Draft version August 21, 2014
Preprint typeset using LATEX style emulateapj v. 04/17/13

1

LATE-STAGE GALAXY MERGERS IN COSMOS TO Z ∼ 1

C. N. Lackner , J. D. Silverman1 , M. Salvato2 , P. Kampczyk3 , J. S. Kartaltepe4 , D. Sanders5 , P. Capak6 ,F. Civano7,8 , C. Halliday9 , O. Ilbert10 , K. Jahnke11 , A. M. Koekemoer12 , N. Lee5 , O. Le Fèvre10 , C. T. Liu13 ,N. Scoville6 , K. Sheth14 , and S. Toft15
Draft version August 21, 2014

ABSTRACTThe role of major mergers in galaxy and black hole formation is not well-constrained. To help address
this, we develop an automated method to identify late-stage galaxy mergers before coalescence ofthe galactic cores. The resulting sample of mergers is distinct from those obtained using pair-finding
and morphological indicators. Our method relies on median-filtering of high-resolution images todistinguish two concentrated galaxy nuclei at small separations. This method does not rely on low
surface brightness features to identify mergers, and is therefore reliable to high redshift. Using mock
images, we derive statistical contamination and incompleteness corrections for the fraction of latestage mergers. The mock images show that our method returns an uncontaminated (< 10%) sample
of mergers with projected separations between 2.2 and 8 kpc out to z ∼ 1. We apply our new method toa magnitude-limited (mF W 814 < 23) sample of 44164 galaxies from the COSMOS HST/ACS catalog.
Using a mass-complete sample with log M∗ /M⊙ > 10.6 and 0.25 < z ≤ 1.00, we find ∼ 5% of systems
are late-stage mergers. Correcting for incompleteness and contamination, the fractional merger rateincreases strongly with redshift as ℜmerge ∝ (1 + z)3.8±0.9 , in agreement both with earlier studies andwith dark matter halo merger rates. Separating the sample into star-forming and quiescent galaxies
shows that the merger rate for star-forming galaxies increases strongly redshift, (1 + z)4.5±1.3 , while
the merger rate for quiescent galaxies is consistent with no evolution, (1 + z)1.1±1.2 . The merger rate
also becomes steeper with decreasing stellar mass. Limiting our sample to galaxies with spectroscopic
redshifts from zCOSMOS, we find that the star-formation rates and X-ray selected AGN activity inlikely late-stage mergers are higher by factors of ∼ 2 relative to those of a control sample. Combining
our sample with more widely separated pairs, we find that 8 ± 5% of star formation and 20 ± 8% of
AGN activity is triggered by close encounters (< 143 kpc) or mergers, providing additional evidence
that major mergers are not the only channels for star formation and black hole growth.
Keywords: galaxies: active – galaxies: formation – galaxies: interactions – techniques: image processing
1. INTRODUCTION

In a hierarchical universe, galaxies grow by accretion ofgas and mergers. Dark matter simulations suggest thatclaire.lackner@ipmu.jp
1 Kavli IPMU (WPI), The University of Tokyo, Kashiwa, Chiba
277-8583, Japan
2 Max-Planck-Institut für extraterrestrische Physik, D-84571
Garching, Germany
3 Institute of Astronomy, Department of Physics, ETH Zürich,
CH-8093 Zürich, Switzerland
4 National Optical Astronomy Observatory, Tucson, AZ 85719,
USA
5 Institute for Astronomy, University of Hawaii, Honolulu, HI
96822
6 California Institute of Technology, Pasadena, CA 91125
7 Harvard-Smithsonian Center for Astrophysics, Cambridge, MA
02138
8 Department of Physics and Astronomy, Dartmouth College,
Hanover, NH 03755
9 23, rue d’Yerres, F-91230 Montgeron, France
10 Aix Marseille Université, CNRS, LAM (Laboratoire dAstrophysique de Marseille), 13388, Marseille, France
11 Max-Planck-Institut für Astronomie, D-69117 Heidelberg,
Germany
12 Space Telescope Science Institute, Baltimore, MD 21218
13 Astrophysical Observatory, CUNY, College of Staten Island,
NY 10314 USA
14 National Radio Astronomy Observatory/NAASC, Charlottesville, VA 22903
15 Dark Cosmology Centre, Niels Bohr Institute, University of
Copenhagen, Copenhagen, DK-2100 Denmark

the halo merger rate (in units per Gyr) increases with
redshift as (1+z)2−3 (Lacey & Cole 1993; Fakhouri et al.
2010). However, identifying merging galaxies and transforming those observations into a galaxy merger rate is
not easy, as is illustrated by the large discrepancies between different methods (see Patton & Atfield 2008; De
Propris et al. 2007; Bell et al. 2006; Jogee et al. 2009;Lotz et al. 2011, and references therein). These discrepancies are mainly due to differences in sample selection and merger identification (see Lotz et al. 2011).
Nonetheless, a precise determination of the merger rateof galaxies is essential to the study of galaxy growth. In
particular, the galaxy merger rate is needed to compare
the growth of galaxies to the growth of dark matter halos. Galaxy mergers may also play an important rolein shaping galaxy morphology (Toomre & Toomre 1972;
Sanders et al. 1988; Barnes & Hernquist 1992; Hopkins
et al. 2009), instigating star formation (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-massive black 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 identifying galaxy mergers. The first class of methods selects
close pairs of galaxies, before the galaxies have merged

2Lackner et al.

(e.g., López-Sanjuan et al. 2013, 2011, 2012; Bundy et al.
2009; Lin et al. 2004, 2010; Patton & Atfield 2008; 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 methods typically select galaxies with projected separations less than
100 h−1
100 kpc. The line-of-sight separation depends onthe method used. Galaxy mergers selected using photometric redshifts include pairs that are widely separated
along the line-of-sight and will never merge (e.g., Kartaltepe et al. 2007; Bundy et al. 2009; López-Sanjuan et al.
2011, 2012). Although these methods cannot identify
individual chance superpositions, superpositions can beeasily accounted for statistically in merger-rate calculations (e.g. Bundy et al. 2009; López-Sanjuan et al. 2011,2012). To better distinguish chance superpositions from
actual mergers, several studies utilize spectroscopic redshifts and identify kinematic pairs of galaxies (e.g., Linet al. 2004; Patton & Atfield 2008; de Ravel et al. 2009;de Ravel et al. 2011; Kampczyk et al. 2013; Ellison et al.
2013; López-Sanjuan et al. 2013). For spectroscopic samples, understanding the completeness of the spectroscopy
as a function of galaxy separation is essential (Kampczyk
et al. 2013; Patton & Atfield 2008; Lin et al. 2004). Although using kinematic pairs eliminates many chance superpositions from a sample of galaxy mergers, spectroscopic samples contain far fewer galaxies than photometric samples and often omit close pairs due to fiber collisions, leading to poorer statistics when measuring galaxy
merger rates.
The second class of methods for finding galaxy mergers looks for morphological signatures during or after amerger (e.g., double nuclei, tidal tails, outer shells). Morphological 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 measures of 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; López-Sanjuan et al. 2009). Visual inspection involves searches for merger signatures, some obvious, suchas double nuclei, and some subtle, such as sharp breaks
in the radial light profile. Measurements, such as the thecentral concentration, asymmetry, and clumpiness (CAS)(Abraham et al. 1994; Conselice 2003), the second moment of the light profile (M20 ) (Lotz et al. 2004), and
the Gini coefficient of the two-dimensional flux distribution (Abraham et al. 2003; Lotz et al. 2004), seek toquantify the morphological signatures of bulges, disks,and galaxy mergers. By comparing visual classification with these quantitative measures, Lotz et al. (2004)
demonstrate that major mergers occupy a distinct part of
the Gini-M20 -concentration-asymmetry space. However,neither visual classification nor non-parametric morphology methods can directly measure the merger mass ratio
or distinguish between major and minor mergers. In fact,
morphology-based methods are sensitive to very minor
mergers and even close passages that cause morphological 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 many
data sets with various selection functions. The resulting fractions of merging galaxies at z ∼ 0.5 vary acrossthe range 1 − 20% and the evolution of the merger rateis either very steep, (1 + z)4 , or non-existent, (1 + z)0 .
Several works address these differences (e.g., Patton &Atfield 2008; Jogee et al. 2009; Lotz et al. 2011). Someof the differences may be due to variations in the parent sample selection with redshift. Samples selected atfixed number density yield a different merger-rate evolution than those selected at fixed stellar mass (Lotz et al.
2011). In addition, the length of time each method is sensitive to a galaxy merger is highly uncertain and varies
greatly as a function of merger-finding method and as afunction of redshift and merger mass ratio. Both photometric pair-finding methods and morphological methods
mis-identify galaxy mergers and often select chance superpositions of galaxies that are widely separated along
the line of sight. Spectroscopic pair studies do greatly
limit the number of line-of-sight pairs. Morphologybased methods often select galaxies in which close passages or very minor mergers caused dramatic morphological disturbances. While most studies correct for these
mis-identifications, the correction factor is difficult to accurately calculate. The typical assumed fraction of misidentified mergers ranges from 0 to 60% (see Lotz et al.
2011, and references therein).
In this work, we present a new quantitative method for
identifying merging galaxies. Our method is in essencea high-pass filter that makes multiple peaks in galaxy
surface brightness profiles easily distinguishable. The
method is designed to select a sample of late-stage mergers in which two galaxy nuclei are still intact and only
separated by a few kpc. In particular, we select galaxies
whose nuclei are separated by 2.2−8 kpc, and expected tomerge within a few hundred Myr (see Lotz et al. 2011).
These galaxies lie at the interface between early-stage
galaxy mergers selected in close pair studies and postmerger galaxies selected based on disturbed morphologies. We show below that our sample of late-stage mergers has little overlap with kinematically selected, more
widely separated pairs. At separations of a few kpc, it isless likely that the galaxy pair is a chance superposition
than at larger separations (e.g. Kartaltepe et al. 2007),
reducing contamination from spurious pairs. Eliminating
pairs that are likely to be spurious mergers, ensures that
our estimate of the merger rate is robust and competitive
with other merger-finding methods, including searches
for spectroscopic pairs. While many galaxies in our sample could be selected by visual inspection, in practicethere is little overlap between mergers identified by otherquantitative morphology methods (e.g., Gini-M20 , asymmetry) and our sample of late-stage mergers. This is
likely because galaxies with two very close, equally-brightcentral peaks do not have abnormally large asymmetryor second moment values.
In addition to the number of merging galaxies, theproperties of merging galaxies are also of much interest. Numerical simulations of merging galaxies demonstrate that major mergers can drive gas toward the center of galaxies leading to enhanced star formation, efficient bulge creation, and AGN activity as some of the gas
is deposited onto the central black hole (e.g., Hernquist
1989; Mihos et al. 1992; Barnes & Hernquist 1992; Hop-3

Galaxy Mergers in COSMOS
kins et al. 2008, 2006). Several observational studies haveshown that merging galaxies typically have enhanced starformation (e.g., Kartaltepe et al. 2012; Robaina et al.
2009; Xu et al. 2012; Kampczyk et al. 2013; Hung et al.
2013). Almost all intensely star-forming systems, suchas luminous infrared galaxies (LIRGS), in the local universe have morphologies consistent with major mergers(Sanders & Mirabel 1996; Wu et al. 1998; Cui et al. 2001;
Kartaltepe et al. 2010). Several studies have also foundthat a larger fraction of close pairs between z ∼ 0 andz ∼ 1.2 have AGN activity than isolated galaxies (e.g.,
Kennicutt & Keel 1984; Keel et al. 1985; Alonso et al.
2007; Silverman et al. 2011; Koss et al. 2011; Ellison et al.
2013; Satyapal et al. 2014, but see Darg et al. 2010a; Liet al. 2008; Ellison et al. 2008). Nonetheless, the majority of low-luminosity AGN activity is not associated withmerging galaxies (e.g., Cisternas et al. 2011; Schawinski
et al. 2011; Kocevski et al. 2012; Kauffmann et al. 2004;
Silverman et al. 2011). Using COSMOS HST images,
Cisternas et al. (2011) find that X-ray selected AGNs
are no more likely to be ongoing or recent major mergers than a control sample of inactive galaxies. Silverman
et al. (2011) examine close kinematic pairs with separations less than 75kpc and find that 18% of X-ray selected
AGN activity since z ∼ 1 is triggered by interactions ofclose pairs. Including late-stage mergers will increase
the completeness of pairs at separations less than 10 kpc
and boost the fraction of AGN associated with merging. Late-stage mergers may help explain a significant
fraction of the AGN activity not currently associatedwith galaxy pairs. Furthermore, understanding galaxy
properties as a function of time to coalescence can help
test numerical models of merging galaxies and black hole
growth (e.g., Hopkins et al. 2006; Di Matteo et al. 2007;
Mihos et al. 1992).
In this study, we apply our method, which selects
galaxies likely undergoing late-stage mergers, to a fluxlimited sample of 44164 galaxies from the COSMOS survey. Since we are looking at high redshift and therefore
require high spatial resolution to separate galaxy pairs,
we apply our pair-finding method to Hubble Space Telescope (HST) images taken as a part of the COSMOS
survey (Scoville et al. 2007; Koekemoer et al. 2007). The
galaxies are selected from the ACS galaxy catalog (Leauthaud et al. 2007). Photometric redshifts, stellar masses,
and absolute magnitudes are taken from the most recent
near infrared-selected COSMOS catalog (Ilbert et al.
2013; McCracken et al. 2012). The data and mergerfinding method are described in detail in §2 and §3. The
sample of 2047 late-stage mergers is presented in Table 2.
Thirty-two of these late-stage mergers are also detectedin X-ray by either Chandra or XMM.
We test the robustness of our method using simulated
images of mergers in §3.1. After demonstrating that
our selection of late mergers is almost independent ofredshift, we calculate the galaxy merger rate as a function of redshift across the range 0.25 ≤ z < 1.0 (§4).
Finally, we analyze the star-formation rates and X-ray
selected AGN fractions for the sub-sample of our datawith spectroscopy from zCOSMOS (Lilly et al. 2007,2009). Unless otherwise noted, we use the cosmology
H0 = 70 km s−1 Mpc−1 , Ωm = 0.25, ΩΛ = 0.75. Whenreferring to other studies, we use units of h−1
100 kpc where

H0 = 100 km s−1 Mpc−1 . 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) initial mass function (IMF).
2. DATA

