Galaxy Pairs in COSMOS -- Merger Rate Evolution Since z=1
C. Kevin Xu, Yinghe Zhao, N. Scoville, P. Capak, N. Drory, Y. Gao
aa r X i v : . [ a s t r o - ph . C O ] N ov Draft 10 ; A
UGUST
26, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
MAJOR-MERGER GALAXY PAIRS IN THE COSMOS FIELD —MASS DEPENDENT MERGER RATE EVOLUTION SINCE Z = 1 C. K
EVIN X U , Y INGHE Z HAO , N. S COVILLE , P. C APAK , N. D RORY , Y. G AO (Accepted Nov. 22, 2011) Draft 10 ; August 26, 2018
ABSTRACTWe present results of a statistical study of the cosmic evolution of the mass dependent major-merger ratesince z = 1. A stellar mass limited sample of close major-merger pairs (the CPAIR sample) was selected fromthe archive of the COSMOS survey. Pair fractions at different redshifts derived using the CPAIR sample and alocal K-band selected pair sample show no significant variations with stellar mass. The pair fraction exhibitsmoderately strong cosmic evolution, with the best-fitting function of f pair = 10 - . ± . (1 + z) . ± . . The best-fitting function for the merger rate is R mg (Gyr - ) = 0 . × (M star / . M ⊙ ) . (1 + z) . / (1 + z / star ∼ – . M ⊙ have undergone ∼ . star ≥ . M ⊙ ) at z ≤
1, major mergers involving star forming galaxies (i.e.wet and mixed mergers) can account for the formation of both ellipticals and red quiescent galaxies (RQGs).On the other hand, major mergers cannot be responsible for the formation of most low mass ellipticals andRQGs of M star < ∼ . M ⊙ . Our quantitative estimates indicate that major mergers have significant impact onthe stellar mass assembly of the most massive galaxies (M star ≥ . M ⊙ ), but for less massive galaxies thestellar mass assembly is dominated by the star formation. Comparison with the mass dependent (U)LIRG ratessuggests that the frequency of major-merger events is comparable to or higher than that of (U)LIRGs. Subject headings: galaxies: interactions — galaxies: evolution — galaxies: starburst — galaxies: general INTRODUCTION
Galaxy mergers have been fascinating astronomers for along time, ever since they were recognized (see the reviewof Schweizer (1996)). Major mergers of galaxies of nearlyequal mass stand out because of the more spectacular tidaland dynamical effects (Toomre 1978), and many nearby ma-jor mergers have been extensively studied (Toomre & Toomre1972; Whitmore et al. 1995; Hibbard & van Gorkom 1996;Hibbard & Yun 1999; Xu et al. 2000; Wang et al. 2004). Ithas been well documented that major mergers can induce en-hanced star formation (Kennicutt et al. 1987; Xu & Sulentic1991), trigger extreme starbursts and active galactic nuclear(AGN) activities (Sanders et al. 1988; Sanders & Mirabel1996; Dasyra et al. 2006), and transform spiral galaxiesinto elliptical galaxies (Toomre 1978; Schweizer 1982;Genzel et al. 2001). They dominate among the extremestarbursts such as luminous infrared galaxies (LIRGs, withSFR > ∼
20 M ⊙ yr - ) and ultra-luminous infrared galaxies(ULIRGs, with SFR > ∼
200 M ⊙ yr - ; Sanders & Mirabel1996). On the other hand, statistically, major mergers playminor roles in the processes such as star formation and massgrowth of z ∼ ∼ Infrared Processing and Analysis Center, California Institute of Tech-nology 100-22, Pasadena, CA 91125, USA Purple Mountain Observatory, Chinese Academy of Sciences, 2 WestBeijing Road, Nanjing 210008, China California Institute of Technology, MC 105-24, 1200 East CaliforniaBoulevard, Pasadena, CA 91125, USA Spitzer Science Center, California Institute of Technology, Mail Stop220-6, Pasadena, CA 91125, USA Instituto de Astronomía, Universidad Nacional Autónoma de México,A.P. 70-264, 04510 México, D.F., México Max-Planck Institut für extraterrestrische Physik, Giessenbachstrasse,85748 Garching, Germany
Patton & Atfield 2008; Domingue et al. 2009), and only ∼
2– 3 percents of star formation rate density (SFRD) in the z=0universe is due to close major mergers (Xu et al. 2010).Are mergers more important in the earlier universe? In-deed, in the hierarchical structure formation paradigm ofthe contemporary cosmology, galaxy and dark matter halo(DMH) merging is one of the most significant processesaffecting the evolution of structures in the early universe,and is largely responsible for the growth of massive darkmatter halos and the buildup of galaxies (Kauffmann et al.1993; Lacey & Cole 1993; Khochfar & Burkert 2005). Manyobservations of intermediate/high redshift peculiar galaxiesand galaxy pairs have found strong evolution in the mergerrate, up to (1 + z)3-6 (Brinchmann et al. 1998; LeFévre et al.2000; Conselice et al. 2003; Bell et al. 2006; Conselice 2006;Conselice et al. 2009; Kampczyk et al. 2007; Kartaltepe et al.2007; Rawat et al. 2008), and show evidence for mergers todominate the total star formation rate in the universe of z > ∼ ∼ (1 + z) . )has been found by other studies of intermediate/high red-shift mergers (Carlberg et al. 2000; Lin et al. 2004; Lotz et al.2008; Robaina et al. 2010; Man et al. 2011), and many au-thors have argued that at z > ∼ > ∼ ≤ r proj ≤
20 h - kpc) major-mergerpairs (stellar mass ratios ≤ . star ≥ M ⊙ ) in thephoto-z range of 0 . ≤ z phot ≤
1. The COSMOS sample hasthe best photo-z’s, measured using data of ∼
30 photomet-ric bands covering the entire UV – infrared range, for morethan 100,000 galaxies with nearly 100 percent completeness(Ilbert et al. 2009). This enables us to obtain a pair samplethat is ∼
70% complete. By comparison the pair samplesin the studies of Patton et al. (2002), Lin et al. (2004), andBundy et al. (2009), using pairs selected from spectroscopicsurveys, are only ∼
10 – 20% complete. Given the rathercomplex spectroscopic selection functions in those studies,the corrections for the incompleteness may lead to substan-tial uncertainties in the results.Photo-z selected pairs of 0 . ≤ z phot ≤ . V ≤ - . ≤
1, be-cause the photo-z’s and stellar mass estimates of z > . ≤ z ≤ Λ -cosmology with Ω m = 0 . Ω Λ = 0 . = 70 (km sec - Mpc - ). THE COSMOS PAIR (CPAIR) SAMPLE
We selected major-merger pair candidates using a parentsample of galaxies constructed from that used by Drory et al.(2009, hereafter D09) in their study of galaxy stellar massfunction (GSMF), which is in turn selected from the COS-MOS photo-z catalog (Ilbert et al. 2009) using the following
Table 1
Parent Samplez min z max Volume log(M min ) Number of Galaxies † (10 Mpc ) (M ⊙ ) SFGs RQGs Total0.2 0.4 0.56 9.0 6787 2039 88260.4 0.6 1.23 9.4 6169 1526 76950.6 0.8 1.92 9.8 6745 1981 87260.8 1.0 2.53 10.2 6610 2287 8897 Note . — : † Number of galaxies with log(M star ) ≥ log(M min ).criteria: 0 . ≤ z ≤
1, K s <
24 and i + AB < . ∆ z = 0 .
2, and into “active” (starforming galaxies, SFGs) and “passive” (red quiescent galax-ies, RQGs) populations according to the SED type of the bestfitting template (Ilbert et al. 2009). The stellar mass of galax-ies, M star , is derived through a stellar population synthesismodel fitting (the Chabrier IMF), using the photo-z and pho-tometric data in the u ∗ (CFHT), B J , V J , g + , r + , i + , z + (Sub-aru), J (UKIRT) and K s (CFHT) bands. Typical uncertaintiesin M star is between 0.1 dex and 0.3 dex at 68% confidencelevel, depending on spectral type and the S/N of the photom-etry (D09). In the four photo-z bins, the completeness limitsfor SFGs and RQGs are log(M star / M ⊙ ) = [8 . , . , . , . star / M ⊙ ) = [8 . , . , . , . min )) on each of the photo-zbins in the parent sample. The mass limit and the number ofgalaxies above the limit are listed in Table 1. There are 34144galaxies in the parent sample.The pair sample is also divided into four photo-z bins. Theselection criteria are: : (1) The primary galaxy has log(M star ) ≥ log(M lim ), withlog(M lim / M ⊙ ) = [9 . , . , . , .
