The dominant role of mergers in the size evolution of massive early-type galaxies since z\sim 1

The dominant role of mergers in the size evolution of massive early-type galaxies since

C. López-Sanjuan Laboratoire d’Astrophysique de Marseille - LAM, Université d’Aix-Marseille & CNRS, UMR7326, 38 rue F. Joliot-Curie, 13388 Marseille Cedex 13, FranceCentro de Estudios de Física del Cosmos de Aragón, Plaza San Juan 1, planta 2, E-44001, Teruel, Spain
clsj@cefca.es Based on observations made at the European Southern Observatory (ESO) Very Large Telescope (VLT) under Large Program 175.A-0839.
   O. Le Fèvre Laboratoire d’Astrophysique de Marseille - LAM, Université d’Aix-Marseille & CNRS, UMR7326, 38 rue F. Joliot-Curie, 13388 Marseille Cedex 13, France    O. Ilbert Laboratoire d’Astrophysique de Marseille - LAM, Université d’Aix-Marseille & CNRS, UMR7326, 38 rue F. Joliot-Curie, 13388 Marseille Cedex 13, France    L. A. M. Tasca Laboratoire d’Astrophysique de Marseille - LAM, Université d’Aix-Marseille & CNRS, UMR7326, 38 rue F. Joliot-Curie, 13388 Marseille Cedex 13, France    C. Bridge California Institute of Technology, MC 105-24, 1200 East California Boulevard, Pasadena, CA 91125 USA    O. Cucciati INAF Osservatorio Astronomico di Trieste, Via Tiepolo, 11, I-34143 Trieste, Italy    P. Kampczyk Institute of Astronomy, ETH Zurich, CH-8093, Zurich, Switzerland    L. Pozzetti INAF Osservatorio Astronomico di Bologna, via Ranzani 1, I-40127, Bologna, Italy    C. K. Xu Infrared Processing and Analysis Center, California Institute of Technology 100-22, Pasadena, CA 91125, USA    C. M. Carollo Institut de Recherche en Astrophysique et Planétologie (IRAP), CNRS, 14, avenue Edouard Belin, F-31400 Toulouse, France    T. Contini Institut de Recherche en Astrophysique et Planétologie (IRAP), CNRS, 14, avenue Edouard Belin, F-31400 Toulouse, France IRAP, Université de Toulouse, UPS-OMP, Toulouse, France    J. -P. Kneib Laboratoire d’Astrophysique de Marseille - LAM, Université d’Aix-Marseille & CNRS, UMR7326, 38 rue F. Joliot-Curie, 13388 Marseille Cedex 13, France    S. J. Lilly Institute of Astronomy, ETH Zurich, CH-8093, Zurich, Switzerland    V. Mainieri European Southern Observatory, Karl-Schwarzschild-Strasse 2, Garching, D-85748, Germany    A. Renzini Dipartimento di Astronomia, Universitá di Padova, vicolo Osservatorio 3, I-35122 Padova, Italy    D. Sanders Institute for Astronomy, 2680 Woodlawn Drive, University of Hawaii, Honolulu, HI 96822, USA    M. Scodeggio INAF-IASF, Via Bassini 15, I-20133, Milano, Italy    N. Z. Scoville California Institute of Technology, MC 105-24, 1200 East California Boulevard, Pasadena, CA 91125 USA    Y. Taniguchi Research Center for Space and Cosmic Evolution, Ehime University, Bunkyo-cho 2-5, Matsuyama 790-8577, Japan    G. Zamorani INAF Osservatorio Astronomico di Bologna, via Ranzani 1, I-40127, Bologna, Italy    H. Aussel CNRS, AIM-Unite Mixte de Recherche CEA-CNRS-Université Paris VII-UMR 7158, F-91191 Gif-sur-Yvette, France    S. Bardelli INAF Osservatorio Astronomico di Bologna, via Ranzani 1, I-40127, Bologna, Italy    M. Bolzonella INAF Osservatorio Astronomico di Bologna, via Ranzani 1, I-40127, Bologna, Italy    A. Bongiorno Max-Planck-Institut für Extraterrestrische Physik, D-84571 Garching b. Muenchen, Germany    P. Capak California Institute of Technology, MC 105-24, 1200 East California Boulevard, Pasadena, CA 91125 USA    K. Caputi Kapteyn Astronomical Institute, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands    S. de la Torre SUPA, Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh EH9 3HJ    L. de Ravel SUPA, Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh EH9 3HJ    P. Franzetti INAF-IASF, Via Bassini 15, I-20133, Milano, Italy    B. Garilli INAF-IASF, Via Bassini 15, I-20133, Milano, Italy    A. Iovino INAF Osservatorio Astronomico di Brera, Via Brera 28, I-20121 Milano, Italy    C. Knobel Institute of Astronomy, ETH Zurich, CH-8093, Zurich, Switzerland    K. Kovač Institute of Astronomy, ETH Zurich, CH-8093, Zurich, Switzerland MPA - Max Planck Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany    F. Lamareille Institut de Recherche en Astrophysique et Planétologie (IRAP), CNRS, 14, avenue Edouard Belin, F-31400 Toulouse, France IRAP, Université de Toulouse, UPS-OMP, Toulouse, France    J. -F. Le Borgne Institut de Recherche en Astrophysique et Planétologie (IRAP), CNRS, 14, avenue Edouard Belin, F-31400 Toulouse, France IRAP, Université de Toulouse, UPS-OMP, Toulouse, France    V. Le Brun Laboratoire d’Astrophysique de Marseille - LAM, Université d’Aix-Marseille & CNRS, UMR7326, 38 rue F. Joliot-Curie, 13388 Marseille Cedex 13, France    E. Le Floc’h Institute for Astronomy, 2680 Woodlawn Drive, University of Hawaii, Honolulu, HI 96822, USA CNRS, AIM-Unite Mixte de Recherche CEA-CNRS-Université Paris VII-UMR 7158, F-91191 Gif-sur-Yvette, France    C. Maier Institute of Astronomy, ETH Zurich, CH-8093, Zurich, Switzerland University of Vienna, Department of Astronomy, Tuerkenschanzstrasse 17, 1180 Vienna, Austria    H. J. McCracken Institut d’Astrophysique de Paris, UMR 7095 CNRS, Université Pierre et Marie Curie, 98 bis Boulevard Arago, F-75014 Paris, France    M. Mignoli INAF Osservatorio Astronomico di Bologna, via Ranzani 1, I-40127, Bologna, Italy    R. Pelló Institut de Recherche en Astrophysique et Planétologie (IRAP), CNRS, 14, avenue Edouard Belin, F-31400 Toulouse, France    Y. Peng Institute of Astronomy, ETH Zurich, CH-8093, Zurich, Switzerland    E. Pérez-Montero Institut de Recherche en Astrophysique et Planétologie (IRAP), CNRS, 14, avenue Edouard Belin, F-31400 Toulouse, France IRAP, Université de Toulouse, UPS-OMP, Toulouse, France Instituto de Astrofísica de Andalucía, CSIC, Apdo. 3004, 18080, Granada, Spain    V. Presotto Universitá degli Studi dell’Insubria, Via Valleggio 11, 22100 Como, Italy SUPA, Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh EH9 3HJ    E. Ricciardelli Instituto de Astrofísica de Canarias, vía Lactea s/n, 38200 La Laguna, Tenerife, Spain Departamento de Astrofísica, Universidad de La Laguna, 38205 Tenerife, Spain    M. Salvato California Institute of Technology, MC 105-24, 1200 East California Boulevard, Pasadena, CA 91125 USA    J. D. Silverman IPMU, Institute for the Physics and Mathematics of the Universe, 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Japan    M. Tanaka IPMU, Institute for the Physics and Mathematics of the Universe, 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Japan    L. Tresse Laboratoire d’Astrophysique de Marseille - LAM, Université d’Aix-Marseille & CNRS, UMR7326, 38 rue F. Joliot-Curie, 13388 Marseille Cedex 13, France    D. Vergani INAF Osservatorio Astronomico di Bologna, via Ranzani 1, I-40127, Bologna, Italy INAF - IASF Bologna, Via P. Gobetti 101, I-40129 Bologna, Italy    E. Zucca INAF Osservatorio Astronomico di Bologna, via Ranzani 1, I-40127, Bologna, Italy    L. Barnes Institute of Astronomy, ETH Zurich, CH-8093, Zurich, Switzerland    R. Bordoloi Institute of Astronomy, ETH Zurich, CH-8093, Zurich, Switzerland    A. Cappi INAF Osservatorio Astronomico di Bologna, via Ranzani 1, I-40127, Bologna, Italy    A. Cimatti Dipartimento di Astronomia, Universitá di Bologna, via Ranzani 1, I-40127, Bologna, Italy    G. Coppa Max-Planck-Institut für Extraterrestrische Physik, D-84571 Garching b. Muenchen, Germany INAF Osservatorio Astronomico di Bologna, via Ranzani 1, I-40127, Bologna, Italy    A. Koekemoer Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218    C. T. Liu Astrophysical Observatory, City University of New York, College of Staten Island, 2800 Victory Blvd, Staten Island, NY 10314, USA    M. Moresco Dipartimento di Astronomia, Universitá di Bologna, via Ranzani 1, I-40127, Bologna, Italy    P. Nair Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 INAF Osservatorio Astronomico di Bologna, via Ranzani 1, I-40127, Bologna, Italy    P. Oesch Institute of Astronomy, ETH Zurich, CH-8093, Zurich, Switzerland UCO/Lick Observatory, Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064    K. Schawinski Department of Physics, Yale University, New Haven, CT 06511, USA Yale Center for Astronomy and Astrophysics, Yale University, PO Box 208121, New Haven, CT 06520, USA    N. Welikala Institut d’Astrophysique Spatiale, Batiment 121, CNRS & Université Paris Sud XI, 91405 Orsay Cedex, France
Submitted February 21, 2012
Key Words.:
Galaxies: elliptical and lenticular, cD — Galaxies:evolution — Galaxies:interactions
Abstract

