C. Scannapieco et al- Feedback and metal enrichment in cosmological smoothed particle hydrodynamics...

8/3/2019 C. Scannapieco et al- Feedback and metal enrichment in cosmological smoothed particle hydrodynamics simulations - I. A model for chemical enrichment

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Feedback and metal enrichment in cosmological smoothedparticle hydrodynamics simulations - I. A model forchemical enrichment

C. Scannapieco, 1, 2 P.B. Tissera, 1,2 S.D.M. White, 3 and V. Springel 31 Instituto de Astronoma y Fsica del Espacio, Casilla de Correos 67, Suc. 28, 1428, Buenos Aires, Argentina 2 Consejo Nacional de Investigaciones Cientcas y Tecnicas, CONICET, Argentina 3 Max-Planck Institute for Astrophysics, Karl-Schwarzchild Str. 1, D85748, Garching, Germany

11 July 2006

ABSTRACTWe discuss a model for treating chemical enrichment by Type II and Type Ia super-nova (SNII and SNIa) explosions in simulations of cosmological structure formation.Our model includes metal-dependent radiative cooling and star formation in densecollapsed gas clumps. Metals are returned into the diffuse interstellar medium by starparticles using a local smoothed particle hydrodynamics (SPH) smoothing kernel. Avariety of chemical abundance patterns in enriched gas arise in our treatment owingto the different yields and lifetimes of SNII and SNIa progenitor stars. In the case of SNII chemical production, we adopt metal-dependent yields. Because of the sensitivedependence of cooling rates on metallicity, enrichment of galactic haloes with metalscan in principle signicantly alter subsequent gas infall and the build up of the stellarcomponents. Indeed, in simulations of isolated galaxies we nd that a consistent treat-ment of metal-dependent cooling produces 25 per cent more stars outside the centralregion than simulations with a primordial cooling function. In the highly-enriched cen-tral regions, the evolution of baryons is however not affected by metal cooling, becausehere the gas is always dense enough to cool. A similar situation is found in cosmolog-ical simulations because we include no strong feedback processes which could spreadmetals over large distances and mix them into unenriched diffuse gas. We demonstratethis explicitly with test simulations which adopt suprasolar cooling functions leadingto large changes both in the stellar mass and in the metal distributions. We also ndthat the impact of metallicity on the star formation histories of galaxies may dependon their particular evolutionary history. Our results hence emphasise the importanceof feedback processes for interpreting the cosmic metal enrichment.

Key words: methods: numerical - galaxies: abundances - galaxies: formation - galax-ies: evolution - cosmology: theory.

1 INTRODUCTION

Over the last decades, our knowledge of the chemical prop-erties of the Universe and, in particular, of galaxies, hasimproved dramatically. Observations of the Local Universe(e.g. Garnett & Shields 1987; Skillman, Kennicutt & Hodge1989; Brodie & Huchra 1991; Zaritsky, Kennicutt & Huchra1994; Mushotzky et al. 1996; Ettori et al. 2002; Tremonti etal. 2004; Lamareille et al. 2004) as well as at intermediateand high redshifts (e.g. Prochaska & Wolfe 2002; Adelberger

E-mail: [email protected] (CS); [email protected](PBT); [email protected] (SDMW); [email protected] (VS)

et al. 2003; Kobulnicky et al. 2003; Lilly, Carollo & Stockton2003; Shapley et al. 2004) have resulted in a quite detailed

picture of the chemical history of the stellar populations andof the interstellar and intergalactic media. It is an importantchallenge for the theory of galaxy formation to explain theseobservational results in the context of the current cosmolog-ical paradigm. Numerical simulations are an important toolto make specic predictions for galaxy formation theoriesand to confront them with observations, because they canaccurately track the growth of structure in the dark matterand baryonic components. It is hence natural to ask whatsuch simulations predict for the chemical properties of theuniverse.

Currently, hydrodynamic cosmological simulations in-

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2 Scannapieco et al.

cluding radiative cooling and star formation, at best,coarsely reproduce the observed properties of galaxies. Theyfail when scrutinised in detail. Among the most prominentproblems are catastrophic angular momentum loss (e.g.Navarro & Benz 1991; Navarro & White 1994) and the dif-culty in nding a consistent modelling of supernova (SN)feedback (e.g. Navarro & White 1993; Metzler & Evrard1994; Yepes et al. 1997; Marri & White 2003; Springel &

Hernquist 2003, hereafter SH03). The rst issue mainly af-fects galaxy morphology, size and kinematics, while the lat-ter primarily inuences the efficiency of star formation. Bothare the subject of intense research. Reproducing the chemi-cal properties of observed galaxies in detail may be viewedas an intertwined third problem.

Regarding the angular momentum problem, recent sim-ulations have shown some promising advances. Domnguez-Tenreiro, Tissera & S aiz (1998) found that the formation of compact stellar bulges can stabilize the discs and therebyprevent the angular momentum loss during violent minormerger events, such that disc systems that resemble observedgalaxies are obtained. Abadi et al. (2003) have also demon-strated the importance of a dense, slowly rotating spheroidal

component, and pointed out its relevance for comparing sim-ulated and observed galaxies consistently. More recently,Robertson et al. (2004) were able to produce large, sta-ble disc systems in their cosmological simulations which arecomparable in size to spiral galaxies. In their approach, theyintroduced a subresolution model for star formation andfeedback which pressurizes the star-forming gas and sta-bilizes discs against fragmentation. We note that all thesestudies agree on the need for a self-consistent treatment of SN feedback as a crucial mechanism to regulate star forma-tion and to reproduce discs similar to observational coun-terparts.