6] for the four red-shift bins, respectively. M lim ’s are 0.4 dex above theM min ’s of the parent sample (Table 1). : (2) the difference in M star between the primary galaxy and thesecondary galaxy is less than 0.4 dex: ∆ log(M star ) ≤ . : (3) the redshift difference between the two components, ∆ z phot = | z priphot - z | , satisfies ∆ z phot / (1 + z priphot ) ≤ . : (4) the projected physical separation (r proj ) is in the range of5 ≤ r proj ≤
20 h - kpc.Compared to the selection criteria for local pairs describedin Xu et al. (2004), we replaced the rest-frame K-band se-lection by a stellar mass selection in criteria (1) and (2).The Spizer-IRAC 3.6 µ m and 4.5 µ m bands, which encom-pass the rest-frame K-band emission for galaxies of 0 . < ∼ z ≤
1, have relatively low angular resolution compared to theHST/ground-based optical and NIR data. Using IRAC datawould have resulted in larger confusion errors in the stellarmass for pairs with separation < ∼ ′′ . At the same time, italaxy Pairs in COSMOS – Merger Rate Evolution Since z = 1 3 Table 2
Sample of Paired Galaxies in COSMOSz min z max Number of Galaxies † log(M lim ) Number of Galaxies with M star ≥ M lim ‡ in iso. in multi. Total (M ⊙ ) in iso. in multi. Total SFGs ∗ RQGs ∗ pairs systems pairs systems0.2 0.4 144 6 150 9.4 128 5
78 550.4 0.6 100 3 103 9.8 93 3
61 350.6 0.8 144 22 166 10.2 126 20
109 370.8 1.0 174 24 198 10.6 131 21
81 71
Note . — : † Including all primaries and all secondaries. : ‡ Including all primaries and those secondaries with log(M star ) ≥ log(M lim ). : ∗ SFGs (“active galaxies”) and RQGs (“passive galaxies”) classifications were taken from D09.was shown in D09 that for field galaxies of z ≤ paired galaxies, found in both isolated pairs and multiple sys-tems. Among them, (including both primaries and secon-daries) have log(M star ) ≥ log(M lim ), and the remaining (90, allsecondaries) have (log(M lim ) - . ≤ log(M star ) < log(M lim ).Statistics of the sample are listed in Table 2. CPAIR SAMPLE: INCOMPLETENESS AND SPURIOUS PAIRSFRACTION
Much of the discrepancies between different results onmerger rate evolution can be attributed to various biases caus-ing incompleteness (missing of true mergers) and contamina-tions of spurious mergers in merger samples. Therefore it isimportant to investigate thoroughly all such biases and correctthem in merger statistics.
Incompleteness due to Missing Very Close Pairs
Photometric data of the photo-z catalog (Ilbert et al.2009) were obtained using the SExtractor in dual mode (Bertin & Arnouts 1996). Images in all bands were degradedto a common PSF of FWHM = 1 . ′′ , and the photometry wasdone with a constant aperture of r = 1 . ′′ (Capak et al. 2007).Because of the limited angular resolution of the photo-z cat-alog, very close pairs with angular sepatation ǫ < ∼ ′′ are in-complete in the pair sample. Exploiting the COSMOS HST-ACS lensing catalog (Leauthaud et al. 2007, 2010), we esti-mated this incompleteness to be [0.01, 0.06, 0.08, 0.20] forthe four redshift bins, with no significant mass dependence.The full analysis can be found in Appendix A. Incompleteness due to Photo-z Errors and SpuriousPairs due to Projection
For pairs of ǫ > . ′′ , major cause of the incompleteness isdue to photo-z errors, which have a non-negligible probabil-ity of being so large that a real pair with ∆ v <
500 km sec - (corresponding to ∆ z / (1 + z) < . ∆ z phot / (1 + z phot ) > .
03 and therefore be missed bythe CPAIR sample. Also, the photo-z selection criterion andthe photo-z errors can introduce spurious pairs whose velocitydifference ∆ v is larger than 500 km sec - . Using Monte Carlosimulations, we estimated the incompleteness and the spuri-ous pair fraction (hereafter SPF) to be [0.21, 0.21, 0.23, 0.25]and [0.07, 0.08, 0.10, 0.09], repectively, for the four refshiftbins. The full analysis is presented in Appendix B. Clustering Effect on Spurious Pair Contaminations
Bell et al. (2006) found that in the COMBO-17 survey, theprojected two-point correlation functions of massive galax-ies with 0 . < z phot ≤ . ∝ r - γ down to r = 15 kpc, with the value of the power-index γ consistent with 2. Based on this result (see alsoRobaina et al. 2010), we made a simple estimation for theeffect of galaxy clustering that was neglected in the MonteCarlo simulations. It should be pointed out that, different fromPatton et al. (2000) and Bell et al. (2006), we assumed thatthe boundary separating physical (i.e. gravitationally bound)and unphysical pairs, r p , is much larger than r = 20 h - kpc,the separation limit in our pair selection. This is because themerger time scales derived by Lotz et al. (2010), as adoptedin this work (Section 5.2), are for close pairs with projected separation r ≤
20 h - kpc.For a given two-point correlation function ξ (r) = (r / r) γ , the C.K. Xu et al. Table 3
Completeness and Reliability Corrections for CPAIR Samplez min z max Completeness Correction Reliability Correctiondue to missing due to photo-z Combined due to random due to due to pairs of Combinedvery close pairs errors projection clustering ∆ v > / sec0.2 0.4 0 . ± .
01 0 . ± .
05 0 . ± .
05 0 . ± .
03 0 . ± .
05 0 . ± .
03 0 . ± . . ± .
03 0 . ± .
05 0 . ± .
05 0 . ± .
03 0 . ± .
05 0 . ± .
03 0 . ± . . ± .
03 0 . ± .
05 0 . ± .
05 0 . ± .
03 0 . ± .
05 0 . ± .
03 0 . ± . . ± .
04 0 . ± .
05 0 . ± .
05 0 . ± .
03 0 . ± .
05 0 . ± .
03 0 . ± . Figure 1.
Illustraction for Eq. 1. r is the maximum projected separa-tion in the pair selection, r p the outer boundary of physical (i.e. gravi-tationally bound) pairs, and r ∆ the distance range along the line-of-sightthat corresponds to the pair selection criterion for the photo-z difference: | ∆ z phot | / (1 + z phot ) ≤ .
03. The shadowed areas are places where spuriouscompanions are located. additional SPF ( η ) due to clustering can be estimated as fol-lows: η = 4 π n R r ∆ r p ( r / r ) γ r dr R arcsin ( r / r )0 sin ( θ ) d θ π n hR r ( r / r ) γ r dr + R r ∆ r ( r / r ) γ r dr R arcsin ( r / r )0 sin ( θ ) d θ i . (1)The numerator on the right-hand side of the equation is theprobability to find spurious companions near a galaxy in bothforeground and background (in the shadowed areas in Fig. 1).Here r ∆ is ∼
100 Mpc, corresponding to the pair selectioncriterion of | ∆ z phot | / (1 + z phot ) ≤ .
03. The denominator isthe probability of finding both real and spurious companionswith a projected separation of r ≤ r . The relations betweenparameters r , r p and r ∆ are illustrated in Fig. 1. For γ = 2 andr << r p << r ∆ , Eq. 1 can be approximated by: η = r / r p π . (2)Assuming r p = 100 h - kpc, Eq. 2 gives η = 0 .
06. It is worthnoting that: (1) η is comparable to the SPF found by theMonte Carlo simulations for the random associations; (2) η is constant against the redshift; (3) given the uncertainties inr p and γ , we shall assume an relatively large error of 0.05 for η ; (4) this correction also applies to pairs selected spectro-scopically because the condition r ∆ >> r p is still valid evenfor the selection criterion of ∆ v ≤
500 km sec - . Fraction of Physical Pairs with ∆ v >
500 km sec - We excluded physical pairs with 500 < ∆ v < ∼ - from the merger rate analysis sincethey have very uncertain and long merger time scales. Thesehigh ∆ v pairs, found in the group/cluster environments(Domingue et al. 2009), are not included in the aboveestimates for projected unphysical pairs. Here we makea separate correction for them. Using local pairs takenfrom Domingue et al. (2009), selected using nearly identicalselection criteria as the CPAIR sample (cf. Section 4) exceptfor that spec-z were used and they include all pairs (isolated or in groups/clusters) with ∆ v spec < - , we findthat the fraction of physical pairs with ∆ v >
500 km sec - is9 . ± .
0% (Appendix C).
Completeness and Reliability of the CPAIR Sample
In Table 3 we listed estimates of the correction factors forsubsamples in the four redshift bins. The combined complete-ness correction factor is the product of that due to missingvery close pairs and that due to photo-z errors. The combinedreliability correction factor, defined as 1 - SPF, is the productof that due to random projections, the additional correctiondue to the clustering effect, and that due to the contaminationof physical pairs with ∆ v >
500 km sec - . The combinedcompleteness correction factor varies in the range of 0.60 –0.78 between the 4 redshift bins. The combined reliabilitycorrection factor ( ∼ .
79) is rather constant against the red-shift.As an independent check, exploiting a sample of spec-zpairs (the ZPAIR sample) selected from the zCOSMOS sur-vey (Lilly et al. 2007), we made an empirical analysis on thecompleteness and reliability of the CPAIR sample. This re-sulted in an estimate of 0 . ± .
12 for the completeness cor-rection factor due to photo-z errors (the incompleteness due tomissing very close pairs cannot be checked with spec-z pairs),which is consistent (within 1- σ ) with the result of the MonteCarlo simulations (Table 3). The estimate for the reliabilitycorrection is also 0 . ± .