Finding late-stage galaxies mergers with two intact nuclei out to z ∼ 1 requires the high resolution available in space-based images. We apply our pair-finding
method to HST/ACS F814W (I−band) images taken as
part of the COSMOS project (Koekemoer et al. 2007;
Massey et al. 2010). The pixel scale in these images in0.03′′ /pixel and the point spread function (PSF) has a
FWHM of ∼ 0.09 pixels, which corresponds to 0.6 kpc
at redshift z = 1. Although our merger-finding method
could be applied to ground-based data, the method requires that stellar concentrations separated by a few kpc
are resolved. In Sloan Digital Sky Survey (SDSS) images,
the median seeing in 1.3′′ , which corresponds to 2.4 kpc
at z = 0.1. Therefore, our method could only be applied to SDSS data at z < 0.1. For ground-based datawith better seeing, the redshift limit could be increased
to z ∼ 0.3. However, to study the evolution of the merger
rate to significant redshift, HST data is necessary.
For each galaxy in the parent sample, we create an
8′′ × 8′′ cutout from the ACS F814W image. Thesecutouts are used to detect late-stage mergers. In thiswork, we use two overlapping samples of galaxies, both
selected from the COSMOS ACS catalog (Leauthaud
et al. 2007). The first sample uses photometric redshifts
and contains ∼ 44, 000 galaxies. The second sample includes ∼ 17, 000 galaxies and uses spectroscopic redshifts
from the zCOSMOS project (Lilly et al. 2007, 2009). Owing to its greater size, we use the photometric sample tostudy the merger rate as a function of redshift. We use
the spectroscopic sample to study the star-formation and
AGN activity in late-stage mergers.
2.1. Photometric Redshift Sample
Our parent galaxy sample is selected from the COSMOS ACS catalog (Leauthaud et al. 2007). We selectall objects classified as galaxies (MU_CLASS = 1) with total magnitudes brighter than I = 23. In the case ofa merger, the total magnitude of the post-merger galaxy
will be brighter than I = 23, while the individual components of the merging galaxy may be up to 5 times fainter(I ≈ 24.7), but still within the magnitude limit of the
COSMOS ACS sample. The magnitude limit is necessary
because the completeness of our merger-finding method
decreases with decreasing signal-to-noise (see §3.1). We
obtain redshifts and stellar masses for the galaxies in
the ACS-selected catalog by matching to the recent Kband selected sample of COSMOS galaxies with photometric redshifts (McCracken et al. 2012; Ilbert et al.
2013). This catalog includes photometric redshifts andstellar masses for 90% of the galaxies in our ACS-selected
sample. The absence of some galaxies is due to slight differences in the observed area and the masking between
the ACS and K−band catalogs. We exclude all galaxies
masked in Ilbert et al. (2013), as these galaxies do nothave reliable photometric redshifts or stellar masses. Ilbert et al. (2013) report a photometric redshift precisionof σ∆z/(1+z) = 0.008 for i+ < 22.5. The final sample
contains 44, 164 galaxies.

4

Lackner et al.

In §5.2, we study the X-ray selected AGN fraction
in late-stage mergers. Unlike Ilbert et al. (2013), we
therefore include known X-ray sources in our parent
galaxy sample. For these sources, we use photometric redshifts from Salvato et al. (2011) for optical/NIR
sources matched to XMM (Brusa et al. 2010) and Chandra (Civano et al. 2012) detections. Depending on thetype of AGN, these photo-zs are computed using different galaxy-AGN hybrid templates, different luminosity
priors, and accounting for source variability. We notethat the Chandra survey only covers ∼ 1/2 of the COSMOS area, although to a greater depth. Out of theparent sample of 44, 164 galaxies, 502 galaxies have an
XMM counterpart, and 573 have a Chandra counterpart, with 282 of these 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 sources identified in XMM, we use stellar masses
computed by Bongiorno et al. (2012). These masses
and photo-zs are most reliable for galaxies that are not
AGN/quasar dominated (type I). For the analysis of the
AGN fraction, we restrict our galaxy sample to systems
that are not AGN-dominated, based on the photo-z templates used. This eliminates galaxies with the least certain photo-zs and stellar masses.
When matching the ACS catalog to the ground-based
K-band selected catalog, 1% of sources (640 sources)that are resolved into 2 galaxies in the HST data are
not resolved in the ground-based data. These galaxies
are clearly possible late-stage mergers with small separations, and cannot simply be removed from the sample.
For these cases, we ensure that the galaxy is includedin the sample only once and use the sum of the I-band
magnitudes for the total magnitude. Because our sample is selected from the ACS catalog, we may be missing
resolved late-stage mergers in which both of the components are below the I−band magnitude limit. However,resolved galaxy pairs make up less than 10% of our final late-stage merger sample, as most of the resolved
pairs are more widely separated than the late-stage mergers selected below. From visual inspection, ∼ 70% of
these resolved galaxy pairs show clear signs of interaction, while the remaining pairs may be chance superpositions. This fraction of chance superpositions agrees wellwith that obtained by other methods (see §4.1). However, by randomly adding galaxies to COSMOS images,
Kampczyk et al. (2007) find the fraction of chance superpositions in a sample of visually selected mergers is
40% at z ∼ 0.7, suggesting that visual inspection cannot
reliably distinguish real mergers from chance superpositions. Because we use visual inspection to ascertain thenumber of chance superpositions, we may underestimate
the fraction of chance superpositions by almost a factorof two.
For chance superpositions in which two galaxies atdifferent redshifts are unresolved by ground-based observations, the photometric redshifts are especially suspect (Bordoloi et al. 2010). Comparing the photometric redshifts to the available spectroscopic redshifts (see§2.2), we find the rate of catastrophic outliers for possible late-stage mergers is 1.6% compared to 1.0% for theentire sample of galaxies in the range 0.25 < zspec. <1.0. However, the catastrophic outlier rate for the latestage merger candidates is still small, and the preci-sion of the photometric redshifts remains unchanged(σ∆z/(1+specz) = 0.004). In this work, we will assume
the photometric redshifts of the late-stage merger candidates are as accurate as those for the entire sample.
The comparison to spectroscopic redshifts does not take
into account that the spectroscopic redshifts of late-stage
mergers may also be suspect, because the galaxies are
typically separated by less than an arcsecond and theirspectra are blended. We visually inspect the spectra oflate-stage mergers and do not find any in which two
merging galaxies are easily discernible in ground-based
spectroscopic data.
2.2. Spectroscopic redshift sample
In §5, we compare the AGN and star-formation
rates (SFRs) of our late-stage mergers to those of
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 (§5.1), we use thebright zCOSMOS 20k bright sample (I < 22.5), whichcontains 16, 467 galaxies with reliable redshifts. Following Lilly et al. (2009), we only use galaxies with redshifts
in the confidence classes 1.5, 2.4, 2.5, 3.x, 4.x, and 9.5,
as well as secondary targets with the same redshift confidences. In principle, the spectroscopic sample should
be a subset of the larger ACS-selected photo-z sample
above. However, differences in masking and the observed
region exclude ∼ 1200 galaxies in the zCOSMOS survey
from the photometric redshift sample described above.
Unlike kinematic pair studies in which both members ofthe merger have measured spectroscopic redshifts, in our
sample of late-stage mergers, we only have one spectroscopic measurement for the entire merging system. Mostof the late-stage merger candidates described below are
separated by less than an arcsecond, so their spectra are
blended. As stated above, we visually inspect a subset ofthe spectra for these galaxies, and find no case in which
two sets of lines (two redshifts) are easily discernible.
In §5.2, we compare the fraction of X-ray selected AGN
in late-stage mergers to the fraction of AGN in kinematic pairs. To simplify the comparison, we use the same
parent sample as Silverman et al. (2011) and Kampczyk
et al. (2013). As in Silverman et al. (2011), we use Chandra observations to identify AGN. Since the Chandra survey (Elvis et al. 2009) only covers ∼ 1/2 of the COSMOS
field, the parent sample of galaxies is smaller. Therefore,
we only examine 10, 681 galaxies from the bright zCOSMOS survey that lie within the Chandra footprint.
Table 1 lists the various parent samples, as well as thetheir properties. We also include the cuts made to thesesamples for the analysis in §4 and §5.
3. MERGING GALAXY SELECTION

To separately detect each component in a merging
galaxy, we run the images through a high-pass filter,
which makes multiple peaks in the flux distribution easily distinguishable. Our procedure, illustrated in Figure
1, is as follows:• We first convolve each postage stamp image witha median ring filter (Secker 1995). This smooths
the image by replacing each pixel with the medianvalue in a ring surrounding that pixel, thus erasing structures on scales larger than the ring. We

5Galaxy Mergers in COSMOS
Table 1
Parent sample properties
Parent sample
photo-zphoto-zphoto-z
spec-zspec-zm(I814W ) limit

z limitslog M∗ /M⊙ limit

Ngal

Nmergerpair sep. limits [kpc]section

< 23
< 23
< 23
< 22.5< 22.5––[0.25,1.0][0.25, 1.05][0.25, 1.05]––> 10.6> 10.4> 10.4

44164
44164
6226
5001
3474

2047
1547
148
166
112

<8
[2.2,8][2.2,8]<8<8§2.1, Table 2a§2.1§4§2.2, 5.1
§2.2, 5.2ba The full sample without any cuts in redshift, mass, or pair separation is very incomplete at high redshift. We do not use it
for any analysis.
b The smaller spectroscopic sample overlaps with the Chandra survey (Elvis et al. 2009), which is used to select X-ray AGNs.

set the inner ring radius to 9 pixels, which is approximately 3 times the PSF width. This sets thesize of the smallest separation we can detect. Atz ∼ 1.0(0.2), 9 pixels corresponds to 2.2(1.1) kpc.
For comparison, in SDSS images at z ∼ 0.1, a 9pixel radius median ring filter could only detectpeaks separated by at least 6 kpc. To apply thismethod to ground-based data, the size of the median ring filter (in pixels) would have to be adjusted
for the seeing.
• We then subtract the smoothed image from theoriginal image. Together, these first two steps create a high-pass filter.
• In the difference image, we select all pixels 5 standard deviations above the noise. Contiguous regions 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 §3.1 that using these detection
thresholds yields a sample of peaks that is relatively complete yet uncontaminated, particularly
for mergers between early-type, bulge-dominatedgalaxies.
Many of the detections returned by this algorithm are
not actually merging galaxies, but rather widely separated galaxies (our postage stamp images span > 50kpc
at z ∼ 1), galaxies with clumpy star formation, spiralarms, or bars. Another source of contamination is edgeon disk galaxies in which a large bulge is bisected bya dusty disk. In order to eliminate most of these spurious mergers, we place further restrictions on the detectedpeaks.
First, we require that the peaks are separated by no
more than 8 kpc. We use this upper limit to restrict the
sample to galaxies that are likely to be mergers, not justclose pairs or chance superpositions. This limit also eliminates the problem of double-counting late-stage mergers,
as widely separated galaxy pairs will be two separate detections in the parent galaxy sample.
To study the fraction of merging galaxies as a functionof redshift, we also implement a lower bound on the peakseparation of 2.2 kpc. This lower limit is set by the sizeof the median ring filter. In this way, we are sensitive
to mergers at similar separations at both low and highredshift. Implementing this lower bound on the peak separation eliminates 25% of the late-stage mergers, mainly
at low redshift.

Second, we remove detected peaks that are faint compared to both the brightest peak in each galaxy and thegalaxy as a whole. We measure the flux in each component simply by summing the flux in the pixels associatedwith the peak. Since this only includes the flux in thecentral region of each merging component, this is an underestimate of the flux in each component. Based onstudies of merger selection in mock images (see §3.1 andAppendix A), we require that every detected peak contain at least 3% of the the total galaxy flux. We demonstrate below that this successfully eliminates 80 − 90% of
the contamination from non-merging galaxies and starforming clumps, without greatly affecting the completeness of our sample. In order to only study major mergers, we require that every detected peak is at least 1/4
as bright as the brightest peak detected for each galaxy.
However, while this cut helps eliminate contaminationfrom minor mergers (see Figure 20), the measured flux
ratio is inaccurate as are cuts based on it. Together, thecuts in flux ratio eliminate 75% of the galaxies that would
otherwise be considered late-stage mergers. However,neither of these cuts significantly affects our completeness, which is determined by the efficacy of the medianring filter. After these cuts, our overall completeness is∼ 20%, but this increases to ∼ 80% for mergers between
bulge-dominated galaxies.
Finally, there are some images that have more than 2
detected peaks. We expect triple merging systems to be
extremely 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
can be eliminated from the late-stage merger sample byrequiring that multiple peaks 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 Pearson
correlation coefficient for the peak centroids is less than
0.5. After all the other cuts have been applied, this cut
eliminates 7% of the detected late-stage mergers (145 of
2, 047).
With these restrictions, we find 2, 047 (1, 547 with separations greater than 2.2 kpc) late-stage mergers withtwo prominent flux peaks in the photo-z sample of 44,164
galaxies. These are listed in Table 2 along with some basic properties of the galaxies and the detected peaks. In
the spectroscopic sample of 16, 467 galaxies, we find 819
merging galaxies, 71 of which are not included in thephoto-z sample due to differences in masking. The latestage mergers in the zCOSMOS sample are also listed
in Table 2. For each late-stage merger, we include the6Lackner et al.