SN explosions are thought to play a fundamental role inthe evolution of galaxies since they are considered the mostefficient and ubiquitous mechanism for the ejection of metalsand energy into the interstellar medium (ISM). Both chem-ical and energy feedback can affect the condensation of gasand consequently the evolution of galactic systems. On onehand, the presence of metals in the ISM affects gas coolingtimes because the radiative cooling rate depends sensitivelyon metallicity (Sutherland & Dopita 1993, hereafter SD93).On the other hand, the release of energy is crucial for reg-ulating star formation through the heating and disruptionof cold gas clouds, and for producing outows which cantransport enriched material into the intergalactic medium(e.g. Lehnert & Heckman 1996; Dahlem, Weaver & Heckman1998; Frye, Broadhurst & Bentez 2002; Rupke, Veilleux &Sanders 2002; Martin 2004). As suggested by observationsand theory, the largest outows (e.g. Larson 1974; White &Rees 1978; Dekel & Silk 1986; White & Frenk 1991) shouldbe able to develop in small systems because of their shal-lower potential wells. Because in hierarchical galaxy forma-tion scenarios large systems are formed by the aggregationof smaller systems, energy feedback from SNe is then ex-pected to have important effects for nearly all systems inthe different stages of galaxy formation.

Modelling of chemical feedback has been addressed al-ready in numerous studies, mostly with the aim to repro-duce the chemical properties of certain types of galaxies, orof clusters of galaxies (e.g. Larson 1976; Tinsley & Larson

1979; Burkert & Hensler 1988; White & Frenk 1991; Burkert,Truran & Hensler 1992; Ferrini et al. 1992; Theis, Burkert& Hensler 1992; Steinmetz & Muller 1994; Kauffmann 1996;Chiappini, Matteucci & Gratton 1997; Kauffmann & Char-lot 1998; Boisser & Prantzos 2000; Valdarnini 2003). As rstshowed by Mosconi et al. (2001), in order to properly modelthe process of metal enrichment in galaxy formation it is nec-essary to consider the full cosmological growth of structure

in which mergers and interactions have important effects onthe star formation process and the dynamical evolution of galaxies (see also Kawata & Gibson 2003; Tornatore et al.2004; Okamoto et al. 2005).

Perhaps the most fundamental motivation for the rele-vance of metal enrichment for galaxy formation is based onthe fact that the cooling rate of baryons depends on metal-licity (SD93). Radiative cooling in turn allows the conden-sation of gas into dense and cold clouds, which form thereservoir of material available for the formation of stars. Aschemical enrichment is a result of star formation, a chem-ical feedback cycle emerges, in which metals can in prin-ciple signicantly accelerate the transformation of baryons

into stars. In hierarchical scenarios these processes dependsignicantly on the chemical prescription adopted (Kaellan-der & Hultman 1998; Kay et al. 2000). These affect galaxyproperties such as the luminosity function (White & Frenk1991). For these reasons, a detailed analysis of the effectsof metal-dependent cooling is clearly important for galaxyformation studies. Substantial numerical challenges in sim-ulations of galaxy formation come from the large dynamicrange required, and from the multiphase character of theISM. Gas in very different physical states coexists in theISM, but the standard formulation of smoothed particle hy-drodynamics (SPH, e.g. Gingold & Monaghan 1977; Lucy1977) is not well suited to deal with this situation. A numberof attempts have been made to solve this problem, rangingfrom an ad-hoc decoupling of phases (e.g. Pearce et al. 1999,2001; Marri & White 2003) to simple analytic sub-resolutionmodels (SH03) that work with an effective equation of state.

Our new model for SN feedback in SPH cosmologicalsimulations has been divided into two stages: chemical andenergy feedback. In this work we address the descriptionof the chemical feedback, which is based on the previousmodel of Mosconi et al. (2001). In a forthcoming paper, wewill present the second part of this work: the implementa-tion of energy feedback in the framework of a multiphasescheme for the ISM, which extends the approach of Marri& White (2003). While a treatment of chemical enrichmentwithout energy feedback is an incomplete picture, we thinkthe complexity of the problem merits a step-wise discussionof our model such that the primary physical effects can bebetter understood.

This paper is organized as follows. In Section 2, we sum-marize the numerical implementation of the chemical model,and in Section 3 we analyse the dependence of the resultson numerical resolution and input parameters, using sim-ulations of isolated galaxies. We then study in Section 4the properties of galaxies formed in cosmological simula-tions and examine how they depend on the chemical model.Finally, in Section 5 we give our conclusions.

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Chemical feedback in SPH 3

2 NUMERICAL IMPLEMENTATION

Our new model for the production and ejection of chem-ical elements by SNe is based in part on the approach inMosconi et al. (2001). We have implemented our schemein the TreePM/SPH code GADGET-2 , an improved versionof the public code GADGET (Springel, Yoshida & White2001) which manifestly conserves energy and entropy whereappropriate (Springel & Hernquist 2002). Note that we donot use the multiphase treatment and the feedback modeldeveloped by SH03 for this code, but we do include theirtreatment of ultraviolet (UV) background. Also, we use adifferent parameterisation for star formation, as describedin detail below.