Context:

Aims:The role of galaxy mergers in massive galaxy evolution, and in particular to mass assembly and size growth, remains an open question. In this paper we measure the merger fraction and rate, both minor and major, of massive early-type galaxies () in the COSMOS field, and study their role in mass and size evolution.

Methods:We use the 30-band photometric catalogue in COSMOS, complemented with the spectroscopy of the zCOSMOS survey, to define close pairs with a separation on the sky plane kpc kpc and a relative velocity km in redshift space. We measure both major (stellar mass ratio ) and minor () merger fractions of massive galaxies, and study their dependence on redshift and on morphology (early types vs late types).

Results:The merger fraction and rate of massive galaxies evolves as a power-law , with major mergers increasing with redshift, , and minor mergers showing little evolution, . When split by their morphology, the minor merger fraction for early-type galaxies (ETGs) is higher by a factor of three than that for late-type galaxies (LTGs), and both are nearly constant with redshift. The fraction of major mergers for massive LTGs evolves faster () than for ETGs ().

Conclusions:Our results show that massive ETGs have undergone 0.89 mergers (0.43 major and 0.46 minor) since , leading to a mass growth of %. We find that mergers can explain % of the observed size evolution of these galaxies since . Another % is due to the progenitor bias (younger galaxies are more extended) and we estimate that very minor mergers () could contribute with an extra %. The remaining % should come from other processes (e.g., adiabatic expansion or observational effects). This picture also reproduces the mass growth and the velocity dispersion evolution of these galaxies. We conclude from these results, and after exploring all the possible uncertainties in our picture, that merging is the main contributor to the size evolution of massive ETGs at , accounting for % of that evolution in the last 8 Gyr. Nearly half of the evolution due to mergers is related to minor () events.

1 Introduction

The history of mass assembly is a major component of the galaxy formation and evolution scenario. The evolution in the number of galaxies of a given mass, as well as the size and shapes of galaxies building the Hubble sequence, provides strong input to this scenario. The optical colour –- magnitude diagram of local galaxies shows two distinct populations: the ”red sequence”, consisting primarily of old, spheroid-dominated, quiescent galaxies, and the ”blue cloud”, formed primarily by spiral and irregular star-forming galaxies (e.g., strateva01; baldry04). This bimodality has been traced at increasingly higher redshifts (e.g., ilbert10), showing that the most massive galaxies were the first to populate the red sequence as a result of the so-called ”downsizing” (e.g., bundy06; pgon08; pozzetti10). These properties result from several physical mechanisms for which it is necessary to evaluate the relative impact. In this paper we examine the contribution of major and minor mergers to the mass growth and size evolution of massive early-type galaxies (ETGs), based on new measurements of the pair fraction from the COSMOS111http://cosmos.astro.caltech.edu/ (Cosmological Evolution Survey, cosmos) and zCOSMOS222http://www.astro.phys.ethz.ch/zCOSMOS/ (lilly07) surveys.

