The Growth and Enrichment of the Intragroup Gas
Lichen Liang, Fabrice Durier, Arif Babul, Romeel Davé, Benjamin D. Oppenheimer, Neal Katz, Mark Fardal, Tom Quinn
MMNRAS , 1–26 (2015) Preprint 9 October 2018 Compiled using MNRAS L A TEX style file v3.0
The Growth and Enrichment of Intragroup Gas
Lichen Liang , Fabrice Durier , Arif Babul , Romeel Dav ´e , , ,Benjamin D. Oppenheimer , Neal Katz , Mark Fardal & Tom Quinn Department of Physics & Astronomy, University of Victoria, BC, V8X 4M6, Canada Physics Department, University of Western Cape, Bellville, Cape Town 7535, South Africa South African Astronomical Observatory, PO Box 9, Observatory, Cape Town 7935, South Africa African Institute of Mathematical Sciences, Muizenberg, Cape Town 7945, South Africa CASA, Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309, USA Astronomy Department, University of Massachusetts, Amherst, MA 01003, USA Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195-1580, USA
Accepted 2015 December 2. Received 2015 November 26; in original form 2015 July 07
ABSTRACT
The observable properties of galaxy groups, and especially the thermal and chemical proper-ties of the intragroup medium (IGrM), provide important constraints on the different feedbackprocesses associated with massive galaxy formation and evolution. In this, the first in a seriesof studies aimed at identifying and exploring these constraints, we present a detailed analy-sis of the global properties of simulated galaxy groups with X-ray temperatures in the range . − keV over the redshift range ≤ z ≤ . The groups are drawn from a cosmologi-cal simulation that includes a well-constrained prescription for galactic outflows powered bystars and supernovae, but no AGN feedback. Our aims are (a) to establish a baseline againstwhich we will compare future models; (b) to identify model successes that are genuinely dueto stellar/supernovae-powered outflows; and (c) to pinpoint features that not only signal theneed for AGN feedback but also constrain the nature of this feedback.We find that even without AGN feedback, our simulation successfully reproduces the ob-served present-day group global IGrM properties such as the hot gas mass fraction, the vari-ous X-ray luminosity-temperature-entropy scaling relations, as well as the mass-weighted andemission-weighted IGrM iron and silicon abundance versus group X-ray temperature trends,for all but the most massive groups. We also show that these trends evolve self-similarly for z < , in agreement with the observations. Contrary to expectations, we do not see any evi-dence of the IGrM undergoing catastrophic cooling. And yet, the z = 0 group stellar mass is afactor of ∼ too high. Probing further, we find that the latter is due to the build-up of cold gasin the massive galaxies before they are incorporated inside groups. This, in turn, indicates thatother feedback mechanisms must activate in real galaxies as soon as their stellar mass growsto M ∗ ≈ a few × M (cid:12) . We show that these must be powerful enough to expel a signifi-cant fraction of the halo gas component from the galactic halos. Gentle “maintenance-mode”AGN feedback, as has been suggested to occur in galaxy clusters, will not do; it cannot bringthe stellar and the baryonic fractions into agreement with the observations at the same time.Just as importantly, we find that stellar/supernovae-powered winds are vital for explainingthe metal abundances in the IGrM, and these results ought to be relatively insensitive to theaddition of AGN feedback. Key words: galaxies: formation, X-rays: galaxies: clusters, galaxies: clusters: general, galax-ies: abundances, methods: N-body simulations
In current schema for the formation of observed cosmic structure,galaxies are often identified as the basic building blocks of cosmicstructure. Early on, this phrase was meant to indicate that struc-ture in the universe can be understood as gravitationally organized assemblages of galaxies in which individual galaxies are merelypassive components, much like bricks in a wall. However, accu-mulating multi-wavelength observations and increasingly detailedtheoretical studies show that galaxies are anything but passive fea-tures of the cosmic landscape. The very processes underlying theformation and evolution of galaxies — star formation, stellar nu- c (cid:13) a r X i v : . [ a s t r o - ph . GA ] D ec L. Liang et al. cleosynthesis, feedback and galactic outflows — also impact thewider environment to such an extent that many of the observedproperties of supra-galactic systems cannot be understood withoutreference to these processes. Understanding how these processesunfold and the extent of their impact on galactic and extragalacticscales is essential for constructing a self-consistent description ofcosmic structure across the hierarchy as well as for accounting fortheir observed properties.Over the years, numerous studies have advanced groups ofgalaxies as the best environments for studying the impact of galax-ies on their surroundings (Renzini 1997; Finoguenov et al. 2002;Ponman et al. 2003; Vikhlinin et al. 2006; Dav´e et al. 2008; Sunet al. 2009; McCarthy et al. 2010, 2011; O’Sullivan et al. 2014, andreferences therein). In the cosmic hierarchy, galaxy groups are thesmallest aggregates of galaxies, with the least massive of these sys-tems comprising only a few luminous galaxies. What makes thesesystems especially interesting is that a significant fraction of thebaryons attached to galaxy groups exists in the form of hot, dif-fuse gas that, at least in the case of the more massive groups in thenearby universe, is amenable to scrutiny via X-ray observations.Given the sizes and masses of groups, the expectation is that galac-tic processes will have affected much of this gas.Of the various properties, the three features that have attractedthe most attention are:(i) The entropy of the hot diffuse gas within R as measuredby the proxy variable S = k B T e /n / e ( c . f ., Balogh et al. 1999):This quantity is much better than temperature or density when itcomes to encapsulating the time-integrated history of heating andcooling to which the gas has been subjected. Ponman et al. (2003),Sun et al. (2009) and Pratt et al. (2010) have found that within R the diffuse gas shows clear evidence of enhanced entropy and agrowing body of work suggests that this most likely is due to non-gravitational heating induced by stellar-powered galactic outflows(Everett et al. 2008; Socrates et al. 2008; Dav´e et al. 2008; Hopkinset al. 2012; Zhang et al. 2014) and/or active galactic nuclei (here-after, AGNs) (Babul et al. 2002; Borgani et al. 2004; McCarthyet al. 2008; Puchwein et al. 2008; Sijacki et al. 2008; McCarthyet al. 2010, 2011; Teyssier et al. 2011; Short et al. 2013; Le Brunet al. 2014; Planelles et al. 2014).(ii) The hot gas fraction within the central regions of thegroups: Vikhlinin et al. (2006); Gastaldello et al. (2007); Sun et al.(2009) find that the hot gas fraction within R is on the aver-age much lower than that in the more massive clusters of galaxies.A lower hot gas fraction can arise as a result of a number of pro-cesses. The hot gas can be depleted by efficient cooling ( c . f ., Lewiset al. 2000; Kravtsov et al. 2005). However, this is not a viable ex-planation for the observations since efficient cooling would alsoresult in stellar fractions that are much higher than observed (Dav´eet al. 2002). A more likely explanation is that the gas, subjectedto non-gravitational heating of the kind described in (i), exists ina more extended equilibrium configuration ( e . g . Crain et al. 2010;McCarthy et al. 2010).(iii) The metal content of the hot diffuse gas: The observediron abundance of approximately ∼ . solar, albeit with a largescatter ( e . g . Edge & Stewart 1991; Peterson et al. 2003; De Grandiet al. 2004; de Plaa et al. 2007), indicates that a significant fractionof the metals produced in galaxies escapes the interstellar mediumin these systems. One way of affecting this transfer is via ram-pressure stripping (Domainko et al. 2006). However, Dav´e et al.(2008, hereafter DOS08) show that this scheme, by itself, is unableto simultaneously account for the observed iron abundance and theoxygen-to-iron ratio in the hot diffuse intragroup medium (here- after, IGrM). DOS08 conclude that the enrichment of the IGrM isthe outcome of metals being flushed out of the galaxies via power-ful galaxy-wide outflows. The outflows must necessarily be power-ful because not only must the winds be carrying a significant frac-tion of the metal-enriched gas but their velocities must be largeenough to ensure that they “slip the surly bonds” of the galaxies’gravity. Additionally, preliminary studies indicate that a fair frac-tion of the metals is ejected typically at epochs prior to the forma-tion of the groups themselves (Oppenheimer et al. 2012; Ford et al.2014).Outflows are ubiquitous in both local as well as high-redshiftgalaxies (see Martin 2005, 2006; Sturm et al. 2011; O’Sullivanet al. 2012; Bradshaw et al. 2013; Veilleux et al. 2013; Williamset al. 2014; Turner et al. 2014; Villar Mart´ın et al. 2014; Sell et al.2014, and references therein). Observations suggest these outflowsmay be due to either stellar or AGN processes. Winds powered byAGNs originate as high-velocity outflows on parsec scales (Poundset al. 2003b,a; Tombesi et al. 2010a,b) and while a growing bodyof observational studies show that these outflows have a profoundimpact on the gas content in the central ∼ kpc of the host galax-ies (Sturm et al. 2011; Veilleux et al. 2013; Villar Mart´ın et al.2014), evidence suggesting that the AGNs can trigger galaxy-wideoutflows capable of flushing the bulk of the metal-enriched, star-forming, interstellar medium (ISM) out of the galaxies remainselusive (Harrison et al. 2014). Recent high-resolution simulationstudies ( c . f ., Faucher-Gigu`ere & Quataert 2012; Gabor & Bour-naud 2014) that track the evolution of the high-velocity nuclearoutflows also find that the resultant winds have very little impacton the extended galactic disk: The nuclear outflow transitions intoan expanding wind of shocked gas within the central ∼ > km/s, and imply a mass outflow ratethat is comparable to the star formation rate. These theoretical andobservational results make a compelling case for stellar-poweredoutflows being the primary mechanism for the dispersal of metalsbeyond the galaxies and an integral feature of all realistic modelsfor cosmic structure formation (Somerville & Dav´e 2014).In a series of papers, Dav´e and collaborators (Oppenheimer &Dav´e 2006; Dav´e, Finlator & Oppenheimer 2006; Finlator & Dav´e2008; Dav´e, Oppenheimer & Sivanandam 2008) have carried outextensive numerical simulation studies to assess the impact of thestellar-powered galactic outflows – based on the momentum-drivenwind scalings of Murray et al. (2005) – over a wide range of cos-mic environments and epochs. They find that this model is able toaccount for a host of observations of which three are especially MNRAS000