Chemical elements are synthesized in stellar interiorsand ejected into the ISM by SN explosions. In order to modelthe production and distribution of metals in the context of the simulations, there are three ingredients we have to con-sider: the SN rate (i.e. number of exploding stars per timeunit), the chemical yields (i.e. chemical material ejected inexplosions) and the typical lifetimes of stars, which deter-mine the characteristic time of the metal release.

In our model, we include a separate treatment of TypeII and Type Ia SNe (SNII and SNIa). These two types of SNe originate from different stellar populations, and havedifferent rates, yields and typical time-scales. We use dif-ferent yields for SNII and SNIa which, in the case of SNII,are metal-dependent. Hence, we will treat SNII and SNIaseparately, owing to the need to model their different char-acteristics. For example, SNII produce most of the chemi-cal elements, except for iron, which is mainly produced bySNIa. Another difference between these two types of SN isthat SNII are the endpoint of the evolution of massive starswith short lifetimes, in contrast to SNIa, which result fromthe evolution of binary systems with lifetimes of 1 Gyr.

We assume that initially gas particles have primordial

abundances: XH = 0 .76 and Y He = 0 .24, and we considerthe enrichment by the following elements, assuming produc-tion only by SNII and SNIa: H, 4 He, 12 C, 16 O, 24 Mg, 28 Si,56 Fe, 14 N, 20 Ne, 32 S, 40 Ca and 62 Zn. Note that we do notconsider nucleosynthesis by intermediate-mass stars. Conse-quently, we will concentrate our analysis on elements such asO or Fe where restricting to SN production may be a goodapproximation. In the rest of this Section, we describe themost important aspects of the chemical model, namely thestar formation and cooling prescriptions, and our scheme forthe production and ejection of metals.

2.1 Star formation

We assume that gas particles are eligible for star forma-tion if they are denser than a critical value ( > =7.0 10 26 g cm 3 , where denotes gas density) and liein a convergent ow (div v < 0)1 . For these particles, weassume a star formation rate (SFR) per unit volume equalto

= c dyn

, (1)

1 See Okamoto et al. (2005) for a different approach.

where c is a star formation efficiency (we adopt c = 0 .1) and dyn = 1 / 4G is the dynamical time of the particle. Webase the creation of new stellar particles on the stochasticapproach of SH03 (see also Lia, Portinari & Carraro 2002).To this end, each gas particle eligible for star formation ina given time-step is assigned a probability p of forming astar particle given by

p =mm 1 exp

c t dyn , (2)

where t is the integration time-step of the code, m is themass of the gas particle, and m is dened as m = m 0 /N gwith m 0 being the original mass of gas particles at the begin-ning of the simulation and N g a parameter which determinesthe number of generations of stars formed from a given gasparticle (we assume N g = 2). If a random number drawnfrom a uniform distribution in the unit interval is smallerthan p , we form a new stellar particle of mass m and re-duce the mass of the gas particle accordingly. Once the gasparticle mass has become smaller than m 0 /N g , we insteadturn it into a star particle. Newly born stars are assumedto have the same element abundances as the gas mass from

which they form.The main advantage of this stochastic approach is thatall particles are either purely stellar or purely gas, whichavoids the use of hybrid particles with both gaseous andstellar components. The latter would articially force thestellar component to evolve dissipately like the gas. Notethat, as a consequence of the star formation scheme, thenumber of baryonic particles in the simulation does not re-main constant. Unlike SH03, we also exchange the massesof heavy elements explicitly between gas and star particles.As a result, the mass spectrum of stellar and gas particles isslightly washed out around otherwise sharp discrete values.

2.2 Chemical production and distribution

Our numerical implementation of the enrichment model hasthree main components: SNII element production, SNIa el-ement production and metal distribution.

SNII element production

In order to estimate the SNII rate we use a Salpeter InitialMass Function (IMF) with lower and upper mass cut-offs of 0.1 and 40 M , respectively, and assume that stars moremassive than 8M end their lives as SNII. For the chem-ical production, we adopt the yields of Woosley & Weaver(1995). These are metal-dependent yields and vary differ-ently for different elements. We use half of the iron yield

of WW95, as it is often adopted (e.g. Timmes, Woosley &Weaver 1995). For the sake of simplicity, in most of our sim-ulations we have assumed that SNII explode (i.e. produceand eject the chemical elements) within an integration time-step of the code (which is typically 106 yr), because SNIIoriginate in massive stars which have very short character-istic lifetimes of the order of 10 7 yr. However, we have alsoanalysed the effect of relaxing this instantaneous recyclingapproximation (IRA) for SNII (see Section 3.2).

SNIa element production

As a progenitor model, we adopt the W7 model of Thiele-

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mann, Nomoto & Hashimoto (1993), which assumes thatSNIa explosions originate from CO white dwarf systems inwhich mass is transferred from the secondary to the primarystar until the Chandrasekhar mass is exceeded and an explo-sion is triggered. It is generally assumed that the lifetime of such a binary system is in the range SNIa =[0 .1, 1 ] Gyr, de-pending on the age of the secondary star (Greggio 1996). Inour model, the material produced by a SNIa event is ejected

when a time SNIa after the formation of the exploding starhas elapsed. We choose this time randomly within a givenrange (in most of our experiments we assume SNIa = [0 .1, 1]Gyr). In order to estimate the number of SNIa, we adopt anobservationally motivated range for the relative ratio of SNIIand SNIa rates (e.g. van den Bergh 1991). We use the chemi-cal yields of Thieleman et al. (1993) for the metal productionitself.