The number density of massive ETGs galaxies with is roughly constant since (pozzetti10, and references therein), with major mergers (mass or luminosity ratio higher than 1/4) common enough to explain their number evolution since (eliche10I; robaina10; oesch10). However, and despite that they seem ”dead” since , two observational facts rule out the passive evolution of these massive ETGs after they have reached the red sequence: the presence of Recent Star Formation (RSF) episodes and their size evolution. In the former, the study of red sequence galaxies in the –optical colour vs magnitude diagram reveals that 30% have undergone RSF, as seen from their blue colours, both locally (kaviraj07) and at higher redshifts (, kaviraj11). This RSF typically involves % of the galaxy stellar mass (scarlata07ee; kaviraj08; kaviraj11). Some authors suggest that minor mergers, i.e., the merger of a massive red sequence galaxy with a less massive (mass or luminosity ratio lower than 1/4), gas-rich satellite, could explain the observed properties of galaxies with RSF (kaviraj09; onti11; desai11).

Regarding size evolution, it is now well established that massive ETGs have, on average, lower effective radius () at high redshift than locally, being and times smaller at and , respectively (daddi05; trujillo06; trujillo07; trujillo11; buitrago08; vandokkum08; vandokkum10; vanderwel08esize; toft09; williams10; newman10; newman12; damjanov11; weinzirl11; cassata11, but see saracco10; and vale10b for a different point of view). Massive ETGs as compact as observed at high redshifts are rare in the local universe (trujillo09; taylor10; cassata11), suggesting that they must evolve since to the present. It has been proposed that high redshift compact galaxies are the cores of present day ellipticals, and that they increased their size by adding stellar mass in the outskirts of the galaxy (bezanson09; hopkins09core; vandokkum10). Several studies suggest that merging, especially the minor one, could explain the observed size evolution (naab09; bezanson09; hopkins10size; feldmann10; shankar11; oser12), while other processes, as adiabatic expansion due to AGNs or to the passive evolution of the stellar population, should have a mild role at (fan10; ragone11; trujillo11). In addition, a significant fraction of local ellipticals present signs of recent interactions (vandokkum05; tal09).

While minor mergers are expected to contribute significantly to the evolution of massive ETGs, there is no direct observational measurement of their contribution yet. As a first effort, jogee09 estimate the minor merger fraction in massive galaxies out to using morphological criteria, and find that the minor merger fraction has a lower limit which is 3 times larger than the corresponding major merger fraction. The minor merger fraction of the global population of galaxies has been studied quantitatively for the first time by clsj11mmvvds in the VVDS-Deep333http://cesam.oamp.fr/vvdsproject/vvds.htm (VIMOS VLT Deep Spectroscopic Survey, lefevre05). They show that minor mergers are quite common, that their importance decrease with redshift (see also lotz11), and that they participate to about 25% of the mass growth by merging of such galaxies. Focusing on massive galaxies, williams11, marmol12, or newman12 study their total (major + minor) merger fraction to , finding also that it is nearly constant with redshift. In this paper we present the detailed merger history, both minor and major, of massive () ETGs since using close pair statistics in the COSMOS field, and use it to infer the role of major and minor mergers in the mass assembly and in the size evolution of these systems in the last Gyr.

The paper is organised as follow. In Sect. 2 we present our photometric catalogue in the COSMOS field, while in Sect. 3 we review the methodology used to measure close pair merger fractions when photometric redshifts are used. We present our merger fractions of massive galaxies in Sect. 4, and the inferred merger rates for ETGs in Sect. 5. The role of mergers in the mass assembly and in the size evolution of massive ETGs is discussed in Sect. 6, and in Sect. 7 we present our conclusions. Throughout this paper we use a standard cosmology with , , Km s Mpc and . Magnitudes are given in the AB system.

2 The COSMOS photometric catalogue

We use the COSMOS catalogue with photometric redshifts derived from 30 broad and medium bands described in ilbert09 and capak07, version 1.8. We restrict ourselves to objects with . The detection completeness at this limit is higher than 90% (capak07). In order to obtain accurate colours, all the images were degraded to the same point spread function (PSF) of . At , the rms accuracy of the photometric redshifts () at is in ), where is the spectroscopic redshift of the sources (Fig. 9 in ilbert09). At the quality of the photometric redshifts quickly deteriorates. Additionally, and because we are interested on minor companions, we require a detection in the band to ensure that the stellar mass estimates are reliable, thus we add the constraint .

Stellar masses of the photometric catalogue have been derived following the same approach than in ilbert10. We used stellar population synthesis models to convert luminosity into stellar mass (e.g., bell03; fontana04). The stellar mass is the factor needed to rescale the best-fit template (normalised at one solar mass) for the intrinsic luminosities. The Spectral Energy Distribution (SED) templates were generated with the stellar population synthesis package developed by bc03. We assumed a universal initial mass function (IMF) from chabrier03 and an exponentially declining star formation rate, ( in the range 0.1 Gyr to 30 Gyr). The SEDs were generated for a grid of 51 ages (in the range 0.1 Gyr to 14.5 Gyr). Dust extinction was applied to the templates using the calzetti00 law, with in the range 0 to 0.5. We used models with two different metallicities. Following fontana06 and pozzetti07, we imposed the prior if age/ (a significant extinction is only allowed for galaxies with a high ). The stellar masses derived in this way have a systematic uncertainty of 0.3 dex (e.g., pozzetti07; barro11mass).

We supplement the previous photometric catalogue with the spectroscopic information from zCOSMOS survey, a large spectroscopic redshift survey in the central area of the COSMOS field. In this analysis we use the final release of the bright part of this survey, called the zCOSMOS-bright 20k sample. This is a pure magnitude selected sample with . For a detailed description and relevant results of the previous 10k release, see zcosmos10k; tasca09; pozzetti10 or peng10. A total of 20604 galaxies have been observed with the VIMOS spectrograph (lefevre03) in multi-slit mode, and the data have been processed using the VIPGI data processing pipeline (scodeggio05). A spectroscopic flag has been assigned to each galaxy providing an estimate of the robustness of the redshift measurement (lilly07). If a redshift has been measured, the corresponding spectroscopic flag value can be 1, 2, 3, 4 or 9. Flag = 1 means that the redshift is 70% secure and flag = 4 that the redshift is % secure. Flag = 9 means that the redshift measurement relies on one single narrow emission line ( or H mainly). The information about the consistency between photometric and spectroscopic redshifts has also been included as a decimal in the spectroscopic flag. In this study we select the highest reliable redshifts, i.e., with confidence class 4.5, 4.4, 3.5, 3.4, 9.5, 9.3, and 2.5. This flag selection ensures that 99% of redshifts are believed to be reliable based on duplicate objects (zcosmos10k).

