The effects of a hot gaseous halo in galaxy major mergers
Benjamin P. Moster, Andrea V. Maccio', Rachel S. Somerville, Thorsten Naab, Thomas J. Cox
MMon. Not. R. Astron. Soc. , 1–23 (2011) Printed 11 November 2018 (MN L A TEX style file v2.2)
The effects of a hot gaseous halo in galaxy ma jor mergers
Benjamin P. Moster , (cid:63) , Andrea V. Macci`o , Rachel S. Somerville , ,Thorsten Naab , T. J. Cox Max-Planck-Institut f¨ur Astronomie, K¨onigstuhl 17, 69117 Heidelberg, Germany Max-Planck Institut f¨ur Astrophysik, Karl-Schwarzschild Straße 1, 85748 Garching, Germany Space Telescope Science Institute, Baltimore MD 21218 Department of Physics and Astronomy, Johns Hopkins University, Baltimore MD 21218 Carnegie Observatories, 813 Santa Barbara Street, Pasadena, CA 91101, USA
11 November 2018
ABSTRACT
Cosmological hydrodynamical simulations as well as observations indicate that spiralgalaxies are comprised of five different components: dark matter halo, stellar disc,stellar bulge, gaseous disc and gaseous halo. While the first four components havebeen extensively considered in numerical simulations of binary galaxy mergers, theeffect of a hot gaseous halo has usually been neglected even though it can containup to 80% of the total gas within the galaxy virial radius. We present a series ofhydrodynamic simulations of major mergers of disc galaxies, that for the first timeinclude a diffuse, rotating, hot gaseous halo. Through cooling and accretion, the hothalo can dissipate and refuel the cold gas disc before and after a merger. This cold gascan subsequently form stars, thus impacting the morphology and kinematics of theremnant. Simulations of isolated systems with total mass M ∼ M (cid:12) show a nearlyconstant star formation rate of ∼ M (cid:12) yr − if the hot gaseous halo is included, whilethe star formation rate declines exponentially if it is neglected. We conduct a detailedstudy of the star formation efficiency during mergers and find that the presence of ahot gaseous halo reduces the starburst efficiency ( e = 0 .
5) compared to simulationswithout a hot halo ( e = 0 . r / surfacebrightness profile at small scales. The consequences on the population of ellipticalgalaxies formed by disc mergers are discussed. Key words: galaxies: elliptical, evolution, haloes, interactions, starburst, structure– methods: numerical, N-body simulation
Galaxy mergers, both major (near-equal mass) and minor(unequal mass), are a generic prediction of structure assem-bly in the Cold Dark Matter (CDM) model (e.g. White& Rees 1978; Davis et al. 1985). Mergers are an impor-tant component of the modern theory of galaxy forma- (cid:63) [email protected] tion and are thought to be a significant physical driver ofmany galaxy properties. Major mergers can transform disc-dominated galaxies into spheroidals (Toomre 1977; Negro-ponte & White 1983; Hernquist 1992; Naab & Burkert 2003;Cox et al. 2006c), enhance star formation (Larson & Tins-ley 1978; Kennicutt et al. 1987; Barnes & Hernquist 1991;Mihos & Hernquist 1994, 1996; Barton Gillespie et al. 2003;Cox et al. 2008) and possibly trigger Active Galactic Nu-clei (AGN) activity (Sanders et al. 1988; Hernquist 1989; c (cid:13) a r X i v : . [ a s t r o - ph . GA ] A p r B. P. Moster et al.
Springel et al. 2005; Hopkins et al. 2006; Johansson et al.2009a; Younger et al. 2009; Debuhr et al. 2010, 2011). Mi-nor mergers can thicken the galactic disc (Quinn et al. 1993;Velazquez & White 1999; Brook et al. 2004; Bournaud et al.2005; Kazantzidis et al. 2008; Villalobos & Helmi 2008; Readet al. 2008; Purcell et al. 2009; Moster et al. 2010) and cre-ate a diffuse stellar halo (Murante et al. 2004; Bullock &Johnston 2005; Bell et al. 2008; Murante et al. 2010). Obser-vations find large samples of recent merger remnants in thelocal universe (Schweizer 1982; Lake & Dressler 1986; Doyonet al. 1994; Shier & Fischer 1998; Genzel et al. 2001; Dasyraet al. 2006) and that ∼ −
10% of low- and intermediate-mass galaxies are in the process of merging (Bridge et al.2010). An average ∼ M ∗ galaxy has experienced about onemajor merger since z ∼ − survey).The different physical properties of elliptical galaxieslead to the viewpoint that the two classes have differentformation histories and form through different mechanisms.Many studies find that collisionless merger simulations leadto slowly rotating, pressure supported, anisotropic remnants(Negroponte & White 1983; Barnes 1988; Hernquist 1992).Along this line of reasoning, Naab et al. (1999), Bendo &Barnes (2000) and Naab & Burkert (2003) argue that fastrotating low luminosity ellipticals are produced by dissipa-tionless minor mergers. However, remnants of dissipationlessdisc galaxies are in conflict with observations, as they do nothave de Vaucouleurs profiles in the inner parts. The reasonfor this is that low phase-space density spirals cannot pro-duce the high central phase-space densities of ellipticals —according to Liouville’s theorem, phase-space density is con-served during a collisionless process (Carlberg 1986). Thisproblem could only be overcome in dissipationless simula-tions by including large bulge components in the progenitorsystems (Hernquist et al. 1993; Naab & Trujillo 2006).Another way to circumvent this problem is to take intoaccount the gas component in the progenitors, which canincrease the phase-space density through radiation (Lake1989). It has been argued by Kormendy & Bender (1996)and Faber et al. (1997) that the observed stellar discs em-bedded in rotating ellipticals (Rix & White 1990; Ferrareseet al. 1994; Scorza et al. 1998; Rix et al. 1999; Lauer et al.2005; Krajnovi´c et al. 2008) experienced dissipation duringtheir formation while non-rotating systems would form frompure dissipationless mergers. This idea has been explored byseveral studies (Bekki & Shioya 1997; Bekki 1998; Naab et al.2006; Jesseit et al. 2009; Hopkins et al. 2008, 2009b,c,d). Fo-cusing on equal mass mergers, Cox et al. (2006b) confirmedthat slowly rotating anisotropic spheroids can be formed indissipationless simulations. Furthermore they show that if amassive gaseous disc is included in the progenitors, a con-sistent fraction of merger orbits leads to systems with sig-nificant rotation. Those remnants are able to reproduce theobserved distribution of projected ellipticities, rotation pa-rameters and isophotal shapes. One open issue is that theseresults rely on a relatively high (possibly too high) gas con-tent in the discs of the merger progenitors and that only afraction of the considered orbits lead to fast rotators. It re-mains unclear whether the abundance of disc galaxies withsuch gas fractions is high enough in order to explain thelarge number of fast rotating elliptical galaxies observed inthe local universe (de Zeeuw et al. 2002; Emsellem et al.2007; Cappellari et al. 2007; Emsellem et al. 2011).The initial conditions for almost all hydrodynamic sim- c (cid:13) , 1–23 ot gaseous halo in major mergers ulations of galaxy mergers performed so far have consideredonly cold gas that is present within the progenitor discs atthe start of the simulation. However, semi-analytic models ofgalaxy formation (Kauffmann et al. 1993; Bower et al. 2006;De Lucia & Blaizot 2007; Monaco et al. 2007; Somervilleet al. 2008b) as well as full cosmological hydrodynamic sim-ulations (e.g. Toft et al. 2002; Sommer-Larsen 2006; Johans-son et al. 2009b; Rasmussen et al. 2009; Stinson et al. 2010;Hansen et al. 2010) both predict a large amount of hot gasin quasi-hydrostatic equilibrium within the gravitational po-tential of the dark matter halo. Smooth accretion of gas fromthese haloes can grow the discs of spiral galaxies (Abadiet al. 2003; Sommer-Larsen et al. 2003; Guo & White 2008).As the gas mainly cools via thermal bremsstrahlung it radi-ates primarily in the soft X-ray band.Since this halo X-ray luminosity depends on the massof the system, observational studies are naturally biased to-wards very massive haloes. Hence, hot gas in massive ellipti-cals has been observed in galaxy groups and clusters and inisolated systems (see Mathews & Brighenti 2003, and refer-ences therein). In smaller haloes, however, the gas temper-ature can be lower than 10 K and thus difficult to observewith current X-ray telescopes, as the radiation is only de-tectable in very soft bands. Still, studies performed in thelast few years have identified X-ray emission from diffusehot gas in various energy bands (Benson et al. 2000; Wanget al. 2003; Strickland et al. 2004; Wang 2005; T¨ullmannet al. 2006; Li et al. 2007; Sun et al. 2009; Owen & Warwick2009). In the MW, X-ray absorption lines produced by localhot gas have been detected in the spectra of several AGN.Sembach et al. (2003) and Tripp et al. (2003) have arguedthat this emission comes from the interface between warmclouds and the ambient hot medium. Given the existence ofhot gaseous haloes around galaxies, it is important to in-clude these in simulations of isolated galaxies and mergers.In the last few years there have been several studiesthat have taken a gaseous halo into account. Mastropietroet al. (2005) and Mastropietro et al. (2009) employ a hot halocomponent to study the hydrodynamic and gravitational in-teraction between the Large Magellanic Cloud and the MW.Sinha & Holley-Bockelmann (2009) ran merger simulationsof galaxies consisting of dark matter and hot halo gas in or-der to study the change of temperature and X-ray luminosityinduced by shocks during the mergers. Those studies, how-ever, use adiabatic simulations, neglecting cooling and starformation. Focusing on isolated systems, Kaufmann et al.(2006) and Kaufmann et al. (2009) simulated systems con-sisting of a dark matter and a hot halo component to studythe evolution and cooling behaviour of the hot halo and theformation of discs via cooling flows. Similarly, Viola et al.(2008) ran simulations of a gas halo embedded in a darkmatter halo to study the cooling process and assess how wellsimple models can represent it. So far, no study has includeda rotating, cooling gaseous halo in merger simulations.The goal of this paper is to test the impact of includingsuch a large gas reservoir on star formation and remnantproperties in major mergers of disc galaxies. For the firsttime we include a gradually cooling hot gas halo (as expectedin a cosmological context) in our galaxy models. We presenta detailed analysis of the effects of this new gas componentand focus our attention on three main quantities: the star formation efficiency during and after the merger, and themorphology and kinematics of merger remnants.The paper is organized as it follows: in section 2 weprovide a brief summary of the
GADGET-2 code and theinitial conditions. We also explain how the initial conditionshave been set up to include a rotating hot gaseous halo,and show the results of simulations constraining the initialspin of this hot halo. In section 3 we present our main re-sults for the major merger simulations, focusing on the dif-ferences between the simulations with and without a hotgaseous component. We present star formation rates, star-burst efficiencies and structural and kinematic properties ofthe remnants. Finally, in section 4 we summarize and dis-cuss our results and compare them to previous studies thathave neglected the gaseous halo.