Metal distribution

We distribute chemical elements ejected in SN explo-sions within the gaseous neighbours of exploding star par-ticles, using the usual SPH kernel interpolation technique(Mosconi et al. 2001). Each neighbouring gas particle re-ceives a fraction of the ejected metals according to its kernelweight. For this purpose, gas particle neighbours of stellarparticles are identied whenever metal distribution has totake place, and smoothing lengths for these stars are cal-culated by setting a desired number of gas neighbours thatshould be enclosed in the smoothing length (we have as-sumed the same criterium used for the smoothing lengths of gas particles). This is particularly important for the enrich-ment by SNIa because of the time delay between the forma-tion of the stars and the ejection of metals. Note that aftera star particle is created, it is only subject to gravitationalforces, unlike the gas particles, which continue to be subject to hydrodynamical forces as well. Consequently, as the

system evolves, star particles can release metals associatedwith SNIa explosions in a different environment from wherethey were born. This, together with the different lifetimesand yields of SNII explosions, can then produce non-trivialvariations in abundance ratios.

2.3 Gas cooling

It is well known that the cooling rate of thin astrophysicalplasmas depends sensitively on metallicity, in such a waythat at a given density, the cooling rate is higher for a highermetallicity. In Fig. 1 we show the cooling function computedby SD93 from primordial (i.e. no heavy elements) to supra-solar abundance ([Fe/H]=+0 .5). As one can see from thisgure, the cooling function can show very large variationswith the metal abundance of the gas, depending on the tem-perature range considered. For example, the usual estimatesof the cooling time ( cool ) for a gas particle at the criticaldensity ( ) and at a temperature of T = 4 104 K yieldthat cool is 50 times larger for primordial gas than for amildly suprasolar medium ([Fe/H]= 0 .5), 18 times largerthan that of a solar abundance one, and still twice as largeas the corresponding time for gas with [Fe/H]= 1.5. Thetemperature range of [10 5 106 ] K shows the largest differ-ences, right in the temperature range relevant to the abun-dant population of dwarf galaxies.

0.5

0.0

-0.5

-1.0

-1.5

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Figure 1. Cooling rates for gas of different metallicities, as givenby the [Fe/H] abundance, from suprasolar ([Fe/H]=0.5) to pri-mordial. The plot is based on data adapted from SD93.

Including effects owing to metal line cooling is there-fore crucial for realistic modelling of galaxy formation be-cause it affects directly the relation between cooling timeand dynamical time of forming galaxies. We therefore in-clude a treatment of radiative cooling consistent with themetal content of the gas component produced by the en-richment model. We use the tables computed by SD93 forthe metal-dependent cooling functions, and interpolate fromthem for other metallicities as needed. For particles with ironabundance larger than 0 .5, we adopt the suprasolar coolingrate (i.e. that for [Fe/H] > +0 .5). In cosmological simula-tions, we also include a redshift-dependent photo-heatingUV background, with an intensity evolution that follows themodel of Haardt & Madau (1996).

3 RESULTS FOR ISOLATED GALAXYMODELS

As rst tests of our model, we consider simulations of iso-lated haloes set up to form disc galaxies at their centre. Thisallows us to examine the dependence of the results on resolu-tion and on different parameters of the chemical enrichmentmodel. The initial conditions consist of a static dark mat-ter potential corresponding to a Navarro, Frenk & White(1996, 1997) prole of concentration c = 20, and a baryonicgas phase initially in hydrostatic equilibrium in this poten-tial. Our typical system has virial mass M 200 = 10 12 h 1 M (h = 0 .7), 10 per cent of which is in the form of baryons(M bar = 10 11 h 1 M ). The initial radius of the system isr 200 = 160 h 1 kpc and the gas has an initial angular mo-mentum characterized by a spin parameter = 0 .1. Wehave followed the evolution of this system for 1 .5 dyn , where dyn = 7 Gyr is the dynamical time at r 200 .

These idealized initial conditions yield a simple model

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for disc formation, which is an ideal test bench for the per-formance and validity of the code, and the dependence of theresults on the free parameters. We stress however that thesemodels are not meant to provide a realistic scenario for thewhole galaxy formation process. Results for full cosmologicalsimulations will be discussed in Section 4, where we analysethe properties of galactic objects formed in cold dark mat-ter (CDM) models with virial masses of M vir 1012 h 1 M ,comparing them also to the results of the idealized tests dis-cussed here.

3.1 Numerical resolution

Both the star formation process and the distribution of met-als can be affected by numerical resolution. Particularly im-portant for our model is the fact that the smoothing lengthof the particles (i.e. the radius which encloses 32 gaseousneighbours) determines the region where the newly releasedchemical elements are injected. Mosconi et al. (2001) foundthat chemical abundances could be oversmoothed in low res-olution simulations because metals are distributed over acomparatively large volume and, consequently, are more ef-ciently mixed with surrounding gas. On the other hand,high numerical resolution could also produce spurious re-sults if the metal mixing mechanism becomes too inefficient.Provided other physical mixing mechanisms are not operat-ing, the simulation results might show an articially largedispersion in gas metallicities.

