:04.7 +2:25:25.3 8 kpcz=0.96 M =−1.77A =0.23G =0.61c)10:00:40.3 +2:47:43.7 8 kpcz=0.94 M =−1.58A =0.14G =0.60d)10:00:49.2 +2:06:12.98 kpcz=0.68 M =−1.10A =0.19G =0.54e)10:00:24.8 +1:39:42.9 8 kpcz=0.84 M =−0.75A =0.21G =0.48f)10:00:17.6 +2:20:48.6 8 kpcz=0.72 M =−0.56A =0.11G =0.45g)09:58:55.3 +2:14:15.6 8 kpcz=0.99 M =−0.67A =0.10G =0.47h)10:01:26.3 +2:23:44.1 Figure 23. Examples of galaxies which are not late-stage mergers but are selected as mergers by the Gini- M method (Lotz et al. 2008a).The redshift range is the same as in Figure 21 The images have the same stretch and scaling as those in Figure 21. Most of these systemswould be characterized as minor mergers, and therefore missed by our method. =−1.64A =0.39G =0.58a)10:02:08.6 +2:26:04.9 8 kpcz=0.99 M =−2.08A =0.36G =0.62b)09:59:39.1 +2:03:42.6 8 kpcz=0.83 M =−0.59A =0.36G =0.06c)10:02:22.0 +2:07:37.1 8 kpcz=0.81 M =−1.50A =0.46G =0.62d)10:02:34.3 +2:26:58.48 kpcz=0.85 M =−1.54A =0.39G =0.53e)09:59:46.9 +2:13:40.5 8 kpcz=0.90 M =−1.87A =0.37G =0.55f)10:01:58.0 +2:29:52.4 8 kpcz=0.83 M =−1.58A =0.37G =0.49g)10:01:47.8 +2:08:15.2 8 kpcz=0.84 M =−1.95A =0.43G =0.61h)10:01:37.5 +1:49:35.7 Figure 24. Examples of galaxies which are not late-stage mergers but are selected as mergers based on their asymmetry around a 180 ◦ rotation ( A > . 35 (see Conselice 2003)). The images have the same stretch and scaling as those in Figure 21. Figure 23 shows instead the galaxies detected as mergers by the Gini- M criterion but not selected as late-stagemergers. Panels b , c , d , g , and h show galaxies with only one bright central peak. The galaxy in panel d may have twobright nuclei, but they are not separable by our method. The peaks detected in panels a and e are too faint comparedto their host galaxy to be included by our method. Our method would characterize these galaxies as star-forming, notmerging. The peaks detected in panel f are separated by slightly more than 8 kpc and are therefore excluded fromour sample.Figure 24 shows galaxies which are selected as mergers based on their asymmetry, but not by our median ring filtermethod. The asymmetric features in almost all of these galaxies are too faint to be detected by our method. 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