Original ImageMedian Filtered Image

10:01:33.6 +01:38:07.5
z=0.58Detected Peaks

1''

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

10:02:09.3 +2:01:27.5
z=0.8410:00:18.8 +2:06:53.3
z=0.31

10:01:39.3 +2:22:23.7
z=0.90

1''

1''

1''

09:58:28.9 +2:27:39.3
z=0.82

09:59:55.7 +2:33:30.9
z=0.73

09:58:22.7 +2:49:24.5
z=0.38

1''

1''

1''

Figure 2. Examples of merging galaxies in the photo-z sample after cuts in peak separation and peak flux. The ×s show peaks found by
the median fing filter. The bottom center image may be an edge-on disk with asymmetric spiral arms instead of a merger.

projected 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 latestage mergers are matched with a Chandra source out of
534 mergers that lie within the Chandra footprint.
Although we are confident that the majority of latestage mergers listed in Table 2 are physical late-stage
mergers, not all the systems identified by our method
will be real mergers. In addition to isolated galaxies
with clumpy central structure, our sample contains lineof-sight superpositions. We show below that these chancesuperpositions represent 30% of the late-stage merger
sample. Without spectroscopic redshifts for each member of the merger or detailed kinematic maps, it is im-

possible to distinguish real late-stage mergers from either widely-separated chance superpositions or isolated
galaxies with complex structures. By tuning the selection criteria to accept smaller peaks, our median-ringfilter method could be used to find galaxies with several
bright clumps instead of late-stage binary mergers.
We note that, other than the pair separation and flux
ratio, all measured properties (e.g., color, redshift, stellar
mass, X-ray flux) are properties of the merger, not theindividual component galaxies. If we categorize galaxies
by stellar mass, merging galaxies are counted with galaxies more massive than either member of the merger. In
this way, late-stage mergers are treated more like postmerger galaxies than pairs of galaxies in the early stagesof merging. This distinction is important to keep in mind

7

Galaxy Mergers in COSMOS

Not selected as mergers

09:58:49.7 +1:57:29.2 09:58:57.0 +1:58:06.7 10:02:10.6 +2:34:59.4
z=0.29z=0.66z=0.81

1''

1''

1''

Figure 3. Examples of galaxies for which multiple peaks are detected, but that are not considered mergers. The ×s show peaks foundby the median ring filter. These galaxies are removed from the merger sample by the cuts explained in §3. These galaxies fail because
the detected peaks are too faint compared to the central peak (left), all but the central peak are too faint compared to the whole galaxy(middle), and the two peaks have a projected separation larger than 8 kpc (right).

when comparing to samples of paired galaxies, in which
properties for the individual galaxies are reported.
Figure 2 shows images of 6 late-stage mergers in thephoto-z sample. Although the galaxy in the lower middle panel may be a spiral galaxy without any merging
activity, the remaining galaxies are clearly mergers at
various separations. The typical peak separation is lessthan 1′′ , demonstrating why our algorithm requires thehigh resolution of space-based data. Figure 3 shows three
examples of galaxies that do not satisfy the cuts on either peak flux ratio, peak separation, or peak Pearson
correlation coefficient. These galaxies are often spiralor barred galaxies. As noted above the median ring filter detects edge-on disk galaxies, in which the bulge isbisected by dust in the disk, as binary mergers. However, these galaxies represent a small contamination. At
fixed SFR, the fraction of late-stage merger candidates is
independent of galaxy ellipticity, a proxy for disk inclination, suggesting our detection algorithm is not biased
by galaxy inclination and dust obscuration.
3.1. Simulated Merger Images

We test our merger detection algorithm on a set of simple mock images of merging galaxies. We create postage
stamps of pairs of galaxies using the HST/ACS images
from the photo-z sample. Each mock image contains 2
random galaxies at the same photometric redshift. We
choose galaxies at the same redshift in order to eliminate line-of-sight chance superpositions, which we address statistically in §4.1. By using real galaxy images
drawn at random, we can create a sample of mergers
with realistic morphologies, magnitudes, and flux ratios.
Note, however, that this method does not include any
surface brightness changes caused by mergers. In particular, we cannot account for the effects optically-brightstar-formation triggered by mergers, or additional obscuration, which may occur with triggered star formation,
will have on our pair detection efficiency. We simply superimpose images of isolated galaxies.
For each pair of galaxies, we make 8 mock images inwhich the galaxies are separated by 0.5, 1.5, 2.0, 2.5,
3.0, 5.0, 7.0, and 10.0 kpc. This allows us to test thecompleteness of our sample as a function of projected
separation. Details of the mock images are discussed inAppendix A. Because the flux limits and separation lim-

its used in this study are derived from these simulations,applications of the median-ring filter method to otherdata sets require new simulations matched to the observations and adjustments to the flux and separation limits
given in §3.
After running these mock merger images through themedian ring filter, we examine the completeness of ourmerger sample as a function of pair separation, redshift,and flux ratio. Unsurprisingly, we find that the efficiency
of detecting late-stage mergers drops precipitously if thepair separation is smaller than ∼ 10 pixels, the size of themedian ring filter (see Figure 18). This motivates using alower bound of 2.2 kpc (9 pixels at z ∼ 1) on the pair separation. The median ring filter selects ∼ 40% of the mockmergers with separations larger than 2.2 kpc to z = 1.
This completeness depends strongly on galaxy morphology. Because the median ring filter smooths away diffuse
structures, our merger-finding method is biased toward
mergers between concentrated, early-type galaxies16 . For
these mergers, our method is 80% complete, while formixed mergers (late+early) and mergers between latetype galaxies, the median ring filter only selects 40%
of mock mergers. After removing contamination, thecompleteness of our selection of early-type mergers is independent of redshift. For late-type galaxies, the completeness drops slightly at higher redshifts (see Figure
17, right panel). For all morphologies together, the completeness drops between z ≈ 0.2 and z ≈ 0.5, as the fraction of early-type galaxies also decreases toward higher
redshift.
In addition to using the mock mergers to study completeness, we can use them to study the contaminationfrom non-merging, clumpy galaxies and minor mergers(see Figure 20). We find that, unlike the completeness, the contamination is essentially independent of redshift. This may be because our merger-finding method isless sensitive to all structures at lower signal-to-noise,
and, therefore, higher redshift. Using artificially redshifted mergers, Kampczyk et al. (2007) find that mergers identified in low-z data do not appear as mergers
at higher redshift due to lower resolution and signal16 We use the ZEST parameter (Scarlata et al. 2007) to ascertain
the morphologies of the galaxies in a mock merger. See §3.3 formore details.

8Lackner et al.
Table 2Late-stage mergers in photo-z + spec-z samples

RA (J2000)a

Dec (J2000)a

149.51058
149.83214
149.83058
150.20693
150.39549
150.51472

2.74338
1.94120
1.902141.68028
2.057542.59320

photo-zb

spec-zcmI d

log M∗ /M⊙ eseparation [′′ ]flux ratio

Chand. log LX f

XMM log LX f

0.49
0.66
0.73
1.11
–
0.37

–
0.70
0.73
–
0.96
–

22.21
22.48
21.25
22.76
21.71
22.71

9.57
9.50
10.95
10.80
10.57
8.81

0.35
0.78
0.62
0.31
0.44
0.36

0.50
0.61
0.31
0.88
0.96
0.34

–
–
42.6
43.8
43.1
–

–
–
–
43.9
–
–

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).
−1
f log L. XMM data from Brusa et al. (2010), Chandra data
X is the X-ray luminosity in the band 0.5 − 10 keV in units of erg sfrom Civano et al. (2012).

to-noise, which may explain the incompleteness of ourmerger selection at high redshift. However, unlike Kampczyk et al. (2007), our merger identification does nottake into account morphological k-corrections. Since
galaxies are less smooth at bluer wavelengths and havea larger fraction of their flux concentrated in smaller regions, our peak-finding method may detect more nonmerging, star-forming galaxies at bluer rest-frame wavelengths, increasing the amount of 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 SFRs, thus again increasing the contaminationfrom non-merging, clumpy star-forming galaxies. The
lack of redshift dependence in the contamination suggests our method is not particularly sensitive to clumpy
star-formation at high redshift, possibly because theseclumps are too small and faint. A better understandingof the effects of morphological k-corrections will require
further study using multi-wavelength data, in particularnear-infrared data at z ∼ 1.
We use the mock mergers to determine the cuts on
both the peak-to-galaxy flux ratio (> 3%) and the peakto-peak flux ratio (> 25%). By implementing thesecuts, we are able to reduce the contamination from nonmerging galaxies to 10%, and the contamination fromminor mergers (flux ratios smaller than 1:4) to 20%.
The median ring filter is naturally less sensitive to minor mergers than major mergers since the faint member of the merger is likely to be below our detection
threshold. These cuts do affect the completeness, decreasing it by a factor of 2 to 20% (see Figure 17). However, the completeness for early-type galaxy mergers islarger unaffected. Removing the cut on peak flux togalaxy flux ratio increases the contamination from nonmerging sources to ∼ 40%, which significantly affects
our results on internal late-stage merger properties (SF,
AGN), which cannot be simply corrected. In calculating
the merger rate (§4), we correct the measured late-stage
merger fractions for contamination and incompleteness.
For all mergers, we take the contamination to be 30%,
independent of redshift. The incompleteness correction

is a function of redshift and merger type and is derived
from Figure 17.
3.2. Caveats

Although our simulations demonstrate the effectiveness of our merger finding, there are several failure modesof the algorithm. First, the method does not distinguish between merging galaxies and chance superpositions. Since we are looking at extremely small separations, we expect the number of chance superpositions tobe small. Although we correct the merger rates in §4 forchance superpositions, we cannot correct the propertiesof mergers for contamination from chance superpositions.
Second, tests with mock merger images show that themedian ring filter is most sensitive to highly concentrated
galaxies. This suggests the merger rate measured forearly-type (quiescent) galaxies is very robust, but themerger rate for late-type (star-forming) galaxies is underestimated by as much as a factor of 3, after accounting for contamination from non-mergers and line-of-sightsuperpositions. Furthermore, the bias toward highly concentrated galaxies may introduce biases in the sample as
a function of redshift. Morphological k-corrections willlead to more disk-dominated, less centrally concentrated,galaxies at high redshift (Kuchinski et al. 2000; Papovich
et al. 2003). Therefore, a bias toward detecting concentrated galaxies is likely to under-report the number oflate-stage mergers at high redshift.
Finally, because we impose a flux ratio cut, our method
cannot detect a merger with only one optically bright
AGN. Therefore, in §5.2, we only compute the AGN
fraction for obscured (Type II) AGN. In addition, thestellar masses and photometric redshifts for Type I AGN
are less certain than for obscured, optically faint AGN.
Thus, removing Type I AGN from the sample improves
the accuracy of our results.
3.3. Comparison with other selection techniques
There are many established methods for selecting
merging galaxies. The simplest methods select galaxies
based on angular separation (e.g., Carlberg et al. 1994;
Zepf & Koo 1989). These methods typically look at sep-

9

Galaxy Mergers in COSMOS

17 The Gini coefficient measures the relative distribution offlux in pixels associated with a galaxy. It is given by G =n
1/ 2f¯n(n + 1) Σni=1 Σj=1 |fi − fj |, where fi is the flux in a pixel,
n is the number of pixels, and f¯ is the mean flux per pixel (Abraham et al. 2003)
18 M
20 is the second moment of the flux around a galaxy’s center22(Σni=1 fi (xi + yi )), only counting the brightest pixels which total
20% of the galaxy’s flux. This is then normalized by the galaxy’s
total second moment, summing over all pixels (Lotz et al. 2004).

0.75
0.70
0.65

mergers
ZEST=1
ZEST=2
ZEST=3

G−M20 Mergers

Gini

0.60
0.55

0.50
0.45
0.40
0.35
0.24
0.18
0.12
0.06
0.00
0.0

fraction

arations of 5 − 100 h−1
100 kpc, and need to be corrected
for chance superpositions and galaxies that are physically close, but will not merge within a Hubble time.
The number of superpositions can be limited by requiringthat the galaxies have similar photometric redshifts (e.g.,
Kartaltepe et al. 2007; Bundy et al. 2009). Spectroscopic
redshifts are also useful in eliminating chance superpositions (e.g., Patton et al. 2002; Patton & Atfield 2008;
Kampczyk et al. 2013; Lin et al. 2004, 2008; Le Fèvre
et al. 2000; de Ravel et al. 2009; de Ravel et al. 2011;
Ellison et al. 2008). However, spectroscopic samples arelimited in size and depth. Furthermore, the late-stage
mergers reported here typically have sub-arcsecond separations. Systems with such small separations will not
be resolved in ground-based spectroscopic studies, evenwhen including pairs that are observed in the same slit
(e.g. Kampczyk et al. 2013). Comparing our results tothe spectroscopically selected pair sample in Kampczyk
et al. (2013), we find only 20% of late-stage mergers arealso kinematic pairs and most of these mergers have separations larger than 2′′ .
Pair samples look for galaxies in the early stages ofmerging. Morphological studies, on the other hand, lookfor evidence of mergers at all stages, including late-stage
mergers and post-merger galaxies. Merger studies basedon morphology rely on either visual classification (e.g.,Kampczyk et al. 2007; Bridge et al. 2010; Darg et al.
2010a; Kartaltepe et al. 2010) or quantitative morphology indicators. Indicators used to distinguish mergers include the Gini coefficient17 and the second moment of thebrightest pixels, M20 18 (e.g., Abraham et al. 2003; Lotz
et al. 2004, 2008a); the galaxy asymmetry and concentration (e.g., Conselice et al. 2009; Shi et al. 2009; LópezSanjuan et al. 2009); and combinations of the above, as
well as parametric fits to galaxy luminosity profiles (e.g.,
Scarlata et al. 2007; Cassata et al. 2005). In particular,
Scarlata et al. (2007) use principle component analysis to
reduce the space spanned by Gini, M20 , concentration,
asymmetry, clumpiness, and galaxy Sérsic index to three
dimensions. Regions in this space are then assigned a
ZEST (Zurich Estimator of Structural Types) type. Thisestimator has been applied to the COSMOS ACS images,
making comparisons to our late-stage merger sample possible.
Figures 4 and 5 show the ZEST classifications of oursample. All morphological values are taken from Scarlata 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, are masked.
We therefore expect that for some mergers, one member of the pair will be masked, decreasing the measured
asymmetry and M20 . However, inspection of the COSMOS ‘clean’ images shows that the majority of late-stage
mergers are considered a single system (see Cisternas
et al. 2011). We limit the sample to galaxies with stel-allmergers−0.5 −1.0 −1.5 −2.0 −2.5 −3.0

M20

Figure 4. Top: Gini coefficient and M20 values for late-stage
mergers (black points). The contours show the parent sample colorcoded by ZEST galaxy type (Scarlata et al. 2007). The sample islimited to galaxies with stellar masses greater than 2.5 × 1010 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 criterion for merging galaxies from Lotz et al. (2004). Most late-stage
mergers lie below this line and would not be detected using the
G − M20 method. Bottom: Distribution of M20 for our sample ofmergers (solid lines) and the parent sample (dashed lines). Colors
indicate ZEST type as in the top panel.

lar masses above 2.5 × 1010 M⊙ and I−band magnitudes
brighter than 23.5. The mass-restricted parent sample isshown by colored contours, while the late-stage mergers
are denoted by black points. In these figures, it is clearthat most mergers are either ZEST type 2 (bulge+disk
galaxies) or ZEST type 3 (irregular). Out of 212 latestage mergers, 28, 112, and 72 are of types 1, 2, and 3, respectively. If the late-stage merger sample had the same
distribution as the parent sample, the expected numberof each type would be 50, 152, and 10. These differencesin ZEST type distribution are shown in the histogramsin Figures 4 and 5.
These histograms show the distributions of M20 andconcentration for late-stage mergers compared to normal
galaxies for each ZEST type. For late-stage mergers classified as spirals, the distribution of M20 is shifted toward
larger values (blue lines), closer to the distribution for
irregular galaxies (green line). This demonstrates that,while the ZEST categorization does not clearly separate
late-stage mergers from spiral galaxies, the morphologies
of late-stage mergers differ measurably from those of regular spiral galaxies. Nonetheless, most mergers are classified as spirals, in agreement with Kampczyk et al. (2007).
Furthermore, most irregular galaxies are not classified asmergers by our method. This is to be expected, since ourmerger selection only identifies major mergers that still
have two nuclei, ignoring other merger signatures.
In Figure 4, the magenta dashed line shows the criterion for merging galaxies from Lotz et al. (2004). This

10

Lackner et al.

. <z ≤0.45

0.00

0 25

0.05
⊙

0.20
0.25
0.30

10
9
8
23 22 21 20 19 23 22 21 20 19 23 22 21 20 19

mergers

0.35 ZEST=1m(IZEST=2

F814W)

0.40 ZEST=3
fraction

∗

M /M

0.15

. <z ≤1.00

0 70

11

log

Asymmetry

0.10. <z ≤0.70

0 45

0.20
all
mergers
0.15
0.10
0.05
0.00
5.0 4.5 4.0 3.5 3.0

Figure 6. The mass completeness of our photometric sample(I < 23) as a function of I814W apparent magnitude in three redshift bins. Quiescent(star-forming) (see §4.4) galaxies are shown inred(blue). Up to z = 0.7, the sample is complete for both populations. Beyond z = 0.7, the completeness drops to ∼ 90%, withmost of the missing galaxies above z = 0.9.