In current schema for the formation of observed cosmic structure,galaxies are often identified as the basic building blocks of cosmicstructure. Early on, this phrase was meant to indicate that struc-ture in the universe can be understood as gravitationally organized assemblages of galaxies in which individual galaxies are merelypassive components, much like bricks in a wall. However, accu-mulating multi-wavelength observations and increasingly detailedtheoretical studies show that galaxies are anything but passive fea-tures of the cosmic landscape. The very processes underlying theformation and evolution of galaxies — star formation, stellar nu- c (cid:13) a r X i v : . [ a s t r o - ph . GA ] D ec L. Liang et al. cleosynthesis, feedback and galactic outflows — also impact thewider environment to such an extent that many of the observedproperties of supra-galactic systems cannot be understood withoutreference to these processes. Understanding how these processesunfold and the extent of their impact on galactic and extragalacticscales is essential for constructing a self-consistent description ofcosmic structure across the hierarchy as well as for accounting fortheir observed properties.Over the years, numerous studies have advanced groups ofgalaxies as the best environments for studying the impact of galax-ies on their surroundings (Renzini 1997; Finoguenov et al. 2002;Ponman et al. 2003; Vikhlinin et al. 2006; Dav´e et al. 2008; Sunet al. 2009; McCarthy et al. 2010, 2011; O’Sullivan et al. 2014, andreferences therein). In the cosmic hierarchy, galaxy groups are thesmallest aggregates of galaxies, with the least massive of these sys-tems comprising only a few luminous galaxies. What makes thesesystems especially interesting is that a significant fraction of thebaryons attached to galaxy groups exists in the form of hot, dif-fuse gas that, at least in the case of the more massive groups in thenearby universe, is amenable to scrutiny via X-ray observations.Given the sizes and masses of groups, the expectation is that galac-tic processes will have affected much of this gas.Of the various properties, the three features that have attractedthe most attention are:(i) The entropy of the hot diffuse gas within R as measuredby the proxy variable S = k B T e /n / e ( c . f ., Balogh et al. 1999):This quantity is much better than temperature or density when itcomes to encapsulating the time-integrated history of heating andcooling to which the gas has been subjected. Ponman et al. (2003),Sun et al. (2009) and Pratt et al. (2010) have found that within R the diffuse gas shows clear evidence of enhanced entropy and agrowing body of work suggests that this most likely is due to non-gravitational heating induced by stellar-powered galactic outflows(Everett et al. 2008; Socrates et al. 2008; Dav´e et al. 2008; Hopkinset al. 2012; Zhang et al. 2014) and/or active galactic nuclei (here-after, AGNs) (Babul et al. 2002; Borgani et al. 2004; McCarthyet al. 2008; Puchwein et al. 2008; Sijacki et al. 2008; McCarthyet al. 2010, 2011; Teyssier et al. 2011; Short et al. 2013; Le Brunet al. 2014; Planelles et al. 2014).(ii) The hot gas fraction within the central regions of thegroups: Vikhlinin et al. (2006); Gastaldello et al. (2007); Sun et al.(2009) find that the hot gas fraction within R is on the aver-age much lower than that in the more massive clusters of galaxies.A lower hot gas fraction can arise as a result of a number of pro-cesses. The hot gas can be depleted by efficient cooling ( c . f ., Lewiset al. 2000; Kravtsov et al. 2005). However, this is not a viable ex-planation for the observations since efficient cooling would alsoresult in stellar fractions that are much higher than observed (Dav´eet al. 2002). A more likely explanation is that the gas, subjectedto non-gravitational heating of the kind described in (i), exists ina more extended equilibrium configuration ( e . g . Crain et al. 2010;McCarthy et al. 2010).(iii) The metal content of the hot diffuse gas: The observediron abundance of approximately ∼ . solar, albeit with a largescatter ( e . g . Edge & Stewart 1991; Peterson et al. 2003; De Grandiet al. 2004; de Plaa et al. 2007), indicates that a significant fractionof the metals produced in galaxies escapes the interstellar mediumin these systems. One way of affecting this transfer is via ram-pressure stripping (Domainko et al. 2006). However, Dav´e et al.(2008, hereafter DOS08) show that this scheme, by itself, is unableto simultaneously account for the observed iron abundance and theoxygen-to-iron ratio in the hot diffuse intragroup medium (here- after, IGrM). DOS08 conclude that the enrichment of the IGrM isthe outcome of metals being flushed out of the galaxies via power-ful galaxy-wide outflows. The outflows must necessarily be power-ful because not only must the winds be carrying a significant frac-tion of the metal-enriched gas but their velocities must be largeenough to ensure that they “slip the surly bonds” of the galaxies’gravity. Additionally, preliminary studies indicate that a fair frac-tion of the metals is ejected typically at epochs prior to the forma-tion of the groups themselves (Oppenheimer et al. 2012; Ford et al.2014).Outflows are ubiquitous in both local as well as high-redshiftgalaxies (see Martin 2005, 2006; Sturm et al. 2011; O’Sullivanet al. 2012; Bradshaw et al. 2013; Veilleux et al. 2013; Williamset al. 2014; Turner et al. 2014; Villar Mart´ın et al. 2014; Sell et al.2014, and references therein). Observations suggest these outflowsmay be due to either stellar or AGN processes. Winds powered byAGNs originate as high-velocity outflows on parsec scales (Poundset al. 2003b,a; Tombesi et al. 2010a,b) and while a growing bodyof observational studies show that these outflows have a profoundimpact on the gas content in the central ∼ kpc of the host galax-ies (Sturm et al. 2011; Veilleux et al. 2013; Villar Mart´ın et al.2014), evidence suggesting that the AGNs can trigger galaxy-wideoutflows capable of flushing the bulk of the metal-enriched, star-forming, interstellar medium (ISM) out of the galaxies remainselusive (Harrison et al. 2014). Recent high-resolution simulationstudies ( c . f ., Faucher-Gigu`ere & Quataert 2012; Gabor & Bour-naud 2014) that track the evolution of the high-velocity nuclearoutflows also find that the resultant winds have very little impacton the extended galactic disk: The nuclear outflow transitions intoan expanding wind of shocked gas within the central ∼ > km/s, and imply a mass outflow ratethat is comparable to the star formation rate. These theoretical andobservational results make a compelling case for stellar-poweredoutflows being the primary mechanism for the dispersal of metalsbeyond the galaxies and an integral feature of all realistic modelsfor cosmic structure formation (Somerville & Dav´e 2014).In a series of papers, Dav´e and collaborators (Oppenheimer &Dav´e 2006; Dav´e, Finlator & Oppenheimer 2006; Finlator & Dav´e2008; Dav´e, Oppenheimer & Sivanandam 2008) have carried outextensive numerical simulation studies to assess the impact of thestellar-powered galactic outflows – based on the momentum-drivenwind scalings of Murray et al. (2005) – over a wide range of cos-mic environments and epochs. They find that this model is able toaccount for a host of observations of which three are especially MNRAS000 , 1–26 (2015) he Growth and Enrichment of Intragroup Gas noteworthy. First, it successfully reproduces the observed mass-metallicity relation in galaxies, along with its second-parameterdependence on star formation, both today and at higher redshifts(Finlator & Dav´e 2008; Dav´e et al. 2011; Hirschmann et al. 2013;Somerville & Dav´e 2014). Second, it also explains the observations(D’Odorico et al. 2013) indicating the widespread enrichment ofthe intergalactic medium (IGM) as early as z ∼ (Oppenheimer& Dav´e 2006; Oppenheimer et al. 2009) and in fact is, as we willshow in a follow-up paper (Durier et al., in preparation), one of themore successful stellar feedback schemes at doing so. Third, it alsoyields iron abundances and the oxygen-to-iron ratios ( i.e. ∼ [Fe/H]and [O/Fe]) in the hot intragroup medium of z = 0 groups thatbroadly match the observations (Dav´e et al. 2008). An alternativeto the momentum-driven model for the kinetic winds is the energy-driven model, the main difference between the two being that themass outflow rate scales as ˙ M wind ∝ σ − in the former case (see § ˙ M wind ∝ σ − in the latter. Theo-retical arguments (Murray et al. 2010; Hopkins et al. 2012) favourthe energy-driven wind scalings for the low to intermediate massgalaxies. And recent simulation studies (Ford et al. 2014; Chris-tensen et al. 2015) suggest that the energy-driven wind model yieldgood agreement with the observed mass-metallicity relation, thestellar mass fraction versus galaxy mass trend, etc. for low to inter-mediate mass galaxies. However, large-scale simulations that treatstellar-powered outflows from all galaxies as energy-driven winds,such as the Illustris simulations (Vogelsberger et al. 2014b,a), tendto produce mass-metallicity relations that are significantly steeperthan observed (Somerville & Dav´e 2014). Since the primary aimof the present work is to examine the emergence of galaxy groups,the massive stellar systems that populate such environments, andespecially the growth and enrichment of the IGrM, we adopt themomentum-drive galactic outflows model .In keeping with this goal, we identify the formation times ofthe z = 0 galaxy group population and compare these to the timeswhen the hot diffuse IGrM in these systems is established as wellas when it is enriched with oxygen, silicon and iron. We also ex-plore whether the stellar-powered winds have any other direct orindirect impact on the properties of the IGrM or, for that matter,any other group properties, beyond just injecting the metals into theIGrM. For instance, one can imagine that the metals, being very ef-ficient coolants, can exacerbate the cooling of the IGrM and giverise to a greater build-up of cold gas and stars in the group cen-tral galaxies. On the other hand, the outflows also heat the IGrM,and if the resultant energy deposition significantly offsets the ra-diative losses, one might expect a reduced IGrM cooling flow ontothe group central galaxy. Since our present simulations do not in-clude AGN feedback, we are especially interested in identifyingrobust trends that are not expected to change with the inclusion ofAGN feedback. One such result (see Section 5) is our findings con-cerning the bulk metallicity of the IGrM and the extent of massrecycling between the IGrM and the galaxies, which sets the stagefor a more detailed analysis of how, where and when the iron andoxygen are introduced into the IGrM in a companion paper (Lianget al., in preparation). The present analysis is useful in other waysalso. It provides detailed insights about where in the hierarchy of For completeness, we note that there are two distinct ways of implement-ing stellar feedback: the “kinetic” approach, which we have adopted, andthe “thermal” approach. For further details about the latter, we refer thereaders to Dalla Vecchia & Schaye (2012); Stinson et al. (2013) (see alsoSchaye et al. 2015; Sokołowska et al. 2015 and references therein). structures the present stellar-powered feedback model first starts