Our final COSMOS catalogue comprises 134028 galaxies at , our range of interest (see Sect. 2.1). Nearly 35% of the galaxies with have a high reliable spectroscopic redshift. For consistency and to avoid systematics, we always use the stellar masses and other derived quantities from the photometric catalogue. We checked that the dispersion when comparing stellar masses from and is dex, lower than the typical error in the measured stellar masses ( dex). Thanks to the methodology developed in clsj10pargoods we are able to obtain reliable merger fractions from photometric catalogues under some quality conditions (Sect. 3). We check that the COSMOS catalogue is adequate for our purposes in Sects. 3.2 and 3.3.

Figure 1: Stellar mass as a function of redshift in the COSMOS field. Red dots are principal galaxies () with in the zCOSMOS area, blue dots are companion galaxies () with in the COSMOS area, and black dots are the red galaxies () with in the COSMOS area. We only show a random 15% of the total populations for visualisation purposes. Green squares mark those galaxies in previous populations with a spectroscopic resdhift. The vertical lines mark the lower and upper redshift in our study, while the horizontal ones the mass selection of the principal (solid) and the companion (dashed) samples.

2.1 Definition of the mass-selected samples

We define two samples selected in stellar mass. The first one comprises 2047 principal massive galaxies in the zCOSMOS area, where spectroscopic information is available, with (, ilbert10) at . The second sample comprises the 23992 companion galaxies with in the full COSMOS area and in the same redshift range. The mass limit of the companion sample ensures completeness for red galaxies up to (drory09; ilbert10). Because of that, we set as the upper redshift in our study, while to probe enough cosmological volume. However, our methodology takes into account the photometric redshift errors (see Sect. 3, for details), so we must include in the samples not only the sources with , but also those sources with in order to ensure completeness in redshift space. Because of this, we set the maximum and minimum redshift of the catalogues to and . We show the mass distribution of our samples as a function of in Fig. 1, and we assume our samples as volume-limited mass-selected in the following.

Our final goal is to measure the merger fraction and rate of massive ETGs, but our principal sample comprises ETGs, spirals and irregulars. We segregate morphologically our principal sample thanks to the morphological classification defined in tasca09. Their method use as morphological indicator the distance of the galaxies in the multi-space (Concentration, Asymmetry and Gini coefficient) to the position in this space of a training sample of 500 eye-ball classified galaxies. These morphological indices were measured in the HST/ACS images of the COSMOS field, taken through the wide F814W filter (koekemoer07). The galaxies in the training sample were classified into ellipticals, lenticulars, spirals of all types (Sa, Sb, Sc, Sd), irregulars, point-like and undefined sources, and then these classes were grouped into early-type (E,S0), spirals (Sa, Sb, Sc, Sd) and irregular galaxies. It is this coarser classification that was considered in building the training set. The unclassified objects were not used for the training. We refer the reader to tasca09 for further details. The morphological classification in the COSMOS field is reliable for galaxies brighter than , and all our principal galaxies are brighter than up to . According to the classification presented in tasca09 our principal sample comprises 1285 (63%) ETGs (E/S0) and 632 (31%) spiral galaxies. The remaining 6% sources are half irregulars (65 sources) and half massive galaxies without morphological classification (65 sources). We stress that the classification of the principal sample is exclusively morphological, without taking into account any additional colour information, i.e., some of our ETGs could be star-forming. We checked that 95% of our massive ETGs are also quiescent (they have a rest-frame, dust reddening corrected colour , ilbert10). Regarding the companion sample, we do not attempt to segregate it morphologically because the morphological classification is not reliable for all companion galaxies (see Sect 4.3, for details).

We used , and automatic indices to classify morphologically the principal galaxy of the close pair systems. However, these indices are affected by interactions, e.g., the asymmetry increases, and we could misclassify ETGs and spirals as irregular galaxies. htoledo05; htoledo06 study how these morphological indices vary on major interactions in the local universe. They find that ETGs are slightly affected by interactions and that interacting ETGs do not reach the loci of irregular galaxies in the space. However, spiral galaxies are strongly affected by interactions and they can be classified as irregulars by automatic methods. Thus, we do not expect misclassifications in our ETGs sample, while some of our irregular galaxies can be interacting spirals. This is in fact observed by pawel12 in the 10k zCOSMOS sample. They find that the fraction of ETGs in close pairs is similar to that in the underlying non-interacting population, while the fraction of spirals/irregulars in close pairs is lower/higher than expected. However, the sum of spirals and irregulars is similar to that in the underlying population, suggesting a spiral to irregular transformation due to interactions.

In summary, the morphology of ETGs is slightly affected by interactions, while some spirals could be classified as irregulars during a merger. Because of this, we define late-type galaxies (LTGs) as spirals + irregulars, thus avoiding any bias due to morphological transformations during the merger process. We show some representative examples of our massive ETGs and LTGs in Fig. 2. The mean mass of both ETGs and LTGs is similar, .

Figure 2: Examples of the typical ETGs (left) and LTGs (right) with in the COSMOS field. The postage stamps show a kpc x kpc area of the HST/ACS F814W image at the redshift of the source, with the North on the top and the East on the left. The pixel scale of the HST/ACS image is 0.05″. The grey scale ranges from 0.5 to 150, where is the dispersion of the sky around the source. The redshift, the concentration () and the asymmetry () of the sources are labelled in the panels.

2.2 Dependence of the photometric errors on stellar mass

The quality of the photometric redshifts in COSMOS decreases for faint objects in the band (ilbert09). In this section we study in details how redshift errors depend on the mass of the sources, since this imposes limits on our ability of measure reliable merger fractions in photometric catalogues (Sect. 3.2). As shown by ilbert10, we can estimate the photometric redshift error () from the Probability Distribution Function of the photometric redshift fit. In Fig. 3 we show the median of galaxies with different stellar masses, from (massive galaxies) to (low-mass galaxies) in bins of 0.2 dex.

Massive galaxies are bright in the whole redshift range under study. Thus, their photometric errors are small up to , . On the other hand, low-mass galaxies are fainter at high redshift than their local counterparts, so their their photometric errors increase with and reach at . We study separately the photometric errors of low-mass red and blue galaxies. We took as red galaxies those with SED (rest-frame, dust reddening corrected) colour , while as blue those with (see ilbert10, for details). Blue galaxies also have up to , while red galaxies have higher photometric redshift errors, with at and at . This different behaviour can be explained by the different mass-to-light ratio () of both populations. Faint () blue galaxies, whose photometric errors are higher, reach masses as low as at . On the other hand, we are in the detection limit for red galaxies at these redshifts (red galaxies have at , Sect. 2.1), explaining their high photometric redshift errors. Similar trends in the COSMOS photometric redshift errors were found by george11. In Sect. 3.2 we prove that our methodology is able to recover reliable merger fractions in COSMOS samples with , as those in our study.