2.5 2.0

1.5

Concentration
Figure 5. Top: Petrosian concentration and asymmetry (about
180 ◦ rotation). Symbols and contours are as in Figure 4. Half ofthe late-stage mergers are of ZEST type 2 (spirals). A late-stage
merger 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. On
average, late-stage mergers of ZEST type 2 (blue lines) are lessconcentrated than typical ZEST=2 galaxies.

criterion is designed for observations in the rest-frame
B−band and is therefore appropriate for the portion of
our sample above z ≈ 0.7. Objects above this line areconsidered mergers, However, only a small fraction oflate-stage mergers are also classified as mergers by the
G-M20 criterion (see also Kartaltepe et al. 2010; Jogee
et al. 2009; Lotz et al. 2011). Similarly, in Figure 5, major
mergers are expected to be highly asymmetric (asymmetry & 0.3), but only a small fraction of our sample oflate-stage mergers have such high asymmetries.
In Appendix B, we further explore the differences between our sample of late-stage mergers and mergers selected based on their Gini, M20 , or asymmetry values.
Some differences may be due to the fact that the Gini,
M20 and asymmetry values reported by Cassata et al.
(2005) are derived from deblended images, which splits
two concentrated nearby galaxies into separated sources.
This eliminates late-stage mergers from the G − M20 andasymmetry-selected samples. Furthermore, the high central concentrations of late-stage mergers selected here biases the asymmetry upward, making their selection as
mergers based on asymmetry less likely. In looking at
mergers selected by Gini-M20 and asymmetry but notby our method, we find that the asymmetry and GiniM20 methods are more sensitive to mergers between latetype galaxies, minor mergers, and small perturbationsin the galaxy flux distribution than our method. Together, these reasons help explain the poor overlap between our sample of late-stage mergers and those derived
using other morphology methods.
4. MERGER RATESIn section §3.1, we demonstrate the completeness andcontamination of our selection of late-stage mergers. By
correcting for these effects, we can compute the major
merger rate as a function of redshift to z = 1. To calculate merger rates, we use the photo-z parent sample, witha few additional restrictions. We limit our parent sample to the approximately volume-limited sample between
0.25 ≤ z < 1.0 and log M∗ /M⊙ > 10.6. The stellar mass
limit is derived by comparing the completeness of ourI−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 catalog
are included in our sample. Figure 6 shows the measured
stellar masses as a function of apparent magnitude in 3
redshift bins. While the sample is mass-complete for the
lower redshift bins, the completeness drops to 82% for
z > 0.9. For the merger-rate analysis, we also remove
all 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 which
136 are late-stage mergers.
4.1. Line-of-sight pairs correction
Before computing the merger rate, we need to correct
the observed number of late-stage mergers for chance superpositions. We do this by computing the expected
number of chance superpositions within 8 kpc of thegalaxies in our sample. This method is outlined in Bundy
et al. (2009). Using the deeper full ACS source catalog(Leauthaud et al. 2007), we compute the expected number of fainter neighbor in an annulus of 2.2 to 8 kpc
around galaxies in the redshift range 0.25 < z < 1.0. In
order to be counted, the fainter galaxy must have a flux
between between 25% and 100% of the primary source,
and together the pair must be brighter than I = 23 andmore massive than 4 × 1010 M⊙ . Summing the expected
number of projected neighbors over the whole sample,
and adjusting the value for the difference in area between
the whole ACS sample and our parent sample, yields an
expected number of chance superpositions of 50. In otherwords, 30% of the 148 late-stage mergers are likely to bechance superpositions. Since the angular-diameter distance, and, therefore, the size of the annulus searched for11

Galaxy Mergers in COSMOS
close pairs, changes slowly with redshift beyond z ∼ 0.5,
the fraction of chance superpositions does not change significantly with increasing redshift. Hence, we correct thefraction of late-stage mergers by a factor of Cl.o.s. = 0.7.
This correction is only statistical and does not allow us todetermine which late-stage mergers are chance superpositions, only the average probability that any late-stage
merger is a spurious pair.
The value of Cl.o.s. given above agrees well with thefraction of chance superpositions found by visually inspecting a fraction of the merger images in §2.1. Our correction factor also agrees well with other values for Cl.o.s.
based on numerical simulations where Cl.o.s. ≈ 0.4 − 1.0(see Kitzbichler & White 2008; Patton & Atfield 2008;
Lotz et al. 2011; Le Fèvre et al. 2000) and visual inspection (Kampczyk et al. 2007). As expected, the fraction ofchance superpositions in our sample is smaller than thatfound by Bundy et al. (2009) using the same method
but a larger search annulus. By including photometric redshift information for both members of a merger,
Kartaltepe et al. (2007) find a smaller correction factor(Cl.o.s. ∼ 15%). However, our method cannot distinguishthe redshifts of the superimposed galaxies. Despite good
agreement with previous studies, the value of Cl.o.s. remains highly uncertain and contributes significantly tothe uncertainty in the merger rates calculated below.
4.2. Contamination and completeness
Using the mock merger images from §3.1, we correct
our sample of late-stage mergers for incompleteness andcontamination. The simulations show that the sample
has a contamination rate of 33 ± 1%, ∼ 20% from minor
mergers 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 multiplying
by 0.67 ± 0.01.
The simulations also demonstrate the incompletenessof our merger-finding method. From Figure 17, the completeness of our sample ranges from ∼ 20% to ∼ 40% as
a function of redshift. Based on the mock mergers, we
compute the completeness in the three redshift bins usedbelow. The correction factor for incompleteness is simply
the inverse of the completeness fraction. In addition toredshift, the completeness of our late-stage merger selection depends strongly on galaxy morphology. In §4.4, we
compute the merger rates for star-forming and quiescentgalaxies separately. In this case, we use completeness corrections derived from the late-type and early-type galaxy
mergers, respectively. While obtaining correct morphologies for artificially superimposed galaxies is trivial, obtaining correct colors requires understanding how thecomponents of the mock merger extinct each other. We
instead assume that the color (SFR) of a merger and themorphology of the merging galaxies are exactly correlated, i.e., there are no star-forming early-type mergers.
This is certainly false, but is likely a small error in lightof the overall uncertainties in the corrections for incompleteness and line-of-sight chance superpositions.
Taken with the line-of-sight pair correction, we correct
the number of late-stage mergers by three factors, Cl.o.s. ,the contamination (0.67 ± 0.01), and the incompleteness1/completeness fraction. Together, we denote these cor-

rections as Cmerge . The values of Cmerge are given in
Table 3 along with the corrected merger fraction fmerge .
The errors in Cmerge are the bootstrap-derived errors in
the completeness and contamination fractions (see Appendix A) and do not include the uncertainty in Cl.o.s. .
The errors on the correction factor are likely underestimated, as they do not include uncertainty in the morphological mix of merging galaxies or in the conversionof flux ratios to mass ratios. The redshift dependence ofCmerge is due entirely to the incompleteness correction.
In §4.5, we examine the measured merger rate without
corrections for incompleteness and contamination in order to determine the sensitivity of our results to these
correction factors.
4.3. Evolution of the merger rate

To calculate the merger rate, we simply count the number of pairs in three redshift bins, chosen such that eachredshift bin spans the same amount of time. Our results
are unchanged if the bins are chosen such that they contain the same number of galaxies. The raw merger fractions are corrected for chance superpositions, contamination, and incompleteness using the correction factor,
Cmerge , given in Table 3. The corrected merger fraction
for our total sample is Cmerge × 136/5894 = 4.8 ± 0.5%,
where Cmerge = 2.1 ± 0.1, and the completeness fraction
is 0.22±0.01. This is comparable to the typical pair fraction found in studies of more widely separated pairs (Linet al. 2004; Kartaltepe et al. 2007; de Ravel et al. 2009;
Bundy et al. 2009; Robaina et al. 2010). and the fraction of morphologically disrupted systems (De Propris
et al. 2007; Conselice et al. 2009; Lotz et al. 2008a). As
noted in §3.3, our sample of late-stage mergers has little
overlap with samples of major mergers selected by visualinspection or other non-parametric methods (asymmetry, etc.). This means the remarkably good agreementin the overall fraction of mergers is difficult to interpret,
and possibly due to chance.
In order to compute the galaxy merger rate, we musttake into account the timescale over which a late-stage
merger could be observed. We calculate the fractional
merger rate defined in (Lotz et al. 2011):ℜmerge = fmerge h

1
i,
Tobs

(1)

where Tobs is the duration of time a merger will be observable. Because Tobs is strongly dependent on themerger/pair selection, using the correct value for Tobs isessential when comparing merger rates based on different techniques (see Lotz et al. 2011). For the late-stage
mergers studied here, Tobs is sensitive to many parameters such as the galaxy masses, gas fractions, orbital parameters, and observational angle. Many pair studies use
the dynamical friction timescale for Tobs (Lin et al. 2004;
Bell et al. 2006; Patton & Atfield 2008; Masjedi et al.
2008). Another way to determine Tobs is using hydrodynamical simulations of galaxy mergers and directly measuring how long close pairs or morphological 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 by 5 − 20 h−1
100 kpc, Lotz
et al. (2011) find hTobs i ≈ 0.33 Gyr, and that hTobs i isessentially independent of galaxy gas fraction, and, there-

12

Lackner et al.

0.35
Table 3
Pair fractions and merger rates
Ngal

Nmgr

Cmergefmergeℜ [Gyr−1 ][0.25, 0.45)[0.45, 0.70)[0.70, 1.00)

867
1644
3383

15
39
82

1.1 ± 0.1
1.8 ± 0.1
2.7 ± 0.1

1.9 ± 0.5%
4.2 ± 0.8%
6.6 ± 0.8%

5.9 ± 1.6%
12.6 ± 2.3%
20.1 ± 2.5%

low mass (10.6 < log M/M⊙ < 10.9) sample
399
782
1766

9
23
42

1.1 ± 0.1
1.8 ± 0.1
2.7 ± 0.1

2.5 ± 0.9%
5.1 ± 1.2%
6.5 ± 1.1%

7.7 ± 2.6%
15.6 ± 3.5%
19.7 ± 3.2%

high mass (log M/M⊙ ≥ 10.9) sample[0.25, 0.45)[0.45, 0.70)[0.70, 1.00)

468
862
1617

6
16
40

1.1 ± 0.1
1.8 ± 0.1
2.7 ± 0.1

1.4 ± 0.6%
3.2 ± 0.9%
6.8 ± 1.1%

4.4 ± 1.8%
9.8 ± 2.6%
20.5 ± 3.4%

star-forming sample[0.25, 0.45)[0.45, 0.70)[0.70, 1.00)

413
763
1131

8
21
36

1.4 ± 0.2
2.0 ± 0.2
3.4 ± 0.3

2.7 ± 1.1%
5.6 ± 1.4%
10.7 ± 2.0%

8.2 ± 3.2%
16.9 ± 4.1%
32.4 ± 6.1%

quiescent sample[0.25, 0.45)[0.45, 0.70)[0.70, 1.00)

454
881
2252

7
18
46

0.6 ± 0.0
0.6 ± 0.0
0.6 ± 0.0

0.9 ± 0.3%
1.1 ± 0.3%
1.3 ± 0.2%

2.6 ± 1.0%
3.5 ± 0.8%
3.9 ± 0.6%

star-forming, low mass (10.6 < log M/M⊙ < 10.9) sample[0.25, 0.45)[0.45, 0.70)[0.70, 1.00)

225
469
660

4
10
22

1.4 ± 0.2
2.0 ± 0.2
3.4 ± 0.3

2.5 ± 1.3%
4.3 ± 1.5%
11.2 ± 2.6%

7.5 ± 4.0%
13.1 ± 4.4%
33.9 ± 7.9%

quiescent, low mass (10.6 < log M/M⊙ < 10.9) sample[0.25, 0.45)[0.45, 0.70)[0.70, 1.00)

243
393
957

2
6
18

0.6 ± 0.0
0.6 ± 0.0
0.6 ± 0.0

0.5 ± 0.3%
0.9 ± 0.4%
1.2 ± 0.3%

1.4 ± 1.0%
2.6 ± 1.1%
3.6 ± 0.9%

star-forming, high mass (log M/M⊙ ≥ 10.9) sample[0.25, 0.45)[0.45, 0.70)[0.70, 1.00)

188
294
471

4
11
14

1.4 ± 0.2
2.0 ± 0.2
3.4 ± 0.3

3.0 ± 1.6%
7.6 ± 2.5%
10.0 ± 2.8%

9.0 ± 4.8%
23.0 ± 7.5%
30.3 ± 8.6%

quiescent, high mass (log M/M⊙ ≥ 10.9) sample[0.25, 0.45)[0.45, 0.70)[0.70, 1.00)

211
488
1295

5
12
28

0.6 ± 0.0
0.6 ± 0.0
0.6 ± 0.0

1.3 ± 0.6%
1.4 ± 0.4%
1.4 ± 0.3%

4.0 ± 1.8%
4.2 ± 1.2%
4.1 ± 0.8%

Note. — The fraction of mergers is corrected by a factor of
Cmerge for line-of-sight superpositions, contamination from minor mergers/non-mergers, and incompleteness. The fractional
merger rate is calculated using hTobs i = 0.33 (Lotz et al. 2011).

fore, redshift. Therefore, Tobs only affects the normalization of the merger rate, not the slope as a function ofredshift. Below, we use the merger observation timescalecomputed by Lotz et al. (2011), hTobs i = 0.33 Gyr. Thisis roughly twice as long as the minimum expected Tobs ,namely the orbital timescale. For mergers with masses
similar to the Milky Way mass, separated by 8 kpc, theorbital timescale is ∼ 0.2 Gyr. Nonetheless, the value ofTobs introduces significant uncertainty in the normalization of the merger rate. Using hTobs i = 0.33, the computed values for ℜmerge are reported in the last column
in Table 3.
Because of the corrected fraction of late-stage mergers,
we find ℜmerge ∝ (1 + z)3.8±0.9 , consistent with, albeitℜmerge [Gyr−1 ]z[0.25, 0.45)[0.45, 0.70)[0.70, 1.00)

this work
Bundy 09de Ravel 09
Conselice 09
Lopez-Sanjuan 09

0.30
0.25
0.20
0.15
0.10
0.05
0.00
0.2

0.4

0.6

0.8

redshift

1.0

1.2

Figure 7. The fractional merger rate as a function of redshift derived from our sample of late-stage mergers (black, filled circles),compared to other stellar-mass-selected studies of merging galaxies. Bundy et al. (2009) and de Ravel et al. (2009) identify merging
galaxies as photometric pairs. López-Sanjuan et al. (2009); Conselice et al. (2009) identify mergers based on galaxy asymmetry.
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 errors shown forour measurements (black) are the statistical errors only, and likely
underestimates, but include the uncertainties in the corrections forcontamination and incompleteness.