tofail and other feedback mechanisms, such as AGN feedback, mightbe needed, and provides clearer requirements for these additionalfeedback mechanisms. These results are informing our current ef-forts to develop new AGN feedback implementation that are morein keeping with both observations as well as theoretical expecta-tions.While on the subject of AGN feedback, we note that severalcollaborations who, like us, are working towards self-consistent,holistic models for the formation and evolution of galaxies, groupsand clusters, have started to incorporate AGN feedback into theirsimulations. Of these, the two initiatives that are the furthest alongare Illustris (Vogelsberger et al. 2014a) and Eagle (Schaye et al.2015; Crain et al. 2015). Each collaboration has its own (very dif-ferent) implementation of AGN feedback just as they each use verydifferent approaches to modelling stellar feedback. Both fare rea-sonably well in terms of matching many of the observed trends andproperties of galaxies. However, each also has its own set of chal-lenges. For example, the AGN feedback scheme implemented inIllustris simulations tends to evacuate too much hot gas from thevicinity of massive galaxies (Genel et al. 2014) while the Eaglesimulations seem to suffer from insufficient expulsion of gas fromthe galaxies at early epochs, which results in the production of toomany stars at early times and correspondingly, a reduced specificstar formation rate at later times (Furlong et al. 2015). Essentially,each approach has its strengths and weaknesses, leaving consider-able room for improvement and further development.The present paper is organized as follows: In Section 2, weprovide a brief description of our simulation setup, discuss how weconstruct our catalog of simulated galaxy groups, and show somegeneral properties of these groups at z = 0 . In Section 3, we dis-cuss the global X-ray properties of our galaxy groups, focusing onthree most commonly discussed group X-ray scaling relations: the(X-ray) luminosity − temperature, the luminosity-mass, the mass-temperature and the entropy-temperature relations. We explore theevolution of the model scaling relations over the redshift range ≤ z ≤ and also compare the z = 0 relations to the obser-vational results. We discuss the baryonic content of the simulatedgroups in Section 4, investigating the variation in the total baryonfraction as well as the stellar and the hot diffuse intragroup mediummass fractions with group mass over the redshift range ≤ z ≤ .We compare these fractions with observational results from bothlow redshift groups as well as more recent results from groups atredshifts out to z ∼ , and we provide a detailed analysis of theassembly of groups’ total mass, IGrM, and stellar mass. We theninvestigate the enrichment of the IGrM in Section 5, looking at thesources of the iron, silicon and oxygen, the abundance ratios, etc.Finally, we summarize and discuss our findings in Section 6. We extracted galaxy groups from a cosmological hydrodynamicsimulation of a representative comoving volume (100 h − Mpc) of a Λ CDM universe with present-day parameters: Ω m , = 0.25, Ω Λ , = 0.75, Ω b , = 0.044, H = 70 km s − Mpc − , σ = 0.83 andn = 0.95. These are based on the WMAP-7 best-fit cosmologicalparameters (Jarosik et al. 2011) and are in good agreement with theWMAP-9 results (Hinshaw et al. 2013).We initialized the simulation volume with dark mat-ter particles and gas particles, implying particle masses of MNRAS , 1–26 (2015)
L. Liang et al. . × M (cid:12) and . × M (cid:12) for the dark matter and gas, re-spectively. In the simulation we assumed a spline gravitational soft-ening length of h − kpc comoving ( . h − equivalent Plummersoftening).The initial conditions for the simulation volume were gen-erated using an Eisenstein & Hu (1999) power spectrum in thelinear regime, and the simulation was evolved from z = 129 to z = 0 using a modified version of GADGET-2 (Springel 2005), acosmological tree-particle mesh-smoothed particle hydrodynamicscode that includes radiative cooling using primordial abundancesas described in Katz, Weinberg & Hernquist (1996) and metal-line cooling as described in Oppenheimer & Dav´e (2006, hereafterOD06). Star formation is modelled using a multiphase prescriptionof Springel & Hernquist (2003). In this prescription, only gas parti-cles whose density exceeds a preset threshold of n H = 0 .
13 cm − are eligible to form stars. The star formation rate follows a Schmidtlaw (Schmidt 1959) with the star formation time-scale scaled tomatch the z = 0 Kennicutt law (Kennicutt 1998). We assume thatthe mass function of forming stars is given by the Chabrier ini-tial mass function (IMF) (Chabrier 2003). According to this IMF,19.8 % of the stellar mass goes into massive ( i . e . ≥ M (cid:12) ) starsthat engender Type II supernovae (Oppenheimer & Dav´e 2008).Over the course of the simulation, we account for mass lossand metal enrichment from Type Ia and Type II SNe as well asthe asymptotic giant branch (AGB) stars. For a detailed discussionof how this was carried out, we refer readers to Oppenheimer &Dav´e (2008, hereafter OD08). An overview is as follows: In thecase of Type II SNe, we use the instantaneous recycling approxima-tion where the mass and the metals are returned immediately to theISM. Type II SN metal enrichment uses the metallicity-dependentyields calculated from the Limongi & Chieffi (2005) supernovamodels. In the case of Type Ia SNe, we allow for both a promptcomponent as well as a delayed component using the model ofScannapieco & Bildsten (2005) in which, the former is tied to thestar formation rate as in the case of Type II SNe, and the latter tothe stellar mass. The mass loss and the enrichment by the promptcomponent is returned to the ISM instantaneously while that dueto the delayed component commences after a delay of . Gyrs.As for the AGB stars, the corresponding mass and metal injectioninto the ISM commences after a delay of Myrs following a starformation event and extends over the subsequent ∼ Gyrs. Asdiscussed by OD08, the most significant impact of the AGB starsis to replenish the ISM. In general, a little more that 50 % of thestellar mass in a Chabrier IMF is returned to the ISM over ∼ Gyrs and 30 % of this comes from the AGB stars. The mass transferfrom AGB stars also returns to the ISM the metals that were previ-ously locked into these stars. Primarily, the metallicity of this gas isthe same as that of ISM from which they were spawned. In detail,however, nucleosynthesis reactions during the AGB phase lead toa slight depletion of the oxygen abundance as well as an enhance-ment of the carbon abundance. To conclude this brief overview,we note that we explicitly track the evolution in the abundancesof four metal species — carbon, oxygen, silicon, and iron. Thesefour species are not only among the most abundant metals in theuniverse, they are also the species most often observed in quasarabsorption line spectra probing the intergalactic medium, in the X-ray spectra of the hot intracluster and intragroup halo gas, as well asthe spectra of the circumgalactic and the interstellar gas in galaxies.In the present study, we will focus primarily on the oxygen, siliconand iron.Our numerical implementation of the kinetic winds pow-ered by stellar feedback is based on the scheme initially devel- oped by Springel & Hernquist (2003), modified to conform to themomentum-driven wind model scalings of MQT05. MQT05 de-scribe a model where the energy and momentum injected into theISM by the stars via stellar winds and supernova explosions, andby radiation pressure produced by the continuum absorption andscattering of photons on the dust grains that are collisionally cou-pled to the gas, propel galaxy-wide winds. A detailed discussionof the model and the particular implementation that we are usinghas been discussed extensively in a series of papers starting withOD06, with updates described in OD08 and Oppenheimer & Dav´e(2009), and has recently been shown to be in general agreementwith the results of recent high-resolution galaxy-scale simulationsof Hopkins et al. (2012, 2014); Muratov et al. (2015) that includeexplicit stellar feedback. For completeness, we briefly summarizebelow the current implementation:The mass outflow rate scales with the star formation rate as ˙ M wind = η ˙ M star where η = (150 km / s) /σ gal is the mass loading factor. Here, σ gal is the galaxy velocity disper-sion. It is used as a measure of the depth of the galaxy’s potentialand is computed using the total mass (baryons+dark matter) of thegalaxies identified over the course of the simulation ( c.f., Oppen-heimer et al. 2010). This means that when a gas particles densityexceeds the threshold for star formation, it is eligible to form starswith some probability P star but at the same time, its probability forbeing incorporated into a wind is P wind = η P star . If a particles ischosen to be in an outflow, it is given a velocity kick v wind , where v wind = 4 . σ gal (cid:112) f L − βσ gal , (1)is orientated parallel to ± v × a , the cross product of the velocityand the acceleration vectors of the particle prior to entrainment.In the above equation, the first term on the right representsthe wind launch velocity — with f L , the luminosity factor in unitsof the galactic Eddington luminosity ( i.e., the critical luminosityfor expelling gas from the galaxy via radiation pressure) given byequation (5) of OD08. As discussed in OD08, this wind launchvelocity is capped by limiting the value of σ gal to σ gal , max = 1400 (cid:18) τ SF (cid:19) km / s , (2)where τ SF is the local star formation timescale, to account for thefact that in the MTQ05 model, starburst luminosities need to reachthe Eddington limit to expel the gas. In practice, we find that thiscap has no impact on winds from galaxies at z > while at lowerredshifts, the median wind velocity from the group central galaxiesis reduced by a constant factor that grows to by z = 0 .The second term (with β = 2 . ) represents an additional ve-locity kick at launch, to simulate the continued dynamical pumpingof the gas in the MQT05 momentum-driven wind model (see OD06and OD08 for details). Since our simulations neither resolve the de-tailed structure of the ISM nor the detailed hydrodynamics of thewind flowing through the ISM, this model assigns the ejected gasparticles an appropriate initial velocity to ensure that the wind hasroughly the expected velocity at large radii. For the same reasons,we also decouple the wind particles hydrodynamically (but not dy-namically) from their surroundings until the local gas density dropsto 10% of the star formation density threshold or for a time dura-tion equal to
200 ( v wind /
100 [km / s]) − Myrs . In real galaxies,this outflow would be expected to flow through the ISM and outof the disk along paths of least resistance — i.e., , along channelsformed by overlapping supernova explosions.We reiterate that our present simulation does not include the
MNRAS000
MNRAS000 , 1–26 (2015) he Growth and Enrichment of Intragroup Gas − − − − − log M vir (M ⊙ ) dn / d l og M ( M p c − ) N gal (cid:42) gal (cid:42) gal (cid:42) gal (cid:42) Figure 1.