Figure 3: as a function of redshift in the mass-selected sample, from (thiner line) to (thicker line) galaxies in bins of 0.2 dex. The black solid line marks the photometric errors of blue galaxies in the lower mass bin, while the black dashed line is for red galaxies in the same mass bin. The vertical line marks the higher redshift in our samples, . The horizontal line marks the median for low-mass galaxies at the high redshift end of our sample , .

3 Close pairs using photometric redshifts

The linear distance between two sources can be obtained from their projected separation, , and their rest-frame relative velocity along the line of sight, , where and are the redshift of the principal (more luminous/massive galaxy in the pair) and companion galaxy, respectively; is the angular separation, in arcsec, of the two galaxies on the sky plane; and is the angular scale, in kpc/arcsec, at redshift . Two galaxies are defined as a close pair if and . The lower limit in is imposed to avoid seeing effects. We used kpc, kpc, and km s. With these constraints 50%-70% of the selected close pairs will finally merge (patton00; patton08; lin04; bell06). The PSF of the COSMOS ground-based images is (capak07), which corresponds to kpc in our cosmology at . To ensure well deblended sources and to minimise colour contamination, we fixed to kpc (). On the other hand, we set to kpc to ensure reliable merger fractions in our study (see Sect. 3.2, for details).

To compute close pairs we defined a principal and a companion sample (Sect. 2.1). The principal sample comprises the more massive galaxy of the pair, and we looked for those galaxies in the companion sample that fulfil the close pair criterion for each galaxy of the principal sample. If one principal galaxy has more than one close companion, we took each possible pair separately (i.e., if the companion galaxies B and C are close to the principal galaxy A, we studied the pairs A-B and A-C as independent). In addition, we imposed a mass difference between the pair members. We denote the ratio between the mass of the principal galaxy, , and the companion galaxy, , as

(1)

and looked for those systems with . We define as major companions those close pairs with , while minor companions those with .

With the previous definitions the merger fraction is

(2)

where is the number of sources in the principal sample, and the number of principal galaxies with a companion that fulfil the close pair criterion for a given . This definition applies to spectroscopic volume-limited samples. Our samples are volume-limited, but combine spectroscopic and photometric redshifts. In a previous work, clsj10pargoods developed a statistical method to obtain reliable merger fractions from photometric catalogues. We recall the main points of this methodology below, while we study its limits when applied to our COSMOS photometric catalogue in Sect. 3.2.

We used the following procedure to define a close pair system in our photometric catalogue (see clsj10pargoods, for details): first we search for close spatial companions of a principal galaxy, with redshift and uncertainty , assuming that the galaxy is located at . This defines the maximum possible for a given in the first instance. If we find a companion galaxy with redshift and uncertainty in the range and with a given mass with respect to the principal galaxy, then we study both galaxies in redshift space. For convenience, we assume below that every principal galaxy has, at most, one close companion. In this case, our two galaxies could be a close pair in the redshift range

(3)

Because of variation in the range of the function , a sky pair at might not be a pair at . We thus impose the condition at all , and redefine this redshift interval if the sky pair condition is not satisfied at every redshift. After this, our two galaxies define the close pair system in the redshift interval , where the index covers all the close pair systems in the sample.

The next step is to define the number of pairs associated at each close pair system . For this, we suppose in the following that a galaxy in whatever sample is described in redshift space by a probability distribution , where is the source’s redshift and are the parameters that define the distribution. If the source has a photometric redshift, we assume that

(4)

while if the source has a spectroscopic redshift

(5)

where is delta’s Dirac function. With this distribution we are able to statistically treat all the available information in space and define the number of pairs at redshift in system as

(6)

where , the integration limits are

(7)
(8)

the subindex 1 [2] refers to the principal [companion] galaxy in system, and the constant normalises the function to the total number of pairs in the interest range

(9)

Note that if or . The function (Eq. [6]) tells us how the number of pairs in the system , , are distributed in redshift space. The integral in Eq. (6) spans those redshifts in which the companion galaxy has for a given redshift of the principal galaxy.

With previous definitions, the merger fraction in the interval is

(10)

where the index spans the redshift bins defined over the redshift range under study. If we integrate over the whole redshift space, , Eq. (10) becomes

(11)

where is analogous to in Eq. (2). In order to estimate the statistical error of , denoted , we used the jackknife technique (efron82). We computed partial standard deviations, , for each system by taking the difference between the measured and the same quantity with the th pair removed for the sample, , such that . For a redshift range with systems, the variance is given by . When we used instead the Bayesian approach of cameron11, that provides accurate asymmetric confidence intervals in these low statistical cases. We checked that for both jackknife and Bayesian methods provide similar statistical errors within 10%.

3.1 Dealing with border effects

When we search for close companions near to the edges of the images it may happen that a fraction of the search volume is outside of the surveyed area, lowering artificially the number of companions. To deal with this we selected as principal galaxies those in the zCOSMOS area, i.e., in the central 1.6 deg, while we selected as companions those in the whole photometric COSMOS area. This maximise the spectroscopic fraction of the principal sample and ensures that we have companions inside all the searching volume.

3.2 Testing the methodology with 20k spectroscopic sources

Following clsj10pargoods, we test in this section if we are able to obtain reliable merger fractions from our COSMOS photometric catalogue. For this, we study the merger fraction in the zCOSMOS-bright 20k sample. The merger fraction in the 10k sample was studied in details by deravel11 and pawel12. We define as the fraction of sources on a given sample with spectroscopic redshift. The 20k sample has , while the COSMOS photometric catalogue has for galaxies. In this section we only use the sources at with a high reliable spectroscopic redshift from the 20k sample.

To test our method at intermediate , we created synthetic catalogues by assigning their measured and to ) random sources of the 20k sample (we denote this case as in the following). To explore different values of , we assigned to the previous random sources a redshift as drawn for a Gaussian distribution with median and , where is the factor by which we increase the initial of the sample. In this case, the redshift error of the source is set to . Then, we measured

(12)

where is the measured merger fraction in the 20k spectroscopic sample at without imposing any mass or luminosity difference and is the merger fraction from the synthetic samples in the same redshift range. When , we repeated the process ten times and averaged the results.