slightly steeper than, results of other studies that findsignificant evolution in the merger rate with redshift (deRavel et al. 2009; Lin et al. 2008; Robaina et al. 2010, but
see Bundy et al. 2009; Lotz et al. 2011). The merger rateis also consistent with the expected merger rate for dark
matter halos, which grow as (1 + z)3−4 (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 7 compares the fractional merger rate for late-stage mergers to other merger
rate studies, including studies using close pairs (de Ravelet al. 2009; Bundy et al. 2009) and galaxy asymmetry(López-Sanjuan et al. 2009; Conselice et al. 2009). The
values plotted are from Lotz et al. (2011) and take into
account differences in Tobs for different merger-finding
methods.
Because the measured merger-rate evolution depends
on the galaxy selection (Lotz et al. 2011), we limit thecomparison to other mass-selected samples. All fourstudies in Figure 7 use mass-selected samples, with mass
limits near log M∗ /M⊙ & 10, which is lower than our
mass limit. For the pair studies, the mass refers to
the mass of the individual merging galaxies, not the final merged galaxy, as is the case in our study. Therefore, care must be taken when comparing these results.
Nonetheless, the agreement between the different methods suggests that above log M∗ /M⊙ ∼ 10, the merger
rate does not depend strongly on galaxy mass. The errors in ℜmerge are statistical errors only and do not include uncertainties in Tobs . A smaller value for Tobs will
increase the measured ℜmerge , and decrease the agreement between our study and previous results. While wehave included the uncertainty in the correction for in-Galaxy Mergers in COSMOSM(NUV)−M(r + )

7
6
5
4
3
2
1
0.2

0.4

0.6

0.8

1.0

M(r + )−M(J)

1.2

1.4

1.6

Figure 8. Color-color diagram for selecting queiscent and starforming galaxies. The cuts are from Ilbert et al. (2013, 2010).
Queiscent galaxies are in the upper left. The data shown is in theredshift range 0.25 < z < 1.0 and with stellar masses > 1010 M⊙ .
The contours show the distribution of the full photo-z sample, with
contours at the 30th , 50th , and 90th percentiles. The points show
the late-stage mergers.

completeness and contamination in our errors, these arelikely underestimated. The error bars show in Figure 7
represent the minimum errors.
4.4. Mergers as a function of color and stellar mass

Since our sample of late-stage mergers is relatively
large, we can explore the evolution of the merger rate
as a function of color and stellar mass. We divide theparent sample into two mass bins, choosing the medianstellar mass, log M/M⊙ = 10.9 as the division. Following
Ilbert et al. (2013), we further divide the sample into quiescent and star-forming galaxies, based on the rest framenear-UV (NUV)−r+ and r+ − J colors, where NUV corresponds to the GALEX filter at 0.23 µm, and r+ refers
to the Subaru r−band. Colors are computed from thebest-fit spectral energy distribution (SED) templates inIlbert et al. (2013). The color cuts for quiescent galaxies
are (NUV − r+ ) > 3(r+ − J) + 1 and (NUV − r+ ) > 3.1(Ilbert et al. 2013, 2010). The color-color diagram in Figure 8 shows these cuts applied to our sample.Our analysis
cannot distinguish the colors of the member galaxies ina late-stage merger. Nonetheless, we classify mergers as‘wet’ (gas-rich) mergers if the total merging system isstar-forming, as ‘dry’ mergers if the merger is quiescent.
Table 3 contains the corrected pair fractions withineach star-forming/stellar mass bin. The fractions andmerger rates reported are those within the limited starforming/stellar mass parent sample. Note that we use
the same Tobs for all sub-samples of galaxies, even thoughTobs is likely to depend on both galaxy mass and color.
Within a single sub-population, Tobs does not depend
strongly on redshift, hence, does not affect the evolutionof the merger rate, only the normalization. The pair fractions reported in Table 3 are corrected for incompletenessand contamination. In addition to a dependence on redshift, Cmerge is different for quiescent and star-forming
galaxies because the completeness of our merger selection
depends on galaxy morphology, and, therefore, color. For
quiescent galaxies, we use the completeness fraction forearly-type galaxies, while for star-forming galaxies, we

13

adopt the completeness of late-type mergers. For quiescent galaxies, Cmerge is independent of redshift, while forstar-forming galaxies, Cmerge increases by a factor of ∼ 2from z ≈ 0.2 to z ≈ 1.0 (see §4.5).
Figure 9 shows the corrected pair fractions for eachsubsample of galaxies as a function of redshift. Fromthese figures it is evident that the merger rates for blue
and red galaxies differ significantly. For blue galaxiesℜmerge ∼ (1 + z)4.5±1.3 , while for red galaxies ℜmerge
is consistent with no evolution, ℜmerge ∼ (1 + z)1.1±1.2 .
This suggests that the evolution in the merger rate forall galaxies is driven by the evolution in the merger rate
for blue galaxies and the increasing contribution of blue
galaxies to the galaxy population at high redshift.
For massive (log M/M⊙ > 10.9), quiescent galaxies,ℜmerge ∼ (1 + z)0.0±1.4 , consistent with no evolution.
The lack of evolution in the merger rate for massive, redgalaxies agrees with results from pair studies (de Ravelet al. 2009; de Ravel et al. 2011; Lin et al. 2008; Bundy
et al. 2009; López-Sanjuan et al. 2011, 2012) and simulations (Kitzbichler & White 2008). As in Lin et al. (2008),
de Ravel et al. (2009) and Darg et al. (2010b), we findthat most mergers are star-forming, and that the fractionof star-forming mergers increases significantly with redshift. Figure 10 shows that dry, quiescent mergers makeup ∼ 20% of all mergers in our sample, once the merger
fractions are corrected for incompleteness and contamination.
It is interesting to note that Figure 9 shows a weakincrease in the fractional merger rate for low-mass, quiescent galaxies (ℜmerge ∝ (1 + z)3.0±2.2 ). However, lowmass quiescent galaxies suffer the most from incompleteness in this I−band selected sample. If the average stellar mass for low mass quiescent galaxies increases as afunction of redshift, then it is unsurprising that the fractional merger rate in the highest redshift bin matches
that of the high-mass quiescent galaxies. This suggeststhat the evolution the low-mass quiescent galaxy merger
rate may be a selection effect.
The fractional merger rate for star-forming galaxies
grows significantly with increasing redshift, ℜmerge ∝(1 + z)3.5±1.8 for high mass galaxies, and ℜmerge ∝(1 + z)5.4±1.7 for low mass galaxies. This demonstrates
the increasing importance of wet major mergers at highredshift, in agreement with previous studies (Li et al.
2008; Bundy et al. 2009; López-Sanjuan et al. 2012,2011). The strongly increasing fraction of star-forming
mergers also agrees with the increase in bright infrared
sources as a function of redshift (Le Floc’h et al. 2005).
This is expected as these sources are often associatedwith mergers (Sanders & Mirabel 1996; Kartaltepe et al.
2010). We show below, however, that this increase in thefraction of SF mergers does not contribute significantly
to the overall increase in SFR with redshift.
As with quiescent galaxies, the merger rate evolution
for low mass galaxies is steeper than for high mass galaxies. Although this may be driven by incompleteness,the steepness of the merger rate for lower mass galaxies suggests that the merger rate depends on halo mass.
Note, however, that the range of masses under study issmall (10.6 ≤ log M/M⊙ . 11). The differences amongℜmerge for star-forming, quiescent, low-mass and highmass galaxies help explain the differences in merger rates

14

Lackner et al.

quiescent galaxies

star−forming galaxies

M ≥10.9logM <10.9
log

12

∗

M ≥10.9logM <10.9
log

12

∗

∗

10

10

8

8

6

6

4

4

2

2

f

merger [%]

∗

0
0.3

0.4

0.5

0.6

0.7

redshift

0.8

0.9

0
0.3

0.4

0.5

0.6

0.7

redshift

0.8

0.9

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,
separated by the color cuts in Figure 8. The solid (empty) symbols show high (low) mass galaxies. Small horizontal offsets are added forvisibility.

log
log

∗

1.6

∗

, M .
., M .

log
log

SF log ∗ ≥10 9quies log ∗ ≥10 9

M <10.9
M <10.9
∗
∗

1.4

3.0

1.2

1.0

/

2.5

/

mergers total [%]3.5

M <10.9
M <10.9, M .
., M .

SF log ∗ ≥10 9quies log ∗ ≥10 9

mergers total [%]

4.0

2.0

1.5

1.0

0.5

0.8

0.6

0.4

0.2

0.0

0.0
0.3

0.4

0.5

0.6

0.7

0.8

0.9

redshift
Figure 10. The fraction of pairs split by galaxy color and mass,
corrected for line-of-sight superpositions, incompleteness and contamination. With these corrections, mergers between star-forming
galaxies dominate at all redshifts, and the number of star-forming
mergers increases significantly with redshift.

found using different parent samples, especially the differences in ℜmerge between mass-limited and luminositylimited samples (e.g., Lotz et al. 2011; Lin et al. 2004).
4.5. Without incompleteness and contamination

corrections
The results in Figures 7 through 10 use late-stage
merger fractions corrected for incompleteness and contamination. While these correction factors are based on
simulations well-matched to the observed data, the cor-

0.3

0.4

0.5

0.6

0.7

0.8

0.9

redshift
Figure 11. As in Figure 10, but the fractions are not corrected
for incompleteness or contamination. Without the incompletenesscorrections, there is no statistically significant increase in merger
activity at high redshifts. Because the correction factor is small forearly-type galaxies, the fraction of queiscent mergers is nearly thesame as in Figure 10.

rections are still uncertain. Thus, we perform the same
analysis, excluding the completeness and contamination
corrections and setting Cmerge = 0.7 for the line-of-sightpairs correction. This only serves to demonstrate theeffect of our correction factors. The simulations clearly
demonstrate the need for incompleteness and contamination corrections, and the measured merger rates arecertainly invalid without any corrections. Without theincompleteness corrections, the overall late-stage merger

Galaxy Mergers in COSMOS
fraction drops by a factor of ∼ 2. Furthermore, the measured evolution in the merger rate disappears if we do notinclude an evolving correction for incompleteness. Figure
11 demonstrates that the fraction of late-stage mergers
only evolves slightly with redshift, fmerge ∝ (1 + z)0.8±0.8This is in contrast to Figure 10, which shows a large
increase in the corrected merger fraction with redshift.
Comparing Figures 10 and 11 also shows that the fraction of quiescent mergers is unchanged by the correction factor for contamination and incompleteness. Thisis unsurprising because our merger sample is complete forearly-type galaxies out to z ∼ 1. The completeness correction mainly affects star-forming galaxies, particularly
at high redshift. Without corrections for contaminationand incompleteness, the merger rates for quiescent andstar-forming galaxies grow as ℜmerge ∝ (1 + z)0.7±1.2
and ℜmerge ∝ (1 + z)1.5±1.2 , respectively. While themerger rate evolution for quiescent galaxies is unchanged,
the merger rate for star-forming galaxies is significantly
lower, and only marginally inconsistent with a flat merger
rate. These results suggest that the non-evolving merger
rate for quiescent galaxies is robust. For star-forming
galaxies, the uncorrected merger rate is a lower limit.
Even if values of the incompleteness we measure using mock merger images are inaccurate, our sample oflate-stage mergers is demonstrably incomplete at highredshift, particularly for late-type, star-forming galaxies.
Therefore, the merger rate for star-forming galaxies will
evolve at least as quickly as (1 + z)1.5±1.2 .
In the above analysis, we use a contamination correction that is independent of redshift and galaxy type (quiescent or star-forming). There are, however, several contamination effects that are likely larger for star-forming
galaxies than for quiescent galaxies. These contaminants may artificially boost the late-stage merger fraction at high redshift. Correcting for these effects will
lower the merger-rate evolution rate. The star-forming
galaxy merger rate is particular sensitive to morphological k-corrections and the overall increase in the fraction of clumpy, star-forming galaxies at high redshift.
This increase in the contamination will lead to an artificial increase in the merger rate for star-forming galaxies at high redshift. However, as demonstrated in §4.1
and Appendix A, the overall contamination rate from
non-merging galaxies is ∼ 10%, while the completenessis only ∼ 20%, and the former only depends weakly on
redshift. We expect the effects of incompleteness to dominate over any effects from contamination, and the resultspresented above to be robust, despite the large correction
for incompleteness and contamination.
5. PROPERTIES OF LATE-STAGE MERGERS

To study the internal properties of late-stage mergers,
we limit our parent sample to galaxies from the spectroscopic zCOSMOS survey (Lilly et al. 2007, 2009). The‘bright’ zCOSMOS sample contains spectra for ∼ 20, 000
galaxies (I < 22.5). The zCOSMOS sample should be
a subsample of the K-band selected sample from Ilbert
et al. (2013) described above, but differences in masking
mean that some zCOSMOS galaxies are missing from thephoto-z sample. To ensure no galaxies are missing, wererun our merger selection algorithm on postage stamps
generated from the zCOSMOS parent sample. The final sample is selected in the same way as that used in

15

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 mergers
to both the parent zCOSMOS sample and more widely
separated kinematic pairs from the same parent sample.
Because these galaxies are observed in zCOSMOS, we
use the spectroscopic redshifts, and stellar masses from
Pozzetti et al. (2010) and Bolzonella et al. (2010). These
stellar masses use the spectroscopic redshifts and arein good agreement with those measured in Ilbert et al.
(2013) using photometric redshifts. For the analysis below, we examine galaxies with M∗ > 2.5 × 1010 M⊙ inthe redshift range 0.25 ≤ z < 1.05, the same mass andredshift range used in kinematic pair studies in zCOSMOS (Silverman et al. 2011; Kampczyk et al. 2013). For
the analysis of the SFR (§5.1), we remove all sources
with a Chandra or XMM detections. This leaves a sample of 4586 galaxies of which 154 are classified as latestage mergers. We use the non-merging galaxies fromthe parent zCOSMOS sample as a control sample. We
first check that the control sample is well-matched to themerger sample in stellar mass and redshift. Since AGN
activity, SFR and, in this sample of galaxies, sSFR (seeMaier et al. 2009), are strong functions of M∗ and z, it
is important that the late-stage merger sample is not biased relative to the control sample. Kolmogorov-Smirnov(K-S) tests show that both the mass and redshift distributions for late-stage mergers and the control sample areindistinguishable.
5.1. Star formation in late-stage mergers
Simulations show that some galaxy mergers lead to enhanced star formation (e.g., Hernquist 1989; Di Matteo
et al. 2007; Mihos & Hernquist 1996; Barnes & Hernquist
1991; Springel et al. 2005; Hopkins et al. 2006). There isalso much observational evidence to support this conclusion. Galaxies identified as mergers are often bluer (e.g.,Kampczyk et al. 2007; Darg et al. 2010a) and show enhanced UV and IR SFR (e.g., Jogee et al. 2009; Robaina
et al. 2009). Spectroscopy confirms that galaxies in close
pairs have higher SFRs than isolated galaxies (e.g., Barton et al. 2000; Lambas et al. 2003; Kampczyk et al. 2013;
Ellison et al. 2013). Studies of far-infrared selected galaxies show that galaxies with very high SFRs are much
more likely to have disturbed morphologies than galaxies
with typical SFRs (e.g., Sanders & Mirabel 1996; Kartaltepe et al. 2010). In this section, we compare the SFR
in late-stage mergers to that of isolated galaxies. Ourcontrol sample of isolated galaxies is simply the set ofzCOSMOS galaxies that are not identified as late-stage
merger candidates.
Figure 12 shows the narrow 4000-Angstrom break(Balogh et al. 1999) for late-stage mergers and the control sample. As expected, at fixed stellar mass, the latestage mergers have a lower median Dn (4000) than thecontrol sample. This is indicative of recent, within thelast Gyr, star formation in the late-stage mergers. A KS test shows that the distributions of Dn (4000) for thelate-stage mergers and the control sample are distinct.
At masses below log M/M⊙ = 10.7, there are almost noquiescent late-stage mergers. This indicates that a significant fraction of star formation may be associated withmergers.
We use the SFR computed from the 24µm flux as mea-

16

Lackner et al.