The mass function of halos with at least three (red), two (blue),one (magenta) luminous galaxies, as well as of the complete halo popula-tion in the simulation volume (black) described in Section 2.2. The dashedvertical line shows our halo mass resolution limit of . × M (cid:12) , cor-responding to 64 dark matter particles. effects of the energy and momentum output of AGNs. As we willshow in Section 4 of the present paper and in the follow-up paper(Paper-II), this deficit does not significantly alter our results abouthow the enrichment of the IGrM unfolds. This is because (1) metalsare flushed out of the galaxies primarily by stellar-powered galac-tic outflows and (2) most of the metals in the IGM and in the hotIGrM are from lower mass galaxies whose evolution is expectedto be only minimally impacted by AGN feedback, if at all. Themost massive galaxies, whose evolution is thought to be stronglyimpacted by AGN feedback and which, in the absence of the latter,build up a much larger stellar mass than their observed counter-parts, contribute approximately of the metals in the hot IGrM.As we show in Section 4, a reduced contribution from these galax-ies due to quenching of star formation by AGN feedback shouldin fact improve the agreement between our simulation results andobservations even further. Each simulation output is analyzed to identify both galaxies as wellas bound halos. We identify bound halos using the spherical over-density (SO) procedure described in Kereˇs et al. (2005): First, as-sociations of dark matter particles are found using a Friends-Of-Friends (FOF) percolation algorithm. Second, after finding the lo-cal potential minima of each association, a sphere is constructedaround these particles and its radius is expanded until the mean en-closed total mass density equals the virial density for the assumedcosmology at the redshift under consideration: ρ m , vir ( z ) = ∆ vir ( z ) · E ( z ) ρ crit (0) , (3)where E ( z ) ≡ H ( z ) /H is the dimensionless Hubble parametergiven by E ( z ) = 1 − Ω m , + (1 + z ) Ω m , , dn / d l og M s t a r ( M p c − ) log M star (M ⊙ ) dn / d l og M s t a r ( M p c − ) . < log M vir ≤ . ⊙ . < log M vir ≤ . ⊙ . < log M vir ≤ . ⊙ Figure 2.
The top panel shows the z = 0 galaxy stellar mass function(GSMF) of all luminous galaxies in the simulated groups, sorted into threemass bins: . < log M vir ≤ . (cid:12) (magenta), . < log M vir ≤ . (cid:12) (blue), and . < log M vir ≤ . (cid:12) (red). For com-parative purposes, we also plot as connected black squares the GSMF forX-ray detected low mass groups spanning the mass range similar to that ofour simulated groups (Giodini et al. 2012). The vertical dashed black lineshows our luminous galaxy stellar mass resolution limit (see text). In antic-ipation of the discussion in § M ∗ > M (cid:12) has been artificially reduced by a factor of 3. and the virial overdensity factor is well-described by the followingfitting function ( c . f ., Babul et al. 2002): ∆ vir ( z ) = 49 + 96Ω m ( z ) + 200Ω m ( z )1 + 5Ω m ( z ) , Ω m ( z ) = Ω m , (1 + z ) − Ω m , + Ω m , (1 + z ) . We will refer to the radius of this sphere as the virial radius, R vir ,and the mass enclosed as the virial mass of the halo, M vir . Occa-sionally, we will reference M ∆ instead of M vir . M ∆ is the enclosedmass inside a sphere centered on the halo center within which themean mass density is ∆ · ρ crit ( z ) = ∆ · E ( z ) ρ crit (0) . Commonlyused values of ∆ are 200, 500 and 2500. The mapping betweenthese different quantities is redshift-dependent. At z = 0 , M vir ≈ . M and M ≈ . M ,R vir ≈ . R , R ≈ . R , and R ≈ . R . In Figure 1, we show the z = 0 mass functions of all halos in MNRAS , 1–26 (2015)
L. Liang et al. the simulation volume (black curve), as well as halos with at leastthree (red), two (blue) and one (magenta) “luminous” galaxies (de-fined below). We identify groups (and clusters) of galaxies as haloscontaining ≥ “luminous” galaxies. On mass scales ≥ M (cid:12) ,nearly all halos have at least 3 galaxies while in the mass range M (cid:12) < ∼ M vir < ∼ M (cid:12) , only a fraction of the halos do.There are a total of 902 groups in our simulation volume at z = 0 .Galaxies in the simulation volume are identified usingthe group-finding algorithm Spline Kernel Interpolative Denmax(SKID) to locate gravitationally bound clumps of star particlesand cold ( T < × K) gas particles that are eligible to formstars ( c . f ., Oppenheimer et al. 2010). We identify a galaxy as “re-solved” if the total mass in cold gas and stars is ≥ . × M (cid:12) and “luminous” if its stellar mass is ≥ . × M (cid:12) , which isequivalent to ≥ star particles.The top panel of Figure 2 shows the average stellar mass func-tion of the luminous galaxies in the simulated groups at z = 0 .We divide the groups into three mass bins: . < log M vir ≤ . (magenta), . < log M vir ≤ . (blue), and . < log M vir ≤ . (red), with 393, 145 and 188 groups in eachbin, respectively. (The sum of these is short of the total num-ber (902) quoted above because the balance of the groups have log M vir ≤ . or > . .) The size of our mass bins were cho-sen to ensure that the intermediate and the most massive mass binsmatch the bins adopted by DOS08 to facilitate comparison withtheir results.For comparison, we also show, as connected black squares,the observed galaxy stellar mass function (GSMF) for the X-raydetected low mass groups in the COSMOS survey (Giodini et al.2012) spanning the similar mass range ( M (cid:12) < M < × M (cid:12) ) to that of our simulated groups (Giodini et al.2012). It is readily apparent that the simulation shows a clear ex-cess of galaxies with large stellar masses. In the lower two massbins, there is typically only one ‘super-sized’ galaxy per group, thecentral galaxy, whose stellar mass exceeds M (cid:12) and it is thesegalaxies that are responsible for the excess. In addition to a ‘super-sized’ central galaxy, the most massive groups also host one (andsometimes, two) ‘super-sized’ satellite galaxies within R vir . Oncloser inspection, we have confirmed that (1) these massive satellitegalaxies were incorporated into the present-day groups via mergerswithin the past 6 Gyrs, (2) they were all central galaxies prior to themerger, and (3) these massive satellites are steadily sinking to thecenter and will eventually merge with the existing dominant centralgalaxy in the group. It is expected that AGN feedback will quenchthe growth of these ‘super-sized’ galaxies. From the resolution limitto approximately M ∗ ≈ M (cid:12) , the GSMF of the group galaxiesin our simulation volume agrees very well with the observations.AGN feedback is believed to play a minimal role in these galaxies;their evolution is principally governed by stellar feedback. To compare the characteristics of our groups to the observations,we compute various X-ray properties of our group halos. Unlessexplicitly noted, we focus exclusively on the properties of the hot(
T > × K ), diffuse IGrM particles.The first of these properties is the rest-frame 0.5-2.0 keV X-ray luminosity within R : L X, . − . . This is computed by summing over the luminosity of the individual IGrM gas parti-cle within a distance r ≤ R of the halo center. The emissioncharacteristics of gas particles is computed using the Astrophysi-cal Plasma Emission Code (APEC) from Smith et al. (2001) as-suming that the gas is optically thin and in collisional ionizationequilibrium. APEC uses the particles mass, SPH-weighted density,temperature and the metallicity as input, and outputs X-ray spectra,from which the luminosity is computed by summing the intensi-ties over the required range of photon energies ( e.g., Z mwq = Σ i Z q , i m i Σ N i m i and Z ewq = Σ i Z q , i L i Σ N i L i , (4)In these equations, “q” is the metal species under consideration, Z q , i is the SPH kernel-weighted abundance of the i th particle, m i is its mass, and L i is the X-ray luminosity of that particle. Thesums run over all IGrM particles within the volume under con-sideration. Additionally, to facilitate comparison between numer-ical and observational results, we scale and report all metal abun-dance estimates in terms of the solar “photosphere abundance” val-ues from Anders & Grevesse (1989): that is, Z O , (cid:12) = 0 . , Z Si , (cid:12) = 0 . and Z Fe , (cid:12) = 0 . .We also compute two different temperature measures of thehot gas in our groups. Observationally, the temperature of the hotgas is determined by fitting its observed X-ray spectrum. Gener-ally, the spectrum within a beam is a composite of the continuumand the line radiation from a range of gas phases with varying tem-peratures and metallicity. Since the vast majority of the observedgalaxy group spectra have been measured using CCDs that do notallow the emission from individual components to be spectrally dis-tinguished, and the statistical quality of the observations is insuffi-cient to detect all the features in the spectrum, and since the spec-trum itself is only available within a limited range of frequencies,the current convention is to compare the composite spectrum withsingle-temperature, single-metallicity thermal plasma models, andassign the temperature of the best-fit model to the observations. Thequestion for theorists is, and has been for years now: what measurebest corresponds to this temperature?The mean emission-weighted temperature ( T X ), which is anaverage of the temperatures of the individual components weightedby their radiative emission contributions is one possibility and infact, is the most commonly used measure in theoretical work. Wetoo compute this temperature but we restrict the weighing to X-rayemission within a relatively narrow energy range. In other words,our emission-weighted temperature is defined as the weighted av-erage temperature of the gas particles, where we use the particles’rest-frame 0.5-2.0 keV X-ray luminosity as the weighting factor.As shown in Figure 3, T X is tightly correlated with group mass and http://cxc.harvard.edu/atomdb/sources apec.htmlMNRAS000