In order to test the effects of numerical resolution, wecarried out simulations of the isolated disc system describedabove using three different initial numbers of gas particles:2500 (R1), 10000 (R2) and 40000 (R3), with mass resolu-tions of 4 107 , 107 and 0 .25 107 h 1 M for R1, R2 andR3, respectively. We have set the gravitational softening to0.4 h 1 kpc. In these three runs we use metal-dependentcooling functions for the gas particles according to the tablesby SD93. In Table 1 we summarize the main characteristicsof these simulations.

In Fig. 2, we show the evolution of the SFRs obtainedfor R1 (dotted line), R2 (solid line) and R3 (dashed line).Most of the stellar mass (92, 88 and 86 per cent in R1,R2 and R3, respectively) is formed at times t < 3 Gyr (43per cent of the dynamical time) in the three runs. Only atlater times, we nd that the lowest resolution test simulation(R1) yields a signicantly lower result for the SFR, indicat-ing that the number of gas particles has dropped so much bythe conversion into stars that discrete effects become appre-ciable. However, the nal stellar mass fractions (i.e. stellarmass formed divided by the total baryonic mass) are verysimilar in R1, R2 and R3.

This can be also appreciated from Fig. 3, where we showthe mass-weighted metallicity proles for R1 (dotted line),R2 (solid line) and R3 (dashed line), in the inner regionand for the stellar (left column) and gaseous (right column)components and for three different times, t = 0 .13 Gyr (up-per panels), t = 2 .5 Gyr (middle panels) and t = 7 Gyr(lower panels). We can see that the stellar abundance pro-les are insensitive to resolution. The mean iron abundancediffers by less than 0 .03 dex between the different simula-tions. Recall that the stellar metallicity of newly formingstars is given by the local gas metallicity. This is directlyvisible at the beginning of the simulation where the gaseous

Figure 2. Evolution of the SFR for our test simulations of iso-lated disc galaxies, as a function of different numerical resolution.R1 (dotted line) has 2500 particles, R2 (solid line) 10000 particles,and R3 (dashed line) 40000 particles.

and stellar components show a similar level of enrichmentin star-forming regions (upper panels in Fig. 3), while atlater stages of the evolution (middle and lower panels) thisconstraint becomes hidden as a result of the superposition

of stars of different ages.However, as can be seen from the right panels of Fig. 3,the mass-weighted metallicity proles for the gas compo-nents show stronger differences with resolution than theirstellar counterparts. At the beginning of the evolution, theproles of the three test simulations are still very similar,although the enriched gas is more spread in the highest-resolution test. However, the gas proles differ more at latertimes when factors such as variations in the consumptiontime of the gas and differences in the spatial distribution of stars begin to affect the radial distribution of metals. At theend of the simulations (lower right panel), the mean gaseousiron abundance for R1 is signicantly lower than those forthe other two simulations. This decrease in the metallicity

is produced by the infall of less enriched gas. This gas is notbecoming dense enough to trigger star formation activity atthe level of R2 and R3, and the infall tends to dilute themetal content in the ISM. Hence, the fact that the gas com-ponent in R1 shows a lower iron abundance is driven by itspoorer gas resolution. Note that as a result of the consump-tion of most of the gas, the nal number of gas particles in R1is very low ( 60 in the inner 30 kpc) and, as a consequence,the distribution of metals in the gas component is stronglyaffected by numerical noise. On the other hand, the resultsfor the tests with 10000 and 40000 particles converge quitewell both in their stellar and gaseous chemical properties.Note that the rms scatter of particles within each radial binis similar for the different tests indicating that, on average,

the metal mixing is not signicantly affected by resolutionif we consider at least an initial number of particles of 2500or more.

3.2 Dependence on assumed supernovacharacteristics

In this Section we analyse the dependence of our results onimportant input parameters of the chemical model, namelythe IRA for SNII, and the rate and lifetimes associated withSNIa. For this purpose we run three additional test simula-tions. In runs P1 and P2, we change the SNIa parameters

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Figure 4. SFR for the experiments of the idealized disc galaxyrun with different SN parameters: R2 (solid line, standard test),P1 (dotted line, higher SNIa rate), P2 (dashed line, IRA for SNIa)and P3 (dashed-dotted line, relaxing the IRA for SNII).

Figure 5. AMR for the stellar component in the tests of the ideal-ized disc galaxy run with different SN parameters: R2 (solid line,standard test), P1 (dotted line, higher SNIa rate), P2 (dashedline, IRA for SNIa), and P3 (dashed-dotted line, relaxing the IRAfor SNII). The error bars correspond to the rms scatter of [Fe/H]around the mean.

metallicity material ([Fe/H] > -0.5) which shows in P1 alower -enhancement compared to that in R2, as expected.

We have also tested the sensitivity of the results on thelifetime of binary systems associated with SNIa. The impor-tance of including SNIa has been previously pointed out byGreggio & Renzini (1983) and Mosconi et al. (2001), amongothers. Motivated by these previous results, we carried out asimulation P2 where we assumed an IRA for SNIa explosions(see Table 1). The main effect of instantaneously releasingthe chemical production of SNIa can be appreciated fromFig. 6, which shows the mean -enhancement of the simu-lated stellar population. These abundance ratios exhibit abehaviour which is in open disagreement with observations(Pagel 1997). Note, however, that these observational resultscorrespond to solar neighbour stars, while the simulated onesinclude information from the whole stellar component.

