Multiple minor mergers: formation of elliptical galaxies and constraints for the growth of spiral disks
aa r X i v : . [ a s t r o - ph ] O c t Astronomy & Astrophysics manuscript no. ms November 5, 2018(DOI: will be inserted by hand later)
Multiple minor mergers: formation of elliptical galaxiesand constraints for the growth of spiral disks
Fr´ed´eric Bournaud , Chanda J. Jog , and Fran¸coise Combes Laboratoire AIM, CEA-Saclay DSM/DAPNIA/SAp – CNRS – Universit´e Paris Diderot, 91191 Gif-sur-Yvette,France Department of Physics, Indian Institute of Science, Bangalore 560012, India Observatoire de Paris, LERMA, 61 Av. de l’Observatoire, F-75014, Paris, FranceReceived; accepted
Abstract.
Multiple, sequential mergers are unavoidable in the hierarchical build-up picture of galaxies, in particularfor the minor mergers that are frequent and highly likely to have occured several times for most present-daygalaxies. However, the effect of repeated minor mergers on galactic structure and evolution has not been studiedsystematically so far. We present a numerical study of multiple, subsequent, minor galaxy mergers, with variousmass ratios ranging from 4:1 to 50:1. The N-body simulations include gas dynamics and star formation. We studythe morphological and kinematical properties of the remnants, and show that several so-called “minor” mergerscan lead to the formation of elliptical-like galaxies that have global morphological and kinematical propertiessimilar to that observed in real elliptical galaxies. The properties of these systems are compared with those ofelliptical galaxies produced by the standard scenario of one single major merger. We thus show that repeatedminor mergers can theoretically form elliptical galaxies without major mergers, and can be more frequent thanmajor mergers, in particular at moderate redshift. This process must then have formed some elliptical galaxiesseen today, and could in particular explain the high boxiness of massive ellipticals, and some fundamental relationsobserved in ellipticals. In addition, because repeated minor mergers, even at high mass ratios, destroy disks intospheroids, these results indicate that spiral galaxies cannot have grown only by a succession of minor mergers.
Key words.
Galaxies: evolution – Galaxies: kinematics and dynamics – Galaxies: formation – Galaxies: interaction– Galaxies: elliptical and lenticular, cD
1. Introduction
Major mergers between spiral galaxies of similar massesare known to form elliptical-like galaxies. The remnantsof such violent events present an r / radial mass pro-file, as observed in elliptical galaxies (de Vaucouleurs1977), and are mainly pressure-supported. This is the casefor equal-mass mergers (e.g. Barnes & Hernquist 1991;Barnes 1992), but more generally for mass ratios rangingfrom 1:1 to 3:1 and even 4:1, studied by Bendo & Barnes(2000), Cretton et al. (2001), Naab & Burkert (2003) andin Bournaud, Jog & Combes (2005b, hereafter paper I).The merger remnant tends to be boxy for 1:1 mergers,while 3:1 and 4:1 mergers mostly result in disky ellipticalgalaxies – that are not disk galaxies, but elliptical galaxieswith a disky isophotal shape. An outer disk-like compo-nent appears in particular for mass ratios of 3:1 and higher(Naab & Trujillo 2006). It can be present even in 1:1 or2:1 merger remnants but is far from being the main contri- Send offprint requests to : F. Bournaud e-mail: [email protected] bution to the total stellar mass. The disk component be-comes more massive with increasing mass ratios. Beyond4:1, mergers do not form elliptical galaxies any longer, butearly-type disk-dominated systems (Bournaud, Combes &Jog 2004, and paper I). They are usually called “minor”mergers, but we have suggested in these earlier works thatone should distinguish between “intermediate” mergers(between 4:1 and around 10:1) that form S0-like galaxies ,and the real “minor” mergers with ratios larger than 10:1,where the remnants can be classified as (disturbed) spiralgalaxies (Quinn, Hernquist & Fullagar 1993; Velazquez &White 1999; Walker, Mihos & Hernquist 1996).Existing studies of multiple mergers have focusedon nearly-simultaneous mergers of several galaxies ofcomparable masses (Weil & Hernquist 1994, 1996; Bekki2001). This typically corresponds to the collapse of a These systems have a disk-like profile, but a massive bulgeand their support is dominated by pressure instead of rotation,unlike spirals, making them rather S0-like (Jog & Chitre 2002;Bournaud et al. 2004) Bournaud et al.: Multiple minor mergers and the formation of elliptical galaxies compact group into one single giant elliptical galaxy.Weil & Hernquist (1994, 1996) have shown that the el-liptical galaxies produced by these events have some kine-matical properties that differ from the remnants of pairmergers, and provide a better explanation for observedproperties. Bekki (2001) has studied the starbursts occur-ring when such events involve gas-rich late-type spirals,and the possible connection with ULIRGs. There is obser-vational evidence that some galaxies are remnants of thecollapse of compact groups (e.g., Borne et al. 2000) or atleast of the simultaneous merging of more than 2 galax-ies (Taniguchi & Shioya 1998). However, these studies arelimited to situations where the different galaxies mergenearly at the same time, and have comparable masses, sothat the merger of only two of them would already haveresulted in the formation of an elliptical galaxy.In this paper, we study a different process: the mul-tiple, sequential mergers of the intermediate and minortypes – hereafter both called “minor” for simplicity – i.e.the mass ratios that do not form elliptical-like galaxies af-ter one single merging event. This corresponds to a givenspiral galaxy that gradually grows by merging with smallercompanions. The mergers are not assumed to occur at thesame time, but one after the other, over a total timescaleof a few Gyrs. We show that a few successive mergerswith mass ratios between 5:1 and 10:1 lead to the grad-ual transformation of spiral galaxies into elliptical-like sys-tems. Under the effects of the sequential mergers, spiralgalaxies become earlier-type spirals, then lenticular S0-like systems, and finally spheroidal objects with globalmorphological and kinematical properties similar to ob-served elliptical galaxies. This new scenario for the for-mation of elliptical galaxies is compared with the resultof the “standard” binary major merger scenario, althoughthe differences are not striking. We also show that eventhe growth of a spiral merging with 50:1 dwarf compan-ions also leads to the progressive destruction of the spiraldisk and the evolution towards S0-like and more frequentlyelliptical-like galaxies, if the initial galaxy is assumed tosignificantly increase its mass by such mergers with dwarfcompanions. Repeated minor mergers occurring alone canthen in theory be an efficient process to form a large num-ber of elliptical galaxies. However, we discuss that in re-ality other processes can reduce this efficiency, in partic-ular to maintain massive disks in spiral galaxies. At thesame time, some elliptical galaxies can likely have formedvia multiple minor mergers, in particular the boxy onesand/or those formed at low redshift when minor mergerslargely dominate major ones.Section 2 contains the details of N-body simulationsand analysis of the results. In Sect. 3, we analyze the prop-erties of the multiple merger remnants as a function ofthe mass ratios and the number of mergers, and study thedifferences with or similarities to the elliptical galaxies re-sulting from major mergers. The implications for galaxyevolution are studied in Sect. 4, and Sect. 5 contains abrief summary of the results of this paper.