.

M /M <10.92

10 52 ≤log

∗

field
mergers

field
mergers

2.5

0.8

cumulative fraction

3.0

P(Dn (4000))

1.0

⊙

2.0
1.5
1.0
0.5
0.0

P(Dn (4000))

2.0

1.00 1.25 1.50
10 92 ≤log ∗

.

1.75

2.00
11 66

M /M < .
⊙

0.4

0.2

0.0
−2

1.5

−1

0

log[sSFR Gyr−1 ]1Figure 13. The cumulative distribution of sSFR for late-stage
mergers and non-interacting galaxies from the zCOSMOS sample.
The sSFR is derived from the Spitzer/MIPS 24µm flux. The median sSFR in late-stage mergers is a factor of 2.1 ± 0.6 higher thanthat in non-interacting galaxies.

1.0
0.5
0.0

0.6

1.00

1.25

1.50

Dn (4000)

1.75

2.00

Figure 12. The distribution of the narrow 4000 Å-break for latestage 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) merging
galaxies. The corresponding vertical lines show the medians ofeach distribution. The median Dn (4000) for late-stage mergers issmaller in both mass bins, indicating most late-stage mergers haveundergone recent star formation.

sured by Spitzer/MIPS (Sanders et al. 2007; Le Floc’h
et al. 2009). The total infrared luminosity, LIR is computed using the SED models from Dale & Helou (2002)
and the photometric redshifts from Ilbert et al. (2009)
and Salvato et al. (2009) for X-ray sources. Below z ∼ 1,
the 24µm flux is an accurate measure of the total infrared
luminosity (e.g., Elbaz et al. 2010). From the infrared luminosity, the total SFR is given by Kennicutt (1998) is
SFR [M⊙ yr−1 ] = 4.5 × 10−44 LIR /L⊙ .

(2)

We only utilize sources with a 24µm-detection and ameasured SFR. This limits our sample to 2318 galaxies, of which 111 are late-stage mergers. Among galaxies
with non-zero 24µm-based SFRs, the fraction of latestage mergers is 4.8 ± 0.5%; in the full zCOSMOS sample, the fraction of late-stage mergers is 3.3±0.3%, which
demonstrates that the fraction of star forming galaxies
in late-stage mergers is higher than in isolated galaxies.
Figure 13 shows the cumulative distributions of thespecific star-formation rate (sSFR) for both late-stage
mergers and galaxies in the control sample. The sSFR
is calculated from the 24µm-based SFR and the stellar
mass from Pozzetti et al. (2010). The measured stellar
mass is increased by a factor 1.8 to account for a difference in IMF: Pozzetti et al. (2010) use a Chabrier IMF
while the SFR is computed assuming a Salpeter IMF(Kennicutt 1998). Figure 13 shows that the distribution of sSFR is skewed to higher values for mergers thanother galaxies in the parent sample. A K-S test showsthat the two distributions of sSFR are distinct. The median sSFR in late-stage mergers is enhanced by a factorof 2.1 ± 0.6 over the sSFR in the parent sample. This
demonstrates that star formation in late-stage mergers
proceeds at only a moderately higher rate than star formation in isolated galaxies. Using the slightly larger anddeeper photo-z parent sample with the same stellar mass
and redshift limits, we find a similar enhancement in the
24µm-derived sSFR in late-stage mergers.
As with the merger rate, the association of late-stage
mergers with star forming galaxies may be affected bycontamination from clumpy, star-forming galaxies, particularly at high redshift. Our peak-finding method may
identify clumpy, star-forming galaxies as late-stage mergers, which would enhance the typical sSFR in late-stage
mergers. However, we show in §4.1 that the contamination from non-merging, but clumpy, galaxies in ∼ 10%.
Furthermore, the enhancement measured here is comparable or less than that measured using other merger
selection methods, strengthening our claim that the contamination from star-forming, isolated galaxies is small.
Kampczyk et al. (2013) draw similar conclusions about
the [O ii] λ3727-derived sSFR in kinematically-selectedclose pairs (see their Figure 13). They find the sSFR
in pairs with separations smaller than 30 h−1
100 kpc is enhanced by factors of 2−4 compared to a stellar mass- andredshift-matched control sample. Using the [O ii] λ3727
emission line as a SFR indicator (Moustakas et al. 2006;
Maier et al. 2009), we also find an enhancement of
2.0 ± 0.5 in the median sSFR in late-stage mergers. The
agreement between the 24µm- and [O ii]-derived sSFRs
suggests that the extinction in late-stage mergers is not
significantly different from that in field galaxies. However, the mean sSFR computed using [O ii] emission is afactor of ∼ 4 lower than the 24µm-derived sSFR.
We can add our sample of late-stage mergers to theGalaxy Mergers in COSMOS
more widely separated pairs in Kampczyk et al. (2013)
to obtain the fraction of star formation due to merging
galaxies separated by less than 30 h−1
100 kpc in the redshift
range 0.25 < z < 1.05. Kampczyk et al. (2013) reportthat 6 ± 1% of galaxies are in kinematic pairs with projected separations smaller than 30 h−1
100 kpc. The sSFR
in these galaxies is enhanced by a factor of 1.9 ± 0.6. In
the same sample, we find 3.3 ± 0.3% of galaxies are latestage mergers, which have sSFRs 2.1±0.6 times above themedian sSFR in the whole sample. Therefore, 18 ± 5%of star formation is associated with mergers, but only
8 ± 5% of all star formation can be considered “excess”
star formation triggered by mergers. This modest enhancement in the star formation due to major mergers
agrees with other studies of visually classified mergers
and close pairs (Robaina et al. 2009; Jogee et al. 2009).
In addition, these results also agree with semi-analytic
models (Somerville et al. 2008), which report that only
7% of star formation is directly associated with major
mergers.
Since the enhancement in sSFR for late-stage mergers is small, we note that these systems are not starburst galaxies. The small shift in the SFR for late-stage
mergers agrees with the analysis by Sargent et al. (2012).
They suggest that the sSFRs for starburst galaxies andmain sequence star-forming galaxies form a double Gaussian, in which the means are offset by only a factor of ∼ 4.
This is in contrast to other definitions of starburst galaxies, requiring SFRs an order of magnitude higher than
predicted by the star-forming main sequence. While themajority of starburst galaxies 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 not starburst galaxies.
5.2. AGN fraction

In addition to triggering star formation, major mergers may drive black hole growth through AGN activity.
Mergers can induce disk instabilities in coalescing galaxies that drive gas to the center of galaxies. This gas isused up in both star formation and feeding the black hole(e.g., Mihos & Hernquist 1996). Many simulations showthat the periods of most intense star formation and blackhole growth occur in late-stage mergers near coalescence(Mihos & Hernquist 1996; Springel et al. 2005; Di Matteo et al. 2007; Johansson et al. 2009). While simulations
suggest that luminous accretion at high rates (i.e. QSOs)
is dominated by major mergers, more than half of lowluminosity (log Lbol. /L⊙ . 11), low-accretion-rate AGN
activity can be fueled by stochastic, non-major merger
processes (e.g., Hopkins & Hernquist 2006; Hopkins et al.
2013). This agrees with studies of AGN host galaxies
that demonstrate that most AGNs occur in galaxies with
undisturbed (non-merging) morphologies (e.g., Cisternas
et al. 2011; Kauffmann et al. 2004; Schawinski et al. 2011;
Liu et al. 2012; Kocevski et al. 2012). Nonetheless, there
are many observations that show some enhancement in
nuclear 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 see Darg
et al. 2010a; Li et al. 2008; Barton et al. 2000). Using spectroscopic pairs out to z ∼ 1, Silverman et al.
(2011) show that the fraction of X-ray selected AGN with

171042 < L0.5−10keV < 1044 erg s−1 increases from 3.8+0.3−0.4 %
for isolated galaxies to 9.7+2.3%
forgalaxies
in
pairs
with
−1.7
a maximum projected separation of 75 kpc and a line-ofsight velocity separation less than 500 km s−1 . Despite
this enhancement, only ∼ 25% of AGN activity occurs
in galaxy pairs, and an even smaller fraction, ∼ 18% of
AGN activity is triggered by close interactions.
We can improve the estimate of the fraction of AGNs
due to merging by including late-stage mergers with thekinematic galaxy pairs in Silverman et al. (2011). To
simplify the comparison, we use a parent sample identical to that of Silverman et al. (2011), and describedabove (log M∗ /M⊙ > 10.4 and 0.25 ≤ z < 1.05). We
select AGN based on their X-ray flux as measured by
Chandra (Elvis et al. 2009). Owning to the limited areaof the Chandra survey, the zCOSMOS parent sample
used here only contains 3474 galaxies of which 112 arelate-stage mergers. The X-ray sources are matched to
optical/IR sources as described in Civano et al. (2012).
As in Silverman et al. (2011), we only consider X-ray
sources with total fluxes (0.5 − 10 keV) greater than1 × 10−15 erg cm−2 s−1 and luminosities brighter than
2×1042 erg s−1 . The latter requirement eliminates galaxies in which the contribution from star formation to the
X-ray flux is not negligible. Ninety-five percent of the Xray sources have luminosities L0.5−10keV < 1044 erg s−1 ,suggesting that most of the AGN hosts we examine are
not AGN-dominated in the optical/NIR, and that thederived properties, especially stellar masses, are reliable(Bongiorno et al. 2012; Salvato et al. 2011). The final
sample contains 164 Chandra X-ray sources, which arecertain to be AGN-dominated. Figure 14 shows the 6late-stage mergers that are also X-ray selected AGN.
The left panel of Figure 15 shows the AGN fraction
as a function of pair separation for our sample of latestage mergers(filled square) and for more widely separated kinematic pairs (Silverman et al. 2011) drawn fromthe same parent sample. We define the AGN fraction as
the fraction of late-stage mergers (close pairs) with associated X-ray sources. We compute the AGN fraction
as in Silverman et al. (2011), equation 1. This formuladown-weights compulsory zCOSMOS targets that are Xray selected and likely to be AGNs (Lilly et al. 2007). It
also accounts for the spatially varying Chandra sensitivity by weighting each AGN by the fraction of galaxies inwhich the measured X-ray flux is below the sensitivity,
i.e., the fraction of galaxies that could host each AGN.
The values for the kinematic pairs in the left panel of
Figure 15 are taken from the Bayesian likelihood analysis in Silverman et al. (2011). This method takes into
account contamination of the control sample by galaxies
in kinematic pairs in which only one member is observed
spectroscopically. Since late-stage mergers fall into a single slit, this more sophisticated approach for calculating
the AGN fraction is unnecessary. We find 6 late-stage
mergers that are also X-ray selected AGN. Although thestatistics are poor, the AGN fraction among late-stage
mergers is 6.4 ± 2.5%. This is marginally consistent with
the AGN fraction in the field, 3.8+0.3−0.4 % (Silverman et al.
2011). At 95% confidence, we find that the AGN fraction
in late-stage mergers is enhanced by less than a factor of
3.0, with a mean value of 1.7 ± 0.7, compared to the control sample, in agreement with (although less stringent

18

Lackner et al.
10:01:52.2 +1:56:08.5

09:59:19.3 +1:54:07.6

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1"

10:01:34.9 +2:03:27.1

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10:00:36.0 +2:28:30.5

1"

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Figure 14. Images of the six late-stage mergers that are also X-ray selected AGN. The (blue) contours show the total (0.5 − 7.0 keV)
flux from Chandra (Elvis et al. 2009). The (cyan) crosses show the position of the two peaks found by our merger-finding method. The
galaxy in the lower middle panel may be a spiral galaxy.