Finally, in order to analyse the effects of the IRA forSNII, we tested a more detailed calculation of the lifetimeof massive stars. To this end, we convolved the IMF with thelifetime of massive stars at different intervals of metallicity(Raiteri, Villata & Navarro 1996). In this way, we obtained arange of mean lifetimes varying with stellar metallicity from6.3 106 yr for Z = 5 10 4 Z to 1.6 107 yr for Z = Z ,where Z denotes mean stellar metallicity and Z is the solarmetallicity. We run a test of our idealized initial condition

Figure 6. [O/Fe] abundance as a function of [Fe/H] for the stellarcomponent in experiments of the idealized disc galaxy run withdifferent SN parameters: R2 (solid line, standard test), P1 (dottedline, higher SNIa rate), P2 (dashed line, IRA for SNIa), and P3(dashed-dotted line, relaxing the IRA for SNII). The error barscorrespond to the rms scatter of [O/Fe] around the mean.

Figure 7. SFR for the idealized disc test run with suprasolar (SC,dashed line), primordial (PC, dotted line) and metal-dependent(R2, solid line) cooling functions.

with the same chemical parameters used in R2 but includingthese metallicity-dependent lifetimes for SNII (P3, see Ta-ble 1). We found no signicant differences between the twotests, either in the SFR or in the iron abundance, as canbe seen from Figs. 4 and 5. The similar behaviour of thesetwo runs is also found in other chemical properties of thesystems, such as the relation shown in Fig. 6. Recall that adrawback of a detailed description of chemical enrichmentcan be its high computational cost, so an important prac-tical goal is to keep the model sufficiently simple to allowits use in large-scale cosmological simulations. While in thiscontext the IRA for SNIa in general cannot reproduce cer-tain observed trends, for SNII it appears to be a simple andsufficiently accurate simplication, at least for these simpletests that do not include energy feedback.

3.3 Effects of metal-dependent cooling

Finally, we performed two more runs of our idealized iso-lated galaxy in order to highlight effects owing to a metal-dependent cooling function. In these ducial tests, we as-sumed a constant metallicity, either primordial (PC) orsuprasolar (SC, [Fe/H]= +0 .5) for the cooling function. Theparameters for star formation and SN rates were the same

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Figure 8. Face-on (left-hand panels) and edge-on (right-hand panels) surface metallicity distribution for the stellar component of theisolated disc galaxy tests run with primordial (PC, upper row), metal-dependent (R2, middle row) and suprasolar (SC, lower row) coolingrate functions. The metallicity scale is also shown.

as in the standard simulation R2 discussed earlier (see Ta-ble 1).

In Fig. 7, we compare the evolution of the SFR for R2(solid line), PC (dotted line) and SC (dashed line). In theearly stages ( t 4 Gyr), the test run with suprasolar abun-

dance cooling function (SC) results in a SFR higher by upto a factor of 3 compared with the simulation R2 with self-consistent cooling function, while the run PC with primor-dial cooling lies lower by up to a factor 1 .5. After the rst4 Gyr, the SFR in the SC run decreases signicantly, indi-

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Figure 11. Oxygen proles for the stellar (left panel) and gaseous (right panel) components in experiments of the idealized disc galaxyrun with different cooling functions: R2 (solid line, metal-dependent cooling), PC (dotted line, cooling function for primordial abundance)and SC (dashed line, cooling function for suprasolar abundance). The error bars correspond to the rms scatter of 12 +log (O/H) aroundthe mean.

M for dark matter and gas particles, respectively. We haveadopted a maximum gravitational softening of 5 h 1 kpcfor dark matter, gas and star particles. We used a metal-dependent, self-consistent cooling function for the gas com-ponent. Table 2 summarizes the main characteristics of thisrun.

In order to test the dependence of our results on mixingprocesses and metal-dependent cooling, we have also carriedout two additional runs with the same parameters, but aconstant metallicity for the cooling function. As a limitingcase of a very enriched medium, in simulation C3 we usedsuprasolar abundance (see Table 2), while in simulation C1

we took primordial cooling in order to model a situationwhere mixing processes are completely absent. These twocases should hence bracket reality.

In our cosmological simulations, we identied galac-tic objects at z = 0 as virialized structures using adensity-contrast criterion with overdensity / 178

0 .60

(White, Efstathiou & Frenk 1993). In our analysis we focuson six haloes with masses similar to the idealized disc testR2 ( 1012 M ). They are resolved with a similar or highernumber of particles ( N 10000, see Table 3). Note that asgas/star particles do not have the same mass, the numberof particles in these components does not, however, trace

the mass. The main properties of these objects are given inTable 4.

In Fig. 12, we compare the star formation histories forthe selected galactic objects in C1 (dotted line), C2 (solidline) and C3 (dashed line), as a function of look-back time,i.e. (z) = 1 [1 + z] 3 / 2 . Note that the global features of the SFRs are preserved in the three runs, although the de-tailed levels of activity are different. In general, the SFRs of the galactic objects formed in C3 are systematically higherthan the corresponding ones in C2, as expected. Note thatbecause galactic objects formed in C3 have higher SFRs thanthose in C2, their nal stellar masses are much larger thanthe corresponding ones in C2 (see Table 4). If we comparethe SFRs obtained for C1 and C2, although the differencesare small, the SFRs in C1 are systematically lower thanthose in C2. It is noteworthy that the impact of metallic-ity on the star formation history seems to depend on theparticular evolutionary histories of the systems, as can beappreciated from Fig. 12.