2. N-body simulations of multiple galaxy mergers
We have used the N-body FFT code ofBournaud & Combes (2003). The gravitational fieldis computed with a resolution of 400pc. We used 4 × particles for the most massive galaxy. The number of par-ticles used for the other galaxy is proportional to its mass.Star formation and time-dependent stellar mass-loss areimplemented as described in Bournaud & Combes (2002).The star formation rate is computed according to thegeneralized Schmidt law (Schmidt 1959): the local star for-mation rate is assumed to be proportional to µ gβ , where µ g is the local two-dimensional density of gas. We chose β = 1 .
5, as suggested by the observational results ofKennicutt (1998) (see also Boissier et al. 2006). The dis-sipative dynamics of the ISM has been accounted for bythe sticky-particles scheme described in Appendix A ofBournaud & Combes (2002). In this paper we employ elas-ticity parameters β t = β r =0.7. Each galaxy is initially made up of a stellar and gaseousdisk, a spherical bulge and a spherical dark halo. The vis-ible mass of the main (target) galaxy is 2 × M ⊙ . Itsstellar disk is a Toomre (1964) disk of radial scalelength5 kpc, truncated at 15 kpc. Gas is distributed in a Toomredisk of scale-length 15 kpc and radius 30 kpc. The bulgeand dark halos are Plummer spheres of radial scalelengths3 kpc and 30 kpc respectively. The dark halo is truncatedat 70 kpc. The bulge-to-total mass ratio is 0.17 (bulge-to-disk: 0.2), and the dark-to-visible mass ratio inside thestellar disk radius is 0.7. This corresponds to a stellar diskof 14 × M ⊙ , gas disk of 2 . × M ⊙ , a bulge of3 . × M ⊙ , and a dark halo of 11 . × M ⊙ (upto r = 70 kpc). The number of particles is 1 . × forstars, 0 . × for gas, and 1 . × for dark matter.The initial velocities of particles for each componentsare computed as in Bournaud & Combes (2003). The ini-tial value of the Toomre parameter is Q = 1 . – the number of merging companions – the mass ratio of each companion – the orbital parameters of each companion ournaud et al.: Multiple minor mergers and the formation of elliptical galaxies 3 The orbital parameters of a merging pair of galaxies havebeen described e.g. by Duc et al. (2000). These authorsdefined two angles θ and Φ for each galactic disk. θ isthe inclination of the orbital plane vs the primary diskplane ( θ = 0 for a prograde encounter in the disk plane, θ = 180 for a retrograde encounter in the disk plane). Φis the azimuthal position of the secondary disk spin axis.We have run series of simulations with Φ fixed to 30 de-grees and a value of θ of either 30 or 180+30 degrees,for each companion (i.e. inclinations of 30 degrees but or-bits either prograde or retrograde). The first encounter isprograde with a corotating companion, the second one isretrograde, with a counter-rotating companion, etc.. Wefixed the encounter velocity to 150 km s − and impactparameter to 45 kpc, both computed at an infinite dis-tance, neglecting the action of dynamical friction beforethe beginning of the simulation . Since the velocity at aninfinite distance is larger than zero, the initial orbits arenot bound but hyperbolic with a total energy larger thanzero, and dynamical friction dissipates the relative kineticof the galaxies, eventually leading to a merger.The choice of an inclination of 30 degrees is made be-cause it is near the statistically average value of the incli-nation angle in spherical geometry. Assuming an isotropicdistribution of the initial orbital planes of galaxies, theprobability of an inclination i is p ( i ) ∝ cos( i ), and theaverage inclination < i > = R ip ( i ) di ≃
30 deg. Thisaverage choice is then representative of orbits that areneither coplanar nor polar. The inclination has not beenvaried in this paper, except for sequences of 10:1 merg-ers as described in Sect. 4.1.1. It is known from paper Iand other studies of major mergers that the properties ofa binary merger remnant depend more on the mass ratiothan the inclination and other orbital parameters; the testin Sect. 4.1.1 confirms that the result of a minor mergersequence depends on the total merged mass more thanthe orbits, even if changing the orbit does result in somevariations of the final properties.In the reference case of one binary equal-mass merger,choosing one orbit orientation (prograde or retrograde)may not be representative; we thus simulated the two casesand kept the average properties in the following study: westill call this “run ” for simplicity, and the propertiesof a merger remnants depend more on the mass ratio itselfthen the orbital parameters (e.g., paper I and other ref-erences in the Introduction). Similarly, for the 3:1 cases,we ran two sequences (prograde-retograde-prograde andretrograde-prograde-retrograde) and kept the average re-sults. For higher mass ratios, we discuss larger number ofmergers so that starting with the first orbit as progradeor retrograde has less influence – the influence of the or-bit orientation is anyway smaller than the influence of These values should be compared to the stellar disk radiusof 15 kpc and circular velocity 180 km s − at the edge of thisdisk, to be applied to smaller/larger galaxies the mass ratio itself (paper I for binary mergers, see alsoSect. 4.1.1 in this paper for multiple mergers). The nomenclature for each run is as follows:
NxM:1 indi-cates that the galaxy has undergone N mergers with com-panions of mass 1 / M of the target galaxy mass.We have simulated mass ratios M of 1, 3, 5, 7, 10, 15, and N varying from 1 to M (by steps of 2 for M =15).In sequences with mass ratios up to 10:1, the mergersare separated in time by ∆ t = 800 Myr. This means thateach interloper will reach its pericenter at an instant com-puted to be ∆ t after the pericenter of the previous ones.In studies of binary mergers over the same range of massratios (paper I) we found that this timescale ensures thateach merger is relatively relaxed before the following oneoccurs – even if the merging/relaxation occurs somewhatmore rapidly for 1:1 cases than 10:1 cases. A time intervalof 2 Gyrs or more would ensure a more complete relax-ation of the each merger before the next one occurs, butthis would lead to total durations longer than the Hubbletime. Actually, multiple mergers are rather expected tooccur in groups or dense cosmological structures, with atotal duration of the merger sequence of a few Gyrs anda somewhat short time interval between mergers.As for 15:1 mass ratios, the injection of fifteen com-panions each 800 Myr would represent a total duration of12 Gyr, which is highly unrealistic, in particular with theadopted mass and gas fraction of the initial target galaxy.We then chose to reduce the time interval between merg-ers to ∆ t = 400 Myr for this 15:1 mass ratio. The firstmerger is only partially relaxed when the second occurs,but the mergers are still subsequent, i.e. the nuclei of thefirst companion is merged when the second companionreaches the outer gas disk at r = 30 kpc.The time interval separating mergers is not varied inthe present paper. We do not find strong differences be-tween the 10:1 (∆ t = 800) and 15:1 (∆ t = 400) mergersequences in the following, suggesting that it has only aminor influence on the main properties of the remnantgalaxies, at least as long as the mergers are sequentialand not simultaneous. Detailed properties like the orbitalstructure could however vary with the time interval sepa-rating the merging events (e.g. Athanassoula 2005); in par-ticular, in the present paper we study subsequent mergersand do not compare to simultaneous mergers.In each run, the final system is evolved 1.5 Gyr afterthe last merger, to ensure full relaxation before any anal-ysis is performed. This way, the simulation cor-responds to five mergers of mass ratio 10:1, separated intime by 800 Myr between their respective pericenter pas-sages, followed by a 1.5 Gyr isolated evolution to ensurethe relaxation of the the final remnant before its prop- In particular, this 800 Myr interval after the first pericenterensures that the nuclei from the first merger have coalescedwhen the second interaction is at its pericenter. Bournaud et al.: Multiple minor mergers and the formation of elliptical galaxies erties are analysed. In the the simulation, thereare 9 intervals of 800 Myr between the mergers and a final1.5 Gyr-long relaxation of the remnant.We also ran a simulation with 50 dwarf compan-ions of mass ratio 50:1, and initial gas mass fraction of30%. This simulation, where the mergers cannot really besubsequent, but overlap over time, is described later inSect. 4.1.2. We do not vary the orbital parameters beyondalternating prograde and retrograde orbits in the mainpart of the paper, but we will describe and discuss the in-fluence of orbital parameters in merger sequencesin Sect. 4.1.1.