12, again consistent (within 1- σ )with the values of the combined reliability correction in Ta-ble 3. The details of the analysis are presented in Appendix D. LOCAL PAIR SAMPLE
Pair statistics in the local universe were carried out usingan updated version of the KPAIR sample by Domingue et al.(2009), a close major-merger pair sample selected in the K-band from cross matches between 2MASS and SDSS-DR5galaxies. The update includes following modifications: : (1) Stellar masses of galaxies in KPAIR and in its parentsample are multiplied by a factor of 10 - . . This isthe average difference between the mass estimated us-ing the total K s band luminosity and a Salpeter IMF(Domingue et al. 2009), and the mass estimated using aKroupa IMF by Kauffmann et al. (2003). Because themass estimated using the Kroupa IMF and that usingthe Chabrier IMF are nearly identical (Kauffmann et al.2003), this modification makes the masses in the localKPAIR sample and those in the CPAIR sample consis-tent. : (2) In order to avoid possible bias due to the local over-density (associated with the local super-cluster), alower redshift cut-off of v ≥ - (z ≥ . z = 1 5 Table 4
Mass Dependent Pair Fractionsz = 0 0 . ≤ z ≤ . . < z ≤ . . < z ≤ . . < z ≤ pair N pg / N G f pair N pg / N G f pair N pg / N G f pair N pg / N G f pair N pg / N G . ≤ log ( M ) ≤ . . ± .
011 2/ 126 0 . ± .
006 44/2034 ...... 0/ 0 ...... 0/ 0 ...... 0/ 09 . < log ( M ) ≤ . . ± .
006 7/ 524 0 . ± .
006 24/1482 0 . ± .
006 44/1977 ...... 0/ 0 ...... 0/ 010 . < log ( M ) ≤ . . ± .
002 41/2775 0 . ± .
010 39/1174 0 . ± .
007 34/1524 0 . ± .
007 71/2542 ...... 0/ 010 . < log ( M ) ≤ . . ± .
002 97/5826 0 . ± .
011 19/ 706 0 . ± .
007 18/ 955 0 . ± .
008 62/1913 0 . ± .
010 110/322911 . < log ( M ) ≤ . . ± .
002 68/4520 0 . ± .
020 6/ 183 (0) 0/ 267 0 . ± .
008 10/ 645 0 . ± .
015 39/105111 . < log ( M ) ≤ . . ± .
007 8/ 417 (0) 0/ 17 (0) 0/ 29 (0) 0/ 65 0 . ± .
029 3/ 103total 0 . ± .
001 223/14188 0 . ± .
010 132/5596 0 . ± .
007 96/4752 0 . ± .
009 143/5165 0 . ± .
011 152/4383 : (3) Pairs with 500 < ∆ v ≤ - are excluded. Mostof these pairs are in cluster environment, and may notbe gravitationally bound. Excluding them improves theaccuracy of the merger rate estimate. : (4) The magnitude limit is set at K s = 12 .
5, the completenesslimit of the KPAIR sample.There are 18,081 galaxies in the parent sample that arebrighter than K s = 12 .
5, of which 14,813 have measured red-shifts (redshift completeness of B z - comp = 0 . . ≤ z ≤ .
1. The new paired galax-ies sample has 221 galaxies, all brighter than K s = 12 . ∆ v spec ≤
500 km sec - . These redshifts are in the range of0 . ≤ z ≤ .
1, with the median of z=0.042. The remain-ing 33 galaxies are in single-redshift pairs (i.e. only one ofthe component galaxies having measured redshift). MASS DEPENDENT MERGER RATES
Pair fraction
The local pair fraction is calculated using the following for-mula:f pair , = B z - comp × (1 - η )A × N + N × (1 - Q spurious )N G , , (3)where B z - comp = 0 .
82 is the redshift completeness of the par-ent sample, A = 0 .
89 the completeness of the local pair sam-ple (Domingue et al. 2009), (1 - η ) = 0 .
94 the clustering re-lated reliability correction factor found in Section 3.3. N and N are numbers of galaxies in pairs of two measuredredshifts and single redshifts, respectively, N G , the num-ber of galaxies in the parent sample with measured redshift(in the range of 0 . ≤ z < . spurious = 0 . = B - comp because pairswith single measured redshifts were included. Also, we sup-plemented the SDSS redshifts of paired galaxies with red-shifts found in the literature and in our own redshift obser-vations (Domingue et al. 2009).The pair fractions in the COSMOS field are estimated asfollows: f pair = Q reli C comp × (1 - D ACS ) × N pg N G , (4)where Q reli = [0 . , . , . , .
78] is the reliability andC comp = [0 . , . , . , .
60] the completeness (for the fourphoto-z bins) of the pair sample, respectively; D
ACS = 0 . pg is the number of interacting galaxies in the pair sample, and N G thenumber of galaxies in the parent sample.The relative error of the pair fraction (i.e. error/f pair ) can beestimated as the quadratic sum of the random error σ rms andthe cosmic variance σ vari7 : σ = σ + σ . (5)The random (binomial statistics) error is σ = 1 - f pair N pg . (6)For the local sample, we adopted the approximation N pg =N + N (1 - Q spurious ). The cosmic variance is given by(Peebles 1980; Somerville et al. 2004): σ = J ( γ ) × (r / r samp ) γ , (7)where r and γ are the parameters in the two-point correla-tion function ξ (r) = (r / r) γ , r samp the radius of the samplingvolume, and J a function of γ :J = 72(3 - γ )(4 - γ )(6 - γ )2 γ . (8)The correlation function parameters for local galaxies of dif-ferent masses were taken from Zehavi et al. (2005). Forgalaxies of z ≥ .
2, we assumed γ = 1 . values by interpolating the measurements for galaxiesof different masses and redshifts by Zehavi et al. (2005),Meneux et al. (2008) and Foucaud et al. (2010). Cosmic vari-ances for the integral pair fractions (i.e. not divided into massbins) were taken from that for galaxies in the mass bin of10 . < log(M star / M ⊙ ) ≤ . ± . . ± . ∆ v ≤ - whereas local pairsin this work are restricted to pairs of ∆ v ≤
500 km sec - ; (2)the application of the clustering related reliability correctionfactor ((1 - η ) = 0 . The pair fraction, f pair , is proportional to the probability of finding asecond galaxy within a spatial separation r from a given galaxy: P(r) =4 π n R r0 [1 + ξ (r)]r dr, where n is the number density of galaxies and ξ thetwo-point correlation function. Hence f pair is proportional to n , and thereforethe cosmic variance has the same effect on f pair as on the number density. C.K. Xu et al. star /M sun )0.000.020.040.060.08 p a i r fr ac ti on z=00.2 Mass-dependent pair fractions in photo-z bins. p a i r fr ac ti on pairs in bin 10.6 Pair fraction evolution. The solid line is the least-square fit tototal pair fraction (pair fraction of all galaxies regardless of the stellar mass)vs. redshift relation, specified by f pair = 10 - . ± . (1 + z) . ± . . Thedashed line is the least-square fit to the pair fractions in the mass bin of 10 . < log(M star / M ⊙ ) ≤ 11, specified by f pair = 10 - . ± . (1 + z) . ± . . for pair fractions to increase with redshift can be seen in allmass bins, though with substantial scatter. The major reasonfor the large scatter is the cosmic variance, given the rela-tively small volume explored by the COSMOS survey in eachphoto-z bin (Table 1). In particular, there is a strong den-sity enhancement in the photo-z bin of 0 . ≤ z < . pair isproportional to the density). Cosmic variance often dominatesthe total error in the pair fraction: its contribution is usually > 50% except in those bins where the number of paired galax-ies, N pg , is less than 10 (hence the random error is large). InFig. 3, we plot the redshift dependence of the integral pairfraction (pair fraction of all galaxies regardless of the stellarmass), and that of the pair fraction for galaxies in the mass bin10 . < log(M star / M ⊙ ) ≤ 11 (the bin encompassing the M ∗ star ).These two results are very close to each other, in agreement star /M sun )0.00.10.20.30.40.50.6 R m g ( G y r - ) z=00.2 Mass-dependent differential merger rate in different photo-z bins. star /M sun )0.000.050.100.150.20 p a i r fr ac ti on z=0 0.2 Comparisons of mass-dependent pair fractions of this work withthose of Bundy et al. (2009). Both results are converted to the f pair for merg-ers of mass ratio, µ , ≤ with our conclusion that the pair fraction does not vary signif-icantly with stellar mass.The least-square fit to the redshift dependence of the inte-gral pair fractions is f pair = 10 - . ± . (1 + z) . ± . . For thepair fractions in the mass bin of 10 . < log(M star / M ⊙ ) ≤ pair = 10 - . ± . (1 + z) . ± . . Differential Major-Merger Rate The differential major-merger rate is the probability foreach galaxy to be involved in a major merger per Gyr: R mg ∝ f pair / T mg , where T mg is the merger time scale in Gyr. Becausethe physical process of a galaxy merger is very complex (seeHopkins 2010b for a review), T mg has been a major sourceof uncertainty in the merger rate studies. In the literature themost common approach has been the approximation of T mg bythe dynamical friction time scale (Binney & Tremaine 1987;Patton et al. 2000; Jiang et al. 2008; Kitzbichler & White2008). Kitzbichler & White (2008) studied the T mg in a semi-alaxy Pairs in COSMOS – Merger Rate Evolution Since z = 1 7 Table 5 Mass Dependent Differential Merger RateMass Bin R mg (Gyr - )z = 0 0 . ≤ z ≤ . . < z ≤ . . < z ≤ . . < z ≤ . ≤ log ( M ) ≤ . . ± . 