All numerical simulations in this work were performed us-ing the parallel TreeSPH-code
GADGET-2 (Springel 2005).Gas dynamics is followed with the Lagrangian smoothedparticle hydrodynamics (SPH Lucy 1977; Gingold & Mon-aghan 1977; Monaghan 1992; Springel 2010) technique, em-ployed in a formulation that manifestly conserves energyand entropy (Springel & Hernquist 2002). Radiative coolingis implemented for a primordial mixture of hydrogen andhelium following Katz et al. (1996), with a spatially uni-form time-independent local photo-ionizing UV backgroundin the optically thin limit (Haardt & Madau 1996).For modelling star formation and the associated heat-ing by supernovae (SN) we follow the sub-resolution multi-phase ISM model developed by Springel & Hernquist (2003).In this model, a thermal instability is assumed to operateabove a critical density threshold ρ th , producing a two-phasemedium which consists of cold clouds embedded in a tenuousgas at pressure equilibrium. Stars are formed from the coldclouds on a timescale chosen to match observations (Kenni-cutt 1998) and short-lived stars supply an energy of 10 ergsto the surrounding gas as supernovae. This energy heats thediffuse phase of the ISM and evaporates cold clouds, suchthat a self-regulated cycle for star formation is established.The threshold density ρ th is determined self-consistently bydemanding that the equation of state (EOS) is continuousat the onset of star formation. In a subset of simulations weinclude SN-driven galactic winds as proposed by Springel &Hernquist (2003). In this model the mass-loss rate carriedby the wind is proportional to the star formation rate (SFR)˙ M w = η ˙ M ∗ , where the mass-loading-factor η quantifies thewind efficiency. Furthermore, the wind is assumed to carrya fixed fraction of the supernova energy, such that there isa constant initial wind speed v w (energy-driven wind).We adopt the standard parameters for the multiphasemodel in order to match the Kennicutt Law as specified inSpringel & Hernquist (2003). The star formation timescaleis set to t ∗ = 2 . A = 1000 and the SN “temperature” to T SN = 10 K. Weemploy a Salpeter (1955) initial mass function (IMF) whichsets the mass fraction of massive stars β = 0 .
1. For the galac-tic winds we adopt a mass-loading factor of η = 2 which is c (cid:13)000
1. For the galac-tic winds we adopt a mass-loading factor of η = 2 which is c (cid:13)000 , 1–23 B. P. Moster et al.
Table 1.
Parameters kept constant for all simulations. Masses are in units of 10 M (cid:12) , scale and softeninglengths are in units of kpc and pc, respectivelySystem M dm M b r d r g r b z c λ N dm N bulge (cid:15) DM (cid:15) stars Z1 80 0.500 2.50 3.75 0.50 0.6 3.64 0.030 500 000 20 000 400 100G3 110 0.890 2.85 8.55 0.62 0.4 6.00 0.050 240 000 20 000 400 100 motivated by observations (Martin 1999; Rupke et al. 2005;Martin 2005), and a wind speed of v w ∼
480 km s − , typi-cal for a Milky Way (MW)-like galaxy at low redshift. Wedo not include feedback from accreting black holes (AGNfeedback) in our simulations. To construct the galaxy models used in our simulations weapply and extend the method described in Springel et al.(2005). Each system is composed of a cold gaseous disc, astellar disc and a stellar bulge with masses M cg , M disc and M b embedded in a halo that consists of hot gas and darkmatter with masses M hg and M dm .The gaseous and stellar discs are rotationally supportedand have exponential surface density profiles. The scalelength of the gaseous disc r g is related to that of the stellardisc r d by r g = χr d . The vertical structure of the stellar discis described by a radially independent sech profile with ascale height z , and the vertical velocity dispersion is setequal to the radial velocity dispersion. The gas tempera-ture is fixed by the EOS, rather than the velocity disper-sion. The vertical structure of the gaseous disc is computedself-consistently as a function of the surface density by re-quiring a balance of the galactic potential and the pressuregiven by the EOS. The spherical stellar bulge is non-rotatingand is constructed using the Hernquist (1990) profile witha scale length r b . The dark matter halo has a Hernquist(1990) profile with a scale length r s , a concentration param-eter c = r vir /r s and a halo spin λ . For MW-like galaxies there are no existing observations thatconstrain the profile of the gaseous hot halo. Therefore, wechoose the observationally motivated β -profile (Cavaliere &Fusco-Femiano 1976; Jones & Forman 1984; Eke et al. 1998)which is commonly used to describe hot gas in galaxy clus-ters: ρ hg ( r ) = ρ (cid:20) (cid:16) rr c (cid:17) (cid:21) − β . (1)It has three free parameters: the central density ρ , the coreradius r c and the outer slope parameter β . The temperatureprofile can be fixed by assuming isotropy and hydrostaticequilibrium inside the galactic potential. The halo temper-ature at a given radius r is then determined by the cumula-tive mass distribution M ( r ) of the dark matter, stellar andgaseous components beyond r and by the density profile ρ hg ( r ) of the hot gas: T ( r ) = µm p k B ρ hg ( r ) (cid:90) ∞ r ρ hg ( r ) GM ( r ) r dr , (2)where m p is the proton mass, G and k B are the gravita-tional and Boltzmann constants and µ is the mean molecularweight.In addition the hot gaseous halo is rotating around thespin axis of the disc. The angular momentum of the hotgaseous halo is set by requiring that the specific angularmomentum of the the gas j hg = J hg /M hg is a multipleof the specific angular momentum of the dark matter halo j dm = J dm /M dm such that j hg = αj dm . A value of α = 1matches the commonly adopted assumption that there is noangular momentum transport between the spherical darkmatter halo and the gaseous halo. The angular momentumdistribution is then assumed to scale with the product ofthe cylindrical distance from the spin axis R and the circu-lar velocity at this distance: j ( R ) ∝ R v circ ( R ). The verticalvelocity of the gas halo particles is set equal to zero. The hot gaseous halo is then described by four parameters:the central density ρ , the core radius r c , the slope parame-ter β and the spin factor α . For the density profile, we adopt β = 2 / r c = 0 . r s (Makinoet al. 1998). Thus there is a central core with a constantdensity and the slope in the outer halo is − ρ such that the bary-onic fraction within r vir (stellar and gaseous discs, bulge andgaseous halo) is the universal value, as this is the maximumfraction that a gaseous halo can achieve. We also test anintermediate case, where we adopt only half of this maximalhot gas mass to investigate whether the results fall betweenthe extreme cases (no and maximal gaseous halo). The re-sults of this test are presented in section 3.4. Note, however,that even for our maximum hot gaseous halo mass we donot violate constraints from X-ray observations; see section4 for a more detailed discussion of this point.This leaves one key free parameter which needs to beconstrained, the spin factor α . In high resolution cosmo-logical simulations one finds that at low redshift ( z ∼ < α is generally larger than 1, as feedback processes preferen-tially remove low angular momentum material from the halo(Governato et al. 2010).In order to fix the spin factor for MW-like galaxieswe model a typical MW-like galaxy at z = 1 and let itevolve to z = 0 using different values for α . We then em-ploy two observational constraints (stellar mass and discsize) to determine the correct α . A typical MW-like galaxywith M dm ( z = 0) ∼ M (cid:12) has a halo concentration of c (cid:13) , 1–23 ot gaseous halo in major mergers Table 2.