Each remnant of a (sequence of) mergers is analyzed,once relaxed, to derive several physical quantities. Webuild projected column-density maps on which we define a”25th- isophote”, its semi-major-axis being the R radiusin the following, commonly called the ”optical radius” inobservations. The conversion of mass density into luminos-ity is calibrated so that the initial target spiral galaxy, seenface-on, has a central surface magnitude µ =21.7 for itsdisk component (not counting the additional luminosityfrom the bulge). This is to be consistent with the Freeman(1970) relation, where this central magnitude is primarlyobserved in B-band, but we do not explicitly assume anywavelength in the analysis of our simulations. We assumethat the mass-luminosity conversion factor does not varyover the duration of our simulations, because we start with15% of gas so that the new stars will represent at most15% of the mass . Most stars are older than the mergingevents, hence have a reasonably constant mass-to-light ra-tio. The 25th isophote is found to include, on average, 82%of the stellar mass of the merger remants in our simula-tions. Once this reference radius R is defined, we canmeasure several fundamental parameters of the multiplemerger remants: – the flattening E . We first derive the “face-on” projec-tion, defined as that minimizing the apparent flatten-ing of the 25th isophote. We then construct projectedmaps for ten “edge-on” projections, and measure theellipticity e ( r ) = 10 × (1 − b/a ) where the axis ratio b/a is obtained from an ellipse-fitting model. We finallykeep the flattening E as the average value of e ( r ) overthe [0 . R ; R ] range for the different projections.This definition is similar to that used in Bournaudet al. 2005b, and roughly equivalent to that used byNaab & Burkert (2003). – the Sersic index n is determined as the best fit over thesame [0 . R ; R ] radial range, averaged for three or-thogonal projections (not restricted to “edge-on” pro-jections as was the case when deriving the flattening E ). actually most new stars formed in mergers lie in the centralkpc, not around R , which results in an even lower contami-nation at this radius – the kinematical parameter V /σ . When building pro-jected images we also compute the velocity distributionalong each line-of-sight, and then derive the averagevelocity V and velocity dispersion σ for each one. Wethen define the V /σ parameter as the column-density-weighted average (equivalent to luminosity-weightedassuming a constant mass-to-luminosity ratio) over the[0 . R ; R ] radial range, and the result is averagedover three orthogonal projections. The V /σ parameteris not measured along a slit, but on all the pixels of afirst momentum map within the chosen radial range,each pixel being weighted by its intensity in the asso-ciated density map. The choice to exclude the centralregions ( r < . R ) from this kinematical analysiswas made to ensure that a disk galaxy will have a V /σ parameter significantly larger than 1. Indeed thislower bound is always larger than 5 kpc in our mergerremnants, which is larger than the bulges of spirals andS0s (even the large and massive bulges of intermediate-mass merger remnants in Bournaud et al. 2004). Thisway the presence of a massive rotating component willresult in a
V /σ >
1, while a value of
V /σ < – the boxiness a . When measuring E from various pro-jections, we also compute the boxiness a ( r ) as a func-tion of the radius, and keep the average value a overthe range [0 . R ; R ]. The choice of 0 . R asthe lower bound ensures that, when a massive diskis present, we really measure its boxiness or diskiness,not that of the bulge (see paper I).
3. Formation of elliptical galaxies in successivemergers
We show in Fig. 1 the morphology and kinematics of the to merger remnants. After one merger ofthis mass ratio, the system resembles an S0 galaxy. It ismade up of a massive disk, thickened by the interaction,and has large velocity dispersions but still with V /σ > n ≃ R / ” profile (deVaucouleurs 1964) than exponential. The morphology ofthis system is hence typical of an elliptical galaxy. At thesame time, the kinematics is dominated by velocity disper-sions with V /σ = 0 . ournaud et al.: Multiple minor mergers and the formation of elliptical galaxies 5 merger sequence, the system has the properties ofa disky elliptical galaxy where a significant residual rota-tion is still observed. With an increased number of minormergers it can become a boxier, slower-rotating ellipticalgalaxy (see. Fig 5). Also note in Fig. 1 that the resid-ual rotation axis also tends to become misaligned to theapparent flattening direction with increasing number ofmergers. The sequences of mergers with various mass ratios havebeen systematically analyzed. The fundamental parame-ters E , n , V /σ , as defined in Sect. 2, are plotted in Figs. 2,3 and 4 for each sequence. The results are given as a func-tion of the number of mergers converted into the “mergedmass” : for instance, when the initial galaxy has mergedwith 3 companions, each of them having a 5:1 mass ratio,this so-called merged mass is 1.6 (1 for the main initialgalaxy and 0.2 for each companion). Using this definitionallows us to directly compare sequences with various massratios. We recall that each multiple merger remnant is an-alyzed after 1.5 Gyr of evolution to make sure that the sys-tem is reasonably relaxed. We do not analyze the poorlyrelaxed systems between the occurrences of two successivemergers or the on-going merger properties in this paper.The first noticeable result is that once the merged massis 2.0 (i.e., the total mass of the companions equal themass of the initial galaxy, as in a 1:1 major merger), thesystem has the properties of a slow-rotating elliptical-likegalaxy, be the companions massive (like 1:1 and 3:1) ormuch more minor (like 15:1). Indeed, all the final systemsafter these sequences of mergers have: – a spheroidal shape with an axis ratio larger than 0.5(class E4 or at most E5) when observed “edge-on”.The shape of the systems is even rounder with otherlines-of-sight. This is measured in the outer parts of thegalaxies (up to R ), so that the systems cannot simplyconsist of spheroidal bulges surrounded by thin disks,but are really spheroid-dominated galaxies – if a thinouter disk is present, it lies beyond the 25th isophoteand/or does not dominate the mass distribution. – a Sersic index of 4.5 on average, thus being muchcloser to the empirical “ R / ” law (de Vaucouleurs1964) than to the exponential profile of a disk galaxy.Here again the measurement is not restricted to thecentral regions but relates to the radial profile up tothe 25th isophote. – a kinematical parameter V /σ smaller than 0.3 (on av-erage 0.2), and are hence not rotationally-supported.Random motion dominates in these multiple mergerremnants as in real elliptical galaxies, and are evenlarger than in the remnant of one single 3:1 merger(which is usually already considered to be an elliptical-like system).