019 0 . ± . 011 ...... ...... ......9 . < log ( M ) ≤ . . ± . 012 0 . ± . 013 0 . ± . 014 ...... ......10 . < log ( M ) ≤ . . ± . 008 0 . ± . 030 0 . ± . 020 0 . ± . 020 ......10 . < log ( M ) ≤ . . ± . 007 0 . ± . 042 0 . ± . 029 0 . ± . 033 0 . ± . . < log ( M ) ≤ . . ± . 011 0 . ± . 107 ...... 0 . ± . 040 0 . ± . . < log ( M ) ≤ . . ± . 046 ...... ...... ...... 0 . ± . analytical model built on the results of the Millennium Simu-lation. They assumed circular orbits to estimate the dynamicalfriction process, and found relatively weak mass and redshiftdependence in the form of T mg ∝ M - . (1 + z / mg using the re-sults of Lotz et al. (2010). They carried out high resolutionhydro-dynamical simulations for a large number of galaxymergers with diverse initial conditions, and derived T mg atdifferent projected separations in a view-angle averaged for-mat. These simulated mergers have line-of-sight velocity dif-ference ∆ v ≤ 500 km sec - , identical to the pairs in our sam-ple. Nine mergers in Lotz et al. (2010) have baryonic massratios ≤ star ≥ . M ⊙ . In the bin of 5 ≤ r proj ≤ 20 h - kpc,these nine mergers have an average merging time scale ofT mg = 0 . ± . 06 Gyr. The three 1:1 mergers in Lotz et al.(2010) have stellar masses in the range of 10 . – 10 . M ⊙ ,and their T mg ’s in the 5 ≤ r proj ≤ 20 h - kpc bin show aweak mass dependence of T mg ∼ M - . , consistent with whatfound by Kitzbichler & White (2008). Because Lotz et al.(2010) did not study the red-shift dependence of T mg , andbecause their sample is too small (3 mergers) to derive ameaningful mass dependence, we adopt the relation foundby Kitzbichler & White (2008), namely T mg ∝ M - . (1 + z / mg = 0 . × (cid:18) M star . M ⊙ (cid:19) - . (cid:16) + z8 (cid:17) . (9)And the differential merger rate for major mergers of massratio ≤ mg = A × f pair / T mg , (10)where A = 1 . 19 is the factor converting the pair fraction in thiswork (for mergers of mass ratio µ ≤ . 5) to that of mergersof mass ratio µ ≤ 3. Here we assumed that f pair ∝ log( µ max )(Appendix E). In Table 5 and Fig. 4 we present our results onR mg .Using the least-square fit to the pair fraction evolution,f pair = 10 - . ± . (1 + z) . ± . , and Eq. 9, we derived a best- fit function for the mass-dependent R mg evolution:R mg (M star , z) = 0 . × (cid:18) M star . M ⊙ (cid:19) . (1 + z) . + z / - ) . (11)Integrating this merger rate over time, we find that the proba-bility for individual galaxies to be involved in a major mergersince z=1 is 0.8 × (M star / . M ⊙ ) . . Accordingly, on aver-age, massive galaxies of M star ∼ – . M ⊙ have undergone ∼ . Comparisons with Previous Results Our results on the mass independence of the local pairfraction (filled circles in Fig. 2) are in agreement with thoseof Domingue et al. (2009) and Patton & Atfield (2008) whilecontradicting Xu et al. (2004), the latter were derived usinga small sample of 19 pairs. For pairs of higher redshifts,Bundy et al. (2009) found a trend of positive mass depen-dence, which was not confirmed by our results. In Fig. 5,our results are compared to those of Bundy et al. (2009). Inorder to compensate the difference in the mass ratios in thetwo works ( µ ≤ . µ ≤ . pair for µ ≤ pair increasesproportionally with log( µ max ). Accordingly, the pair fractionsfrom this work were scaled up by a factor of 1 . 19 = log(3) / . . 80 = log(3) / . 6. The results of Bundy et al. (2009)might have suffered from large uncertainties: Those obtainedusing their “method I” (projected pairs without any redshiftinformation for the companions), which are plotted in Fig. 5,were based on pair samples with high contaminations ( ∼ 60 –70%) of unphysical pairs; and those from their “method II”(spectroscopic and/or photometric redshifts for both compo-nents) were based on small samples (3 to 15 paired galax-ies in each mass/redshift bin). de Ravel et al. (2009) claimedevidence for strong mass dependence of the evolutionary in-dex of the pair fraction, in the sense that low mass pairs havestrong pair fraction evolution (m = 3 . ± . 54) and high masspairs have weak evolution (m = 0 . ± . . ± . 01) in optically faint pairs (M B ≤ - - Qz,Q=1.11) and for weak evolution (m = 1 . ± . 76) in opti-cally bright pairs (M B ≤ - . - Qz). But the low evolu-tionary index of the bright pairs was obtained only when theyincluded in their fit the z=0 pair fraction of de Propris et al.(2007), one of the highest local pair fraction in the literature(Fig. 6). Indeed, when being calculated in the same way asfor the evolutionary index of faint pairs (i.e. fitting only highz data points), the index of bright pairs is m = 3 . ± . 68, C.K. Xu et al.consistent with that for faint pairs. c l o s e m a j o r- m e r g e r p a i r fr ac ti on this work Bundy 09Lin 08 m = . + - . Bell 06 de Ravel 09de Propris 07 Patton 08Kartaltepe 07 m = . + - . m = . + - . Figure 6. Comparisons of observed pair fractions in the literature. When itis appropriate, results of different authors were corrected so they are consis-tent with a common definition of close major-merger pairs with the maximumprojected separation of r proj , max = 20 h - kpc and the maximum primary-to-secondary mass ratio µ max = 3. Results of pair samples of different r proj , max were corrected by assuming f pair ∝ (r proj , max ) - γ with γ = 2 (Bell et al. 2006).For example, results of Lin et al. (2008) were divided by a factor of 1 . proj , max = 30 h - kpc. The results of Bell et al. (2006)had r proj , max = 30 kpc, corresponding to r proj , max = 21 h - kpc for h = 0 . proj , max = 20 h - kpc and therefore no correction was ap-plied. Results of pair samples of different mass ratio limits were correctedby assuming f pair ∝ log( µ max ) (Fig. E-1). These include results of this work(log( µ max ) = 0 . µ max ) = 0 . µ max ) = 0 . In Fig. 6, our results on the cosmic evolution of the in-tegral pair fraction are compared with those taken from theliterature. It shows that the evolutionary rate derived fromour results is in between those for the strong evolution (e.g.the result of K07) and for weak evolution (e.g. the result ofLin et al. 2008), respectively. Actually, our pair fractions inthe photo-z bins of z = 0 . > 3) for theincompleteness. The color based pre-selection of their red-shift surveys may indeed introduce biases in the pair selection,given the significant influence of galaxy-galaxy interaction onoptical colors (Larson & Tinsley 1978).In the literature, pair fractions are often compared tomerger fractions estimated using counts of peculiar galax-ies (Conselice et al. 2003, 2009; Lotz et al. 2008; Jogee et al.2009). In general the latter are higher than the former, be-cause (1) Contaminations from irregular galaxies (Jogee et al.2009); (2) morphologically selected merger samples based G ( G y r) this workBundy+09 Conselice+09Lotz+08 dotted line: model (Hopkins 2010) Figure 7. The redshift dependence of Γ = 1 / R mg . The values of morpholog-ical based merger studies of Conselice et al. (2009) and of Lotz et al. (2008)were taken from Fig. 7 of Conselice et al. (2009). R mg ’s of Bundy et al.(2009) were scaled down by a factor of 0 . 80 = log(3) / . µ ≤ star /M sun )-6.0-5.5-5.0-4.5-4.0-3.5-3.0 l og ( R V ) ( M p c - d e x - G y r - ) average merger rate (0.3 Data points with error bars are mass-dependent volume mergerrates in different redshift bins. The dashed line is the average growth rate ofellipticals between z=0.3 – 0.9 and dotted line that of RQGs, estimated usingthe mass function of Ilbert et al. (2010). The solid line is the average volumemerger rate calculated using Eq. 12 by replacing R mg with its best fit (Eq. 11)and averaged over the same redshift range of 0.3 – 0.9. on the G – M method (Lotz et al. 2008, 2010) includeminor mergers; (3) the merger time scales for morpholog-ically selected merger samples based on the CAS methodare longer than the merger time scales of close major-mergerpairs (Conselice et al. 2009). Given the different merger timescales for close pairs and for peculiar galaxies, it is moreappropriate to compare the differential merger rates R mg .In Fig. 7 we compare the inverse of the R mg , Γ = 1 / R mg (Conselice et al. 2009), of morphologically selected mergersby Conselice et al. (2009) and by Lotz et al. (2008) with thatof M ∗ star galaxies (log(M ∗ star / M ⊙ ) ∼ . 