Parameters for the different simulation runs. Masses are in units of 10 M (cid:12) , and softening lengthsare in units of pc.Run f gas M disc M cg M hg α N disc N cg N hg (cid:15) gas θ Z1 0.40 2.00 1.33 0.0 - 100 000 33 333 0 140 -Z1A1 0.40 2.00 1.33 12.0 1 100 000 33 333 375 000 140 -Z1A2 0.40 2.00 1.33 12.0 2 100 000 33 333 375 000 140 -Z1A4 0.40 2.00 1.33 12.0 4 100 000 33 333 375 000 140 -Z1A8 0.40 2.00 1.33 12.0 8 100 000 33 333 375 000 140 -G3 0.23 4.11 1.20 0.0 - 100 000 15 000 0 140 30 ◦ G3f0 0.00 5.31 0.00 0.0 - 130 000 0 0 - 30 ◦ G3f4 0.40 3.20 2.11 0.0 - 80 000 25 000 0 140 30 ◦ G3f8 0.80 1.07 4.24 0.0 - 30 000 50 000 0 140 30 ◦ G3h 0.23 4.11 1.20 11.0 4 100 000 15 000 175 000 140 30 ◦ G3hf0 0.00 5.31 0.00 11.0 4 130 000 0 175 000 140 30 ◦ G3hf4 0.40 3.20 2.11 11.0 4 80 000 25 000 175 000 140 30 ◦ G3hf8 0.80 1.07 4.24 11.0 4 30 000 50 000 175 000 140 30 ◦ G3hX 0.23 4.11 1.20 5.5 4 100 000 15 000 87 500 140 30 ◦ c = 8 .
43 at z = 0 (Macci`o et al. 2008) which fixes both pa-rameters of the Hernquist profile. Assuming that the haloprofile does not change from z = 1 to the present, wecan compute the virial mass and the halo concentrationgiven the higher background density at z = 1, resultingin M dm , z=1 = 8 . × M (cid:12) and c z =1 = 3 .
64. Using theredshift-dependent stellar-to-halo mass relation derived byMoster et al. (2010), converted to a Salpeter IMF, we as-sign a stellar mass of M ∗ ,z =1 = 2 . × M (cid:12) to the system.Distributing 80% of this stellar mass into the exponentialdisc yields a stellar disc mass of M disc = 2 . × M (cid:12) anda bulge mass of M b = 5 × M (cid:12) . A bulge scale length of r b = 0 . M ∗ = 2 . × M (cid:12) at z = 1 have a gas fractionof f gas = M cg / ( M cg + M disc ) = 0 . M cg = 1 . × M (cid:12) . The scale lengthfor the stellar disc at z = 1 is set to r d = 2 . λ = 0 .
03 assuming the scalings of Mo et al. (1998). Weassume that the scale length of the gaseous disc r g is a factorof χ = 1 . z = 0 . r vir is M hg = 1 . × M (cid:12) ,such that the baryonic fraction within r vir is the universalvalue. The system is modeled with N dm = 500,000 darkmatter, N disc = 100,000 stellar disc, N cg = 33,333 gaseousdisc, N bulge = 20,000 bulge and N hg = 375,000 gaseoushalo particles. We set the gravitational softening length to (cid:15) = 100 pc ,
140 pc and 400 pc for stellar, gas and dark mat-ter particles, respectively. We summarize the parametersthat are kept constant for all simulations in Table 1, andparameters that differ for the various simulation runs aresummarized in Table 2.In order to fix the angular momentum of the gaseoushalo, we run five simulations with different values of the spin factor α . These include: one simulation with no gaseous haloat all (Z1), and simulations with α = 1 , , z = 1 to z = 0 which corresponds to 7 . M dm = 0 . × M (cid:12) at z = 0 . M ∗ = 4 × M (cid:12) and the mean observedscale length for galaxies of this stellar mass is r d = 2 .
82 kpc.We require that the stellar mass and scale length measuredin the simulations should obey these constraints.We show the results of the simulations in Figure 1. Forthe simulation without a gaseous halo the evolution of thescale length agrees well with the observed values at z ∼ > . z = 0. This shows that the hot gaseoushalo is very important in order to reproduce the SF historyof spiral galaxies like our MW, by providing an extendedsupply of cold gas that can fuel ongoing star formation.The simulations including a gaseous halo show a muchlarger SFR, with the value depending on the initial spin fac-tor α . For low values of α = 1 and 2, the stellar mass of thegalaxy increases too fast and becomes too large at z = 0, c (cid:13) , 1–23 B. P. Moster et al.
Figure 1.
Upper panel:
Stellar mass as a function of time fordifferent values of the spin parameter for the hot gas halo α . Thevalues measured in the simulations (lines) are compared to theobservational constraints from Moster et al. (2010, bold line andshaded area). Lower panel:
Disc scale length as function of timefor different α . Symbols show the observed values by Barden et al.(2005). Only the simulation with α = 4 agrees well with bothconstraints. while the scale length quickly decreases and reaches valuesthat are much smaller than the observed ones. These effectsare due to the low angular momentum of the halo gas at thestart of the simulation. When the gas cools, it is no longersupported by pressure, but only by angular momentum. Thismeans that a lower initial angular momentum results in alower orbital distance and thus in a lower scale length. Ad-ditionally, since the centrifugal barrier is lower, much morematerial can reach densities where SF is active which yieldsa much higher SFR and thus a larger stellar mass. For valuesof α ∼ <
3, too much material concentrates at small distancesfrom the galactic centre which results in overly massive andtoo compact discs compared to observations. On the otherhand, large values of α = 8 yield a stellar disc which is notmassive enough and which has a scale length that is toolarge. Due to the larger initial angular momentum the cool-ing gas can retain large orbital distances. This also leadsto much less dense star-forming material and thus to lowerstellar masses. For values of α ∼ >
6, we find that gas settlesin discs that are too large and does not form enough starscompared to observations.The model that agrees best with the observational con-straints is the one with a spin factor of α = 4. For this valuewe find a stellar mass and a scale length which are consistentwith the observational constraints for MW-like galaxies. As a result we use this value throughout the rest of this paperfor all systems, which are all in the halo mass range of theMilky-Way. We note that different values of α (represent-ing different merger histories, feedback efficiencies, etc.) caneasily result in a range of stellar masses and scale length, inagreement with the spread of these quantities for observedspiral galaxies. To study equal mass mergers of disc galaxies we adopt thegalaxy model G3 used by Cox et al. (2008), which is tuned tomatch SDSS observations of local spirals. The stellar mass ofthis galaxy was chosen to be M ∗ = 5 × M (cid:12) . The bulge-to-disc ratio of B/D = 0 .
22 is taken from de Jong (1996),resulting in a stellar disc mass of M disc = 4 . × M (cid:12) and a bulge mass of M b = 8 . × M (cid:12) . The gas fractionin the disc of 0 .
23 is motivated by the gas-to-stellar massscaling relation from Bell et al. (2003) and yields a massfor the cold gaseous disc of M cg = 1 . × M (cid:12) . The sizesof the stellar disc and bulge were chosen to agree with thestellar mass-size relation of Shen et al. (2003) resulting in r d = 2 .
85 kpc and r b = 0 .
62 kpc. The scale length of thegaseous disc was assumed to be a factor of χ = 3 larger thanthat of the stellar disc, such that r g = 8 .
55. The scale heightof the stellar disc was set to z = 0 . M dm = 1 . × M (cid:12) and a concentrationparameter of c = 6. In order to explore the effects of differentinitial progenitor gas fractions on starbursts and remnantmorphologies we construct additional galaxy models withmodified disc gas fractions of 0%, 40% and 80% (G3f0, G3f4and G3f8). In some simulations we extend this model to alsoinclude a hot gaseous halo (G3hf0, G3h, G3hf4, G3hf8) witha mass of M hg = 1 . × M (cid:12) within r vir and a hot gas spinfactor of α = 4. In addition, we construct a system with onlyhalf of the maximal hot gas mass, i.e. M hg = 5 . × M (cid:12) within r vir (G3hX). We set the gravitational softening lengthto (cid:15) = 100 pc ,
140 pc and 400 pc for stellar, gas and darkmatter particles, respectively.We follow Cox et al. (2008) and choose a nearly un-bound elliptical orbit with an eccentricity of (cid:15) orbit = 0 . r min = 13 . d start = 250 kpc . The resulting interactions arefast and nearly radial, consistent with merger orbits foundin cosmological N -body simulations (Benson 2005; Khochfar& Burkert 2006). We employ a prograde orbit; the spin axesof the first galaxy and the orbital plane are aligned whilethe second galaxy is inclined by θ = 30 ◦ with respect tothe orbital plane. We evolve all simulations for 5 Gyr, suchthat the remnant galaxies are relaxed and do not show anyobvious signs of a recent merger event. At this initial distance the two hot gaseous haloes are al-ready penetrating each other. This, in principle, could reduce thestrength of the shock at the boundaries of the haloes during themerger. We explicitly tested this by running a simulation with d start = 500 kpc and found no difference in the temperature anddensity profiles. This is not surprising because of the very lowdensity of the hot gas in the outer regions ( r >
125 kpc).c (cid:13) , 1–23 ot gaseous halo in major mergers Figure 2.
Projected surface density for the stellar component (upper two rows) and the gaseous component (lower two rows) for themerger without hot gaseous haloes and without stellar winds as viewed in the orbital plane. Each panel measures 200 kpc on a side andthe time in Gyr is displayed in the upper left corner of each panel. The right-hand panels in the second and bottom columns show a sideview of the final merger remnant. The images were created with splash (Price 2007).