Merged mass (nb of mergers) E ( fl a t enn i ng ) orbitalscatter Fig. 2.
Evolution of the apparent flattening of the relaxedmerger remnants seen edge-on, along sequences of merg-ers with various mass ratios. All systems evolve from theinitial thin disk to spheroidal galaxies. The flattening ap-pears to depend on the merged mass, more than the massratio of the mergers: for instance 6 mergers of mass ratio10:1 or 3 mergers of mass ratio 5:1 (that both correspondto a merged mass of 1.6) both lead to the formation of anE5 system. Only the 15:1 systematically forms flatter sys-tems, but the difference remains small and several mergersof this type still form spheroidal galaxies. The values for1:1 and 3:1 mass ratios are averaged between progradeand retrograde orbits as detailed in the text. The “orbitalscatter” shows the (1 σ ) dispersion of the result for the sequence when orbital parameters are varied (asdetailed in Sect. 4.1.1).There are differences from one case to the other, butthey are not larger than the variations from one line-of-sight to another one for each given system, and much be-low the differences between standard elliptical and spiralgalaxies. The main observable properties, in projection, ofthese remnants from multiple mergers are typical of ellip-tical galaxies, even if each merger is really minor (like 10:1or 15:1) and would by itself alone have kept the system inthe form of a (disturbed) spiral galaxy.A merged mass of 2.0 is not required to form anelliptical-like galaxy. This is known to be the case for the“major” unequal-mass 2:1 and 3:1 binary mergers. A set ofcriteria to consider that a merger remnant is an ellipticalgalaxy can be: – a flattening of E6 or less when observed edge-on, i.e.thicker than any disk galaxy. – a kinetic energy mainly in the form of random motion,i.e. V /σ < – a Sersic index larger than 3, i.e. the luminosity profileis closer to elliptical-like than to an exponential disk –an this cannot relate only to a central bulge since theinner regions are not included in our measurement.Thus, elliptical-like systems are obtained as soon as themerged mass is 1.3–1.4, i.e. the total mass of the compan- Bournaud et al.: Multiple minor mergers and the formation of elliptical galaxies
Fig. 1.
Comparison of the initial spiral galaxy (here seen after 1 billion year of isolated evolution) and the relaxedmerger remnants of one to four 10:1 mergers. The density maps (left) are in logscale. The velocity and dispersion fieldsare shown in linear scale, with color code ranging from -150 (black) to +150 km s − (white) for the velocity maps, andfrom 0 (black) to 200 km s − (white) for the velocity dispersion. The contour intervals are 35 km s − in the velocityand dispersion fields. The system is viewed under the projection that maximizes its apparent flattening parameter E at each timestep: other projections make the system appear rounder, with generally lower rotational velocites.ions is at least 30% of that of the initial galaxy. This isin agreement with binary mergers up to 3:4 or 4:1 alreadyproducing elliptical galaxies (Bournaud et al. 2005b – po-tentially with faint outer disks: Naab & Trujillo 2006),but this also indicates than two mergers with mass ratio5:1 or three mergers with mass ratio 10:1 are enough totransform a spiral galaxy into an elliptical galaxy. These systems then resemble the low-mass elliptical galaxies thathave a higher degree of residual rotation than the giant el-liptical galaxies (e.g., Naab & Burkert 2003). An increas-ing number of mergers finally keeps on evolving them into ournaud et al.: Multiple minor mergers and the formation of elliptical galaxies 7 Merged mass (nb of mergers) orbitalscatter V / ! ( k i ne m a t i cs ) Fig. 3.
Evolution of the
V /σ parameter along sequencesof mergers of various mass ratios. All systems evolve fromthe initial rotating disk to remnants supported by increas-ing velocity dispersion. The kinematics of these multiplemerger remnants appears to depend on the merged massmore than the mass ratio of the mergers. The velocity dis-persion becomes larger than the rotation velocity whenthe merged-mass is larger than ∼ Merged mass (nb of mergers) n ( S e r s i c i nde x ) orbitalscatter Fig. 4.
Evolution of the Sersic index n in the[0 . R ; R ] radial range. Starting from n ∼ systems, together with astill decreasing degree of rotation.Thus, multiple minor mergers can form elliptical galax-ies that look like both the real observed ellipticals and the these systems are rounder regarding their global flattening E , but this does not imply that the diski-/boxiness is washedout (see Sect. 3.3). major merger remnants, from their shape (flattening), ra-dial profile (Sersic index) and kinematics ( V /σ ). Theseelliptical-like galaxies are never flatter than E7, like thereal ellipticals and the major merger remnants. This isbecause the increase of the equatorial velocity dispersionis not achieved without a large increase of the vertical dis-persions, too, which makes the final system much thickerthan its progenitors.With the parameters studied so far, no major system-atic difference exists compared to major mergers, providedthat the total merged mass is the same. This can be in-terpreted as follows: the energy dissipated by dynamicalfriction is to first order equal to the relative kinetic energyof the merging galaxies (i.e. their mass and relative veloc-ities). The merging of an equal-mass pair thus releases thesame energy through dynamical friction as ten subsequent10:1 mergers. The kinetic energy dissipated by dynami-cal friction heats the stellar systems. The same amount ofheating is thus obtained in the two cases (binary 1:1 vs. se-quence of ten 10:1 merger), which explains the similar
V /σ final values. Kinematical heating in galaxy mergers is gen-erally close to isotropic, thus the different cases also leadto the same amount of vertical heating of the initial disk,which explains the similar flattening of the merger rem-nants of various origins. Finally, the rather similar Sersicindexes suggest that the final degree of relaxation is sim-ilar, even though it is reached through gradual stages. Adetailed study of the dynamics and stellar orbits duringon-going mergers will however be needed to fully under-stand the similarities and differences between the violentrelaxation of major mergers and the step-by-step relax-ation through multiple minor mergers.
Elliptical galaxies are often classified according to var-ious parameters. A fundamental one, that relates totheir formation history, is the diskiness/boxiness param-eter a , which quantifies the 4th Fourier component inthe azimuthal decomposition of their projected isophotes(e.g., Bender & Moellenhoff 1987). Two classes of ellipti-cal galaxies are generally distinguished: – the “disky” elliptical galaxies ( a >
0) are not diskgalaxies but have an isophotal shape recalling that ofdisks, although at a much lower degree. These are gen-erally low mass elliptical galaxies, with a significantamount of rotation (
V /σ up to 0.5–1). In binary mergerscenarios, these are mainly produced by 3:1–4:1 merg-ers. – the “boxy” elliptical galaxies ( a < V /σ generally limited to 0.1 or 0.2). In binary merger sce-narios, they result mainly from equal-mass 1:1 mergers We define a as the coefficient of the cos (4 θ ) componentin the azimuthal decomposition of the isophotes. Bournaud et al.: Multiple minor mergers and the formation of elliptical galaxies Merged mass (nb of mergers) -0.200.20.40.60.81 a4 ( bo xy ne ss ) orbitalscatter Fig. 5.