8, Ilbert et al. (2010))alaxy Pairs in COSMOS – Merger Rate Evolution Since z = 1 9 Table 6 Mass Dependent Volume Merger RateMass Bin log(R V ) (Mpc - dex - Gyr - )z = 0 0 . ≤ z ≤ . . < z ≤ . . < z ≤ . . < z ≤ . ≤ log ( M ) ≤ . - . ± . - . ± . 09 ...... ...... ......9 . < log ( M ) ≤ . - . ± . - . ± . - . ± . 08 ...... ......10 . < log ( M ) ≤ . - . ± . - . ± . - . ± . - . ± . 08 ......10 . < log ( M ) ≤ . - . ± . - . ± . - . ± . - . ± . - . ± . . < log ( M ) ≤ . - . ± . - . ± . 17 ...... - . ± . - . ± . . < log ( M ) ≤ . - . ± . 18 ...... ...... ...... - . ± . in close major-merger pairs in this work and in Bundy et al.(2009). The Γ parameter derived using paired galaxies inour sample (the inverse of Eq. 11) and that of Conselice et al.(2009) derived using morphologically selected mergers are invery good agreement. The higher Γ values of Bundy et al.(2009) are likely due to the relatively long merging time scalethey adopted from Kitzbichler & White (2008). On the otherhand, the low Γ values and lack of evolution of Lotz et al.(2008) are because of the inclusion of minor mergers in theirsample. Our results are in good agreement with the predic-tion of the default (semi-empirical) model of Hopkins et al.(2010b). MAJOR MERGERS, ELLIPTICAL GALAXY FORMATION, ANDGALAXY ASSEMBLY Mass Dependent Volume Merger Rate The volume merger rate, R V , measures the frequency ofmerger events in a given volume in the universe. Here wedefine the mass dependent R V in terms of the stellar mass ofthe merger remnant , which is the total stellar mass of the twogalaxies involved in the merging (ignoring the mass of starsformed during the merger):R V (M star , z) = 0 . × R mg (M star / . , z) φ (M star / . , z) , (12)where φ (M , z) is the GSMF of galaxies in the parent sam-ple (D09), the factor of 0.5 is due to the fact that every ma-jor merger event involves two galaxies of similar mass. Wealso assume that on average the mass of a merger remnant is0.2 dex higher than that of individual galaxies involved in themerger. This is because, under the assumption that mass ra-tio distribution is flat (Appendix C), pairs in our sample hasa mean mass ratio of 0.2 dex. Therefore the logarithm of themean ratio between the total mass of a pair and that of theprimary is log(1 + - . ) ≃ . 2. Our results on the R V arepresented in Table 6.In Fig. 8 we compare our results with the average growthrate of elliptical galaxies (dashed line) and that of RQGs (dot-ted line) between z=0.3 – 0.9, estimated using the differ-ences between their GSMFs at z=0.3 and z=0.9, taken fromIlbert et al. (2010), divided by 3.88 Gyr (the time span corre-sponding to the redshift interval of [0.3,0.9]). The solid lineis the average volume merger rate calculated using Eq. 12 byreplacing R mg with its best fit (Eq. 11) and averaged overthe same redshift range of 0.3 – 0.9. It shows that majormergers can fully account for the formation of both massiveellipticals and RQGs (M star ≥ . M ⊙ ). This contradictsBundy et al. (2009) who concluded that the major-merger rateis too low to fully explain the formation of RQGs since z=1.The major reason for the contradiction is due to the differ-ence in the adopted merger time scales in this work and in Bundy et al. (2009): Our T mg , derived from the results ofLotz et al. (2010), is about a factor of 2 shorter than that usedby Bundy et al. (2009). There is also a difference in the for-mation rates of ellipticals and RQGs adopted in this work (es-timated from results of Ilbert et al. (2010)) and in Bundy et al.(2009). The latter is about 50 – 100% higher than the former.We define “dry mergers” (“wet mergers”) as those in pairsor multiple systems consisted of only RQGs (SFGs), and“mixed mergers” the rest of galaxies in the pair sample. InFig. 9 we compare the volume merger rates of dry merg-ers, and those of wet and mixed mergers combined, to theformation of ellipticals. Our results show that wet/mixedmergers alone can account for the formation rate of mas-sive ellipticals and RQGs, even for the most massive ones ofM star ≥ . M ⊙ . Our results are consistent with Lin et al.(2008), who also found that the wet and mixed mergers dom-inated over the dry mergers since z ∼ star ≥ . M ⊙ . For most mas-sive galaxies with M star ≥ . M ⊙ , the major-merger rateagrees very well with the two formation rates (in this mass0 C.K. Xu et al. star /M sun )-6.0-5.5-5.0-4.5-4.0-3.5-3.0 l og ( R V ) ( M p c - d e x - G y r - ) average growth rate ofRQGs (0.3 Figure 9. Left: Mass-dependent volume merger rates of wet (S+S) and mixed (S+E) mergers, in different photo-z bins. The dashed line is theaverage growth rate of ellipticals between z=0.3 – 0.9 and dotted line that of RQGs, both being estimated using results of Ilbert et al. (2010). Right: Mass-dependent volume merger rates of dry (E+E) mergers. star /M sun )-0.4-0.20.00.20.40.60.8 / f d f / d t ( G y r - ) DA08 merger: z=0.5DA08 merger: z=1DA08 SFR: z=0.5DA08 SFR: z=1major merger contribution(0.3 Figure 10. Fractional change rate of the GSMF. The solid line is our resulton the mean ˆ φ merger (contribution of major mergers, see Eq. 13) over 0 . < z < . 9. The dotted and dashed lines are results of Drory & Alvares (2008)on the contribution of mergers (including both major and minor mergers) atz=0.5 and z=1, respectively. The dot-dashed and dot-dot-dot-dashed linesare results of Drory & Alvares (2008) on the contribution of star formation atz=0.5 and z=1, respectively. range most ellipticals and RQGs belong to the same popula-tion of red elliptical galaxies). In the mass range of 10 . ≤ M star ≤ . M ⊙ , the major-merger rate is slightly higherthan both formation rates. Two factors may be responsible forthis: (1) Remnants of some gas-rich wet mergers may remainto be blue disk galaxies (Hopkins et al. 2009). (2) Dry merg-ers, contributing most in this mass range, may move some redellipticals to higher mass.Fig. 8 and Fig. 9 also show that most (i.e. ∼ / 3) oflow mass ellipticals and RQGs (M star < ∼ . M ⊙ ) are notproduced by mergers. Many authors have argued that thesegalaxies are mostly quenched satellite galaxies whose gashalos are stripped by much more massive central galaxies star /M sun )-6.0-5.5-5.0-4.5-4.0-3.5-3.0-2.5 l og ( R V ) ( M p c - d e x - G y r - ) (U)LIRGs: 0.2 The volume rates of (U)LIRGs (10 . < L IR / L ⊙ < . ), indifferent redshift and stellar mass bins. Estimated using data taken fromKartaltepe et al. (2010) and assuming a (U)LIRG time scale of 140 Myr. Thesolid line is the average mass dependent volume merger rate (this work), iden-tical to that in Fig. 8. (van den Bosch et al. 2008; Peng et al. 2010). Impacts of Major Mergers on Galaxy Assembly Mergers shift galaxies from lower mass bins to higher massbins in the GSMF. The efficiency of this process is clearlycritical for the hierarchical structure formation paradigm.Drory & Alvares (2008) tried to answer this question via com-parisons between observed GSMF variation against redshiftand that predicted by the SFR vs. z relation which was wellestablished (in particular for z ≤ φ merger to evaluate thealaxy Pairs in COSMOS – Merger Rate Evolution Since z = 1 11impact of major mergers on the GSMF φ :ˆ φ merger (M star ) = R V (M star ) /φ (M star ) - R mg (M star ) , (13)where φ (M star ) is the GSMF (D09), R V (M star ) the volumemerger rate defined in Eq. 12, and R mg the differential mergerrate estimated using Eq. 11.In Fig. 10 we compare our results with those ofDrory & Alvares (2008). The solid line is our result on themean ˆ φ merger (M star ) over 0 . < z < . 