T > × K ), diffuse IGrM particles.The first of these properties is the rest-frame 0.5-2.0 keV X-ray luminosity within R : L X, . − . . This is computed by summing over the luminosity of the individual IGrM gas parti-cle within a distance r ≤ R of the halo center. The emissioncharacteristics of gas particles is computed using the Astrophysi-cal Plasma Emission Code (APEC) from Smith et al. (2001) as-suming that the gas is optically thin and in collisional ionizationequilibrium. APEC uses the particles mass, SPH-weighted density,temperature and the metallicity as input, and outputs X-ray spectra,from which the luminosity is computed by summing the intensi-ties over the required range of photon energies ( e.g., Z mwq = Σ i Z q , i m i Σ N i m i and Z ewq = Σ i Z q , i L i Σ N i L i , (4)In these equations, “q” is the metal species under consideration, Z q , i is the SPH kernel-weighted abundance of the i th particle, m i is its mass, and L i is the X-ray luminosity of that particle. Thesums run over all IGrM particles within the volume under con-sideration. Additionally, to facilitate comparison between numer-ical and observational results, we scale and report all metal abun-dance estimates in terms of the solar “photosphere abundance” val-ues from Anders & Grevesse (1989): that is, Z O , (cid:12) = 0 . , Z Si , (cid:12) = 0 . and Z Fe , (cid:12) = 0 . .We also compute two different temperature measures of thehot gas in our groups. Observationally, the temperature of the hotgas is determined by fitting its observed X-ray spectrum. Gener-ally, the spectrum within a beam is a composite of the continuumand the line radiation from a range of gas phases with varying tem-peratures and metallicity. Since the vast majority of the observedgalaxy group spectra have been measured using CCDs that do notallow the emission from individual components to be spectrally dis-tinguished, and the statistical quality of the observations is insuffi-cient to detect all the features in the spectrum, and since the spec-trum itself is only available within a limited range of frequencies,the current convention is to compare the composite spectrum withsingle-temperature, single-metallicity thermal plasma models, andassign the temperature of the best-fit model to the observations. Thequestion for theorists is, and has been for years now: what measurebest corresponds to this temperature?The mean emission-weighted temperature ( T X ), which is anaverage of the temperatures of the individual components weightedby their radiative emission contributions is one possibility and infact, is the most commonly used measure in theoretical work. Wetoo compute this temperature but we restrict the weighing to X-rayemission within a relatively narrow energy range. In other words,our emission-weighted temperature is defined as the weighted av-erage temperature of the gas particles, where we use the particles’rest-frame 0.5-2.0 keV X-ray luminosity as the weighting factor.As shown in Figure 3, T X is tightly correlated with group mass and http://cxc.harvard.edu/atomdb/sources apec.htmlMNRAS000 , 1–26 (2015) he Growth and Enrichment of Intragroup Gas − − log T x (keV) l og M v i r ( M ⊙ ) N ≥ ≥ Figure 3. M vir − T X relation of galaxy groups with at least three (red)and two (blue) luminous galaxies. T X is tightly correlated with M vir andfollows the scaling relation: M vir ∝ T . X . Groups that lie significantly offthis relationship are located near larger systems and are “contaminated” bythe latters’ hot diffuse gas. Excluding groups with fewer than three lumi-nous galaxies, eliminates most of these “contaminated” halos. we will use the mass ( M vir , M or M ) or the mean emission-weighted temperature ( T X ) interchangeably when referring to orcategorizing the group halos.Observationally, group and cluster hot gas temperatures aredetermined by identifying a single-temperature thermal modelwhose spectrum best matches the observed spectrum. Reproducingthis procedure is sufficiently involved, especially if the observedspectrum is an integrated output of gas that spans a range of temper-atures, that most theoretical studies have, until relatively recently,tended to rely on T X as a stand-in. A decade ago, Mazzotta et al.(2004) showed that for clusters of galaxies, T X is generally biasedhigh by as much as ∼
25% compared to the observationally deter-mined integrated X-ray temperatures and introduced an alternateweighting scheme leading to a new temperature measure, whichwe will refer to as the “spectroscopic” temperature ( T spec ), whichis intended to be directly comparable to the observationally deter-mined temperature, at least in the case of the hot ( T > keV)intracluster gas. Vikhlinin (2006) has since extended the approachto cooler groups and here we will use their algorithm. As demon-strated by Vikhlinin (2006), T spec is an accurate estimate (to withina few percent) of the fitted temperature of a multiphase plasma withcomponents whose temperatures and metallicities span the rangeexpected in group and cluster environments.We compute the two temperatures mentioned above ( T X and T spec ) using either all the hot diffuse particles within R or onlythose within the radial range . R ≤ r ≤ R . The lat-ter measures will be referred to as “core-corrected” and identifiedwith subscript “corr” (short for ‘corrected’). Observational studiesof groups typically quote “core-corrected” temperatures.Comparing T spec to T X , we find that in the small ( ≤ keV)groups, the two agree with each other to within ∼ T spec nor T X is an unbiased measure of the actual mean temperature of the gas, which is much better approximated via amass-weighted average.Finally, we point out that to compare the X-ray scaling rela-tions for our simulated groups across different redshifts, we adoptthe common convention in the literature and plot quantities moti-vated by the self-similar model of group and cluster halos (Kaiser1986). In this model, the scaling relations are preserved when usingthe quantities L X ( z ) E ( z ) − , M ∆ ( z ) E ( z ) and S ∆ ( z ) E ( z ) / ,where E ( z ) ≡ H ( z ) /H is the dimensionless Hubble parame-ter ( c.f., equation 3), instead of L X ( z ) , M ∆ ( z ) and S ∆ ( z ) . Theself-similar model assumes that the profiles describing the inter-nal structure of all groups and clusters have the same functionalform, with the gas properties created through gravitational collapsealone, so that these properties scale only with the system mass andthe critical density at the time of observation. Strictly speaking, theself-similar model is an anachronism in that it does not account forprocesses like radiative cooling or heating of the gas by stellar (orAGN) winds and jets, or for a variation in the IGrM fraction withhalo mass. As a result, the observed scaling with mass deviatesfrom the predictions of this model. Nonetheless, the observed scal-ing with redshift (for moderate redshift values) agrees surprisinglywell with the self-similar predictions, suggesting that over limitedperiods of time the systems may well be evolving in a self-similarfashion. For further details, we refer the readers to § In this section, we discuss some of the global properties of galaxygroups, focusing on the observed X-ray scaling relations, of thesimulated z = 0 groups and compare these to those of simulatedgroups at earlier epochs ( z = 0 . to . ), and to available observa-tions. As we shall show, even in the absence of AGN feedback, thepresent model does remarkably well in accounting for the observa-tions. In the absence of feedback and cooling flows, the X-ray luminosityon the group scale ought to scale with the mean gas temperatureof the IGrM as L X ∝ T (Balogh et al. 1999; Babul et al. 2002).This relationship is flatter than the more familiar L X ∝ T scalingin situations where bremsstrahlung dominates the X-ray emissionbecause at temperatures less than 1 keV recombination radiation isas important, if not more, than bremsstrahlung. The observed scal-ing relationship for groups, L X ∝ T , however, is much steeper(Helsdon & Ponman 2000), indicating that either heating (Baloghet al. 1999; Babul et al. 2002) and/or cooling (Voit & Bryan 2001)has significantly altered the hot X-ray gas distribution. Both pro-cesses eliminate the denser, lower entropy, X-ray bright, gas.Figure 4 shows the rest-frame . − . keV X-ray luminos-ity emitted within the central R versus the mean core-correctedspectroscopic temperature (solid lines) for the simulated groupsat redshifts z = 0 (black), . (blue), (red), (green) and (cyan). Once cosmic evolution is taken into account, the group L X − T spec , corr curves at z ≤ essentially lie on top of eachother. At higher redshifts, however, the groups – at a given tempera-ture – are less luminous than predicted by the self-similar evolutionmodel. These trends can be understood in terms of the behaviourof the hot gas fraction in the groups that we will discuss in the nextsubsection. MNRAS , 1–26 (2015)
L. Liang et al. − − − log T spec , corr (keV) l og L x , . − k e V E ( z ) − ( e r g s − ) z = 0z = 0.5z = 1z = 2z = 3 mass-weighted temperaturespectroscopic temperatureemission-weighted temperature Figure 4.