14

AGN Fraction [%]

12
10
8
6
4
2
0

0

50

100

150

proj. separation [kpc]

0.4 0.6 0.8 1.0

redshift

Figure 15. Left: The fraction of AGN in galaxy pairs at various
projected separations. The 3 rightmost points are from Silverman
et al. (2011) (see their Figure 5). The empty symbol is the fieldvalue, corrected for unidentified kinematic pairs. The square shows
the AGN fraction in late-stage mergers (6 mergers). The points areplotted at the median separation in each bin, and the horizontal
error bars denote the interquartile range (25%−75%) of the galaxies
in each bin. Right: The AGN fraction in pairs in two redshift bins.
The squares denote late-stage mergers. There are no late-stage
mergers in the low redshift bin and the error bar denotes the 1σ
upper limit. The filled and empty circles are the AGN fraction
in pairs separated by < 75kpc, and the field, respectively, and aretaken from Silverman et al. (2011). Note that in this panel, the field
AGN fractions are not corrected for contamination by kinematic
pairs and should be ∼ 0.5 − 1% lower.

than) Cisternas et al. (2011).
Given the upper limit on the enhancement of AGN
activity associated with late-stage mergers, we can compute an upper limit for the AGN activity triggered bymergers. Following the same procedure as §5.1, the latestage merger fraction in this sample is 3.0 ± 0.3% and theenhancement in the AGN fraction is at most a factor of 3
above the control sample. Therefore, the fraction of AGN
activity associated with late stage-mergers is < 9.0±0.9%
and the fraction of AGN activity triggered by late-stage
mergers is at most 6.0 ± 0.9%. Using the measured meanvalue for the AGN enhancement (1.7 ± 0.7), the fraction of AGN activity triggered by late-stage mergers is2±2%. While Silverman et al. (2011) find approximately
1/4 of AGN are associated with kinematic pairs closer
than 143 kpc, only 17.8+8.4−7.4 % of AGN can be directly
contributed to the pair interaction. Combining the kinematic pairs with our late-stage mergers gives a total fraction of AGN activity triggered by mergers of ∼ 20 ± 8%.
As expected, including late-stage mergers does not significantly increase the fraction of AGN activity producedby major mergers.
The right panel in Figure 15 shows the AGN fraction
in pairs divided into two redshift bins of 0.25 ≥ z < 0.65
and 0.65 ≥ z < 1.05. Among late-stage mergers, all 6 Xray selected AGN occur above z = 0.65. This boosts the
AGN fraction at high redshift to 11.5 ± 4.2%, which isstatistically above the value for the field, and comparable
to the boost seen for kinematic pairs separated by lessthan 75 kpc (Silverman et al. 2011). Note that in theright panel of Figure 15, the field AGN fraction is notcorrected for contamination by kinematic pairs in which
only one galaxy is observed. Since kinematic pairs have

19

Galaxy Mergers in COSMOSa larger AGN fraction than the field sample, correcting
for this contamination will likely lower the field AGN
fraction by ∼ 0.5 − 1%. Below z ∼ 0.65, none of ourlate-stage mergers are also X-ray AGN. The error bar in
Figure 15 shows the 1σ upper limit for the AGN fraction,
which is consistent with the AGN fraction in the field,
albeit with large uncertainty. Although our results ruleout a decrease in the merger rate at close separations,and suggest some enhancement in the AGN fraction atz & 0.7, a larger sample is required to determine if any
enhancement in the AGN rate for late-stage mergers is
statistically significant.
From the X-ray and optical images alone, it is unclear whether any 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 fromthe sample above since its measured stellar mass is below
2.5 × 1010 M⊙ . However, our method does select CID-42
as a late-stage merger. We have examined the spectra
for the 6 mergers with AGN and find no evidence for velocity offsets, suggesting that only one of the black holes
in the system is actively accreting. Nonetheless, since
the late-stage mergers are selected to have two, concentrated central cores, this sample would be well-suited tosearches for galaxies with dual AGN.
5.2.1. AGN in the photo-z sample

We can check the fraction of mergers with AGN using
the photo-z sample. For the photo-z sample, we use thesame stellar mass and redshift cuts as the spectroscopic
sample. We exclude X-ray sources that are best-fit by aType I AGN/QSO template (Salvato et al. 2011).Since
we identify late-stage mergers based on the flux ratio of
two central peaks, our method is poorly suited to selecting companions of bright Type I AGN, in which theoptical flux is dominated by a single point source. Thismeans that the AGN fraction reported here is for lowerluminosity, obscured AGN, not bright Type I AGN.
Using the photo-z sample, we find 8 late-stage
mergers that are Chandra-detected X-ray AGN with
L[0.5−10 keV] > 2 × 1042 erg s−1 , 4 of which are also identified in the spectroscopic sample. The missing 2 galaxies are excluded because of differences in the masking in
the K−band and I−band selected catalogs, used for thephoto-z and spec-z samples (see Ilbert et al. 2013; Lilly
et al. 2007). These 8 late-stage mergers yield an AGN
fraction of 5±2%, consistent with the AGN fraction fraction found above and that in the field. Because of thehigh degree of overlap between the photo-z and spec-z
galaxy samples, all our results on the AGN fraction arehighly correlated and do not add significant statisticalpower. Complete coverage of the COSMOS area with
Chandra will improve the statistics of these results by afactor ∼ 2 and yield a larger sample of AGNs associatedwith mergers (Civano et al., in prep).
As with the star-formation rates, we find that, although AGN activity may be slightly enhanced in latestage mergers, mergers do not drive the majority of AGN
activity, hence black hole growth. Including late-stage
mergers along with more widely separated pairs, only
∼ 20% of AGN activity is triggered by mergers, and latestage mergers are responsible for at most 6% of AGN activity. The small fraction of AGN activity associatedwith close pairs agrees with previous studies (Ellison

et al. 2013; Alonso et al. 2007) and suggests that minor mergers and secular processes within galaxies drive
the majority of low-luminosity AGN activity. Similarly,
while the SFR of late-stage mergers is typically higher
than that of isolated galaxies, the enhancement is lessthan a factor of 2 and only 8 ± 5% of star formation canbe contributed to kinematic pairs and late-stage mergers. The similarity between the AGN enhancement andSFR enhancement in merging galaxies (see also Silverman et al. 2011) suggests that star formation and AGN
activity may be physically coupled, as expected from simulations of gas-rich major mergers (Mihos & Hernquist
1996; Barnes & Hernquist 1992; Hernquist 1989; Hopkins
et al. 2006, 2008).
It is possible that our focus on late-stage mergers ignores other phases of galaxy merging with larger enhancements in AGN activity and star formation (seeScudder et al. 2012). The bright QSO phase may occur when the two nuclei are closer to coalescence (e.g.
Di Matteo et al. 2005; Hopkins et al. 2008). However, by combining kinematic pairs with late-stage mergers, we can observe galaxy mergers from separations of
100 h−1
100 kpc until shortly before coalescence. Furthermore, the 0.5 − 8 keV X-ray selection for AGN may exclude highly obscured AGN, which would be visible in
the infrared (e.g., Satyapal et al. 2014) or harder X-ray
bands (e.g., Koss et al. 2011). Using WISE-selected AGN
in SDSS, Satyapal et al. (2014) find an enhancement of
the AGN fraction in nearby post-merger galaxies of a factor 10−20, suggesting the AGN in late-stage mergers arehighly obscured. Nonetheless, the low enhancement in
X-ray selected AGN and star formation activity in latestage mergers and kinematic pairs reconfirms the resultsthat galaxy and black hole growth are not solely driven
by major mergers.
6. SUMMARY

Although mergers of dark matter halos underpin theories of structure and galaxy formation, the actual role ofgalaxy mergers is less clear. In this work, we seek to expand the study of merging galaxies to galaxy pairs withsmall separations. By including late-stage mergers withsamples of more widely separated (as of yet not merging) pairs, we can obtain a clearer understanding of therole of mergers in galaxy evolution since z ≈ 1. To that
end, we develop a method to identify late-stage galaxy
mergers using HST images.
We utilize a high-pass filter that easily detects thebright, concentrated, central cores of both member galaxies of a merger before coalescence. By implementing
limits on the flux ratio and brightness of the measured
peaks, we are able to produce a clean sample of 2055
galaxy mergers from COSMOS ACS I−band images ofgalaxies brighter than I = 23. These late-stage mergers have two intact galaxy nuclei that are separated byless than 8 kpc. If we restrict the parent sample to a
mass-complete (log M∗ /M⊙ > 10.6) sample of galaxies in
the redshift range 0.25 < z < 1.0, with pair separations
between 2.2 and 8 kpc, we find 136 late-stage mergers,which represents 2.3 ± 0.2% of the massive galaxy population, or 4.8 ± 0.5% when corrected for contaminationand incompleteness. The sample of late-stage mergers
identified here is distinct from other samples of merging
galaxies, such as kinematic pairs, and morphologically20

Lackner et al.

disrupted galaxies identified by CAS or Gini/M20.
We create mock images of mergers by placing two
real galaxies in one postage stamp and use these to test
the completeness and contamination in our sample. Although the sample suffers little from contamination (10%from clumpy, non-merging galaxies and 20% from minor
mergers), we only successfully select ∼ 20% of all major mergers, and the selection efficiency decreases withincreasing redshift. Our method is most successful formergers between concentrated early-type galaxies, selecting 80% of all simulated mergers, independent of redshift.
Using our sample of late-stage mergers, we study boththe evolution of the merger rate and the properties ofmerging galaxies. Our results can be summarized as follows:• For galaxies with stellar masses above log M/M⊙ >10.6, we find that the fraction of mergers evolves asfmerge ∝ (1 + z)3.8±0.9 when corrected for incompleteness, and contamination from minor mergers,
non-mergers and line-of-sight superpositions. Despite uncertainties in the sample completeness andthe merger timescale, Tobs , the normalization of thefractional merger rate, ℜmerge , agrees well with thatfound in previous studies. The measured evolution
in the merger rate becomes significantly flatter if
we remove the redshift-dependent correction for incompleteness of the sample, ℜmerge ∝ (1+z)0.8±0.8 .
• Dividing the sample into quiescent, star-forming,
low-mass, and high-mass galaxies, we find that themerger rate for star-forming galaxies is a strong
function of redshift, ℜmerge ∝ (1 + z)4.5±1.3 , whilethat for quiescent galaxies is a mild function of redshift, consistent with no evolution, (1 + z)1.1±1.2 .
Therefore, among massive galaxies, the increase in
the total merger rate is driven by the increase in
the merger rate for star-forming galaxies and by
the larger fraction of massive star-forming galaxies
at high redshift. Lower mass (10.6 < log M/M⊙ <10.9) galaxies also exhibit a steeper merger rate
evolution than higher mass (log M/M⊙ > 10.9)
galaxies of (1 + z)5.1±1.3 compared to (1 + z)2.7±1.1.
These results use different corrections for completeness for star-forming (late-type) mergers and quiescent (early-type) mergers. Although the merger
rate slopes are not as steep without the corrections for incompleteness, the merger rate for starforming (low-mass) galaxies still evolves more with
redshift than that of quiescent (high-mass) galaxies. This shows that the differences in the merger
rates as a function of stellar mass and SFR are robust. Furthermore, these differences suggest thatmeasurements of the merger rate as a function ofredshift are very sensitive to the sample of galaxies.
• Examining the properties of late-stage mergers,
we find that the SFR in late-stage mergers withlog M∗ /M⊙ > 10.4 is enhanced by a factor of
2.1 ± 0.6 compared to non-interacting galaxies.
This is similar to the enhancement found for kinematic galaxy pairs using the same parent sample(Kampczyk et al. 2013). Only 18 ± 5% of star formation between z = 0.25 and z = 1.05 is associatedwith late-stage mergers or pairs separated by lessthan 30 h−1
100 kpc. However, the excess star formation that can be attributed to major mergers is only
half of that.
• The AGN fraction in late-stage mergers at z > 0.5
is enhanced by a factor of 2.2±0.8 compared to thefield. For the entire redshift range, 0.25 < z < 1.05,
we do not measure a statistically significant enhancement in AGN activity. At most, the AGN
activity in late-stage mergers between 0.25 < z <1.05 is enhanced by a factor of 3 above the activity
in field galaxies. Together with more widely separated pairs, 20 ± 8% of AGN activity is induced bymergers at separations less than 143 kpc. The fraction of AGNs triggered by late-stage mergers andkinematic pairs is similar to the fraction of SFR activity triggered by the same class of mergers. Thissuggests that the processes responsible for star formation and AGN activity in major mergers may becoupled, indicating a co-evolution scheme (Jahnke
et al. 2009; Cisternas et al. 2011; Schramm & Silverman 2013).
The measurement of the blue galaxy merger rate is particularly sensitive to morphological k-corrections and theincreasing fraction of blue, star-forming, clumpy galaxies at high redshift. Because galaxies appear clumpier atblue rest-frame wavelengths and the entire galaxy population contains more clumpy, star-forming galaxies athigh redshift, we expect our peak-finding method to detect more late-stage merger candidates at high redshift.
We plan to address this by applying our peak-finding
method near-infrared data WFC3 HST data from the
CANDELS survey (Koekemoer et al. 2011; Grogin et al.
2011). Performing this study at longer wavelengths may
also help increase the completeness of our merger sample. Galaxies appear more bulge-dominated and concentrated at longer wavelengths and our merger-finding
method is significantly more sensitive to mergers between
concentrated, early-type galaxies than mergers between
late-type galaxies.
Although we have examined the SFRs and X-ray emission of late-stage mergers, resolved properties of themergers require additional data. For instance, we have asample of ∼ 20 late-stage mergers with significant X-ray
detections and 2 concentrated central cores. Although
the X-ray detection cannot resolve the merging galaxies,
these sources provide an excellent parent sample for spectroscopic searches for dual AGN (e.g., Comerford et al.
2009; Liu et al. 2010; Civano et al. 2010). By focusing only on X-ray AGN, we are only studying a subset
of AGN. There are many AGN selected in IRAC (Donley et al. 2012), radio (Smolčić et al. 2008), and optical/infrared (Fiore et al. 2008; Dey et al. 2008) data. Increasing 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 also increases using AGN selected in
the optical, infrared, or radio.
Obtaining a sample of late-stage mergers in the redshift
range 1 . z . 2 would allow us to continue to measure
the evolution of the merger rate at higher redshifts. Recent spectroscopic studies suggest that the merger rate

Galaxy Mergers in COSMOS
increases quickly beyond z ∼ 1 (e.g., López-Sanjuan et al.
2013; Tasca et al. 2014). Expanding the sample to higher
redshift requires high resolution and signal-to-noise datain the near infrared. Switching to the longer wavelengths
eliminates the effects of morphological k−corrections, as
there is evidence that galaxies typically have more structure at shorter wavelengths (e.g., Kuchinski et al. 2000).
Near-infrared WFC3 HST data from the CANDELS survey (Grogin et al. 2011; Koekemoer et al. 2011) could
be used for such a study. Additionally, since the starformation and AGN activity also continue to grow with
redshift, expanding the sample of mergers to higher redshift will increase the statistical significance of the sample of late-stage mergers with ongoing star formation and
AGN activity. This will help determine the role of major mergers in the growth of galaxies and super-massive
black holes at their peak epoch of formation.

21

We thank the referee for their insightful comments
which greatly improved this work. We also thankRichard Massey and Kevin Bundy for helpful comments
on a draft. This work was supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. ST acknowledges support fromthe Lundbeck Foundation. The Dark Cosmology Centre is funded by the Danish National Research Foundation. This research has made use of the NASA/IPAC
Infrared Science Archive, which is operated by the Jet
Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics andSpace Administration. This research made use of APLpy,
an open-source plotting package for Python hosted at
http://aplpy.github.com

APPENDIXAPPENDIX A: SIMULATED MERGER IMAGESIn order to test our merger-finding algorithms, we create a sample of mock mergers by coadding real galaxy images
from 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,
the mock mergers 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 merger
in the images. Since our method is sensitive to only the brightest features in merging galaxies, this omission is
likely unimportant. Below, we focus on mergers with total masses larger than 4 × 1010 M⊙ and in the redshift range
0.25 < z < 1.0. These are the cuts in §4 and ensure the sample is complete at all redshifts.

late-late merger
z=0.69late-late merger
z=0.85

8 kpc

8 kpc

early-late merger
z=0.34early-early merger
z=1.04

8 kpc

8 kpc

Figure 16. Example mock merger images. The circles show the position of the coadded galaxies, while the crosses show the positions of
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 ratio of
the two galaxies is below our detection threshold.