We explored several cases with our synthetic catalogues. For example, we assumed that all sources in the synthetic principal catalogue (subindex 1) and in the companion one (subindex 2) have a photometric redshift, , and that . We also considered more realistic cases, as and for principals, and and for companions. We found that is higher than 10% for kpc close pairs for and realistic values of . We checked that % for and kpc, justifying the upper limit imposed in Sect. 2.2. For higher the method overestimates the merger fraction by about 50% in the case. Because we are interested on faint companions, we set kpc in the following to ensure reliable merger fractions.

On the other hand, we found that the of the is % of the measured value, i.e., two times lower than the estimated %. Because of this, and to ensure reliable uncertainties in the merger fractions, we impose a minimum error in of 10%, and we take as final merger fraction error .

In the next section we test further our methodology by comparing the merger fraction from a spectroscopic survey () against that in COSMOS from our photometric catalogue.

Figure 4: Merger fraction of galaxies as a function of luminosity difference in the band, , at (top) and (bottom) for kpc close pairs. Diamonds are from present work in COSMOS (photometric catalogue) while dots are from VVDS-Deep (LS11, spectroscopic catalogue). The black solid lines in both panels show the maximum and minimum merger fractions, including errors, when we split the COSMOS field in VVDS-Deep size subfields (0.5 deg).

3.3 Comparison with merger fractions in VVDS-Deep: cosmic variance effect

In a previous work in VVDS-Deep, LS11 measured the merger fraction of galaxies with spectroscopic redshifts, where and accounts for the evolution of the luminosity function with redshift, as a function of luminosity difference in the band, . As an additional test of our methodology, in this section we compare the merger fraction in the COSMOS photometric catalogue with that measured by LS11 down to , reaching the minor merger regime in which we are interested on. To minimise the systematic biases, we used the same redshift ranges, and , close pair definition ( kpc), principal sample (), and companion sample () than LS11. We checked that the photometric redshift errors are up to for faint companion galaxies (see Sect. 3.2). Note that LS11 use kpc, while we take kpc. Hence, we recomputed the merger fractions in VVDS-Deep for kpc. We show the merger fractions from COSMOS and VVDS-Deep for different values of in Fig. 4.

We find that VVDS-Deep and COSMOS merger fractions are in excellent agreement in the first redshift range, while in the second redshift range some discrepancies exist, with the merger fraction in COSMOS being higher than in VVDS-Deep at . However, both studies are compatible within error bars. Note that merger fraction uncertainties in COSMOS are times lower than in VVDS-Deep because of the higher number of principals in COSMOS. We checked the effect of comic variance in this comparison. For that, we split the zCOSMOS area in several VVDS-Deep size (0.5 deg) subfields and measured the merger fraction in these subfields. The maximum and minimum values of in these subfields, including errors, are marked in Fig. 4 with solid lines. We find that, within , there is a zCOSMOS subfield with merger properties similar to the VVDS-Deep field. Because the zCOSMOS subfields are contiguous, this exercise provides a lower limit to the actual cosmic variance in the COSMOS field (e.g., moster11). Hence, we conclude that our methodology is able to recover reliable minor merger fractions from photometric samples in the COSMOS field.

4 The merger fraction of massive ETGs in the COSMOS field

The final goal of the present paper is to estimate the role of mergers (minor and major) in the mass assembly and size evolution of massive ETGs. To facilitate future comparison, we present first the merger properties of the global massive population in Sect. 4.1. Then, we focus in the ETGs population in Sect. 4.2.

The evolution of the merger fraction with redshift up to is well parametrised by a power-law function (e.g., lefevre00; clsj09ffgoods; deravel09),

(13)

so we take this parametrisation in the following.

4.1 The merger fraction of the global massive population

We summarise the minor, major and total merger fractions for galaxies in the COSMOS field in Table 1 and we show them in Fig. 5. We defined five redshift bins between and both for minor and major mergers. The ranges , and are dominated by Large Scale Structures (LSS, kovac10), so we use these LSS as natural boundaries in our study. This minimises the impact of LSS in our measurements, since the merger fraction depends on environment (lin10; deravel11; pawel12). We identify a total of 56.2 major mergers and 71.1 minor ones at . Note that the number of mergers can take non integer values because of the weighting scheme used in our methodology (Sect. 3). We compare the previous number of mergers (measured as , Eq. [11]) with the total number of close pair systems (), obtaining that the fraction of real close pairs over the total number of systems is %. We find that

  • The minor merger fraction is nearly constant with redshift, . The least-squares fit to the minor merger fraction data is

    (14)

    The negative value of the power-law index implies that the minor merger fraction decreases slightly with redshift, but it is consistent with a null evolution (). This confirms the trend found by LS11 for bright galaxies, and by jogee09 and lotz11 for less massive () galaxies, and extend it to the high mass regime.

    Figure 5: Major (dots), minor (squares) and total (major + minor, triangles) merger fraction of galaxies as a function of redshift in the COSMOS field. Dashed, solid and dott-dashed curves are the least-squares best fit of a power-law function, , to the major (), minor () and total () merger fraction data, respectively.
  • The major merger fraction of massive galaxies increases with redshift as

    (15)

    This increase with contrasts with the nearly constant minor merger fraction. In Fig. 6 we compare our measurements with those from the literature for massive galaxies and for kpc close pairs. deravel11 measure the major merger fraction by kpc spectroscopic close pairs in the 10k zCOSMOS sample, so their sample is included in ours. Because they assume a different inner radius than us, we apply a factor 2/3 to their original values (see Sect. 5, for details). Both merger fractions are in good agreement, supporting our methodology. Note that our uncertainties are lower by a factor of three than those in deravel11 because our principal sample is a factor of four larger than theirs. xu12 measure the merger fraction from photometric close pairs also in the COSMOS field. They provide the fraction of galaxies in close pairs with , so we apply a factor 0.7 to obtain the number of close pairs (this is the fraction of principal galaxies in their massive sample) and a factor 1.6 to estimate the number of systems (the merger fraction depends on as , as shown by LS11, and for massive galaxies in COSMOS, Sect. 6.2). On the other hand, bundy09 and bluck09 measure the major () merger fraction in GOODS444http://www.stsci.edu/science/goods/ (Great Observatories Origins Deep Survey, giavalisco04) and Palomar/DEEP2 (powir) surveys, respectively. These studies are also in good agreement with our values, with the point at from bluck09 being the only discrepancy. The least-squeres fit to all the close pair studies in Fig. 6 yields similar parameters to those from our COSMOS data alone, Eq. (15).