X-ray luminosity − T relation for simulated groups at z = 0 (black), z = 0 . (blue), and z = 1 (red), z = 2 (green), and z = 3 (cyan). The solid lines show the scaling relationship between the X-ray lu-minosity that is emitted by gas within R and the core-corrected spectro-scopic temperature. The error bars indicate 1- σ scatter. The dotted and thedashed curves show the mean L X − T for the z = 0 simulated groups,where T is the mass-weighted and emission-weighted temperature (bothcore-corrected), respectively. Squares, stars and triangles show observedlow redshift group data from Osmond & Ponman (2004), Pratt et al. (2009)and Eckmiller et al. (2011), respectively. We plot all the groups in Osmond& Ponman (2004) including those with a small radial extent in observableX-rays (i.e. their H sample). Luminosity in the Pratt et al. (2009) and Eck-miller et al. (2011) data is corrected to the . − keV band. Focusing on the mean L X − T spec , corr relationship for oursimulated z = 0 groups, we note that this is in good agreementwith the observations for T spec , corr < ∼ keV. In this low tempera-ture regime, the luminosity scales as L X ∝ T . , corr . The steepnature of this relationship is partly due to the use of spectroscopictemperature. The spectroscopic temperature can differ considerablyfrom the true temperature. To illustrate this, we plot in Figure 4 the L X − T relationship for our z = 0 simulated groups using the core-corrected mass-weighted temperature ( T mw – black dotted curve).For T < ∼ keV, L X ∝ T . . The difference between this relation-ship and the self-similar expectation ( L X ∝ T ) suggests that thegroups have been subjected to some process that has a greater im-pact on the IGrM in groups with the shallowest potential wells (lowtemperatures) and less so on the gas in groups with the deepest po-tential wells (high temperatures). Both heating (or preheating) ofthe IGrM by the galactic outflows, which will cause the gas to ex-pand out of (or resist falling into) the shallowest potential wells,as well as the removal of the IGrM by radiative cooling, are plausi-ble mechanisms. At this point, we cannot distinguish between thesetwo. For T > . keV, the L X − T based on the spectroscopic andthe mass-weighted temperatures converge, implying that in massivegroups, the former is a good measure of the latter. Both scaling re-lations also start to flatten as bremsstrahlung grows in importance.However, we note that compared to the observations, the high mass For consistency, we use the same mass-concentration relationshipadopted by Leauthaud et al. (2010). l og L x , . − . k e V E ( z ) − ( < R )( e r g s − ) log M E(z) (M ⊙ ) z = 0z = 0.5z = 1z = 2z = 3 Figure 5. L X − M relation for simulated groups at z = 0 (black), z = 0 . (blue), z = 1 (red), z = 2 (green), and z = 3 (cyan). The error barsshow 1- σ scatter. The circles, stars and squares show data from Eckmilleret al. (2011), Pratt et al. (2009), and Leauthaud et al. (2010), respectively.The hydrostatic mass estimates from the first two studies have been cor-rected for the hydrostatic bias (Hoekstra et al. 2015) and L X, bol from Prattet al. (2009) have been converted to L X, . − . . We also convert theweak-lensing M values from Leauthaud et al. (2010) to M using anNFW profile, and we scale their luminosities using the median value of L X, . − . ( < R ) /L X, . − . ( < R ) for our simulatedgroups. The observed groups at z ≤ . , . < z ≤ . , and z > . are plotted as black, blue and red symbols, respectively. simulated groups are more luminous, and/or a bit cooler. This sug-gests that the hot gas in these systems is denser than in real systems.In the scenario where the galactic outflows really do impact the gasdensity in shallow wells, the emergence of overluminous groups astheir halo mass approaches (and exceeds) M ≈ M (cid:12) suggeststhat the outflows have become ineffectual and another mechanismis necessary.For illustrative purposes, we also plot L X − T relationshipfor the z = 0 groups using the mean emission-weighted tempera-ture ( T X – black dashed curve). Until relatively recently, this wasthe relationship used to compare model L X − T to observations.For the lowest temperature groups, the emission-weighted and thespectroscopic temperatures are nearly equal, and the two L X − T curves track each other. For T > . keV, the emission-weighted L X − T X deviates from that based on the spectroscopic temperatureand remains in good agreement with the observations. This agree-ment, however, is spurious since the observations are based on thespectroscopic temperature, and indicates a need for caution: Thecomparison between the T X − based relation for simulated groupsand the T spec − based observations masks the need for an additionalheating or redistribution mechanism in the more massive groups.It is instructive to compare our results to those of the “stel-lar feedback only” run from the OWLS collaboration (referred toas the “Reference Model” in McCarthy et al. 2010 and as the“ZCool+SF+SN model” in McCarthy et al. 2011). This model(hereafter referred to as OWLS-stars) primarily accounts for onlySNe feedback, which is implemented via the kinetic wind model ofDalla Vecchia & Schaye (2008), where the mass loading factor isfixed to constant ( η = 2 ) instead of varying inversely with galaxyvelocity dispersion as in our model and the wind velocity is also set MNRAS000
X-ray luminosity − T relation for simulated groups at z = 0 (black), z = 0 . (blue), and z = 1 (red), z = 2 (green), and z = 3 (cyan). The solid lines show the scaling relationship between the X-ray lu-minosity that is emitted by gas within R and the core-corrected spectro-scopic temperature. The error bars indicate 1- σ scatter. The dotted and thedashed curves show the mean L X − T for the z = 0 simulated groups,where T is the mass-weighted and emission-weighted temperature (bothcore-corrected), respectively. Squares, stars and triangles show observedlow redshift group data from Osmond & Ponman (2004), Pratt et al. (2009)and Eckmiller et al. (2011), respectively. We plot all the groups in Osmond& Ponman (2004) including those with a small radial extent in observableX-rays (i.e. their H sample). Luminosity in the Pratt et al. (2009) and Eck-miller et al. (2011) data is corrected to the . − keV band. Focusing on the mean L X − T spec , corr relationship for oursimulated z = 0 groups, we note that this is in good agreementwith the observations for T spec , corr < ∼ keV. In this low tempera-ture regime, the luminosity scales as L X ∝ T . , corr . The steepnature of this relationship is partly due to the use of spectroscopictemperature. The spectroscopic temperature can differ considerablyfrom the true temperature. To illustrate this, we plot in Figure 4 the L X − T relationship for our z = 0 simulated groups using the core-corrected mass-weighted temperature ( T mw – black dotted curve).For T < ∼ keV, L X ∝ T . . The difference between this relation-ship and the self-similar expectation ( L X ∝ T ) suggests that thegroups have been subjected to some process that has a greater im-pact on the IGrM in groups with the shallowest potential wells (lowtemperatures) and less so on the gas in groups with the deepest po-tential wells (high temperatures). Both heating (or preheating) ofthe IGrM by the galactic outflows, which will cause the gas to ex-pand out of (or resist falling into) the shallowest potential wells,as well as the removal of the IGrM by radiative cooling, are plausi-ble mechanisms. At this point, we cannot distinguish between thesetwo. For T > . keV, the L X − T based on the spectroscopic andthe mass-weighted temperatures converge, implying that in massivegroups, the former is a good measure of the latter. Both scaling re-lations also start to flatten as bremsstrahlung grows in importance.However, we note that compared to the observations, the high mass For consistency, we use the same mass-concentration relationshipadopted by Leauthaud et al. (2010). l og L x , . − . k e V E ( z ) − ( < R )( e r g s − ) log M E(z) (M ⊙ ) z = 0z = 0.5z = 1z = 2z = 3 Figure 5. L X − M relation for simulated groups at z = 0 (black), z = 0 . (blue), z = 1 (red), z = 2 (green), and z = 3 (cyan). The error barsshow 1- σ scatter. The circles, stars and squares show data from Eckmilleret al. (2011), Pratt et al. (2009), and Leauthaud et al. (2010), respectively.The hydrostatic mass estimates from the first two studies have been cor-rected for the hydrostatic bias (Hoekstra et al. 2015) and L X, bol from Prattet al. (2009) have been converted to L X, . − . . We also convert theweak-lensing M values from Leauthaud et al. (2010) to M using anNFW profile, and we scale their luminosities using the median value of L X, . − . ( < R ) /L X, . − . ( < R ) for our simulatedgroups. The observed groups at z ≤ . , . < z ≤ . , and z > . are plotted as black, blue and red symbols, respectively. simulated groups are more luminous, and/or a bit cooler. This sug-gests that the hot gas in these systems is denser than in real systems.In the scenario where the galactic outflows really do impact the gasdensity in shallow wells, the emergence of overluminous groups astheir halo mass approaches (and exceeds) M ≈ M (cid:12) suggeststhat the outflows have become ineffectual and another mechanismis necessary.For illustrative purposes, we also plot L X − T relationshipfor the z = 0 groups using the mean emission-weighted tempera-ture ( T X – black dashed curve). Until relatively recently, this wasthe relationship used to compare model L X − T to observations.For the lowest temperature groups, the emission-weighted and thespectroscopic temperatures are nearly equal, and the two L X − T curves track each other. For T > . keV, the emission-weighted L X − T X deviates from that based on the spectroscopic temperatureand remains in good agreement with the observations. This agree-ment, however, is spurious since the observations are based on thespectroscopic temperature, and indicates a need for caution: Thecomparison between the T X − based relation for simulated groupsand the T spec − based observations masks the need for an additionalheating or redistribution mechanism in the more massive groups.It is instructive to compare our results to those of the “stel-lar feedback only” run from the OWLS collaboration (referred toas the “Reference Model” in McCarthy et al. 2010 and as the“ZCool+SF+SN model” in McCarthy et al. 2011). This model(hereafter referred to as OWLS-stars) primarily accounts for onlySNe feedback, which is implemented via the kinetic wind model ofDalla Vecchia & Schaye (2008), where the mass loading factor isfixed to constant ( η = 2 ) instead of varying inversely with galaxyvelocity dispersion as in our model and the wind velocity is also set MNRAS000 , 1–26 (2015) he Growth and Enrichment of Intragroup Gas to a constant, km/s. Comparing the resultant L X − T X for thesimulated groups ( c.f., right panel of Figure 6 in McCarthy et al.2010), we find that the groups in the OWLS-stars run are about afactor of ∼ more luminous than our groups at T ≈ . keV, andabout a factor of ∼ more luminous than our groups at T ≈ keV.While our results match the observed L X − T X relationship, theirslie systematically above the observations and define a shallowertrend. A comparison with the results shown in McCarthy et al.