To create mock-merger postage stamps, we randomly select 2400 galaxies from our photo-z sample. For each selectedgalaxy, we select at random a second galaxy at approximately the same photometric redshift (∆z < 0.02) as the first
selected galaxy. This ignores any contamination from chance superpositions at widely different redshifts, which we
address statistically in §4.1. We then coadd the HST/ACS postage stamp images of these galaxies. For each galaxy
pair, we make 8 postage stamps with different separations between the galaxy centers, spanning from 0.1 to 10 kpc.
Using the ZEST morphology parameter (Scarlata et al. 2007), we create 3 additional samples of 1200 mock mergers
with specific morphologies: a sample of mergers between two early-type galaxies (ZEST=1), a sample between latetype galaxies (ZEST=2), and a mixed sample (ZEST=1 and 2). We apply the median ring filter to all these mock

22

Lackner et al.

late-laterandom1.0
completeness fraction

completeness fraction

1.0

early-early
early-late

0.8
0.6
0.4

early-early
early-latelate-laterandom

0.8
0.6
0.4

0.2

0.2

0.0
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

redshiftredshift

Figure 17. The completeness of the late-stage major mergers in simulated images as a function of redshift, before applying cuts in flux
ratio 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. The other lines show the completenesses 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 ZEST
parameter. The errors are derived by bootstrap resampling. The completeness is a stronger function of morphology than redshift.

images and examine the results. Figure 16 shows four example mock-merger images. The circles √denote the twogalaxies that have been super-imposed. Owing to the coaddition, these mock images are a factor of 2 noisier thanthe original images. However, because we are creating merger images by coadding images from our sample, the mockmergers are up to a factor of 2 brighter than the real galaxies in the sample. These effects approximately cancel out
and we neglect the differences in signal-to-noise ratio 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 selection
is particularly incomplete for mergers among late-type galaxies, in which neither galaxy has a dominant bulge. The
left panel of Figure 17 indicates our completeness as a function of redshift (black solid line). In this figure, we examine
the completeness for major mergers (> 1 : 4) with separations between 2.2 and 8.0 kpc, without applying any cuts influx ratio, while the right panel includes cuts in flux ratio (see below). Beyond z ∼ 0.5, our method only detects 20%of the mock late-stage mergers. Dividing the sample by the ZEST morphology of the merging galaxies shows that thecompleteness 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 to detect apeak. When comparing the merger rates of early- and late-type galaxies, we find they have very different completenessfractions. Furthermore, the decrease in the completeness up to z ∼ 0.5 leads to an underestimate of the merger-rate
evolution, as we are missing about twice as many galaxies at high redshift than at low redshift.
Figure 18 shows the completeness as a function of pair separation, similarly divided by galaxy morphology. For all
morphologies, the completeness is independent of pair separation beyond ∼ 2 − 3 kpc. This is driven by the size ofthe median ring filter (2.2 kpc at z = 1). The lower panel shows the fractional error in our measurement of the pair
separation. For large separations, the separation is well-measured. However, for small real separations, the measured
separation is typically too large. By cutting off the pair separations at 2.2 kpc, we introduce some contaminationfrom pairs at smaller separations, particularly at lower redshifts. Determining the exact fraction of this contamination
would require knowledge of the spectrum of real pair separations, which we have not included in these simulations.
However, we can assume that the number of mergers at small separations is smaller than those at large separations
and that this contamination is small. In particular, the contamination from other galaxy structures and minor mergers
is likely to be much larger, and can be measured using our simulated merger images.
Because our mock-merger images use real galaxies, we can ascertain how often galactic sub-structures, such as bars,
spiral arms, and star-forming clumps, are selected by the median ring filter. These features are typically fainter thangalaxies, and by applying a cut to the ratio of the peak flux to the total galaxy flux, we can eliminate a substantial
fraction of the contamination for galaxy substructure. Figure 19 shows the distribution of peak fluxes for peaks
associated with merging galaxies and peaks associated with galaxy substructure. The substructure peaks are typically
fainter. To eliminate these detections, we require that the detected peaks contain at least 3% of the total galaxy flux.
This reduces the contamination by extraneous peaks to ∼ 10%, while keeping the completeness of detected peaks at∼ 80%. Lowering this threshold to 0.5% does not significantly affect our results. Before applying our method todifferent 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 of

23

fractional error

completeness fraction

Galaxy Mergers in COSMOS
early-early
early-late

1.0late-laterandom

0.8
0.6
0.4
0.2
0.0
3
2
1
0
−1

0

1

2

3

4

5

6

7

8

separation [kpc]Figure 18. Top: The completeness of the mock mergers as a function of pair separation. Note that each galaxy pair was simulated at a
discrete set of separations. The completeness drops sharply for separations comparable to the median ring filter size. The different lines
show the completeness for different morphologies of the members of the merger, as in Figure 17. The vertical line shows the cut made inseparation at 2.2 kpc. 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 < 2.2 kpc.

1400
1200

real galaxies
other peaks

number

1000
800
600
400
200
0
10-4

10-1
10-3
10-2
100
peak flux/total galaxy flux

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%.

minor mergers, we build a sample of 2400 mock mergers in which one member of the pair is brighter than I = 20.5.
This ensures that, from a sample of galaxies with I < 23, we select a realistic distribution of merger ratios down to
1 : 10. Note that our algorithm only measures the flux ratio of the merger, not the underlying mass ratio, which
requires color information about the separate galaxies. The conversion between flux ratio and mass ratio is mostfraught in the case of mixed mergers, i.e., mergers between star-forming and quiescent galaxies. However, in our mockmerger images, we find that the real flux ratio of a merger is on average strongly correlated with the mass ratio, andthat the flux ratio of 0.25 corresponds approximately to a mass ratio of 0.25.
Figure 20 shows the contamination rates for our sample of detected mergers, including major and minor mergers,
as well as false positives, i.e. mergers made of star-forming clumps instead of the two galaxies inserted into the mock
image. We exclude mergers with a observed flux ratio smaller than 0.25. Overall, 70% of the detected late-stage

24

frac. of detected pairs

Lackner et al.

1.0

detected mergers
non mergers
minor mergers

0.8
0.6
0.4
0.2

fractional error

0.0
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
meas. flux ratio
2
1
0
−1
0.0

0.2

0.4

0.6

0.8

1.0

real flux ratio
Figure 20. Top: The fraction of detected mergers that 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 that 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.

mergers are real major mergers, and only 10% of mergers are false positives, as expected from the peak-to-total flux
cut explained above. The total fraction of minor mergers is 20%, and the contamination is worse at lower flux ratios.
The lower panel in Figure 20 shows the fractional error in the measured flux ratio. While the measured flux ratio
correlates with the real flux ratio, the errors are extremely large, particularly at small real flux ratios. More accurate
measurements of the flux ratio could be obtained by fitting a late-stage merger with two realistic galaxy profiles
centered on each detected peak. However, in this work, we only use the measured flux ratio to discriminate between
major 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 mergers
than major mergers, and that many minor mergers are eliminated by the peak-to-total flux cut of 3%. Both of theseeffects 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. These
cuts are important since they significantly decrease the contamination from star-forming clumps and minor mergers.
Using the results of Figures 17 and 20, we can correct the measured late-stage merger fractions for incompletenessand contamination and use the corrected fractions to determine the merger-rate evolution. In studying the 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 will mask any
differences between the field population and the merger population.
APPENDIX B: COMPARISON OF MEDIAN RING FILTER SELECTION TO CAS AND GINI-M20 SELECTION

To better understand the poor overlap between our sample of late-stage mergers and mergers selected based on theirGini (G), M20 and asymmetry (A) values, we examine a small random set of galaxy images. A galaxy is considered amerger by the Gini-M20 method if G > −0.12M20 + 0.38 (Lotz et al. 2008a). A galaxy is considered a merger basedon its asymmetry if A > 0.35 (Conselice 2003). The morphology measurements G, M20 , and asymmetry (A) values
are taken from Cassata et al. (2005). Note that the deblending done by Cassata et al. (2005) leads to different values
for the morphology metrics than those derived directly from the images shown here. However, because we are looking
for merging, deblending close pairs may not always be desirable, and we include differences in the deblending as partof our comparison.
The Gini-M20 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-corrections
need to be taken into account. By using galaxies at redshifts above z ∼ 0.6, the observed I−band images are close
to the rest frame B−band images and corrections to the measured G, M20 , and A can be neglected. We do include a
correction of δA = 0.05 for the effect of surface-brightness dimming at high redshift (see Conselice et al. 2009; Conselice
2003; Conselice et al. 2003).

25

Galaxy Mergers in COSMOSa)10:01:07.8 +1:55:55.5 b)10:02:48.1 +2:33:57.6 c)09:58:31.7 +2:17:46.7 d)10:01:49.2 +2:10:36.1
M20 = −1.09 z=0.61
M20 = −1.17 z=0.84
M20 = −1.70 z=0.93
M20 = −1.70
z=0.84

A =0.13
G =0.41

8 kpc

A =0.11
G =0.44

8 kpc

A =0.13
G =0.54

8 kpc

A =0.21G =0.50

8 kpce)09:59:48.6 +2:20:30.6 f)10:01:43.2 +2:05:12.7 g)10:01:53.7 +2:02:23.1 h)10:01:38.6 +1:39:00.2
M20 = −2.39 z=0.66
M20 = −1.92 z=0.95
M20 = −1.53 z=0.80
M20 = −1.73
z=1.00A =0.04
G =0.55

8 kpc

A =0.34
G =0.55

8 kpc

A =0.24
G =0.51

8 kpc

A =0.17
G =0.51

8 kpc

Figure 21. Examples of galaxies which are late-stage mergers but are not detected as mergers by the Gini-M20 method (Lotz et al.
2008a). We only examine galaxies with z > 0.6 in order to minimize the effects of morphological k-corrections to the rest frame 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.

a)10:02:51.8 +2:40:26.1 b)10:00:36.0 +2:28:30.6 c)10:01:17.7 +2:00:14.1 d)10:02:42.7 +2:44:26.3
M20 = −1.69 z=0.69
M20 = −1.65 z=1.00
M20 = −1.98 z=0.97
M20 = −2.33
z=0.61

A =0.20
G =0.49

8 kpc

A =0.19
G =0.44

8 kpc

A =0.19
G =0.61

8 kpc

A =0.04
G =0.54

8 kpce)09:59:13.2 +1:52:39.6 f)09:58:47.4 +1:53:44.1 g)10:01:11.2 +2:29:02.1 h)10:00:25.3 +2:17:51.4
M20 = −1.80 z=0.78
M20 = −1.26 z=0.78
M20 = −1.13 z=0.94
M20 = −0.88
z=0.99A =0.21G =0.57

8 kpc

A =0.19
G =0.43

8 kpc

A =0.17
G =0.45

8 kpc

A =0.26
G =0.45

8 kpc

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 > 0.35, (see Conselice 2003)). We use the asymmetry measurements from Cassata et al. (2005) and include a correction of 0.05
for the surface brightness dimming (Conselice et al. 2009). We only use galaxies with z > 0.6, which limits the morphological k-corrections
when comparing to the rest frame B-band. The images have the same stretch and scaling as those in Figure 21.

Figure 21 shows late-stage mergers selected by our method that are not selected by the Gini-M20 criterion. Panels b,
c, d, g, and h show galaxies with Gini and M20 values close to the division line. In panel a, the detected peaks are wellseparated from the main galaxy and are likely a separate system. In panels e and f , the central peaks are sufficiently
separated to be deblended before measuring the morphology. This will lower the M20 coefficient in particular. In
general, the galaxies our merger method selects are highly concentrated, which leads to lower M20 values than forother mergers.
Figure 22 shows late-stage mergers with A < 0.35 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. Nevertheless, wenote that an equal-mass merger between two similar galaxies will be symmetric about an 180◦ rotation, which may

26

Lackner et al.
a)10:01:54.9 +2:24:16.5 b)10:02:04.7 +2:25:25.3 c)10:00:40.3 +2:47:43.7 d)10:00:49.2 +2:06:12.9
M20 = −1.34 z=0.90
M20 = −1.81 z=0.96
M20 = −1.77 z=0.94
M20 = −1.58
z=0.93

A =0.25
G =0.55

8 kpc

A =0.14
G =0.60

8 kpc

A =0.23
G =0.61

8 kpc

A =0.14
G =0.60

8 kpce)10:00:24.8 +1:39:42.9 f)10:00:17.6 +2:20:48.6 g)09:58:55.3 +2:14:15.6 h)10:01:26.3 +2:23:44.1
M20 = −1.10 z=0.84
M20 = −0.75 z=0.72
M20 = −0.56 z=0.99
M20 = −0.67
z=0.68A =0.19
G =0.54

8 kpc

A =0.21G =0.48

8 kpc

A =0.11
G =0.45

8 kpc

A =0.10G =0.47

8 kpc

Figure 23. Examples of galaxies which are not late-stage mergers but are selected as mergers by the Gini-M20 method (Lotz et al. 2008a).
The redshift range and the image stretch and scaling are the same as in Figure 21. Most of these systems would be characterized as minor
mergers, and therefore missed by our method.

a)10:02:08.6 +2:26:04.9 b)09:59:39.1 +2:03:42.6 c)10:02:22.0 +2:07:37.1 d)10:02:34.3 +2:26:58.4
M20 = −1.64 z=0.99
M20 = −2.08 z=0.83
M20 = −0.59 z=0.81
M20 = −1.50
z=0.94

A =0.39
G =0.58

8 kpc

A =0.36
G =0.62

8 kpc

A =0.36
G =0.06

8 kpc

A =0.46
G =0.62

8 kpce)09:59:46.9 +2:13:40.5 f)10:01:58.0 +2:29:52.4 g)10:01:47.8 +2:08:15.2 h)10:01:37.5 +1:49:35.7
M20 = −1.54 z=0.90
M20 = −1.87 z=0.83
M20 = −1.58 z=0.84
M20 = −1.95
z=0.85

A =0.39
G =0.53

8 kpc

A =0.37
G =0.55

8 kpc

A =0.37
G =0.49

8 kpc

A =0.43
G =0.61

8 kpc

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 > 0.35 (see Conselice 2003)). The images have the same stretch and scaling as those in Figure 21.

contribute to the low A values of systems in panels d and g. As with the galaxies in Figure 21, the galaxies shown
here are highly concentrated, which also tends to lower the asymmetry value.
Figure 23 shows instead the galaxies detected as mergers by the Gini-M20 criterion but not selected as late-stage
mergers. 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 that are selected as mergers based on their asymmetry, but not by our median ring filter
method. The asymmetric features in almost all of these galaxies are too faint to be detected by our method. These
are frequently mergers with a late-type galaxy, which, as shown above, our method often overlooks. The mergers

Galaxy Mergers in COSMOS

27

in panels e and g both have flux ratios below our threshold of 0.25 and would be considered minor mergers. Manyof the galaxies not detected by our method but detected by other methods are mergers in which one component issignificantly fainter than another, or the companion is no longer visible and only other tracers of the merger remain.
The former will include major mergers with different mass-to-light ratios for each merger component, i.e. mergers
between quiescent and star-forming galaxies. This suggests that our merger-finding method may be complementary
Guo, Q. & White, S. D. M. 2008, MNRAS, 384, 2
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