    Figure 6: Major () merger fraction for galaxies from kpc close pairs. The dots are from present work, triangles are form deravel11 in the zCOSMOS 10k sample, squares from xu12 in the COSMOS field, pentagons from bluck09 in the Palomar/DEEP2 survey, and diamonds from bundy09 in the GOODS fields. Some points are slightly shifted when needed to avoid overlap. The dashed line is the least-squares best fit of a power-law function, , to the major merger fraction data in the present work.
    Figure 7: Major merger fraction as a function of redshift. The dots are from present work for galaxies from kpc kpc close pairs. The triangles are from kar07 in the COSMOS field for galaxies from kpc kpc close pairs. The stars are from bridge10 in the CFHTLS by morphological criteria for galaxies, and crosses are from jogee09 for galaxies by morphological criteria in GEMS (upward arrows mark those points that are lower limits). The dashed line is the least-squares best fit of a power-law function, , to the major merger fraction data in the present work. The dotted line is the evolution from kar07, .

    For completeness, if Fig. 7 we compare our major merger fractions with other works that are either based on morphological criteria or come from luminosity-selected samples. Regarding morphological studies, bridge10 provide the major merger fraction of galaxies in two CFHTLS555http://cfht.hawaii.edu/Science/CFHLS/ (Canada-France-Hawaii Telescope Legacy Survey, cfhtls) Deep fields, including the COSMOS field. They perform a visual classification of the sources, finding 286 merging systems of that mass. In their work, jogee09 estimate a lower limit of the major merger fraction of galaxies in the GEMS666http://www.mpia-hd.mpg.de/GEMS/gems.htm (Galaxy Evolution From Morphology And SEDs, rix04) survey. We cannot compare directly the merger fractions from these two morphological studies with ours because of the different methodologies (e.g., bridge10; lotz11). Thus, we translate their merger rates into the expected close pair fraction following the prescriptions in Sect. 5. Giving the uncertainties in the merger time scales of both methods and the difficulties to assign a precise mass ratio to the merger candidates in morphological studies, the merger fractions from bridge10 and jogee09 are in nice agreement with our results.

    kar07 estimate the merger fraction of luminous galaxies () in the COSMOS field. They take these luminous galaxies to define the principal and the companion sample, i.e., they are incomplete for low luminosity major companions near the selection boundary. We find that both studies in the COSMOS field are compatible in the common redshift range (). The different evolution of the major merger fraction in both works, in kar07 vs in our study, is due to the data. We conclude that both studies are consistent, even if a direct quantitative comparison is not possible because of the different sample selection and companion definition.

  • The fit to the total merger fraction is

    (16)

    This evolution is slower than the major merger one, reflecting the different properties of minor and major mergers. We compare our total merger fractions with others in the literature in Fig. 8. marmol12 study the total merger fraction of massive galaxies by kpc close companions. The merger fraction depends on the search radius as (LS11), so we translate the merger fractions provided by marmol12 to our search radius. On the other hand, newman12 measure the merger fraction of galaxies from kpc close pairs. The values from both close pair studies are consistent with ours. Also the results of williams11 suggest a slow/null evolution in the total () merger faction of massive galaxies up to .

    Figure 8: Total (major + minor, ) merger fraction as a function of redshift. Dots are from the present work in the COSMOS field for galaxies, diamonds are from marmol12 for massive galaxies, squares are from newman12 for galaxies, crosses are from jogee09 for galaxies by morphological criteria, and inverted triangles are from lotz11 for galaxies by morphological criteria. The dashed line is the least-squares best fit of a power-law function, , to the total merger fraction data in the present work.

    Regarding morphological studies, jogee09 estimate the total () merger fraction of galaxies in the GEMS survey. Their values, , are consistent with ours. We also show the merger fraction from lotz11 for galaxies in the AEGIS777http://aegis.ucolick.org/ (All-Wavelength Extended Groth Strip International Survey, davis07) survey. The different methodologies between these works and ours, and the different stellar mass regimes probed, make direct comparisons difficult (see bridge10; lotz11, for a review of this topic). In summary, previous work is compatible with a mild evolution of the total merger fraction, as we observe.

Merger fraction
Table 1: Minor, major and total merger fraction of galaxies

4.2 The merger fraction of ETGs

We summarise the minor and major merger fractions for both massive () ETGs and LTGs in the COSMOS field in Tables 2 and 3, respectively, while we show them in Fig. 9. We defined five redshift bins between and for ETGs, as for the global population, but only three in the case of LTGs because of the lower number of principal sources. We do not split the companion sample by neither morphology or colour in this section, and we study the properties of the companion galaxies in Sect. 4.3.

We assume in the following for the minor merger fraction, as for the global population (Sect. 4.1). The mean minor merger fraction of ETGs is , while for LTGs. There is therefore a factor of three difference between the merger fractions of early type and late type populations. LS11 also find a similar result when comparing the minor merger fraction of red and blue bright galaxies.

On the other hand, the major merger fraction of ETGs is also higher than that of LTGs by a factor of two. The fit to the major merger data yields

(17)
(18)

Because we only have three data points for LTGs and of the high uncertainty in the first redshift bin, the reported value of for massive LTGs is only tentative. Nevertheless, that the major merger fraction of LTGs evolves faster than that of ETGs is in agreement with previous studies which compare early-types/red and late-types/blue galaxies (e.g., lin08; deravel09; bundy09; chou10; LS11).

As shown by lotz11, the merger rate evolution depends on the selection of the sample, with samples selected to prove a constant number density population over cosmic time showing a faster evolution () than those with a constant mass selection (). To check the impact of the selection in the merger fraction of ETGs, we computed the major and minor merger fraction of ETGs with (-selected sample, in the following). As shown by vandokkum10, this provides a nearly constant number-density selection for massive galaxies. We find that the major and minor merger fractions from the -selected sample are compatible with those from the mass-selected sample. Regarding their evolution, the major merger fraction evolves faster in the -selected sample, , that in the mass-selected sample, , as expected. The minor merger fraction remains the same, (-selected sample) vs (mass-selected sample). In addition, we checked that the results presented in Sect. 6 remain the same when we use the merger fractions from the selected sample instead of those from the mass-selected one. Therefore, we conclude that the selection of the massive ETGs sample has limited impact in our results.

In summary, the merger fraction of massive () ETGs, both major and minor, is higher by a factor of 2-3 than that of massive LTGs (see also marmol12, for a similar result). We estimate the merger rate of ETGs in Sect. 5.