9. In this redshift range,major mergers (as opposed to star formation) have significantimpact to the galaxy mass assembly only for the most mas-sive galaxies with M star > ∼ . . The GSMF change due tomajor mergers dominates that due to star formation only atM star > ∼ . . For less massive galaxies with M star < . the GSMF change due to major mergers is negligible (ampli-tude ≤ 10 % Gyr - ) in comparison to that due to star for-mation. For these galaxies, our result is much flatter thanthat of Drory & Alvares (2008) for the GSMF change ratedue to mergers at both z=0.5 and z=1. For massive galax-ies (M star > ∼ . ) we find much steeper mass dependencethan Drory & Alvares (2008). The major reason of the dis-crepancy is due to the difference between the redshift depen-dent GMSFs used in this work (Drory et al. 2009) and thosein Drory & Alvares (2008), the latter were derived using datafrom earlier FDF/GOODS surveys. MAJOR MERGERS AND (U)LIRGS Kartaltepe et al. (2010) carried out a study of luminousIR galaxies (LIRGs: 10 < L IR / L ⊙ < ) and ultra-luminous IR galaxies (ULIRGs: L IR / L ⊙ > ) in the S-COSMOS survey (Sanders et al. 2007). We neglect ULIRGsof L IR / L ⊙ > . since very few galaxies have such highIR luminosities, and the AGN fraction increases rapidly withthe L IR among these galaxies (Kartaltepe et al. 2010). Takinggalaxies with 10 . < L IR / L ⊙ < . from their sample andadopting a (U)LIRG time scale of 140 Myr (Kartaltepe et al.2010), we estimate the (U)LIRG rates in different stellar massbins and in the redshift range of 0 . < z < . 0. The results arepresented in Fig. 11, compared with the average mass depen-dent volume merger rate.The mass dependence of (U)LIRG rates in all photo-z binshave the shape of the log-normal function, peaking at a ratherconstant mass of ∼ log( M ∗ star / M ⊙ ) = 10 . 8. In the low photo-z bin (0 . ≤ z ≤ . 4) (U)LIRGs are less frequent, consis-tent with the fact that (U)LIRGs are very rare in the lo-cal universe (Sanders & Mirabel 1996). The average massdependent volume merger rate is above or comparable tothe (U)LIRG rates in all redshift and mass bins, and there-fore it is possible that most of the (U)LIRGs in this red-shift range are major-mergers, just like their local counter-parts (Sanders & Mirabel 1996). Using morphological classi-fications, Kartaltepe et al. (2010) found that > ∼ 50% of their(U)LIRGs are major-mergers. This means that the merger-induced (U)LIRG rates are even more below the averagemerger rate, in particular for M star < ∼ . and M star > ∼ . ,than being depicted in Fig. 11. Hence, it is likely thata large fraction of major-mergers, in particular those withM star < ∼ . or M star > ∼ . , may not become (U)LIRGs.It is interesting to note that the most massive mergers ofM star > ∼ . M ⊙ have rather low (U)LIRG rate. Most of them are wet or mixed mergers, but many probably have rel-atively low gas content. Galaxies of lower mass (M star ∼ M ⊙ ) also have low (U)LIRG rate because their gas massis not adequate to sustain the very high SFR of the extremestarbursts in (U)LIRGs. SUMMARY We have presented results of a statistical study on the cos-mic evolution of the mass dependent major-merger rate sincez = 1. A stellar mass limited sample of major-merger pairs(the CPAIR sample) was selected from the archive of theCOSMOS survey. It includes 617 galaxies in pairs/multiple-systems with stellar mass ratios µ leq2 . 5, projected separa-tions in the range of 5 ≤ r proj ≤ 20 h - kpc, and in the photo-zrange of 0 . ≤ z phot ≤ . 0. The pair selection was based onphoto-z, with the criterion of ∆ z phot / (1 + z phot ) ≤ . 03, andon visual inspections of the HST-ACS images. The CPAIRsample is divided into four photo-z bins of [0 . ≤ z ≤ . . < z ≤ . 6, 0 . < z ≤ . 8, 0 . < z ≤ . ± . 05, 0 . ± . . ± . 05, 0 . ± . 05] and a reliability correction factor of[0 . ± . 06, 0 . ± . 06, 0 . ± . 06, 0 . ± . pair = 10 - . ± . (1 + z) . ± . .The merger time scale was taken from the simu-lation results of Lotz et al. (2010): T mg / Gyr = 0 . × (M star / . M ⊙ ) - . (1 + z / µ ≤ mg / Gyr - = 0 . × (M star / . M ⊙ ) . (1 + z) . / (1 + z / star ∼ – . M ⊙ have undergone ∼ . star ≥ . M ⊙ )at z ≤ 1, major mergers involving star forming galaxies (i.e.wet and mixed mergers) can fully account for the formationrates of both ellipticals and red quiescent galaxies (RQGs),lending support to models that link both bulge formation andSFR quenching to major mergers (e.g. Hopkins et al. 2008).On the other hand, major mergers cannot be responsible forthe formation of most low mass ellipticals and RQGs ofM star < ∼ . M ⊙ . Dry mergers contribute negligibly to themajor-merger rate in all mass and photo-z bins. Major merg-ers have significant impact to the stellar mass assembly of themost massive galaxies (M star ≥ . M ⊙ ). For less massivegalaxies the stellar mass assembly is dominated by the starformation.Comparisons with mass dependent (U)LIRG rates in differ-ent redshift bins suggest that the frequency of major-merger2 C.K. Xu et al.events is comparable or higher than that of (U)LIRGs. Mostlow mass mergers (M star < ∼ . M ⊙ ) and most very massivemergers (M star > ∼ . M ⊙ ) may not become (U)LIRGs. Acknowledgments : This work is based on observations withthe NASA/ESA Hubble Space Telescope , obtained at theSpace Telescope Science Institute, which is operated byAURA Inc, under NASA contract NAS 5-26555; and SpitzerSpace Telescope, which is operated by the Jet PropulsionLaboratory, California Institute of Technology under NASAcontract 1407; also based on data collected at : the SubaruTelescope, which is operated by the National AstronomicalObservatory of Japan; the XMM-Newton, an ESA sciencemission with instruments and contributions directly fundedby ESA Member States and NASA; the European SouthernObservatory under Large Program 175.A-0839, Chile; KittPeak National Observatory, Cerro Tololo Inter-American Ob-servatory, and the National Optical Astronomy Observatory,which are operated by the Association of Universities for Re-search in Astronomy, Inc. (AURA) under cooperative agree-ment with the National Science Foundation; the National Ra-dio Astronomy Observatory which is a facility of the NationalScience Foundation operated under cooperative agreementby Associated Universities, Inc ; and the Canada-France-Hawaii Telescope with MegaPrime/MegaCam operated as ajoint project by the CFHT Corporation, CEA/DAPNIA, theNRC and CADC of Canada, the CNRS of France, TERAPIXand the Univ. of Hawaii. C.K.X acknowledges Kevin Bundyfor constructive discussions and Alexie Leauthaud for helpsin analyzing the COSMOS HST-ACS lensing catalog. ZaraScoville is thanked for proofing the English of the manuscript.Y.Z. and Y.G. are grateful for the financial support from theNSF of China (grants 10833006 and 10903029). Y.Z. thanksIPAC for the hospitality and the financial support during hisvisit. REFERENCESBamford, S. P. et al. 2009, MNRAS, 393, 1324Barnes, J. E. 1988, ApJ, 331, 699Bell, E. F., Papovich, C., Wolf, C., et al. 2005, ApJ, 625, 23Bell, E. F., Phleps, S., Somerville, R. S., R.S., et al. 2006, ApJ, 652, 270Bell, E. F. et al. 2007, ApJ, 663, 834Bensen, A. J. et al. 2003, ApJ, 599, 38Bertin, E. & Arnouts, S. 1996, A&AS, 117, 393Binney, J. & Tremaine, S. 1987, Galactic Dynamics (Princeton: PrincetonUniv. Press)Bridge, C. R., Appleton, P. N., Conselice, C. J., et al. 2007, ApJ, 659, 931Brinchmann, J., Abraham, R., Shade, D., et al. 1998, ApJ, 499, 112Bundy, K. et al. 2009, ApJ, 697, 1369—. 2010, ApJ, 719, 1969Capak, P., Abraham, R. G., Ellis, R. S., Mobasher, B., Scoville, N., Sheth,K., & Koekemoer, A. 2007, ApJS, 172, 284Carlberg, R. G., Cohen, J. G., Patton, D. R., et al. 2000, ApJL, 532, 1Conselice, C. J. 2006, ApJ, 638, 686Conselice, C. J., Bershady, M. A., Dickinson, M., & Papovich, C. 2003, AJ,126, 1183Conselice, C. J., Yang, C., C., & Bluck, A. F. L. 2009, MNRAS, 394, 1956Daddi, E. et al. 2010, ApJL, 714, 118Dasyra, K. M. et al. 2006, ApJ, 638, 745de Propris, R. et al. 2007, ApJ, 666, 212de Ravel, L. et al. 2009, A&A, 498, 379Domingue, D. L., Xu, C. K., Jarrett, T. H., & Cheng, Y.-H. 2009, ApJ, 695,1559Drory, N. & Alvares, M. 2008, ApJ, 680, 41Drory, N. et al. 2009, ApJ, 707, 1995Ellison, S. L., Patton, D. R., Simard, L., et al. 2010, MNRAS, 407, 1514Faber, S. M. et al. 2007, ApJ, 665, 265 Flores, H., Hammer, F., Thuan, T. X., et al. 1999, ApJ, 517, 148Foucaud, S., Conselice, C. J., Hartley, W. G., et al. 2010, MNRAS, 406, 147Genzel, R. et al. 2001, ApJ, 563, 527Hammer, F., Flores, H., Elbaz, D., et al. 2005, A&A, 430, 115Hibbard, J. E. & van Gorkom, J. H. 1996, AJ, 111, 655Hibbard, J. E. & Yun, M. S. 1999, ApJ, 522, 93Hopkins, P. F. et al. 2008, ApJS, 75, 390—. 2009, ApJ, 691, 1186—. 2010a, ApJ, 724, 915—. 