We have simulated the fiducial major merger using fourdifferent sets of ingredients: one without stellar winds andwithout hot gaseous halo (G3G3), one with stellar windsand no gaseous halo (G3G3w), one without winds but witha gaseous halo (G3G3h) and finally one with winds and a gaseous halo (G3G3wh). The surface density in the orbitalplane is shown in Figures 2 (G3G3) and 3 (G3G3wh) forthe stellar component (upper panels) and the gaseous com-ponent (lower panels).The discs become tidally distorted as they reach firstpericentre ( t ∼ . c (cid:13) , 1–23 B. P. Moster et al.
Figure 3.
Similar to Figure 2, but for the simulation with stellar winds and hot gaseous haloes. form bar-like structures. Due to dynamical friction, orbitalenergy decreases while the spin of the haloes increase, whichresults in an almost radial orbit after the first encounter.During the second encounter ( t ∼ . ∼
150 Myr). The stellar remnant is more flattened c (cid:13) , 1–23 ot gaseous halo in major mergers Figure 4.
The rows from top to bottom show the total SFR, SFR normalized by the SFR of both isolated galaxies, the mass of densestar-forming gas available, the new stellar mass formed during the simulation, the burst mass, the gas fraction in the disc and thebulge-to-total ratio for the fiducial simulations G3G3, G3G3w, G3G3h and G3G3wh, from left- to right-hand side. The results for themergers are shown by the solid red lines and for the combined isolated galaxies by the dotted blue lines. All SFRs are given in M (cid:12) yr − and all masses in 10 M (cid:12) . than in the G3G3 run. In addition, after the merger there isstill a large reservoir of hot gas left in the halo which has re-ceived most of the orbital angular momentum. This massivehot halo can reform a much more prominent cold gaseousdisc after the merger which is thinner than in the G3G3run. In both simulations we find several tidal condensationswhich form from loosely bound tidal material and consist ofgas and new stars. In this and the following section we study the effects of stel-lar winds and the hot gaseous halo on the SFRs and theefficiency of the starburst. For this we compare the SFRsand the new stellar mass that forms during the simulationsbetween the four merger simulations and for the progeni-tor galaxies evolved in isolation. We investigate the effect ofincluding stellar winds but no hot halo, a hot halo but nowinds, and both winds and a hot halo.The star formation history for each of our four fiducial c (cid:13) , 1–23 B. P. Moster et al. mergers is shown in the first row of Figure 4. The simulationwithout stellar winds and no gaseous halo (G3G3) agreesvery well with the results of Cox et al. (2008): The SFR ofthe merger (solid line) is clearly enhanced compared to theisolated runs (dotted line). The maximum SFR during themerger ( ∼ M (cid:12) yr − ) is 30 times larger than the summedSFR of the isolated discs ( ∼ . M (cid:12) yr − ), as shown in thesecond row of Figure 4. The starburst starts shortly beforethe final coalescence and after the merger, the SFR quicklydrops ( ∼
500 Myr) to the value of two isolated discs. Wefind that in both cases the SFR after 3 Gyr ( < M (cid:12) yr − )is very low compared to the SFR at the beginning of thesimulation ( ∼ M (cid:12) yr − ). This is due to the limited amountof remaining cold gas, which has no source of refuelling. Weshow the amount of cold star forming gas (i.e. cold gas whichalso fulfills the density criterion ρ > ρ th ) in the third rowof Figure 4. The amount of dense star-forming gas stronglyincreases just before the burst, due to the torques driving gasinto the nucleus. This star-forming gas reservoir is largelyconsumed in the burst.The SFR in the simulation with stellar winds included(G3G3w) drops much more rapidly for the isolated galax-ies, as cold gas is expelled from the disc by the winds. After ∼ ∼ M (cid:12) yr − ) that is ∼
30 times larger thanthe summed SFR of the isolated discs ( ∼ . M (cid:12) yr − ). Withrespect to the simulation with no winds, the absolute valueof the SFR during the starburst is five times lower. Theduration of the starburst is also significantly increased withrespect to the windless case. This result was already demon-strated by Cox et al. (2006c), although using a different im-plementation of stellar feedback. The SFR in the merger isalways larger than in the isolated case and equals that of theisolated discs only at the end of the simulation. The amountof dense star-forming gas is lower than in the no wind caseduring the burst. After the burst, however, there is as muchstar-forming gas available as in the G3G3 run, leading to asimilar SFR. The reason for the longer duration of the star-burst is that during the starburst, the wind prevents some ofthe gas from reaching the dense nucleus of the galaxy. Thismaterial is then located in a halo around the galaxy andcan subsequently cool and accrete onto the disc, leading toa higher SFR.In the run without winds, but with a hot gaseous halo(G3G3h), the SFR for the isolated galaxy stays relativelyconstant during the simulation ( ∼ M (cid:12) yr − per galaxy),as the cold gas in the disc is constantly refuelled throughcooling from the halo. The starburst in the merger has anenhanced SFR of ∼ M (cid:12) yr − , which is a factor of fivetimes larger than the summed SFR of the isolated discs.However, after the burst the SFR drops to a value that islower with respect to the isolated case ( ∼ M (cid:12) yr − ). Thereason for this is the lower amount of star-forming gas avail-able after the burst. This means that the cold gas at thecentre of the galaxy which is compressed and quickly usedup during the burst, is not immediately replenished, indi-cating that there is a process that hinders the accreting gasfrom becoming dense and forming stars.Finally, the SFR for the isolated galaxies in the sim-ulation including winds and a gaseous halo (G3G3wh) isalso relatively constant ( ∼ M (cid:12) yr − per galaxy), but lower than in the G3G3h case due to the stellar winds which re-move dense gas from the centre. Although in the mergercase there is clearly an enhanced SFR, the peak is not asprominent and the burst is spread over a much larger timeinterval than in the other cases. With respect to the iso-lated case, the maximum SFR ( ∼ M (cid:12) yr − ) is enhancedby only a factor of three. After the burst, the SFR decreasesagain and reaches a value that is similar to that of the twoisolated systems. The reason for this is that the amount ofdense star-forming gas is the same in both runs.In summary we can point out two major effects: (1) Insimulations with stellar winds, the starburst is spread over amuch larger time interval than in the windless case. This isdue to the removal of cold gas from the dense star-formingregion in the centre. This material is ejected into a haloaround the galaxy and can then cool and accrete back tothe centre which results in an enhanced SFR. (2) In sim-ulations that include a hot gaseous halo the enhancementof the SFR in a merger with respect to isolated galaxies ismuch smaller than in systems that do not include a gaseoushalo. The reason is the continuous accretion of cold gas fromthe halo and the resulting higher SFR in the isolated discs.In simulations without this accretion, most of the gas is al-ready used up by the time of the merger and the rest is thenquickly converted into stars during the burst resulting in ahigh SFR. Isolated galaxies, however, have a very low SFRat the corresponding time, which results in a large differencebetween merging and isolated galaxies. If the gaseous halo istaken into account, the isolated galaxies also have a consid-erable SFR, such that the difference between the enhancedSFR during mergers and isolated systems is no longer aslarge. In order to quantify the merger-driven star formation it iscommon to focus on quantities based on the overall gas con-sumption rather than details of the time-dependent star for-mation history, since the latter depends on the adopted feed-back model. Various authors have made use of the ‘burstefficiency’ e which is defined as the fraction of cold gasconsumed during the merger minus the fraction of coldgas consumed by the constituent galaxies evolved in isola-tion (Cox et al. 2008; Somerville et al. 2008b). This def-inition is then useful to predict the additional mass dueto the starburst as a function of initial cold gas mass. Anequivalent definition is e = M burst /M cold , where the ‘burstmass’ M burst = M ∗ , new (merger) − M ∗ , new (isolation) is thestellar mass that formed due to the merger and M cold isthe mass of cold gas in the galaxy before the merger. Thetwo main quantities to determine the burst efficiency arethus burst mass and the cold gas mass. It is important atwhich time these quantities are defined: the cold gas masshas to be defined just before the final coalescence where thegas will lose angular momentum. The burst mass has to bedefined just after the merger, i.e. when the SFR of the merg-ing system is at the same level of the isolated galaxies again,otherwise it depends on the amount of time that has elapsedafter the merger. c (cid:13) , 1–23 ot gaseous halo in major mergers Figure 5.
The rows from top to bottom show the SFR, the SFR normalized by the SFR of both isolated galaxies, the new stellar massformed in the simulation, the burst mass, the cold gas mass, the gas fraction in the disc and the bulge-to-total ratio for the simulationsG3G3, G3G3h and G3G3wh from the left- to right-hand side. The various lines represent different initial cold gas fractions in the disc.All SFRs are given in M (cid:12) yr − and all masses in 10 M (cid:12) . In the fourth row of Figure 4 we show the new stellar massformed during the simulation for the isolated (dotted line)and the merger case (solid line). The difference between theisolated and the merger lines is shaded. In the fifth row weplot the burst mass and in the sixth row, we show the coldgas fraction in the disc f gas = M cold / ( M cold + M ∗ , disc ). The new stellar mass formed in the simulation G3G3 isenhanced during the starburst, such that the burst mass is M burst = 0 . × M (cid:12) . With a cold gas mass just beforethe burst of M cold = 1 . × M (cid:12) (for both galaxies) thisresults in a starburst efficiency of e = 0 .
68. Due to the stellarwinds, the starburst in the G3G3w case is less efficient: it hasa burst mass of M burst = 0 . × M (cid:12) and a cold gas mass c (cid:13) , 1–23 B. P. Moster et al. before the burst of M cold = 0 . × M (cid:12) which results in anefficiency of e = 0 .