(2011) indicates that this difference is due to a larger IGrM compo-nent within R in the OWLS-stars groups and possibly that theIGrM is more centrally concentrated and hence, denser. We willcomment on this further in the next section where we discuss theIGrM and the baryon fractions in our groups.Finally, we note that the error bars on the simulation resultsindicate 1- σ scatter above and below the mean. The scatter in theobservational data is significantly larger. There are a number of pos-sible reasons for this difference. First, our simulations are missingAGN feedback and one can imagine that the variations introducedby yet another heating/redistribution mechanism could increase thedispersion in the X-ray luminosity of the simulated groups at a fixedtemperature (see, for example, McCarthy et al. 2010). The observa-tions, however, are also not homogeneous. For instance, we plot allgroups in Osmond & Ponman (2004), including those in which theX-ray emission is only detected to a relatively small radial extent.This can artificially enhance the scatter. In fact, most group sam-ples, including the ones plotted, are not statistically representative(O’Sullivan et al. 2014) and the inhomogeneities and biases willalso be reflected in the scatter.Figure 5 shows the L X − M trends for the simulated groups atredshifts z = 0 (black), z = 0 . (blue), z = 1 (red), z = 2 (green)and z = 3 (cyan). This time we plot the rest-frame 0.1-2.4 keV X-ray luminosity to facilitate comparison with available observations.Like the L X − T spec , corr curves, once cosmic evolution is takeninto account through the dimensionless Hubble parameter E ( z ) ,the L X − M curves for the z ≤ group populations scale as L x ∝ M . and essentially lie on top of each other, implying a self-similar evolution over this redshift range. Like the L X − T spec , corr relations, the higher redshift curves lie off those at z ≤ and thedeviation goes in the same direction. The groups at a given valueof M E ( z ) – note that temperature and M E ( z ) are equivalentmeasures of the depth of the gravitational potential well – are lessluminous than predicted by the self-similar evolution model and theunderlying reasons, on which we will elaborate when we discussthe behaviour of the hot gas fraction in the groups, are also thesame.There are two different types of observational data shown inthe plot: One set (black circles and stars), where the group massesare in fact hydrostatic mass estimates derived from the X-ray mea-surements by Eckmiller et al. (2011) and Pratt et al. (2009), respec-tively, and another (black, blue and red squares), where the massesare derived using weak lensing methods (Leauthaud et al. 2010). Itis well known that the hydrostatic masses typically underestimatethe true mass and to facilitate a fair comparison with our actual mass determinations, we have corrected the Pratt et al. (2009) andEckmiller et al. (2011) masses using the bias factor determined byHoekstra et al. (2015) (see also Mahdavi et al. 2013). Our numer-ical results are in good agreement with the observational results.Moreover, the fact that the L X − M trends delineated by the black,blue and red points show no significant offsets from each other sug-gests that the evolution of the observed group L X − M relation isconsistent with that predicted by the self-similar model over the − − − l og [ M E ( z ) ] ( M ⊙ ) log T spec , corr (keV) z = 0z = 0.5z = 1z = 2z = 3 Figure 6. M − T spec , corr relation for simulated groups at z = 0 (black), z = 0 . (blue), z = 1 (red), z = 2 (green), and z = 3 (cyan). The er-ror bars show 1- σ scatter. The black squares and triangles show the resultsfrom Sun et al. (2009) and Eckmiller et al. (2011). The hydrostatic massestimates given in these two studies have been corrected for the hydrostaticbias (Hoekstra et al. 2015). We also note that the temperatures in the lat-ter study are not always extracted in a consistent, systematic fashion. Thediamonds show results from Kettula et al. (2013); their masses are weak-lensing estimates. The observed groups at z ≤ . and . < z ≤ . are plotted as black and blue symbols, respectively. redshift range ≤ z < , which is also in agreement with ournumerical results.Figure 6 shows the M − T spec , corr trends for the simulatedgroups at redshifts z = 0 (black), z = 0 . (blue), z = 1 (red), z = 2 (green) and z = 3 (cyan). Once cosmic evolution is takeninto account, all the curves, even those for z > groups, lie on topof each other. The shape of these curves differs from that shownin Figure 3 because there we had plotted mass versus emission-weighted temperature whereas here we are using the core-corrected spectroscopic temperature. Comparing the M − T relation for oursimulated z = 0 groups to that of OWLS-stars groups ( c.f., Figure 5of McCarthy et al. 2010, – this figure shows mass versus emission-weighted temperature whereas we plot mass versus spectroscopictemperature), we find that the two are in excellent agreement witheach other once the differences between the two temperatures at T spec , corr > ∼ . keV are accounted for.As in Figure 5, we plot corrected hydrostatic masses (squaresand triangles) and masses derived from weak lensing analyses(black and blue diamonds). Within the scatter, all the data (weaklensing and X-ray based, present-day and at moderate redshift)are consistent with each other. Focusing on measurements with T spec , corr > . keV, the scaling of mass with temperature canbe well described by M ∝ T . , corr , which is consistent withthe self-similar scaling relationship. The numerical trends, on theother hand, are steeper in the neighbourhood of keV but flattensat both higher and lower temperatures. In spite of this, the numer-ical results are consistent with the observations except perhaps forthe most massive groups with M > ∼ M (cid:12) . In these massivesystems, the temperature in the simulated systems seems to be a bitcooler than that in the observed systems. We note that this diver- MNRAS , 1–26 (2015) L. Liang et al. gence at the high mass end is also present in the L X − T spec , corr plot. At various points in the preceding discussion, we have notedthat the trends exhibited by the simulated groups in the L X − T spec , corr − M space are the consequences of two different typesof processes: (1) the structure of the intergalactic medium that col-lapses to form the IGrM and, therefore, the properties of the IGrMitself, are altered by the galactic outflows from an earlier ( z > )generation of galaxies; and (2) heating and/or cooling processes oc-curring once the groups form can convert the cooler, denser, X-rayluminous gas into either hotter, more diffuse (and therefore, lessluminous) gas, or into cold, dense gas that is effectively dark inthe X-rays. To gain insights into the relative importance of theseeffects, we examine the entropy of the hot X-ray emitting gas. Entropy is a very useful physical quantity to consider when theIGrM is subject to cooling and heating processes because the for-mer typically lowers the entropy while the latter always raises it.This is not the case with either density or temperature because heat-ing can cause the gas to expand, potentially lowering both quan-tities (see McCarthy et al. 2008, for a more detailed discussion).Additionally, the gas distribution will tend to organize itself so thatthe lowest entropy gas is at the group centre and the highest is atthe group periphery. On the other hand, in the present situation,there is an additional complication to keep in mind: If cooling isable to cause the low entropy IGrM in the center to drop out andsettle in the central galaxy, higher entropy gas from further out willflow in to take its place and the entropy in the centre will appear“enhanced” unless cooling is able to erode the entropy of this in-flowing gas as quickly as it flows in. This effect was first seen inthe numerical simulation by Lewis et al. (2000) and discussed morefully by Voit & Bryan (2001).In Figure 7, we show the cosmic expansion corrected gas en-tropy at R (top panel) and R (bottom panel), in present-daygroups (black solid curve) as well as for groups at z = 0 . (blue), z = 1 (red), z = 2 (green), and z = 3 (cyan), as a functionof the integrated core-corrected spectroscopic temperature of theIGrM within R . We also plot entropy estimates from the X-rayobservations of Sun et al. (2009), computed using the deprojectedtemperature and electron density profiles. To be precise, we are not plotting the actual thermodynamic specific entropy, but rather itswidely accepted proxy given by S ( r ) = k B T spec ( r ) n e ( r ) / , (5)where k B is the Boltzmann constant, and T spec ( r ) and n e ( r ) are,respectively, the spectroscopic temperature and the electron num-ber density within a thin spherical shell at radius r . We shall, here-after, refer to S ( r ) as ‘entropy’.Focusing first on the R , we see that scaled entropy sys-tematically declines with time. The change is much greater at highredshifts ( z > ) than at low redshifts ( z < ) and also, muchmore stronger in groups with shallow potential wells than in thosewith deep potential wells. Both results are primarily driven by theevolution in the IGrM density at R . For group halos of a given The ‘entropy proxy’ (S) and the thermodynamic specific entropy (s) arerelated to each other as ds ∝ d ln S (see Balogh et al. 1999). − − − log T spec , corr (keV) l og S E / ( z )( k e V c m ) z = 0z = 0.5z = 1z = 2z = 3 l og S E / ( z )( k e V c m ) S S Figure 7.