Evolution of the a parameter versus the mergedmass along several merger sequences. The elliptical-likegalaxies formed with merged masses up to ∼ . a parameter for the multiplemerger remnants from several projected images (same as V /σ ). The average results for the various simulated massratios are shown in Fig. 5. Once again, the result dependsmainly on the total merged mass with little dependenceon how it is merged. For instance, two or three successivemergers of mass ratio 7:1 produce the same final low diski-ness as one single 3:1 merger, while 10 minor 10:1 mergersresult in a boxiness comparable, on average, to an equal-mass 1:1 merger. Note that, just like a remnant, a remnant can appear slightly disky depending onthe viewing direction (see the 1- σ scatter in Fig. 5) but willmore frequently appear boxy, with on average a ∼ -0.1 –-0.2. Nevertheless, a trend can be noted for lower massratios, in particular 10:1 and 15:1, to converge less rapidlytowards negative a parameters. This indicates that theless violent relaxation in minor mergers is less efficient indestroying the disky underlying orbital structure. The dif-ference remains small after several 10–15:1 mergers, butthis suggests that very minor mergers at higher mass ratiosmight be less efficient in forming boxy elliptical galaxies.This trend could also be increased by the higher gas massfraction in lower mass galaxies, because this gas tends toreform disky structures in elliptical galaxies, which canreduce the boxiness.Our result extends the trend observed in 1:1 vs 3:1 bi-nary mergers, namely an increase in the boxiness with themerged mass. This trend still holds when several mergersare repeated in time. Thus, boxy elliptical galaxies can be formed either in the merging of pairs of nearly-equal-massgalaxies, but also by the merging of several lower massgalaxies. Lima-Neto & Combes (1995) had found that re-peated mergers tend to wash out any particular shape(boxy or disky) of elliptical galaxies. The apparent con-tradiction can relate to the much lower resolution availableto these authors, but also that they studied only collision-less and simultaneous major mergers, which is a largelydifferent process.We actually find here that an increasing number ofsubsequent mergers does increase the boxiness. In thesame vein, (Naab, Khochfar & Burkert 2006b) find thatan elliptical galaxy that undergoes another merger (withanother elliptical galaxy in their simulations) can havea slight increase in its boxiness, too. Binary mergers ofdisk galaxies cannot account for the most massive ellipti-cal galaxies being boxy: even collisionless, perfectly equal-mass 1:1 mergers generally do not result in very boxysystems. The formation of such giant boxy ellipticals canthen more likely result of from several re-mergers, the firstones forming an elliptical galaxy and the last ones mak-ing it more and more boxy. This mechanism is at workin the simulations by Naab et al. (2006b), and our results(Fig. 5) further indicate that the sequential mergers do notneed to be equal-mass nor even major : several 3:1 mergerscan form a boxy elliptical galaxy, and a sufficient numberof 7:1 mergers can as well. An alternative scenario to formmassive boxy elliptical galaxies might be the simultaneousmerger of several galaxies in a dense proto-cluster environ-ment, as in the simulations by Weil & Hernquist (1994,1996): the morphological properties of massive ellipticalgalaxies formed this way remain to be studied in detail.We at least show that repeated mergers can explain theboxiness of large ellipticals, which binary major mergers ofdisks alone fail to explain. It is possible that the giant el-lipticals first formed from major mergers at high redshift,then continued to grow with repeated minor mergers withlower-mass galaxies, hence gradually increasing their box-iness. Up to now, we have analyzed only the projected proper-ties of the multiple merger remnants. These can be directlymeasured in observed galaxies. The three-dimensional or-bital structure of elliptical galaxies cannot be directly ob-served, but there is some evidence that the rotation ofelliptical galaxies is generally not large enough to supporttheir flattening (Binney 1982), so that their stellar velocitydispersion has to be anisotropic. Yet, the actual anisotropyof the orbits cannot be accurately inferred from observableparameters alone. And indeed, it is only recently that nu-merical simulations of major mergers revealed the largeradial anisotropy of the stellar orbits in elliptical galaxies,in particular in the outer regions. This anisotropy resultsin a decrease of the observed velocities (along the line-of- ournaud et al.: Multiple minor mergers and the formation of elliptical galaxies 9 sight) in the outer regions, so that the actual mass contentof elliptical galaxies had been underestimated – in partic-ular their dark matter content (Dekel et al. 2005).In the multiple merger remnants, we measured theanisotropy parameter β = 1 − (cid:18) σ θ σ r (cid:19) where σ θ and σ r are respectively the tangential and ra-dial velocity dispersions with respect to the galaxy masscenter. The result is shown, on average over all directionsbut as a function of radius, in Fig. 6. The elliptical-likegalaxies formed in multiple minor mergers tend to have alarger radial anisotropy than those formed in one singlemerger bringing the same total mass.A possible explanation of the higher radial anisotropyfound in multiple minor merger remnants can be thatthe stars and gas clouds in smaller companions have alower angular momentum than in a massive one. Then,the resulting remnants have a lower angular momentumper star, which results in more eccentric orbits, i.e. higherradial velocity at a given radius. As a result, higher radialanisotropies would tend to increase the dynamical massof elliptical galaxies (Dekel et al. 2005) if some of themhave been formed by multiple minor mergers, but the or-der of difference expected from Fig. 6 would not exceeda few tens of percent. However, a study including vari-ous orbits and initial morphologies is required to confirmwhether the anisotropy is systematically higher in multi-ple minor merger remnants. Indeed, Athanassoula (2005)shows that many parameters can significantly influencethe orbital structure of the merger remnant, including thetime interval between subsequent collisions in group merg-ers. Moreover, the radial anisotropy is unlikely to keepincreasing with higher numbers of minor mergers, giventhat Athanassoula (2005) finds lower anisotropy in rem-nants whose progenitors are already elliptical.
4. Discussion
Single binary mergers with mass ratios of 5:1 and largerdo not form remnants with elliptical-like properties, butdisk galaxies: these are “minor” mergers, or the “interme-diate” mergers forming S0-like galaxies (Bournaud et al.2005b). But when several mergers of this type occur, thesystem shows increasing velocity dispersion, together witha rounder and more concentrated morphology (lower E and higher n ). Hence, both the morphological and kine-matical properties of these multiple minor merger rem-nants are similar to those of observed elliptical galaxies.An elliptical-like galaxy is formed when the total mass ofthe companions is 30–40% of the mass of the main initial Radius (kpc) -0.200.20.40.6 β ( an i s o t r op y pa r a m e t e r) Fig. 6.