Figure 9: Major (upper penel) and minor (lower panel) merger fractions of galaxies as a function of redshift and morphology. Dots are for ETGs, while squares are for LTGs. Dashed (solid) lines are the best fit to the ETGs (LTGs) data, while dotted lines are the fits for the global population.
Merger fraction
Table 2: Minor and major merger fraction of ETGs with
Merger fraction
Table 3: Minor and major merger fraction of LTGs with

4.3 Colour properties of companion galaxies

In this section we attempt to identify the types of galaxies in the companion population. As the morphological classification is not reliable for all companions because they are faint, we instead use a colour selection. We took as red (quiescent) companions those with SED (rest-frame, dust reddening corrected) colour , while as blue (star-forming) those with (see ilbert10, for details), and we measured the fraction of red companions () of massive galaxies at .

We find that % of the companions of the whole principal sample are red, while % are blue. Furthermore, the red fraction remains nearly the same for minor (%) and major (%) companions. When we repeated the previous study focusing on massive ETGs as principals, we find %, both for minor and major companions. Because % of our massive ETGs are also red, most of the ETG close pairs are ”dry” (i.e., red - red).

5 The merger rate of massive ETGs in the COSMOS field

In this section we estimate the minor () and major () merger rate, defined as the number of mergers per galaxy and Gyr, of massive ETGs. We recall here the steps to compute the merger rate from the merger fraction, focusing first on the major merger rate.

Following deravel09, we define the major merger rate as

(19)

where the factor takes into account the lost companions in the inner kpc (bell06) and the factor is the fraction of the observed close pairs that finally merge in a typical time scale . We take . The typical merger time scale depends on and can be estimated by cosmological and -body simulations. In our case, we compute the major merger time scale from the cosmological simulations of kit08, based on the Millennium simulation (springel05). This major merger time scale refers to major mergers ( in stellar mass), and depends mainly on and on the stellar mass of the principal galaxy, with a weak dependence on redshift in our range of interest (see deravel09, for details). Taking as the average stellar mass of our principal galaxies with a close companion, we obtain Gyr for kpc and km s. We assumed an uncertainty of 0.2 dex in the average mass of the principal galaxies to estimate the error in . This time scale already includes the factor (see patton08; bundy09; lin10, LS11), so we take in the following. In addition, LS11 show that time scales from kit08 are equivalent to those from the body/hydrodynamical simulations by lotz10t, and that they account properly for the observed increase of the merger fraction with (see also deravel09). We stress that these merger time scales have an additional factor of two uncertainty in their normalisation (e.g., hopkins10mer; lotz11).

The minor merger rate is

(20)

where . Following LS11, we take from the body/hydrodynamical simulations of major and minor mergers performed by lotz10t; lotz10gas. As for major mergers, we assume and .

We summarise the major and minor merger rates of massive ETGs in Table 4, and show them in Fig. 10. We parametrise their redshift evolution as

(21)
Merger rate
(Gyr)
Table 4: Minor and major merger rate of ETGs with

Assuming for minor mergers, as for the merger fraction (Sect. 4.2), we find . The fit to the major merger rate of massive ETGs is

(22)

Our results imply that the minor merger rate is higher than the major merger one at . In addition, the minor and major merger rates of massive ETGs are % higher than for the global population.

In Fig. 10 we also show the minor and major merger rates of red bright galaxies measured by LS11. We find that red galaxies have similar merger rates, both minor and major, than our massive ETGs. This suggests that massive red sequence galaxies have similar merger properties: nearly 95% of our ETGs are red, while the mean mass of the red galaxies in LS11 is , a factor of two less massive than our ETGs, . The study of the merger properties of the red sequence galaxies as a function of stellar mass is beyond the scope of this paper and we explore this issue in a future work.

Figure 10: Major (upper panel) and minor (lower panel) merger rate of ETGs as a function of redshift. Filled symbols are from the present work, while open ones are from LS11 in VVDS-Deep for red galaxies. Dashed lines are the best fit to the ETGs data, while dotted lines are the fits for the global population.

6 The role of mergers in the evolution of massive ETGs since

In this section we use the previous merger rates to estimate the number of minor and major mergers per massive () ETG since (Sect. 6.1) and the impact of mergers in the mass growth (Sect. 6.2) and size evolution (Sect. 6.3) of ETGs in the last 8 Gyr.

6.1 Number of minor mergers since

We can obtain the average number of minor mergers per ETG between and as

(23)

where in a flat universe. The definition of for major mergers is analogous. Using the merger rates in previous section, we obtain , with and between and . The number of minor mergers per massive ETGs since is therefore similar to the number of major ones. Note that these values and those reported in the following have an additional factor of two uncertainty due to the uncertainty on the merger time scales derived from simulations (Sect. 5).

The number of major mergers per red bright galaxy measured by LS11 is , higher than our measurement, while the number of minor mergers is similar, . The discrepancy in the major merger case can be explained by the evolution of the merger rate in both studies, since LS11 assumed and we measure .

On the other hand, LTGs have a significantly lower number of mergers, , with and . We refer the reader to LS11 for the discussion about the role of major and minor mergers in the evolution of LTGs. In their work, pozzetti10 find that almost all the evolution in the stellar mass function since is a consequence of the observed star formation (see also vergani08), and estimate that mergers since per galaxy are needed to explain the remaining evolution. Their result is similar to our direct estimation for the global massive population (ETGs + LTGs), , but they infer . This value is half of ours, , pointing out that close pair studies are needed to understand accurately the role of major/minor mergers in galaxy evolution.

6.2 Mass assembled through mergers since

Following LS11, we estimate the mass assembled due to mergers by weighting the number of mergers in the previous section with the average major () and minor merger () mass ratio,

(24)

To obtain the average mass ratios we measured the merger fraction of massive ETGs at for different values of , from to . Then, we fitted to the data a power-law, , and used the prescription in LS11 to estimate the average merger mass ratio from the value of the power-law index . Following those steps we find for massive ETGs in COSMOS, while the average merger mass ratios are and , similar to those values reported by LS11. With all previous results we obtain that mergers with increase the stellar mass of massive ETGs by % since . LS11 find % for red bright galaxies in VVDS-Deep, consistent with our measurement within errors. We note that they use band luminosity as a proxy of stellar mass, so their value is an upper limit due to the lower mass-to-light ratio of blue companions. bluck12 study the major and minor () merger fraction of massive galaxies at in GNS888http://www.nottingham.ac.uk/astronomy/gns/ (GOODS NICMOS Survey, conselice11). They extrapolate their results to lower redshifts, estimating % for mergers. Their value is in good agreement with our measurement, but its large uncertainty prevents a quantitative comparison.

The relative contribution of major/minor mergers to our inferred mass growth is 75%/25% because the average major merger is three times more massive than the average minor one, as already pointed out by LS11. In their cosmological model, hopkins10fusbul predict that the relative contribution of major and minor mergers in the spheroids assembly of