45. This shows that any parametrizationof the starburst efficiency depends on the stellar wind modeland its parameters.In the simulation with a gaseous halo and no winds themass of the merging system also increases during the burstwith respect to the isolated systems. It has a burst massof M burst = 0 . × M (cid:12) and a cold gas mass before theburst of M cold = 1 . × M (cid:12) resulting in an efficiency of e = 0 .
51. The presence of the hot gaseous halo thus reducesthe efficiency of SF, although the absolute SFR is larger inthis case. In addition, as the SFR of the merger remnantis lower than that of the isolated systems after the burst,the summed stellar mass of the isolated galaxies increasesfaster, such that both simulations have the same stellar massat t ∼ . ∼ t ∼ . t ∼ . ∼
70% higher than in theisolated run. This leads to a cooling time which is ∼ M burst = 0 . × M (cid:12) and with a cold gas mass before theburst of M cold = 1 . × M (cid:12) the efficiency is e = 0 . Up to now we have studied mergers with just one fixed initialgas fraction in the disc (23%). In the following section westudy how our results depend on the initial progenitor gasfraction. It has been shown by Hopkins et al. (2009a) thatthe dominant process that removes angular momentum fromthe gas during a merger is the lag between the stellar barand the gaseous bar. In very gas rich systems, the stellarmass density is low and the stellar bar is weak or absent. Inthis case, as shown by Robertson et al. (2006a) and Hop-kins et al. (2009a), even major mergers may produce littleenhancement in star formation activity and may result in adisc-dominated remnant. Thus, based on merger simulationswith no winds and no hot halo, we expect the star forma-tion efficiency in the burst and the remnant morphology toscale with the initial gas fraction in the progenitors. For thisstudy we use our fiducial models, and keep the total mass ofthe disc fixed but modify the gas content in the disc to 0%,23%, 40% and 80%. All other parameters remain unchangedfrom the fiducial values. c (cid:13) , 1–23 ot gaseous halo in major mergers Table 3.
Burst efficiency for different gas fractions.Run f g , init a f g , burst b M gas c M burst d ee G3G3 0.23 0.16 1.253 0.849 0.678G3G3f4 0.40 0.25 2.119 1.365 0.644G3G3f8 0.80 0.41 3.809 2.448 0.643G3G3hf0 0.00 0.14 1.371 0.553 0.403G3G3h 0.23 0.18 1.920 0.968 0.504G3G3hf4 0.40 0.24 2.640 1.218 0.461G3G3hf8 0.80 0.38 3.580 2.220 0.620G3G3whf0 0.00 0.11 1.048 0.400 0.382G3G3wh 0.23 0.11 1.446 0.636 0.440G3G3whf4 0.40 0.11 1.287 0.672 0.522G3G3whf8 0.80 0.26 1.405 0.224 0.159 a gas fraction in the initial disc b gas fraction in the disc just before the starburst c cold gas mass just before the starburst in 10 M (cid:12) d burst mass just after the starburst in 10 M (cid:12) e starburst efficiency The results are plotted in Figure 5 for the simulationsG3G3, G3G3h and G3G3wh from left- to right-hand side.From top to bottom the SFR, the SFR normalized by theSFR of both isolated galaxies, the new stellar mass formedin the simulation the burst mass, the cold gas mass, the gasfraction in the disc and the bulge-to-total ratio are shown asa function of time. In order to compute the burst efficiency,we use the cold gas mass and gas fraction just before thestarburst, and the burst mass just after it. The resultingquantities are given in Table 3.For the case without winds and gaseous halo (G3G3)we find that the starburst efficiency decreases slightly withincreasing gas fraction. This means that if more gas is avail-able in the disc, it is harder to convert all of the gas intostars during the burst. If a hot gaseous halo is included,however, the starburst becomes more efficient with increas-ing gas fraction. In order to explain this it is important tostate that the efficiency mainly depends on the amount ofcold gas available for the starburst. This material is of coursenot the total mass of cold gas in the simulation, but onlythe cold gas in the nucleus, where the burst occurs. Thusthe efficiency is a strong function of the spatial distributionof the cold gas.In the G3G3 series, the fraction of the cold gas at thecentre ( < f gas . Both the gaseoushalo and the winds reduce the burst efficiency. When thegaseous halo is included, the efficiency decreases with de-creasing gas fraction, as the initial dense disc is replaced byaccreted gas from the halo which is spatially much more ex-tended. When stellar winds are also included, the efficiencyfor systems with a high initial gas fraction in decreased,since the winds prevent the formation of a massive stellardisc before the merger, which is needed to form a stellar barthat can drag the gas to the centre of the burst. Having investigated how the SFR changes during themerger, we now focus on the properties of the merger rem-nant at the end of the simulation. To this end, we decomposethe stellar particles into a spheroidal and a disc componentusing the following method. For every particle, we computethe angular momentum along the spin axis and divide thisby the angular momentum the particle would have on a cir- c (cid:13)000
Burst efficiency for different gas fractions.Run f g , init a f g , burst b M gas c M burst d ee G3G3 0.23 0.16 1.253 0.849 0.678G3G3f4 0.40 0.25 2.119 1.365 0.644G3G3f8 0.80 0.41 3.809 2.448 0.643G3G3hf0 0.00 0.14 1.371 0.553 0.403G3G3h 0.23 0.18 1.920 0.968 0.504G3G3hf4 0.40 0.24 2.640 1.218 0.461G3G3hf8 0.80 0.38 3.580 2.220 0.620G3G3whf0 0.00 0.11 1.048 0.400 0.382G3G3wh 0.23 0.11 1.446 0.636 0.440G3G3whf4 0.40 0.11 1.287 0.672 0.522G3G3whf8 0.80 0.26 1.405 0.224 0.159 a gas fraction in the initial disc b gas fraction in the disc just before the starburst c cold gas mass just before the starburst in 10 M (cid:12) d burst mass just after the starburst in 10 M (cid:12) e starburst efficiency The results are plotted in Figure 5 for the simulationsG3G3, G3G3h and G3G3wh from left- to right-hand side.From top to bottom the SFR, the SFR normalized by theSFR of both isolated galaxies, the new stellar mass formedin the simulation the burst mass, the cold gas mass, the gasfraction in the disc and the bulge-to-total ratio are shown asa function of time. In order to compute the burst efficiency,we use the cold gas mass and gas fraction just before thestarburst, and the burst mass just after it. The resultingquantities are given in Table 3.For the case without winds and gaseous halo (G3G3)we find that the starburst efficiency decreases slightly withincreasing gas fraction. This means that if more gas is avail-able in the disc, it is harder to convert all of the gas intostars during the burst. If a hot gaseous halo is included,however, the starburst becomes more efficient with increas-ing gas fraction. In order to explain this it is important tostate that the efficiency mainly depends on the amount ofcold gas available for the starburst. This material is of coursenot the total mass of cold gas in the simulation, but onlythe cold gas in the nucleus, where the burst occurs. Thusthe efficiency is a strong function of the spatial distributionof the cold gas.In the G3G3 series, the fraction of the cold gas at thecentre ( < f gas . Both the gaseoushalo and the winds reduce the burst efficiency. When thegaseous halo is included, the efficiency decreases with de-creasing gas fraction, as the initial dense disc is replaced byaccreted gas from the halo which is spatially much more ex-tended. When stellar winds are also included, the efficiencyfor systems with a high initial gas fraction in decreased,since the winds prevent the formation of a massive stellardisc before the merger, which is needed to form a stellar barthat can drag the gas to the centre of the burst. Having investigated how the SFR changes during themerger, we now focus on the properties of the merger rem-nant at the end of the simulation. To this end, we decomposethe stellar particles into a spheroidal and a disc componentusing the following method. For every particle, we computethe angular momentum along the spin axis and divide thisby the angular momentum the particle would have on a cir- c (cid:13)000 , 1–23 B. P. Moster et al.
Figure 6.
Upper panels : Surface density profiles averaged over 100 projections for all, old and new stars from left- to right-hand side.
Lower left panel : Surface density profiles of the cold gas as seen face-on.
Lower middle panel : 3d density profiles of the hot gaseoushaloes.
Lower right panel : 3d density profiles of the dark matter halo. The various lines show the different simulations: G3G3 (no winds,no gaseous halo), G3G3w (with winds, no gaseous halo), G3G3h (no winds, with gaseous halo) and G3G3wh (with winds, with gaseoushalo). The dotted vertical lines indicate three times the softening length and hence the resolution limit. cular orbit at the same radius. The spherical component isthen distributed around a value of zero, while the disc com-ponent is centred at unity, such that the two componentscan be separated easily (Abadi et al. 2003). In the lowerpanels of Figure 4, we plot the resulting bulge-to-total ratio
B/T = M bulge /M ∗ for the four fiducial runs. In all simula-tions the disc component just after the starburst is almostcompletely destroyed. In the runs without the gaseous halo,the B/T after the burst is ∼ . B/T after the burst is also ∼ .
9, but then decreases to ∼ . ∼ .
85 for G3G3wh. The reason forthis is that due to the accretion of gas from the halo, a muchlarger cold gaseous disc can form after the burst which leadsto a much larger stellar disc. Because of the stellar winds inG3G3wh, cold gas is subsequently removed from the disc,leading to a lower mass stellar disc at the end of the simula-tions and thus to a larger
B/T compared to G3G3h. Still, allfour remnant systems are still very much bulge dominated.We also find that the bulge-to-total ratio decreases withincreasing initial gas fraction. However, even for f g , init = 0 . B/T = 0 .