Anisotropy parameter β for an equal-mass majormerger remnant (1:1) compared to remnants of multipleminor mergers ( and ). The radial variationsof the anisotropy are qualitatively similar in these systems,but the remnants of multiple minor mergers have a higherradial anisotropy in their outer regions.galaxy (merged mass = 1.3–1.4). This has been estab-lished for 5:1 to 15:1 companions, but the simulation with50:1 companions presented below indicates that this resultextends to smaller companions, too. Multiple minor merg-ers are thus a new pathway for the formation of ellipticalgalaxies without major mergers.The sequences of mergers in our simulations describedso far alternate prograde and retrograde companions. Theimpact parameter, velocity, and inclination were not fixedat particularly low or high values, and are thus expectedto give representative results. Furthermore, we know frompaper I and other studies of binary mergers that the globalproperties of a merger remnant are more influenced by themass ratio of the merging galaxies than the other param-eters. For instance, the properties of a binary 3:1 mergerremnant vary with the orbit, but the variations are gen-erally smaller than the typical differences with binary 1:1or 5:1 remnants. Yet, the influence of orbital parametersmay a priori be more important for multiple mergers, be-cause the total angular momentum provided to the systemcan change, influencing the residual rotation of the mergerremnant.We have then repeated our simulation withall companions on prograde orbits, all companions on ret-rograde orbits, all companions at inclination θ = 0 (alter-nating prograde and retrograde orbits as in the fiducialrun), and all companions at θ = 65 degrees. The typ-ical variation of the various properties E , V /σ , n and a corresponding to these changes in orbits is shown inFigs. 2 to 5. We then notice that: (i) for a given mergedmass (for instance vs ) the differences be-tween the mass ratios are below this orbital scatter, but (ii) the evolution of the morphological parameters alongthe merger sequences is larger than the scatter related toorbital parameters, hence it is a significant general result. Fig. 7.
Schematic description of the nature of the binaryand multiple merger remnants, as a function of the num-ber of mergers and the mass ratio. Orbital parametershave not been varied in this paper, except for 10:1 merg-ers, but we know from paper I that the properties of amerger remnant depend on the mass ratio more than theorbital parameters, so this scheme should give a repre-sentative estimate of the number of mergers required totransform a disk galaxy (Sp or S0) into an elliptical-likesystem. The ellipticals formed for instance by merg-ers or sequences are generally boxy on average (they appear disky as well under some projections), andtheir boxiness is moderate. An increasing degree of boxi-ness can be obtained with an increasing number of merg-ers. These results were established for a gas mass fractionof 15% within stellar disks but to first order can be appliedto all systems that are not initially strongly gas-dominated(see text).The fact that a sequence produces slow-rotatingand (slightly) boxy ellipticals, on average, while a sequence results in a disky rotating elliptical is a robustresult that is not much affected by the variations of orbitalparameters. Only the case where all the mergers occur onprograde orbits gives a somewhat higher
V /σ , but this isa rather unlikely case. In major mergers too, some orbitscan preserve massive disk-like structures (for instance inthe case of NGC 4550, Pfenniger 1997). Similarly, a suc-cession of ten minor mergers with all companions coplanarand corotating to the main galaxy would likely form anS0 or disky E rather than a boxy E, but such unlikelycases can only explain specific situations without beingrepresentative of the majority of real mergers.In Fig. 7, we briefly summarize the properties of thebinary and multiple merger remnants, as a function of themass ratio and number of mergers, according to the sim-ulations of this paper and that of paper I. Real situationscan obviously be more complex, but from what we saidabove, we can expect for instance that a sequence will form an elliptical-like galaxy whose averageproperties are similar to the and remnants.
Here we present a simulation where the same initial spi-ral galaxy as before merges with 50 companions each of1/50th of its initial mass. The parameters are the same asfor the other simulations, except that:– the mergers cannot be fully subsequent; they are uni-formly distributed over a 8 Gyr period.– the dwarf companions initially contain 30% of their vis-ible mass in gas.The relaxed remnant of this multiple minormerger sequence is displayed in Fig. 8, viewed along theline-of-sight giving the largest apparent flattening (whichis E = 6 . V /σ ∼ . confirms that theformation of elliptical-like galaxies can still be achievedwith high mass ratios. In detail the merger rem-nant is slightly flatter and has a somewhat higher residualrotation than the other cases; the discrepancy is not majorand likely results from the higher gas fraction in the 50:1companions. Thus, a large number of mergers with veryhigh mass ratios still form elliptical-like galaxies, at leastwhen the size/concentration of galaxies is scaled as in ourmodel (which assumes M ∝ R and a constant centralsurface density). Resolution tests should be performed inthe future to further explore the case of such very smallcompanions. A few 10 particles per galaxy is usually be-lieved to provide a viable large-scale description for majormergers, but in the 50:1 cases the small companion galaxycontains only 2 × stellar particles. High mass ratios aredifficult to model for this reason, and a lack of resolutioncould for instance smooth their gravitational potential andunderestimate their effects. The initial gas mass fraction in the initial spiral galaxyand in the 1:1 to 15:1 companions is 15% in our models:the mergers are not “dry”, but higher gas fractions couldstill be encountered in real mergers at high redshift and/orin low-mass companions. A high fraction of gas in mergerstends to preserve the diskiness and somewhat higher resid-ual rotation (Naab, Jesseit & Burkert 2006a; Jesseit et al.2007) because the gas can be stripped before the galaxycollision, making it less violent, and also because gas canfall back into a disk where it will form new stars after ournaud et al.: Multiple minor mergers and the formation of elliptical galaxies 11
Fig. 8.
Projected mass density, veloc-ity and dispersion fields for a relaxed merger remnant, viewed alongthe projection resulting in the largestapparent flattening ( E = 6 . − , on the velocity dispersion fieldthey are 100, 120 and 140 km s − . Notethe misalignment between the residualrotation and apparent flattening axis. Fig. 9.