In Fig. 13, we show the mean stellar mass fraction f (r )as a function of radius, estimated from the six selected galac-tic objects in C1 (dotted line), C2 (solid line) and C3 (dashedline). As in Section 3.3, the distribution function for eachgalactic object was calculated by summing up the stellarmass in bins of radius normalized to the total baryonic mass

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Table 2. Chemical model parameters for the cosmological tests: initial number of gas and dark matter particles N gas and N DM , typicallifetimes associated with SNII ( SNII ) and SNIa ( SNIa ) in Gyr, rate of SNIa and cooling functions adopted.

Test N gas = N DM SNII SNIa Rate SNIa Cooling Function

C1 512000 0 0 .1 5 0.0015 PrimordialC2 512000 0 0 .1 5 0.0015 Metal-dependentC3 512000 0 0 .1 5 0.0015 suprasolar

Figure 12. SFR for the six selected galactic objects from the cosmological simulations run with primordial (dotted line), metal-dependent(solid line) and suprasolar (dashed lines) cooling functions.

Table 3. Number of dark matter ( N DM ), gas ( N gas ), and stars ( N star ) within the virial radius for the six galactic objects (GLOs)identied in the cosmological tests run with primordial (C1), metal-dependent (C2) and suprasolar (C3) cooling functions.

C1 C2 C3

GLO N DM N gas N star N DM N gas N star N DM N gas N star

1 8591 2149 12838 8552 1881 13382 8739 1486 193682 5454 1337 7573 5482 1270 8013 5684 1431 123133 21816 8947 24218 21790 6930 27105 22275 2442 434304 5738 1858 7785 5656 1740 8240 5840 1569 119565 8738 2724 12385 8688 2451 13362 8934 1736 204656 4980 1506 7868 4966 1476 8166 5150 1512 10482

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Table 4. Virial mass ( M vir ), stellar mass ( M star , both in 10 10 h 1 M ) and optical radius ( r opt in h 1 kpc) for the six galactic objects(GLOs) identied in the cosmological tests run with primordial (C1), metal-dependent (C2) and suprasolar (C3) cooling functions.

C1 C2 C3

GLO M vir M star r opt M vir M star r opt M vir M star r opt

1 139.28 13.74 15.05 138.81 14.35 14.20 146.70 20.72 15.702 87.79 8.11 15.38 88.52 8.58 14.15 95.98 13.16 14.99

3 352.44 25.91 13.31 351.07 29.06 12.51 365.50 46.56 12.404 93.04 8.32 14.30 92.09 8.79 13.47 98.26 12.80 12.735 142.10 13.26 12.06 141.79 14.30 11.78 151.09 21.89 10.906 81.63 8.40 12.38 81.70 8.72 12.58 86.71 11.20 14.71

within the corresponding bin. As we found for the tests of theisolated galaxies, there are clear differences between the re-sults for the three runs. Although in the inner 10 h 1 kpc thesimulations yield similar stellar fractions, within 40 h 1 kpc,galactic objects in C2 have transformed a larger fraction of the gas into stars compared with those in C3, while galacticobjects in C1 show the opposite behaviour. At larger radii,the mean distribution function of stellar mass for the galac-

tic objects in C3 is signicantly larger than its counterpartfor C2, indicating that as a result of the higher cooling effi-ciency, the gas in C3 has been transformed into stars furtheraway from the centre of mass of the objects. Conversely, theprimordial run shows fewer stars in the outer region. Notethat efficient energy feedback is needed to prevent excessivestar formation in the outer regions, as it can be observedfrom Fig. 13.

In order to assess how these differences affect the chem-ical properties of the formed galactic objects, we analysedthe metal indicator 12 + log(O / H) for the gaseous and stel-lar components in C1, C2 and C3. Consistent with our re-sults for the idealized disc tests, we found that the metallic-ity of the stellar components is not sensitive to the coolingfunction adopted, in contrast to the gaseous components.In Fig. 14 we compare the gaseous oxygen proles for thegalaxy samples in C1 (dotted lines), C2 (solid lines) and C3(dashed lines). Although there is a trend for systems in C3 tohave a higher level of enrichment and atter mass-weightedabundance proles compared to their counterparts in C2 andC1, how much metals affect these relations seems to dependon the particular history of evolution of each galaxy, as canbe inferred from Figs. 12 and 14.

Finally, for a comparison with observational results, weperformed linear regression ts to the gaseous oxygen pro-les of our simulated galactic objects within the optical ra-dius. By denition, the optical radius encloses 83 per cent of the baryonic stellar mass within the virial radius. In Fig. 15,we show the zero-point of these ts as a function of the cor-responding slopes for the galactic objects in C1 (triangles),C2 (diamonds) and C3 (asterisks). We also include obser-vational results from Zaritsky et al. (1994, lled circles).In general, the properties of the simulated galactic objectsagree reasonably well with the range obtained in observa-tional studies. However, the simulated galactic objects iden-tied in C2 tend to have steeper proles and higher zero-points compared with observations. Conversely, galactic objects in C3 exhibit atter proles. A similar behaviour wasalso found in our tests for the isolated disc galaxies runwith primordial (PC, squared triangle), metal-dependent

Figure 13. Mean stellar mass fraction as a function of radius forthe six selected objects in the cosmological simulations run withprimordial (C1, dotted line), metal-dependent (C2, solid line) andsuprasolar (C3, dashed line) cooling functions as a function of radius.