2010b, ApJ, 715, 202Huertas-Company, M. et al. 2010, A&A, 515, 3Ilbert, O. et al. 2009, ApJ, 690, 1236—. 2010, ApJ, 709, 644Jiang, C. Y. et al. 2008, ApJ, 675, 1095Jogee, S., Miller, S. H., Penner, K., et al. 2009, ApJ, 697, 1971Kampczyk, P. et al. 2007, ApJS, 172, 329Kannappan, S. J. et al. 2009, AJ, 138, 579Kartaltepe, J. S. et al. 2007, ApJS, 172, 320—. 2010, ApJ, 721, 298Kauffmann, G., S, D. M. W., & Guiderdoni, B. 1993, MNRAS, 264, 201Kauffmann, G. et al. 2003, MNRAS, 341, 33Kennicutt, R. C., Keel, W., van der Hulst, J., et al. 1987, AJ, 93, 1001Khochfar, S. & Burkert, A. 2005, MNRAS, 359, 1379Kitzbichler, M. G. & White, S. D. M. 2008, MNRAS, 391, 1488Koekemoer, A. M. et al. 2007, ApJS, 172, 196Kormendy, J. & Kennicutt, R. C. 2004, ARA&A, 42, 603Lacey, C. & Cole, S. 1993, MNRAS, 262, 627Larson, R. B. & Tinsley, B. M. 1978, ApJ, 219, 46Leauthaud, A. et al. 2007, ApJS, 172, 219—. 2010, ApJ, 709, 70LeFévre, O., Abraham, R., & Lilly, S. J. 2000, MNRAS, 311, 565Lilly, S. J. et al. 2007, ApJS, 172, 70Lin, L., Koo, D. C., Wilmer, C. N. A., et al. 2004, ApJL, 617, 9Lin, L., Patton, D. R., & Koo, D. C. 2008, ApJ, 681, 232Lotz, J. M., Davis, M., Faber, S. M., S.M., et al. 2008, ApJ, 672, 177Lotz, J. M., Jonsson, P., Cox, T. J., & Primack, J. R. 2010, MNRAS, 404,575Man, A. W. S. et al. 2011, arXiv:1109.2985Martig, M. et al. 2009, ApJ, 707, 250Melbourne, J., Koo, D. C., & Flóch, E. L. 2005, ApJL, 632, 65Meneux, B. et al. 2008, A&A, 478, 299Patton, D. R. & Atfield, J. E. 2008, ApJ, 685, 235Patton, D. R., Pritchet, C. J., & Carlberg, R. G. 2002, ApJ, 565, 208Patton, D. R. et al. 2000, ApJ, 536, 153Peebles, P. 1980, The Large-Scale Structure of the Universe (Princeton:Princeton Univ. Press)Peng, Y. et al. 2010, ApJ, 721, 193Rawat, A. et al. 2008, ApJ, 681, 1089Robaina, A. R., Bell, E. F., van der Well, A., et al. 2010, ApJ, 719, 844Sanders, D. B. & Mirabel, I. F. 1996, ARA&A, 34, 749Sanders, D. B. et al. 1988, ApJ, 325, 74—. 2007, ApJS, 172, 86Schweizer, F. 1982, ApJ, 252, 455Schweizer, F. 1996, in Saas-Fee Advanced Course, Vol. 26, Galaxies:Interactions and Induced Star Formation, ed. D. Friedli, L. Martinet, &D. Pfenniger (Berlin and Heidelberg: Springer-Verlag), 105Scoville, N. Z. et al. 2007, ApJS, 172, 1Somerville, R. S., Lee, K., C., H., C.Ferguson, & Gardner, J. P. 2004, ApJL,600, 171Somerville, R. S. et al. 2008, MNRAS, 391, 481Toomre, A. 1978, in The Evolution of Galaxies and Stellar Populations, ed.B. M. Tinsley & R. B. Larson (New Haven: Yale Univ. Press), 401Toomre, A. & Toomre, M. 1972, ApJ, 178, 623van den Bosch, F. C. et al. 2008, MNRAS, 387, 79Wang, Z. et al. 2004, ApJS, 154, 193Whitmore, B. C. et al. 1995, AJ, 109, 960Xu, C., Gao, Y., Mazzarella, J., Lu, N., Sulentic, J. W., & Domingue, D. L.2000, ApJ, 541, 644Xu, C. & Sulentic, J. W. 1991, ApJ, 374, 407Xu, C. K., Domingue, D., Cheng, Y., Lu, N., Huang, J., Gao, Y., Mazzarella,J. M., Cutri, R., Sun, W., & Surace, J. 2010, ApJ, 713, 330Xu, C. K., Sun, Y. C., & He, X. T. 2004, ApJ, 603, L73Zehavi, I., Zheng, Z., & Weinberg, D. 2005, ApJ, 630, 1Zheng, X. Z., Hammer, F., Flores, H., et al. 2004, A&A, 421, 847 alaxy Pairs in COSMOS – Merger Rate Evolution Since z = 1 13 APPENDIX A. INCOMPLETENESS DUE TO MISSING VERY CLOSE PAIRS — ANALYSIS e ( a r cs e c ) < 5 h -1 kpc> 20 h -1 kpc photo-z pair candidatesACS pairs missed by photo-z sample Figure A-1. Plot of the angular separation ǫ vs. redshift relation for pair candidates (open diamonds), and for very close ACS pairs that are missed by the photo-zpair candidate sample (plus symbols). In order to estimate how many pairs with ǫ < ∼ ′′ are missing in our sample, we carried out an analysis exploiting the COSMOSHST-ACS lensing catalog (Leauthaud et al. 2007, 2010). It includes 1 . × galaxies detected by HST-ACS in the F814 band(hereafter i ACS band), with an angular resolution of FWHM = 0 . ′′ (Leauthaud et al. 2007). From this catalog, we selected asample of “very close ACS pairs” through the following procedure: : (1) Find the match in the HST-ACS lensing catalog for every D09 galaxy of log(M star ) ≥ log(M lim ) (see Section 2 for thedefinition of M lim ) with a searching radius of 0 . ′′ and the criterion of | i ACS - i AB , D09 | ≤ : (2) Around the ACS matches of D09 galaxies, we search for ACS pairs with three criteria: (i) | ∆ i ACS | ≤ ǫ < . ′′ ;(iii) r proj ≥ - kpc. star /M sun )0.00.20.40.60.81.01.21.4 fr ac ti on Figure A-2. Comparison of mass distributions of CPAIR galaxies and of galaxies in the single photo-z ACS pairs ( ǫ < ′′ ) with 0 . < z phot < . 0, including 31of the 47 “very close” ACS pairs. The procedure selected 222 very close ACS pairs. Among them, 171 pairs have both component galaxies with photo-z matches,including 53 pairs found in the photo-z pair sample and the remaining 118 pairs consisting of galaxies of discordant photo-z’s orwith mass ratios larger than 2.5. In the remaining 51 pairs, 4 are multi-peak single galaxies in the ACS images. The final samplehas 47 pairs in which only one of two galaxies was detected in the photo-z catalog. These pairs, shown in Fig. A-1 by red crosses,4 C.K. Xu et al.have the average angular separation < ǫ > = 1 . ′′ with the standard deviation of σ = 0 . ′′ . Fig. A-1 also shows that, for pairs of z > . 5, the lower boundary for the pair separations, r proj ≥ - kpc, corresponds to a angular separation of ǫ ∼ ′′ .We then used Monte Carlo simulations to estimate the expected number of spurious pairs in the sample of very close ACSpairs, utilizing the 138001 galaxies in D09 sample. In each of the 100 simulations, we randomly put these galaxies in a 1.7 deg region, with all other properties of the galaxies, including the photo-z and stellar mass, intact. We then search companions aroundeach of the galaxies of log(M star ) ≥ log(M lim ) in the simulated sample according to the following criteria: | ∆ i AB | ≤ ǫ < . ′′ , and (iii) r proj ≥ - kpc. Spurious pairs that do not pass the four pair selection criteria in Section 2 were then counted.These simulations found a mean spurious pair number of 103.3 with a 1- σ dispersion of 7.0. As described above, the number ofconfirmed spurious pairs of photo-z galaxies in the sample of very close ACS pairs is 118. This number is slightly higher thanthe mean total number of spurious pairs (103.3 ± . 0) predicted by the Monte Carlo simulations, perhaps due to galaxy clustering.Thus majority of 47 single photo-z ACS pairs are in fact real and not chance superpositions. Indeed their ACS images very oftenshow signs of interaction. In what follows we shall make the conservative assumption that all 47 ACS pairs are real major-mergerpairs.There are N ACS = [1 , , , 31] single photo-z ACS pairs in the four photo-z bins. The corresponding incompleteness due tomissing of very close pairs, estimated according to the ratio N ACS / (N photo - z + N ACS ) (N photo - z being the number of photo-z paircandidates), is 0.01 ± . 01, 0.06 ± . 03, 0.08 ± . 03, and 0.20 ± . 04 for the four photo-z bins, respectively. As a check, we foundno significant difference between the stellar mass distributions of galaxies in the ACS single photo-z pairs and of those in theCPAIR sample in the redshift bin of 0 . < z phot < . B. INCOMPLETENESS DUE TO PHOTO-Z ERRORS AND SPURIOUS PAIRS DUE TO PROJECTION — MONTE CARLO SIMULATIONS -0.10 -0.05 0.00 0.05 0.10 d z phot /(1+z phot )05101520 pe r c en t age histogram -- parent sample with spec-z (5001)curve -- Lorentz func. ( g =0.0056+-0.0004) Figure B-1. Plot of (z phot - z spec ) / (1 + z spec ) distribution of 5001 galaxies in the parent sample that have spec-z. The red solid curve is the best-fit Lorentzianfunction. We examine the accuracy of the photo-z using the spectroscopically measured redshift (hereafter spec-z) of galaxies in theparent sample that were observed in the zCOSMOS survey (Lilly et al. 2007). zCOSMOS includes a magnitude-limited survey(zCOSMOS-bright) for about 20,000 galaxies of i AB < . . < z < . 2, covering 1.7 deg COSMOS includes 10643galaxies. There are 5001 matches (matching radius = 2”) between galaxies in the parent sample (Table 1) and zCOSMOS sourceswith reliable spec-z measurements (z-class indices being 4’s, 3’s, 9.5, 9.4, 9.3, 2.5, 2.4 or 1.5). This is 19.5% of 25711 galaxies inthe parent sample that have i AB < . 