Average velocity and velocity dispersion for the merger remnant shown in Fig. 8, taken along a 1kpc-width slit aligned with the apparent major axis. Thesystem is supported by large velocity dispersions similarto those observed in elliptical galaxies.the merger. However, major mergers rarely preserve diskgalaxies similar to real spirals. Indeed, even cases start-ing with pure gas disks in a coplanar co-rotating situation(the best case to preserve most of the angular momentum)end up with about half the mass in a spheroidal compo-nent (see e.g., Springel & Hernquist 2005). More realis-tic orbits will have more mass in the spheroid, and morerealistic initial gas fractions will reduce the subsequentdisk re-formation so that even more mass will end up ina spheroid, making the galaxy elliptical-like (there canbe an outer disk component, formed for instance by gasfalling-back, but not dominating the mass). So gas-richmajor mergers are still expected to form elliptical galax-ies, even if their detailed properties show differences. Onlyextreme situations with very high initial gas fractions canpreserve an (early-type) disk (see also Robertson et al.(2006)), which can be representative only of primordialgalaxies at very high redshift, but not of most galaxies at z ∼
1. Our simulations, even with 30% gas for the 50:1case, can have a low-mass disk component but not a finalmass distribution dominated by an exponential disk.As for multiple minor mergers, except at very high red-shift z >>
1, gas mass fractions are not expected to belarger than 50%, except perhaps in some exceptional casesor in LSB galaxies. Then the pre-existing stars, represent- ing more than half of the mass, will to first order end-upin the spheroidal component after a sufficient number ofminor mergers. Only the stars born during and after themergers potentially end up in a disk, but not all of them(for instance not those formed during the first merger ina sequence of ten mergers), so that the disk componentcannot dominate the mass distribution – which it does inspiral galaxies. Thus, at redshift z ∼ The global properties of the multiple minor merger rem-nants resemble those of binary major mergers. It is thusdifficult to infer from the projected properties of an ellip-tical galaxy its past formation mechanism. The differencesbetween multiple minor and major mergers are not largerthan the scatter related to orbits and other parameters.The orbital structure can be different, but it is unclearwhether there is a systematic difference, because manyparameters that may also influence the anisotropy of themerger remnants have not been varied in this paper.Differences may more likely be found using more de-tailed parameters, like the h of the projected velocity dis-tribution (Gonz´alez-Garc´ıa, Balcells & Olshevsky 2006),the λ R parameter defined by Emsellem et al. (2007) whichcouples the resolved kinematics to the density profile andrevealed different families of early-type galaxies, or corre-lations of several such parameters. Such detailed compar-isons with advanced parameters are beyond the scope ofthe present paper which studies whether merger remnantsare elliptical-like or not, but will be important for futurestudies. time (Gyr) S F R ( M o y r - ) Fig. 10.
Star formation history in binary major mergers(1:1, for the prograde and retrograde orbits) and for asuccession of 7:1 minor mergers.Another major difference lies in the star formationhistory of these systems. Indeed, minor mergers triggerbursts of star formation (e.g., Cox 2004; Cox et al. 2007)that are comparatively less intense than in major merg-ers (see Di Matteo et al. 2007a, regarding the intensity ofstarbursts in major mergers). As a result, the star for-mation history of multiple minor merger remnants largelydiffers from that of a binary major merger, as illustratedin one case in Fig. 10. This difference may however be-come smaller if the successive minor mergers occurredwith smaller time intervals or simultaneously.
Beyond their fundamental properties studied above (massprofile, kinematics, isophotal shape), the real ellipti-cal galaxies are also observed to be described by rela-tions between these fundamental parameters. An impor-tant scaling relation is the so-called fundamental plane(Faber et al. 1987). Most scaling relations are defined overthe complete mass (or luminosity) range of elliptical galax-ies, while our simulations explore only a restricted massrange (a factor of two between the initial and final masses),making it irrelevant to test the viability of multiple minormergers by a comparison with these relations. This is alsothe case for major merger simulations, and simulationscovering the full mass range of ellipticals in a cosmologi-cal context would be required.An observed fundamental relation of ellipticals thatcan be tested in our simulations is the ellipticity – veloc-ity dispersion (
E, V /σ ) relation (Binney 1982), which doesnot explicitly span a large mass range. In our simulationsof multiple minor mergers, we find in Fig. 11 that a rathertight relation exists between E and V /σ for the ellipticalremnants of multiple minor mergers – and even for thosethat we classify as disks (spirals or S0s) after for instanceone single 7:1 merger or two 15:1 mergers. The multiplemerger mechanism then appears to form elliptical galax-
E (flattening) V / ! ( k i ne m a t i cs ) Fig. 11.
Relation between the velocity dispersion (mea-sured via the
V /σ parameter) and ellipticity (flattening E )along the multiple minor merger sequences with variousmass ratios, and the reference major mergers. Evolutionwith increasing number of mergers is from top-right tobottom-left.ies that are viable with regard to this observed relation.The fact that all fundamental parameters have a similarevolution along all mergers sequences, whatever the massratio is (Figs. 2 to 5), suggests that other parametric re-lations exist too. Note however that we cannot check inour simulations whether higher- or lower-mass ellipticalswould still lie on the relation shown in Fig. 11 and notoffset from it.The mass of spheroids (bulges and ellipticals), of-ten traced by central velocity dispersion, is known tocorrelate with the mass of central black holes (e.g.,Kormendy & Richstone 1995), probably mostly grownduring rapid accretion QSO phases (Yu & Tremaine2002). Major mergers can directly fuel a central black holeby rapid gas accretion (Di Matteo et al. 2007b), while mi-nor mergers would rather lead to more moderate inflows(see the star formation history in major vs multiple mi-nor mergers in Fig. 10). Still, minor mergers can increasethe mass of a central black hole by the merging of severalsmaller black holes - those initially at the center of theprimary target galaxy and each companion: then the rela-tion between the central black hole mass and the spheroidmass could a priori be preserved in the elliptical galaxiesformed by multiple minor mergers. Repeated minor mergers, even with rather high mass ra-tios, are thus a mechanism that can form spheroids hav-ing the properties of the real observed elliptical galaxies.Multiple minor mergers is then a possible mechanism to ournaud et al.: Multiple minor mergers and the formation of elliptical galaxies 13 form elliptical galaxies without major mergers, at leastwithin the theoretical frame where binary and repeatedmergers plus internal evolution are the only phenomenondriving the evolution of galaxies. The real evolution ofgalaxies is more complex, because galaxy-galaxy mergersand internal evolution are not the only driving mecha-nisms, and we now discuss how repeated minor mergerscan be placed in a more complete description of galaxyevolution.