85, while for the lower f g , init =0 .
23 case the final bulge-to-total ratio is only slightly higher:
B/T = 0 .
9. This is mainly due to the low SFR after theburst, so that the mass in the new stellar disc that formsafter the merger is very low ( M ∗ = 5 × M (cid:12) for the 80percent gas case) as can be seen in the third row of Figure5. The final bulge-to-total ratio in the simulations with ahot gaseous halo is very similar in all runs, independentof the initial cold gas fraction and whether stellar winds are enabled. The reason for this is that the SFR after themerger does not depend on the initial cold gas mass anddistribution, but only on the accretion rate after the merger.As the latter only depends on the mass, temperature andprofile of the hot gaseous component, the SFRs are verysimilar for all runs, as can be seen in the first row of Figure5. As a result the mass in the new stellar disc that forms afterthe merger is very similar in all simulations which yields verysimilar bulge-to-total ratios.In order to study how the stellar mass is distributedwithin the merger remnants, we compute the azimuthallyaveraged surface density profiles for old, new and all stars,where old stars are the stellar particles which were presentbefore the burst (i.e. particles created for the initial condi-tions and particles formed through SF) and new stars arethose stellar particles that formed through SF during and af-ter the burst. The upper panels of Figure 6 show the resultsfor the four fiducial runs. The profiles for all stars at scalesbeyond ∼ r / profile. The slope is identical for all runsand only the normalization of G3G3h is higher than thatof the other runs, as the stellar mass before the burst wasalready much larger. This can also be concluded from theprofiles of the old stars: as the mass of the old stellar com-ponent is very similar for all runs, except for G3G3h, theirfinal profiles have the same normalization. The contributionfrom new stars at these scales is very small for all runs. Thesurface density profiles in the outer parts are in agreementwith profiles obtained by dissipationless simulations (Naab c (cid:13) , 1–23 ot gaseous halo in major mergers & Trujillo 2006), which shows that the gas physics plays anegligible role far from the centre.At small scales ( R ∼ < ∼ r / pro-file and show neither a cusp nor a core. Our simulations arein agreement with previous studies (Kormendy et al. 2009;Hopkins et al. 2008, 2009b,c), who find that including a largefraction of cold gas in merger simulations leads to a steeperslope in the centre (‘extra light’) and to a lower S´ersic indexthat is distinct from the main body. However, in contrastto simulations that do not include a hot gaseous halo wefind that large amounts of cold gas are not required in theprogenitor discs, as gas can be accreted from the halo afterthe merger resulting in the formation of a dense stellar core.In the lower left panel of Figure 6 we show the face-on density profiles of the cold gas component. In the G3G3run, the profile of the gas disc is very flat up to 15 kpc buthas a very dense central concentration ( R < −
50 kpc, the densityin the G3G3wh run is a little higher, as gas that is heatedand ejected from the disc by the winds is added to the hotgas reservoir and accumulated at these scales. For the runswithout an initial gaseous halo, we see that a hot halo formsdue to the merger. In the G3G3 run this hot halo formsfrom gas that is shock-heated during the merger and hasexpanded into the halo (Cox et al. 2006a). In the G3G3wrun, the density of this halo is enhanced by the materialejected by the wind. The dark matter profile is nearly indis-tinguishable for all four runs: an NFW-like profile modifiedby the baryonic contraction, with a slightly higher centraldensity for systems with a gaseous halo.
Having determined the mass distribution of the merger rem-nants, we now study their kinematic properties, i.e. howmuch the remnants are supported by rotation. The ellipticalshape of a rotating galaxy can be understood as a result offlattening induced by rotation. The elliptical structure of anon-rotating galaxy, however, must be supported by some-thing other than rotation, most likely by velocity anisotropy. This trend can be visualized by plotting the rotation veloc-ity v maj divided by the central velocity dispersion σ againstthe ellipticity (cid:15) . In this anisotropy diagram v maj /σ is a mea-sure of the rotational support and (cid:15) indicates the deviationfrom a circle.An analytic relation between the intrinsic ellipticity (cid:15) intr and ( v maj /σ ) edge for edge-on projections has been derivedby Binney (2005). For a given anisotropy of the system δ one can plot a distinct line in the (cid:15) – v maj /σ plane. For afixed amount of rotation, the intrinsic ellipticity is lower inisotropic systems and larger in anisotropic systems. For anobserved galaxy at a given inclination, the observed elliptic-ity and ( v maj /σ ) obs can be computed from the intrinsic ellip-ticity and ( v maj /σ ) edge (see Binney & Tremaine 1987, § (cid:15) = 0), no rotation can be observed, whileedge-on ( (cid:15) = (cid:15) intr ) the observed rotation velocity is maximal.In order to compute the three quantities (cid:15) , v maj and σ ,for our simulated remnants, we follow Cox et al. (2006b) andrefer to this work for details. Here, we give a brief outlineof the procedure. First, the stellar particles are projectedonto a plane as if observed from a random viewing angle.Then we determine the isodensity contour that encloses halfof the stellar mass and fit an ellipse to it. The ellipticityis computed as (cid:15) = 1 − b/a , where a is semi-major and b the semi-minor axis of the ellipse. A slit is then placedalong the major axis with a length of 3 a and a width of a/ v maj is defined as the average absolutevalue of the maximum and minimum mean velocity alongthe slit and σ as the average dispersion of the bins within a/
2. Figure 7 shows the resulting anisotropy diagram for ourfiducial merger remnants. The left panel compares the fourruns and shows v maj /σ vs. (cid:15) for 1000 random projections foreach remnant. In each panel we plot the location of edge-on oblate galaxies with different anisotropy δ as given bythe analytic recipe (solid lines). For each simulated remnantwe compute the intrinsic ellipticity and the corresponding( v maj /σ ) edge indicated by the black symbol. The anisotropyof the remnant can be obtained by finding the line on whichthe symbol lies. The dashed lines indicate projections withdifferent inclinations for the analytic galaxy model and tracethe projections of the simulations very well.The merger simulation with no winds and no gaseoushalo leads to a remnant which is only slowly rotating, witha maximum rotation velocity of ∼
50 km s − and a maxi-mum v maj /σ of ∼ .
25. This means that the G3G3 remnantis mostly supported by velocity dispersion and not by rota-tion. The intrinsic ellipticity and the anisotropy parameterare relatively large ( (cid:15) intr = 0 .
49 and δ = 0 . (cid:15) and the observed rotationvelocity of the disc are maximal. When viewed face-on, onecannot observe any rotation of the disc. For the simulationwith winds, the stellar disc is much smaller, leading to aneven smaller disc contribution to the rotation. This resultsin lower values for v maj /σ and an anisotropy diagram whichis similar to that of a remnant in a dissipationless simula- c (cid:13) , 1–23 B. P. Moster et al.
Figure 7.
Anisotropy diagram: v max /σ vs. ellipticity, where v max is the maximum rotation velocity measured in a slit along the majoraxis and σ is the velocity dispersion averaged within half of the half-mass radius. The ellipticity is measured at the half mass isophote. Left panel:
Comparison between the four fiducial simulations, where every point corresponds to one projection. The solid lines are thelocations expected for edge-on oblate galaxies with different anisotropy δ = 0 , . , . . . , .
5. The black symbols indicate the intrinsicellipticities. The dashed lines give the projections for different inclinations.
Right panel:
Comparison between the simulation with windsand a gaseous halo and data from observed elliptical galaxies. The contours indicate the 10%, 50%, 70% and 90% probability of findinga merger remnant in the enclosed area. The solid line plots edge-on models with δ = 0. tion. The intrinsic ellipticity and the anisotropy parameterare even larger ( (cid:15) intr = 0 .
53 and δ = 0 .
45) than in the sim-ulation without winds.When a gaseous halo is included, v maj /σ increasesstrongly with increasing (cid:15) , which can be explained by themore massive stellar disc that forms after the merger. Whenviewed edge-on, the stellar disc dominates within the slit inwhich the velocity is measured and thus leads to a highermean rotation velocity. The remnant has an intrinsic ellip-ticity of (cid:15) intr = 0 .
56 and corresponds to a galaxy modelwith an anisotropy parameter of δ = 0 .
3. This indicatesthat the elliptical shape of the remnant at the half-massisophote ( R ∼ v maj /σ , however, the remnant isstill partly supported by rotation. It has an intrinsic ellip-ticity of (cid:15) intr = 0 .
49 and an anisotropy parameter of δ = 0 . v maj /σ − (cid:15) space that the simulated rem- nant can cover. First, by decreasing (increasing) the windefficiency, we can achieve larger (smaller) values of v maj /σ for a given (cid:15) , up to the limit of no winds (G3G3h), thusreproducing the observed remnants with a large rotationalsupport. Second, by lowering the initial mass of the gaseoushalo, we can achieve smaller values of v maj /σ for a given (cid:15) and can thus reproduce the observed remnants with a smallrotational support. Note that by employing the universalbaryonic fraction in the initial conditions we have used anupper limit for the mass of the gaseous halo. Through feed-back, it is possible to decrease the mass of the halo beforethe merger. See section 3.4 for a discussion. Finally, we study how the shape of the isophotes changewhen a hot gaseous halo is included in the merger simula-tions. To this end, we measure the deviations of the isoden-sity contour of a projection to a fitted ellipse. The residu-als are expanded in a Fourier series and the Fourier coeffi-cient a is computed. Positive values of a indicate discyisophotes, while negative values indicate boxy isophotes.The results of this analysis are shown in Figure 8, whichplots the ellipticity against the shape parameter a (nor-malized by the semi-major axis and multiplied by a factorof 100) for our fiducial simulations with 1000 projectionseach. The left panel compares the four runs. The simula-tions with no winds and no gaseous halo can appear discyor boxy, depending on the viewing angle, with a tendencytowards boxy isophotes. If winds are included, the isophotescan still be discy, however, they are more boxy on average.When a gaseous halo is included, the shape of the isophotesis more discy, especially at high ellipticities. If both winds c (cid:13) , 1–23 ot gaseous halo in major mergers Figure 8.