5. Fig. B-1 shows (z phot - z spec ) / (1 + z spec ) of the 5001 galaxies. The distribution, an estimateof the photo-z error distribution (the spec-z error < ∼ 100 km sec - , Lilly et al. 2007), has a 1 . × median( | z phot - z spec | / (1 + z spec )) =0 . γπ + ((x - x ) /γ ) , (B1)with x = (z phot - z spec ) / (1 + z spec ), γ = 0 . ± . = 0 . ± . i AB = 22 . 5. In the pair candidates, factions of0.032, 0.061, 0.168, 0.352 of the sample are fainter than i AB = 22 . i AB = 22 . 5, the probability (simulated by a randomnumber generator) being equal to the observed fraction of such galaxies in the photo-z bin. For galaxies brighter than i AB = 22 . phot / (1 + z phot ) was assigned to it using a random number generator with weighted probability distribution functiongiven by a Lorentzian with x = 0 and γ = 0 . i AB = 22 . 5, the random error was generated accordingto a Lorentzian function with x = 0 and γ = 0 . ≃ . × . / . . / . 007 is the ratio between the photo-z accuracies for galaxies of 22 . ≤ i AB < 24 and of i AB < . 5, Ilbert et al. 2009). We ignored the real velocity difference andalaxy Pairs in COSMOS – Merger Rate Evolution Since z = 1 15 phot I A B ( m a g ) black dots --- parent samplered squares --- galaxies in pair candidates Figure B-2. The i-band magnitude ( i AB ) vs. photo-z plot. Galaxies in the pair candidates are shown by red squares, and galaxies in the parent sample (Table 1)by black dots. The dashed line marks the boundary of i AB = 22 . assumed that the photo-z difference in a pair is purely due to photo-z errors. The completeness factor was estimated by thefraction of simulated pairs with | ∆ z phot / (1 + z phot ) | ≤ . 03. According to the simulations, the completeness correction factor is[0 . ± . , . ± . 06, 0 . ± . 05, 0 . ± . 05] in the four photo-z bins.Another set of Monte Carlo simulations (each consisting of 1000 repeats) were carried out to estimate the SPF due to projection,utilizing the 138001 galaxies in D09 sample. Here we pretended that the photo-z’s in that sample are 100% accurate, and thenadded errors to them using the same algorithm as described above. The sky coordinates of the galaxies were also randomized,filling a 1.7 deg region uniformally. The other properties of the galaxies, including the stellar mass, were left intact. We thenselected pairs from this simulated parent sample by applying the four selection criteria presented in Section 2. Spurious pairswere identified when the “true velocity difference”, calculated using the “true redshifts” (i.e. the photo-z’s without added error),is > 500 km sec - . In the four photo-z bins, the simulations found [7 . ± . 8, 6 . ± . 5, 11 . ± . 3, 11 . ± . 4] spurious pairs.Dividing these numbers by the numbers of photo-z pair candidates, the predicted SPF in the four photo-z bins are 0 . ± . . ± . 03, 0 . ± . 03 and 0 . ± . 03, respectively. C. DISTRIBUTION OF LINE-OF-SIGHT VELOCITY DIFFERENCE OF MAJOR-MERGER PAIRS d v| (km/sec)0.00.20.40.60.81.0 c u m u l a t i v e d i s t z=0 K-band selected pairs (135) d v distribution Figure C-1. Cumulative distribution of ∆ v of major-merger pairs, derived using a sample of z=0 K-band selected pairs (Domingue et al. 2009). ∆ v spec ≤ - . Here we exploit these data to determine the cumulative distribution of ∆ v and, in particular, the fraction of pairs with500 < ∆ v ≤ - . We assume that all pairs with ∆ v > - are spurious. In the sample of Domingue et al.(2009), which is 0 . 82% complete for the spec-z, 135 pairs have measured v spec for both components and v spec > - (excluding pairs in the local super-cluster). The cumulative distribution of ∆ v of these pairs is plotted in Fig. C-1. From thisdistribution, we found that the fraction of pairs with ∆ v > 500 km sec - is 9 . 6% with a random error of 2 . 5% (binomial statistics).It should be pointed out that the ∆ v distribution is sensitive to the environment and to the pair separation (Ellison et al. 2010).Therefore caution should be taken when applying the result here to other pair samples. D. INCOMPLETENESS AND SPURIOUS PAIRS FRACTION — A COMPARISON WITH SPEC-Z PAIRS We made a comparison between pairs in the CPAIR sample and a sample of spec-z pairs (ZPAIR sample) selected fromthe zCOSMOS survey (Lilly et al. 2007). In principle, this comparison applies only to galaxies brighter than i AB = 22 . 5, themagnitude limit of zCOSMOS. However, most of galaxies in photo-z pairs are brighter than i AB = 22 . i AB < . ∆ v spec < 500 km sec - . Thisresults in an empirical estimate for the SPF of 2 / 14 = 0 . 14, or a reliability of 0 . 86, with a binomial uncertainty of ± . ∆ z phot / (1 + z phot ) > . 03 but ∆ v spec < 500 km sec - . As shown in Fig. D-1, the primary of ZPAIR-03 is a close pair itself, and its large z phot error (Table D-1) is likely due to confusion in the photometric data. ZPAIR-07, having ∆ z phot / (1 + z phot ) = 0 . ∆ v < 500 km sec - in the ZPAIR sample.This results in a completeness for the CPAIR sample of 12 / 14 = 0 . 86, with a statistical error 0.12. E. DISTRIBUTION OF PRIMARY-TO-SECONDARY MASS RATIO OF CLOSE PAIRS pri /M N p a i r Differential distributions of log( µ ) ( µ = M pri / M ) of close pairs (5 ≤ r proj ≤ 20 h - kpc) in three mass bins. Derived using pair candidatesselected in a volume limited sample of galaxies with redshift in the range of 0 . ≤ z ≤ . Right: Normalized cumulative distributions of log( µ ) ( µ = M pri / M )of the same close pairs. In the parent sample of CPAIR, galaxies in the photo-z bin of 0 . ≤ z phot ≤ . star = 10 . M ⊙ . Using this volume limited sample and applying the same pair selection criteria in Section 2except for expanding the mass ratio limit to log( µ max ) = 1 . 0, where µ = M pri / M nd is the mass ratio, we selected pair candidates(including both major and minor pairs) in three mass bins: 10 . < log(M pri / M ⊙ ) ≤ . 4, 10 . < log(M pri / M ⊙ ) ≤ . 8, and10 . < log(M pri / M ⊙ ) ≤ . 2. Assuming that completeness and reliability corrections for these pair candidates do not depend onthe mass ratio µ , we calculated the differential and cumulative log( µ ) distributions of these close pairs (5 ≤ r proj ≤ 20 h - kpc). Theresults are plotted in Fig. E-1. It shows that the flat distribution, i.e. df pair / d log( µ ) = constant, is a reasonably good approximation.It is worth noting that our result is different from that of Ellison et al. (2010), who found a mass ratio distribution for SDSS pairsthat is tilted toward low µ pairs (i.e. major mergers). However, their result is affected significantly by the “missing secondary”bias, causing severe incompleteness of the µ ∼ 10 minor-mergers in their sample.alaxy Pairs in COSMOS – Merger Rate Evolution Since z = 1 17 Figure D-1. HST-ACS (F814) images of close major-merger pairs in zCOSMOS survey (ZPAIRs in Table D-1). The size of all images is 20 ′′ × ′′ . Thecrosses mark the positions of component galaxies in the pairs. Notes : ZPAIR-03 and ZPAIR-07 are not in the CPAIR (photo-z pairs) sample. The large neighborin ZPAIR-14 is likely a foreground galaxy. ZPAIR-16 is in a compact group of galaxies (three in this group were included in the CPAIR sample). Table D-1 Pairs in Z-COSMOS Survey (ZPAIR)ZPAIR ∆ v spec RA Dec z spec , zclass z phot , log(M star , )ID (km sec - ) (degree) (degree) (M ⊙ ) ∆ z phot / (1 + z phot ) RA Dec z spec , zclass z phot , log(M star , )(degree) (degree) (M ⊙ )01 43 149.713610 2.019610 0.6444 4.5 0.6518 10.920.012 149.713950 2.019773 0.6441 4.5 0.6324 10.8302 218 149.839700 1.929228 0.3722 3.5 0.3856 10.800.020 149.838780 1.930125 0.3711 4.5 0.3585 10.7603 † 70 150.009050 2.274964 0.4726 2.5 0.5769 11.050.071 150.008210 2.275954 0.4730 2.5 0.4645 10.7804 ∗ 817 150.107580 2.556516 0.5038 3.5 0.4915 10.330.004 150.107510 2.557509 0.4990 3.5 0.4969 10.2105 73 150.115480 1.975120 0.4385 4.5 0.4431 10.450.025 150.115680 1.976216 0.4381 3.5 0.4069 10.0506 65 150.126060 1.913758 0.7360 2.5 0.7168 11.170.003 150.125690 1.913726 0.7365 3.5 0.7108 11.1507 † 11 150.168760 2.315481 0.8524 2.5 0.7921 10.970.031 150.168890 2.316234 0.8523 1.5 0.8473 10.9408 220 150.196380 2.371582 0.6834 4.5 0.6783 10.860.003 150.196460 2.370591 0.6850 22.5 0.6726 10.6409 103 150.230880 1.845002 0.6226 2.5 0.6072 10.670.014 150.230550 1.844713 0.6233 3.5 0.5840 10.6010 118 150.258800 1.988773 0.7258 2.5 0.7168 10.700.001 150.258510 1.988547 0.7267 2.5 0.7191 10.3211 ∗ Note . — : † Missing in the CPAIR sample. : ∗ Spurious pairs (with ∆ v spec > km sec -1