Disk galaxies are observed to increase their size andmass between z = 1 and z = 0. At redshift 1,stellar disks had on average smaller truncation radii(Trujillo & Pohlen 2005) and smaller exponential scale-lengths (e.g., Elmegreen et al. 2007b). Their mass mustthen have increased in significant proportions over the last ∼ ∼ vis ∼ M ⊙ and above plus their massive dark mat-ter halo cannot achieve this, as shown for instance by oursimulation with 50:1 mergers.Cold gas can be accreted directly from cosmological fil-aments for galaxies whose total mass (including the darkhalo) does not exceed ∼ M ⊙ (Birnboim & Dekel2003; Dekel & Birnboim 2006) and even for more massivegalaxies but less regularly (Birnboim, Dekel & Neistein2007); and it can explain the morphological properties ofdisk galaxies in our Local Universe (Bournaud & Combes2002; Bournaud et al. 2005a). Moreover, the growth ofdisks is observed to be inside-out (e.g., Trujillo & Pohlen2005), which cannot be easily explained by a (minor)merger-driven growth, but can result from the accretionof gas if the lower angular momentum material is accretedfirst, and higher angular momentum gas accreted at laterstages. Gas falling-back from large radii after the merg-ers (in particular gas from tidal tails) appears not to bemassive enough to refuel a massive disk, even in our 50:1cases with gas-rich companions. A low-mass disk compo-nent can be fueled this way, but a disk dominating thetotal mass distribution cannot be maintained without theadditional accretion of external gas.That spiral disks have been able to grow from z = 1 to z = 0 thus implies that some phenomenon favor the per-sistence of their disks, like the accretion of cold gas. Then, the process of progressive disk destruction and transfor-mation into ellipticals by repeated minor mergers could becompensated for by other processes, like cold gas accre-tion, which would increase or maintain massive disk com-ponents around/within the heated stellar spheroid. But inour simulations the galaxy evolution is driven only by mi-nor mergers, and this leads to a progressive transformationof disk galaxies into elliptical-like spheroids. The standard “major merger” scenario for the formationof elliptical galaxies is usually assumed to produce a frac-tion of elliptical galaxies roughly consistent with that ob-served (e.g., Mamon 1992; Baugh, Cole & Frenk 1996). Anadditional mechanism has been proposed by Naab et al.(2007), but is mainly expected to be at work in the EarlyUniverse forming primordial elliptical galaxies.Successions of several minor mergers are more likelythan binary major mergers – see Khochfar & Silk (2006),Maller et al. (2006), and estimates in paper I – at leastat redshift z <
1. The number of elliptical galaxies isthen a priori expected to increase significantly throughthis alternative mechanism. But then the number of el-liptical galaxies present in the Universe today would bemuch larger than observed. Even among field spiral galax-ies, which have significantly grown over the past 8 billionyears, many would have become elliptical and lenticulargalaxies. Another process is then required to prevent thesuccession of minor mergers from systematically trans-forming disk galaxies into ellipticals as soon as their massis increased by a few ten of percents, otherwise this mech-anism together with binary major mergers would resultin an excess of elliptical galaxies. Still, there should be atleast some ellipticals formed by multiple minor mergersat low redshift; van Dokkum (2005) finds a large fractionof mass ratios larger than 4:1 in the mergers undergonerecently by field ellipticals.Observationally, on-going minor mergers are not un-common at z = 0, but also at z ∼
1: for instance a largefraction of the interacting systems at z ∼ the boxiness of giant ellipticals, as discussed previously(Section 3.3), and there is further evidence that ellipti-cal galaxies did not all form from binary major merg-ers (Naab & Ostriker 2007). Repeated major mergers ingroups may have formed them too, but these are less likelythan multiple minor mergers. Thus, successions of minormergers likely participated in the formation of some of theelliptical galaxies seen today.Elliptical galaxies have a higher frequency of globularclusters (GCs) relative to their stellar mass than spiralgalaxies (Harris 1991; van den Bergh 2001). The forma-tion of GCs can be triggered by strong shocks associatedwith starbursts, as suggested by van den Bergh (1979) andstudied by Jog & Solomon (1992). Major mergers trig-ger stronger starbursts, while the shocks and starburstsare less intense (but repeated) during the successive mi-nor mergers (see Sect. 4.1.4), potentially forming differentnumbers of GCs – which models resolving GC formationcould confirm. This could be a way to disentangle theelliptical galaxies formed by major and repeated minormergers.
5. Conclusion
In this paper, we have shown that the succession of minorgalaxy mergers (mass ratios larger than 4:1) leads to thegradual transformation of spiral galaxies into elliptical-likegalaxies. This is the case both for the truly minor mergers(mass ratios above 10:1, a single merger of this type formsa spiral) and the “intermediate” mergers (mass ratios be-tween 4:1 and 10:1, a single merger of this type forms anS0-like galaxy, e.g. paper I). The remnants of repeatedmergers with these mass ratios have a spheroidal shape, aradial profile close to the “ R / ” empirical profile of ellipti-cals, and are supported by large velocity dispersions V /σ .This is true even for very low-mass companions (up to50:1 in one of our simulations), and the relaxed remnantresembles an elliptical galaxy as soon as the total massadded by successive mergers exceeds 30–40% of the massof the main initial spiral. The global properties of the mul-tiple merger remnants depend more on the total mergedmass than on the mass ratio of each merger, and for in-stance a merger sequence resembles a rem-nant more than a . These properties can vary withthe orbital parameters and morphology of the progenitorgalaxies, but not widely. In particular, only extremely gas-rich systems, or companions on peculiar orbits, may keepdisk-dominated galaxies after several minor mergers, butthis should not be the most frequent case except at veryhigh redshift. A noteworthy dynamical result is that thefinal properties of the remnant (radial profile, flattening,kinematics) are to first order independent of whether itis formed by a single merger, a sequence, ora
10 x 10:1 sequence, so as long as the final mass hasincreased by the same factor.Multiple, sequential minor mergers provide a new the-oretical pathway to form elliptical galaxies without majormergers. In a purely hierarchical scenario, a succession of several minor mergers is more likely than one single binarymerger, and must then have formed some of the ellipticalgalaxies seen today. Repeated minor mergers also providea possible explanation for some specific features, in par-ticular the boxiness of the largest ellipticals, that are notexplained by the standard major mergers (1:1-3:1).However, minor mergers repeated in time would tendby themselves to produce too many elliptical galaxies.Moreover if field galaxies were to grow only by hierarchicalmerging, most spirals would have been transformed intoellipticals over the last 8 Gyr, even if these mergers wereminor ones. It is then required that another process par-ticipates in the growth of galaxies, braking down or revers-ing the minor-merger-driven evolution towards early-typespheroids. This process is likely to be accretion of cold gas,either in a completely diffuse phase, or in small gas-richclumps – but not dwarf galaxies bounded by their darkmatter haloes that would have destroyed massive disks.While we present a new mechanism for the formationof elliptical galaxies in a purely hierarchical context, wealso conclude that its efficiency must be somewhat limited:the evolution of galaxies cannot be purely merger-driven,and a large fraction of their mass cannot have been ac-quired through mergers, even minor ones with small com-panions. The growth of spiral galaxies at low and moder-ate redshifts must have rather been a competition betweenthese minor mergers and accretion of cold gas. Some ofthe present-day ellipticals likely formed by multiple minormergers, but this process cannot be much more efficientthan binary major mergers, otherwise it would result inan excess of elliptical galaxies.Cosmological simulations of restricted volumes canreach a resolution similar to that of the generic galaxysimulations presented in this paper (see in particularNaab et al. 2007), but not over large samples that can beused for statistical purposes. At the opposite, large-volumecosmological simulations may lack the resolution neededto reproduce the effects of repeated minor mergers in a re-alistic way, because this requires that the dwarf compan-ions are sufficiently resolved. However, these simulationscan provide accurate predictions of the evolution historyof galaxies (mass ratios of mergers, time intervals, andrate of diffuse gas accretion). The possibility of formingellipticals but keeping most field galaxies as spirals at thesame time, in high-resolution galaxy models taking intoaccount these large-scale cosmological predictions, couldbe a future test of cosmological models.
Acknowledgements.
We are very grateful to the anonymousreferee whose critical comments helped us present the methodand results clearly. Stimulating discussions on this work withAvishai Dekel and Eric Emsellem and comments from ThorstenNaab on an earlier version of this manuscript are gratefully ac-knowledged. We are happy to acknowledge the support of theIndo-French grant IFCPAR/2704-1. The N-body simulationswere computed on the NEC-SX8R of the CEA/CCRT com-puting center and the NEC-SX8 of CNRS/IDRIS.ournaud et al.: Multiple minor mergers and the formation of elliptical galaxies 15