Ellipticity (cid:15) vs. characteristic shape parameter a , both measured at the half mass isophote. Left panels:
Comparison betweenthe four fiducial simulations, where every point corresponds to one projection.
Right panel:
Comparison between the simulation withwinds and a gaseous halo and data from observed elliptical galaxies. The contours indicate the 10%, 50%, 70% and 90% probability offinding a merger remnant in the enclosed area. and a gaseous halo are present the isophotal projections aremostly discy. However, at low ellipticities ( (cid:15) < .
3) the prob-ability for boxy and discy isophotes is equal.As a result, we find that including a gaseous halo re-sults in more cold gas at the centre, leading to more discyisophotes. This is in agreement with results by Springel(2000), Cox et al. (2006b) and Naab et al. (2006), whofind that mergers with gas increase the fraction of discyisophotes. Naab et al. (2006) argue that the reason for thelack of boxy projections in simulations with gas is the differ-ent behaviour of minor-axis tube orbits (which are the dom-inant family around the half-mass radius) in axisymmetricand triaxial potentials. Dissipational mergers lead to moreaxisymmetric potentials, and in those, minor-axis tubes lookless boxy and more discy in all projections. Additionally, thefraction of box orbits and boxlets, which can support a boxyshape, is reduced.The right panel of Figure 8 compares the remnant of theG3G3wh run to data from observational samples (Benderet al. 1988; Rothberg & Joseph 2006; Cappellari et al. 2007).The contours give the 10%, 50%, 70% and 90% probabilityof finding a G3G3wh merger remnant in the enclosed area.The simulated merger remnant agrees very well with theisophotal shapes of observed ellipiticals. At low ellipticities,there are both discy and boxy projections, with an equalprobability. At higher ellipticities ( (cid:15) > .
4) the chances tofind boxy isophotes are very small. These trends are similarto those seen in the observational data.
In the previous sections we have employed model galaxieswith a maximal hot gas halo, i.e. we chose the hot gas masssuch that the baryonic fraction within r vir was the universalvalue. This was done in order to demonstrate the maximumeffect this hot gaseous halo can have on the SFR, the star- burst efficiency and the remnant morphology, in comparisonto the case in which the hot gas is neglected. Of course, bothcases are the relative extremes, as feedback can decrease themass of hot gas in the halo before the merger. Thereforewe run a merger simulation in which we used only half ofthe ‘full’ halo mass (G3G3whX) as an intermediate case andcompare it to the simulations with the extreme hot gas cases(G3G3w and G3G3wh) in order to check whether the resultsof the intermediate case fall between the extreme cases. Thisadditional simulation is evolved for 8 Gyr with enabled stel-lar winds and using the same orbital parameters as in theprevious runs.On the left-hand-side of Figure 9, we show the SFRsduring the merger normalized by the SFRs of the respec-tive isolated galaxies and the new stellar mass formed dur-ing the simulations. The left, middle and right panels showthe runs without a hot gaseous halo, with the ‘full’ hot gasmass and with half of the ‘full’ hot gas mass, respectively.The G3G3whX simulations has a maximum SFR that isenhanced by a factor of ∼ ∼
30 and ∼
3, respectively. The new stellar mass that has formed by t = 5 Gyr is 1 . × M (cid:12) for the G3G3whX runs, whilein the runs G3G3w and G3G3wh the stellar mass formed is0 . × M (cid:12) and 3 . × M (cid:12) . This shows that the starformation in the run with half of the ‘full’ hot gas mass isan intermediate case between the two extremes.With a burst mass of M burst = 0 . × M (cid:12) and acold gas mass before the burst of M cold = 0 . × M (cid:12) thestarburst efficiency for the G3G3whX run is e = 0 .
44. Thisvalue is very close to the values obtained for the G3G3wand G3G3wh runs, e = 0 .
45 and e = 0 .
44, respectively.This means that in the case with stellar winds, the starburstefficiency does not depend strongly on the hot gaseous halomass. c (cid:13)000
44, respectively.This means that in the case with stellar winds, the starburstefficiency does not depend strongly on the hot gaseous halomass. c (cid:13)000 , 1–23 B. P. Moster et al.
Figure 9.
Left panels : The two rows show the SFR normalized by the SFR of both isolated galaxies and the new stellar mass formed inthe simulation for the simulations G3G3w, G3G3wh and G3G3whX, from left- to right-hand side. The results for the mergers are shownwith solid lines and for the combined isolated galaxies by the dotted lines. All masses are in 10 M (cid:12) . Right panels : v max /σ vs. ellipticity(anisotropy diagrams, cf. Figure 7). The four panels show a comparison between the simulations G3G3w, G3G3wh and G3G3whX at t = 5 Gyr and G3G3whX at t = 8 Gyr. On the right-hand side of Figure 9, we compare the kine-matic properties of the merger remnants, plotting anisotropydiagrams for the runs G3G3w, G3G3wh and G3G3whX at t = 5 Gyr and for G3G3whX at t = 8 Gyr. While the sim-ulation including the ‘full’ hot gas mass forms a remnantthat is supported by rotation, the simulation with half ofthe ‘full’ hot gas mass is only slowly rotating after 5 Gyr.However, when evolved to 8 Gyr, the rotational support ofthe system has increased, although not as much as in thecase with the ‘full’ hot gas mass. The reason for this is thatin the G3G3whX run, the lower hot gas mass leads to slowercooling and accretion and thus to a lower SFR. Thereforeit takes longer to form a prominent stellar disc after themerger, and it is this disc that is responsible for the rotation.As a result we see that the model with half of the ‘full’ hotgas mass can lead to a rotationally supported remnant aswell, although it takes longer and the amount of rotation isless then for the model that employs the universal baryonicfraction within r vir .Haloes in the Universe have baryonic fractions betweenthe extreme cases (universal fraction and no hot gas at all).The actual value will depend on the merger history of a givensystem, the amount of feedback during its evolution and itsenvironment. We conclude that our results for the extremecases thus give upper and lower limits for actual galaxiesand the results for the simulation with half of the ‘full’ hotgas mass are one possible example within these limits. We investigated the role of a cooling gaseous halo in mergersimulations using the parallel TreeSPH-code
GADGET-2 .To do this we have extended the initial conditions to includea hot gaseous halo (in addition to a dark matter halo, a stel- lar bulge and a disc consisting of stars and cold gas). Weadopted the observationally motivated β -profile to describethe hot gas and required the halo to be in hydrostatic equi-librium. Furthermore the gaseous halo is rotating around thespin axis of the disc. We have fixed the initial angular mo-mentum of the hot gas by requiring that the specific angularmomentum of the gas halo is a multiple α of the specific an-gular momentum of the dark matter halo and treated α asa free parameter.Cosmological simulations without cooling, star forma-tion, or feedback show that the spin parameter of hot gaswithin dark matter haloes is the same as that of the darkmatter (van den Bosch et al. 2002), which would correspondto α = 1. However, it has been shown that if this hot gascollapses to form a disc while conserving its angular momen-tum, the disc profiles do not match observations — there istoo much low angular momentum material (van den Bosch2001; Bullock et al. 2001). These results are supported bythe results of our simulations: if we allow hot gas with α = 1to cool and form a disc in an isolated halo, we do not repro-duce the observed size vs. stellar mass relation for discs (ourdiscs are too small). It has been suggested that winds couldpreferentially remove low angular momentum material, re-sulting in a higher average specific angular momentum forthe gas relative to the dark matter ( α > α for our hot haloes.This was done by modelling a typical MW-like galaxyat z = 1 and letting it evolve in isolation up to z = 0 us-ing different values of α . We employed two observationalconstraints, stellar mass and disc scale length, in order to c (cid:13) , 1–23 ot gaseous halo in major mergers determine the correct α . The results for the control sim-ulation without a hot halo disagreed drastically with theobservations, which supports the importance of the gaseoushalo. Simulations with a low value of α showed both an in-crease of stellar mass which was too large and scale lengthsthat were too small compared to observations. Large valuesof α led to overly large discs and stellar masses that weretoo low. Only a value of α ∼ . erg s − (Wang et al. 2003; Strickland et al. 2004;Wang 2005; T¨ullmann et al. 2006; Li et al. 2007; Sun et al.2009; Owen & Warwick 2009). These observational limitshave been compared to the X-ray luminosities found in cos-mological hydrodynamic simulations by Rasmussen et al.(2009). They found no tension between simulations and ob-servations (for a simulated MW-like galaxy they found 0 . ∼ erg s − ). In a recent pa-per Crain et al. (2010) showed that disc galaxies in sim-ulations develop gaseous haloes with an associated X-rayluminosity that is in good agreement with the observationalconstraints. They argue that this lower X-ray luminosityis due to the density profile of the hot gas not followingthat of the dark matter and being much less centrally con-centrated as a result of energy injection from SNae. Simi-larly, we can compute X-ray luminosities for our assumedhot gas haloes. To do this we integrate the emissivity overthe volume of the halo in the 0 . L X = 2 , × erg s − , respectively. We thus con-clude that even our maximal gaseous haloes are not in con-flict with X-ray observations.We have used MW-like galaxy models including agaseous halo in a series of binary merger simulations. Wehave run all mergers both with and without galactic windsusing the ‘constant wind’ model of Springel & Hernquist(2003), where the mass-loss rate carried by the winds is pro-portional to the SFR and the wind speed is constant. How-ever, this model has some deficiencies as the wind speedfor low mass galaxies is the same as for high mass galaxies resulting in too much heating for low mass systems. Morerecent models have been developed that attempt to over-come these problems and present a more realistic match toobserved quantities, e.g. momentum driven winds (Oppen-heimer & Dav´e 2006), in which the mass loading factor andwind velocity are functions of the internal galaxy velocitydispersion. However, since our study focussed on equal massgalaxies, and our galaxies do not change their internal veloc-ity dispersions significantly over the course of the simulation,we doubt that introducing such scalings would significantlyeffect our results.We have studied the impact of a gaseous halo and stellarwinds on the SFR using four ‘fiducial’ runs: without gaseoushalo and without winds (G3G3), without gaseous halo butwith winds (G3G3w), without winds but with a gaseous halo(G3G3h) and with both winds and gaseous halo (G3G3wh).We found that in simulations without a gaseous halo, themaximum SFR during a starburst is ∼
30 times larger thanthat of the constituent galaxies evolved in isolation. When agaseous halo is included, this enhancement is much smaller(factor of ∼ e = 0 .