(R2, squared diamond) and suprasolar (SC, squared aster-isk) cooling functions. The fact that these simulations donot reproduce the whole observed range of gradients couldbe related to the lack of a treatment of energy feedbackby SNe. The latter, if realistically modelled, is expected totrigger mass outows from the star-forming regions into thehalo. Since these regions are highly enriched, metals may betransported outwards, affecting the metallicity distributionsand attening the metallicity proles. Our simulation runwith suprasolar cooling function was performed in order toassess the effects of the presence of metals in these outerregions on the gas cooling, mimicking an extreme case of metal enrichment by energy feedback.

5 CONCLUSIONS

We have implemented a new model for chemical evolutionwithin the cosmological SPH code GADGET-2 . We accountfor nucleosynthesis from SNIa and SNII separately. Radia-tive cooling of the gas according to self-consistent metallicityvalues is realized by means of precomputed look-up tables.Our implementation was designed to allow a reasonably ac-curate treatment of the main features of stellar evolutionwhile still not becoming computationally too expensive.

Using a number of test simulations both of isolatedgalaxies and of cosmological structure formation, we havevalidated our implementation and established some rst ba-sic results for the effects of chemical enrichment. An impor-tant consequence of the presence of metals is the increase in

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Figure 14. Oxygen proles for the gaseous components of the six selected galactic objects from the cosmological simulations run withprimordial (dotted lines), metal-dependent (solid lines) and suprasolar (dashed lines) cooling functions. The error bars correspond to therms scatter of 12 + log(O/H) around the mean.

the cooling efficiency that it can cause, leading to acceler-ated star formation. In our isolated galaxy simulations, theSFR for test runs with metal-dependent cooling functioncan be up to a factor of 1 .5 higher than the correspondingone for a test with a primordial cooling function, and upto a factor of 3 lower than the one for suprasolar cooling.We found that these differences do not originate in the gasin the central regions, because it is already cold and denseanyway. Instead, the differences are caused by more diffusegas at outer radii which has yet to cool. Here the increaseof the cooling efficiency allows condensation of gas and starformation to occur further away from the centre of the sys-tems.

An important implication of this result is that strongeffects owing to metal-dependent cooling can only be ex-pected when heavy elements are efficiently transported andmixed into diffuse gas that has yet to cool. In our cosmolog-ical simulations, which lacked a physical model for energyfeedback, such a large-scale spreading of metals only occursat a low level. As perhaps was to be expected, we found thatsimulations with metal-dependent cooling produced similarresults as simulations with a primordial cooling function. Weexpect however that this could be very different if a modelfor efficient metal distribution is added to our simulations.An explicit demonstration of this has been provided by our

test simulation where we assumed suprasolar cooling ratefunctions, resulting in substantially elevated star formationactivity and different abundance proles. Note that in thispaper we explored galaxy scale systems which cool very effi-ciently. Larger effects from chemical mixing are expected inmore massive haloes such as clusters of galaxies (White &Frenk 1991; De Lucia, Kauffmann & White 2003).

We have also tested the impact of a number of assump-tions made in our model, and the relevance of numericalparameters. Relaxing the IRA for SNII has only a negligi-ble effect and does not change the chemical properties of thesimulated systems. However, as also shown by previous work(e.g. Raiteri, Villata & Navarro 1996; Chiappini et al. 1997;

Mosconi et al. 2001), the chemical properties of both thestellar populations and the ISM are sensitive to the time-delay associated with SNIa explosions. In agreement withprevious results, we found that the latter must be includedin order to be able to reproduce the observed chemical prop-erties of galaxies.

We have shown that chemical enrichment can signif-icantly modify the chemical and dynamical properties of forming galactic systems. However, the strength of the inu-ence of metals on galaxy formation might also depend on thephysics of energy feedback. If the latter is neglected, as wehave done here, metals are not mixed widely in gas that has

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Theis C., Burkert A., Hensler G., 1992, A&A, 265, 465Thielemann F.K., Nomoto K., Hashimoto M., 1993, in Prantzos

N., Vangoni-Flam E., Casse N., eds, Origin and Evolution of the Elements. Cambridge University Press, Cambridge, p.299.

Timmes F.X., Woosley S.E., Weaver T.A., 1995, ApJS, 98, 617Tinsley B.M., Larson R.B., 1979, MNRAS, 186, 503Tornatore L., Borgani S., Matteucci F., Recchi S., Tozzi P., 2004,

MNRAS, 349, L19Tremonti C.A. et al., 2004, ApJ, 613, 898Valdarnini R., 2003, MNRAS, 339 , 1117Van den Bergh S., 1991, ApJ, 369, 1White S.D.M., Efstathiou G., Frenk C.S., 1993, MNRAS, 262,

1023White S.D.M., Frenk C.S., 1991, ApJ, 379, 52White S.D.M., Rees M.J., 1978, MNRAS, 183, 341Woosley S.E., Weaver T.A., 1995, ApJS, 101, 181Yepes G., Kates R., Khokhlov A., Klypin A., 1997, MNRAS, 284,

235Zaritsky D., Kennicutt R.C.Jr., Huchra J.P., 1994, ApJ, 420, 87

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