68 while for G3G3w itis only e = 0 .
45, showing that the efficiency depends on thewind model and its parameters. The presence of a gaseoushalo reduces the efficiency in G3G3h to e = 0 .
51. In addi-tion, the SFR after the burst is lower than the SFR of theconstituent galaxies evolved in isolation, resulting in a rem-nant stellar mass that is lower than that of the two isolatedgalaxies. This occurs for two reasons: first, the specific angu-lar momentum of the hot gas after the merger is higher thanthat of the isolated systems, due to the acquisition of orbitalangular momentum. This leads to a higher centrifugal bar-rier and thus to a lower accretion rate and SFR. Second,due to shocks that occur during the merger, the tempera-ture of the gaseous halo in the merger case is higher thanin the isolated case, leading to a longer cooling time anda lower SFR. The fact that two non-merging galaxies canhave a larger stellar mass than if they had merged poses achallenge for semi-analytic models, which generally assumethat a merger always leads to enhanced star formation.We have also studied how the starburst efficiency de-pends on the initial cold gas fraction in the progenitors andfound that without a gaseous halo, it decreases with increas-ing gas fraction. Higher gas fractions imply a lower stellarmass, which suppresses the formation of a stellar bar thatcan remove angular momentum from the gas Hopkins et al.(2009a). If a hot gaseous halo is present, however, the star-burst efficiency increases with increasing gas fraction, as the c (cid:13)000
51. In addi-tion, the SFR after the burst is lower than the SFR of theconstituent galaxies evolved in isolation, resulting in a rem-nant stellar mass that is lower than that of the two isolatedgalaxies. This occurs for two reasons: first, the specific angu-lar momentum of the hot gas after the merger is higher thanthat of the isolated systems, due to the acquisition of orbitalangular momentum. This leads to a higher centrifugal bar-rier and thus to a lower accretion rate and SFR. Second,due to shocks that occur during the merger, the tempera-ture of the gaseous halo in the merger case is higher thanin the isolated case, leading to a longer cooling time anda lower SFR. The fact that two non-merging galaxies canhave a larger stellar mass than if they had merged poses achallenge for semi-analytic models, which generally assumethat a merger always leads to enhanced star formation.We have also studied how the starburst efficiency de-pends on the initial cold gas fraction in the progenitors andfound that without a gaseous halo, it decreases with increas-ing gas fraction. Higher gas fractions imply a lower stellarmass, which suppresses the formation of a stellar bar thatcan remove angular momentum from the gas Hopkins et al.(2009a). If a hot gaseous halo is present, however, the star-burst efficiency increases with increasing gas fraction, as the c (cid:13)000 , 1–23 B. P. Moster et al. initial dense gas disc is replaced by accreting gas from thehalo which is spatially much more extended. Systems withhigher initial gas fractions retain more of their initial densegas at the time of the merger which then leads to a moreefficient burst. If winds are also included, the formation ofmassive stellar discs in very gas rich galaxies is preventedsuch that the starburst efficiency is again decreased.Our simulations are closely related to prior studies onthe efficiency of starbursts in binary galaxy mergers, andit is important to compare the results of our simulationswithout gaseous haloes or winds to those obtained by Coxet al. (2008) and Hopkins et al. (2009a), which also neglectedthese effects. Using the same progenitor galaxies (G3) buta different star formation model, Cox et al. (2008) find astarburst efficiency for G3G3 of e = 0 .
5. However, in thedefinition of e , they have used the gas fraction at the startof the simulation rather than just before the burst. As thegas fraction decreases until the time of the burst, the effi-ciency would increase to e = 0 .
67 for our definition. This isin excellent agreement with our value of e = 0 .
68. Hopkinset al. (2009a) used a large suite of simulations to developan analytic model for the burst efficiency. For our orbit,mass ratio and gas fraction this model predicts an efficiencyof e = 0 .
74. However, this small difference ( ∼ < q = 0 .
25; see Springelet al. 2005 for details). As a result, more gas can lose angu-lar momentum and fall to the centre during the starburst,increasing the starburst efficiency.We have also addressed the question of how the gaseoushalo affects the morphology of merger remnants. Analysingthe systems ∼ B/T ∼ r / profile at small scales, sys-tems with a hot halo match the observed profile. The reasonis the new stellar disc which leads to a higher surface densityat the centre.A kinematic analysis of the merger remnants showedthat if the progenitor galaxies contain only ∼
20% cold gasand no gaseous halo, our chosen orbit leads to a remnantwhich is slowly rotating and only supported by velocity dis-persion. When a gaseous halo is included, however, the ro-tational support of the remnant strongly increases. This canbe also explained by the presence of a massive stellar discin the centre that forms after the merger. The rotation ofthis disc contributes to the total rotational support in amass-weighted average and leads to a larger potential at thecentre, which causes ‘old’ stars to fall towards the centreand to increase their rotational velocity due to conservationof angular momentum. We have further studied the impactof the gaseous halo on the isophotal shape of the remnantsand found that including a gaseous halo leads to remnantsthat are more discy on average. We found that both thekinematic structure and the isophotal shape of the remnantswith a gaseous halo agree very well with observed ellipticals. Studying the effects of cold gas fraction in progenitorgalaxies on the kinematic structure of major merger rem-nants, Cox et al. (2006b) conclude that in order to formrealistic low-luminosity elliptical galaxies in merger simula-tions, the progenitor galaxies must have high gas fractionsof ∼ r / stellarsurface brightness profile at small scales and the formationof fast rotators which dominate the local early-type popu-lation (e.g. Emsellem et al. 2011). However, this leads tothe opposite problem for massive ellipticals: if a hot gaseoushalo (expected in all progenitor galaxies) always leads to arotationally supported system, how can slow rotators form?Traditionally they have been expected to form only in discmergers with mass ratios of 1:1 or 1:2 (see Jesseit et al. 2009;Bois et al. 2010, for a detailed discussion). This is relatedto the problem of how elliptical galaxies can have low SFRsand red colours as observed, if a gaseous halo leads to thecontinuous accretion of cold gas and thus to ongoing SF. Incontrast to observed elliptical galaxies the remnants in oursimulations including the gaseous halo have relatively highSFRs and young stellar populations. This general problemhas been discussed by Naab & Ostriker (2009) who concludethat elliptical galaxies can only form through a merger oftypical disc galaxies if they have merged more than 3 − c (cid:13) , 1–23 ot gaseous halo in major mergers the remnant will have neither have ‘extra light’ in the centrenor rotation. In this case, fast rotators could still form fromdisc mergers with high mass ratios (e.g. Barnes 1998; Naab& Burkert 2003). Another possibility is that AGN feedbackis delayed, so that the merger remnant can form a disc beforethe cold gas is removed.Moreover, we have not included cosmological accretionfrom outside the initial virial radius of the halo, which willbe very significant at high redshift ( z > ACKNOWLEDGEMENTS
We thank Hans-Walter Rix, Glenn van de Ven, Arjen vander Wel, Volker Springel, Tom Abel, and Simon White forenlightening discussions and useful comments on this work.We also thank Volker Springel for providing the code used asa basis to create the initial conditions. The numerical sim-ulations used in this work were performed on the PIA andTHEO clusters of the Max-Planck-Institut f¨ur Astronomieand on the PanStarrs2 clusters at the Rechenzentrum inGarching. BPM thanks the Space Telescope Science Insti-tute for hospitality and financial support for his visit. BPMalso acknowledges a travel grant from the German ResearchFoundation (DFG) within the framework of the excellenceinitiative through the Heidelberg Graduate School of Fun-damental Physics.
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