Gas entropy at R (top panel) and R (bottom panel) ofthe simulated groups at z = 0 (black), z = 0 . (blue), z = 1 (red), z = 2 (green) and z = 3 (cyan), as a function of core-corrected spectro-scopic temperature. The error bars show 1- σ scatter. The observational dataof the low redshift sample from Sun et al. (2009, hereafter S09) is shownby black squares. The dashed lines in the top and bottom panels representthe power-law fits to the S − T relation at the two different radii for thefull group+cluster sample from S09, with a power law index of 1 and 0.74,respectively. temperature, if we take the present-day value of IGrM density at R as a reference, then we are led to conclude that the IGrMdensity at R at an earlier epoch is not E ( z ) times the present-day value, as would be expected if the IGrM density were evolv-ing self-similarly. Rather, it is lower than the expected value andhence, the cosmic expansion corrected entropy is higher. Put an-other way, the halos at z = 3 are IGrM poor (relative to the totalmatter). As the halos grow, they encompass additional dark andbaryonic matter but the ratio of baryons-to-dark matter is largerthan the universal value. In effect, the groups are recapturing someof the baryons that were ejected from their member galaxies at ear-lier times, in addition to the usual complement associated with theaccreting dark matter (reminiscent of the “outside-in” IGM enrich-ment scenario of Oppenheimer et al. 2012). The higher tempera-ture groups are able to recapture a greater fraction of the previouslyexpelled baryons at an earlier time ( z > ) than the lower temper-ature groups. The outcome of this differential accretion of baryonsand dark matter is that the density of hot gas in the groups evolvesdifferently from self-similar expectations – i.e., until z ≈ , afterwhich the evolution of the entropy and the density for all the group MNRAS000
Gas entropy at R (top panel) and R (bottom panel) ofthe simulated groups at z = 0 (black), z = 0 . (blue), z = 1 (red), z = 2 (green) and z = 3 (cyan), as a function of core-corrected spectro-scopic temperature. The error bars show 1- σ scatter. The observational dataof the low redshift sample from Sun et al. (2009, hereafter S09) is shownby black squares. The dashed lines in the top and bottom panels representthe power-law fits to the S − T relation at the two different radii for thefull group+cluster sample from S09, with a power law index of 1 and 0.74,respectively. temperature, if we take the present-day value of IGrM density at R as a reference, then we are led to conclude that the IGrMdensity at R at an earlier epoch is not E ( z ) times the present-day value, as would be expected if the IGrM density were evolv-ing self-similarly. Rather, it is lower than the expected value andhence, the cosmic expansion corrected entropy is higher. Put an-other way, the halos at z = 3 are IGrM poor (relative to the totalmatter). As the halos grow, they encompass additional dark andbaryonic matter but the ratio of baryons-to-dark matter is largerthan the universal value. In effect, the groups are recapturing someof the baryons that were ejected from their member galaxies at ear-lier times, in addition to the usual complement associated with theaccreting dark matter (reminiscent of the “outside-in” IGM enrich-ment scenario of Oppenheimer et al. 2012). The higher tempera-ture groups are able to recapture a greater fraction of the previouslyexpelled baryons at an earlier time ( z > ) than the lower temper-ature groups. The outcome of this differential accretion of baryonsand dark matter is that the density of hot gas in the groups evolvesdifferently from self-similar expectations – i.e., until z ≈ , afterwhich the evolution of the entropy and the density for all the group MNRAS000 , 1–26 (2015) he Growth and Enrichment of Intragroup Gas halos is consistent with self-similar evolution. We will examine thedensity and entropy profiles in detail in a follow-up paper. How-ever, this general behaviour also explains the self-similar evolutionof the L X − T spec , corr and L X − M from z = 0 to z = 1 and then,the decrease in the amplitude of the (cosmic expansion corrected)scaling relation from z = 1 to z = 3 ( c.f., Figures 4 and 5). Athigher redshifts, the groups of a given temperature or M E ( z ) (bothare equivalent measures) are not as luminous as they ought to be ifthey were evolving self-similarly because the IGrM is not as denseas self-similarity would predict.In contrast with S , S evolves somewhat differently.The scaled entropy evolves self-similarly from z ≈ to the presentand even between z = 3 and z = 2 , the change is relatively mild.The core regions tend to form earlier and we expect that they willsettle down into a steady-state configuration at an earlier epoch.DOS08 compared the core entropies of groups in a simulation withand without outflows and found that the gas in the former case hadhigher entropy. This is a non-trivial result. As we mentioned above,it is not unexpected to see elevated entropies at R in simula-tions with cooling, star formation and inefficient stellar feedback(hereafter Cool+SF simulations – for more details about such sim-ulations, see Lewis et al. 2000; Kravtsov et al. 2005, and DOS08),relative to a non-radiative simulation ( c.f.,
Figure 10 of Lewis et al.2000). The inclusion of outflows, however, could just as easily haveled to still higher core entropies, or lower core entropies. As DOS08explain, the latter can occur if heating from the outflows just bal-ances cooling, and the low-entropy gas remains in place unchanged, i.e., it is neither removed via cooling nor raised to a higher adiabat.The outflows in our simulations, on average, heat the IGrM at leastclose to the centre of the groups.Comparing S and S entropy results for our simulatedgroups to the observations, we find that the IGrM entropy at R in our massive groups is consistent with the observations. Sun et al.(2009) find that the observed S values scale with the integratedcore-corrected spectroscopic temperature of the gas within R as S ∝ T spec , corr (dashed line) across their full sample of groupsand clusters. Our simulation results also follow the same scaling for T spec , corr > . keV. Below this threshold, S in the simulatedgroups flattens. This flattening is because of a decrease in the IGrMdensity with decreasing group mass. We will discuss this furtherin the next subsection. At R , Sun et al. (2009) find that theobserved entropy scales as S ∝ T . , corr (dashed line). The S of the groups in the simulated sample is less steep, scalingwith temperature as S ∝ T . , corr , and the simulated groupsat the high mass end have approximately lower core entropiescompared to the observations. One explanation is that the density ofIGrM in the cores of the massive simulated groups is slightly higherthan in real groups and this, in turn, would explain why massivesimulated groups seem to be somewhat more X-ray luminous thantheir real counterparts.Comparing our entropy results to those of groups in theOWLS-stars run (see Figure 2 in McCarthy et al. 2010), we findthat entropy at R in the two simulations is very similar. At R , however, the entropy in the OWLS groups is lower thanin our groups by approximately − . This supports our pre-vious conjecture that the IGrM in OWLS groups is more centrallyconcentrated than in our groups, which in turn would explain thedifferences in the X-ray luminosities of the two group populations.Overall our stellar-powered wind model fares remarkably wellwhen it comes to matching the observed group L X − T spec , corr − M scaling relations except perhaps in the most massive groups. Thebehaviour of the IGrM entropy at R and R suggests that the principal variable governing the behaviour of these relationships inour simulated groups is the IGrM density. We now turn to direct determinations of the total baryon fractionas well as the stellar and the IGrM gas mass fractions in the sim-ulated groups to confirm whether the IGrM density behaves as wehave argued above, and try to understand the reasons behind itsbehaviour. The partitioning of the baryons between stars and hotgas is interesting in and of itself. We know that our model is notable to suppress the overproduction of stars in the largest galaxiesin the groups ( c.f.,
Figure 2) but by looking into the issue morecarefully, we hope to understand when and where the model startsto fail. Additionally, we also quantify the assembly of the groupsusing several different measures.
The sequence of plots in the left panel of Figure 8 shows the to-tal baryon,
T > × K , hot, diffuse gas (IGrM), stellar, andcold gas fractions in simulated groups at z = 0 , as function ofthe total group mass. All the quantities are computed with R to facilitate comparisons with the observations. The plots in theright column show the same mass fractions within R to illus-trate their behaviour across group populations at different redshiftsas well as beyond just the inner regions of the halos. The colouredlines show the results for groups at z = 0 (black), . (blue), . (red), . (magenta), . (green) and . (cyan). On the x -axis,we plot M E ( z ) so that we can compare populations of ha-los with potentials of similar depths across the different epochs.Baryon properties, as well as the impact of feedback and radia-tive cooling, both tend to be strongly correlated with the depth ofthe halos’ gravitational potential well. For completeness, we notethat we have tracked the evolution of individual groups in the rightcolumn of Figure 8 and find that once formed, they do not sim-ply evolve vertically in these plots. Rather, they move both verti-cally up or down (depending on the quantity under consideration)with decreasing redshift, transitioning from one coloured line to thenext, while also generally sliding to the right along the x -axis. Thisis because the masses of individual groups generally grow fasterthan expected under the self-similar growth model; i.e., they in-crease faster than M ( z group ) [ E ( z group ) /E ( z )] , where z group is the redshift at which the most massive progenitor halos of thepresent-day groups first acquire three luminous galaxies and as perour definition, become ‘groups’. Consequently, the potential wellof individual groups tend to deepen towards the present.In the first panel of both columns, we investigate the totalbaryon fraction. The solid line indicates the cosmological baryonfraction of Ω b / Ω m = 0 . for the simulation. The red trian-gles, blue squares, golden circles and orange stars in the left panelshow observational estimates of the fraction of mass in hot gas andstars, which for massive groups is essentially the same as the to-tal baryon fraction, from Lin et al. (2003), Giodini et al. (2009,revised ), Gonzalez et al. (2013), and Lagan´a et al. (2013), respec- The results for Giodini et al. (2009) shown in Figure 8 differ from thosein their paper because they have been revised as suggested by Leauthaudet al. (2012). See also discussion in Giodini et al. (2012). The stellar massesresults presented are derived using the Chabrier IMF.MNRAS , 1–26 (2015) L. Liang et al. M b a r / M M I G r M / M M c o l d / M log M (M ⊙ ) M ∗ / M M b a r / M M I G r M / M M c o l d / M log M E(z)(M ⊙ ) M ∗ / M z = 0z = 0.5z = 1z = 1.5z = 2z = 3 Figure 8.
Left column: Stellar and gas mass fractions within R in simulated z = 0 groups. Top panel : Total baryonic fraction. The black line indicatesthe cosmological value, Ω b / Ω m = 0.176. The symbols (see text for details) show observational estimates for hot gas + stars. Error bars depict 1- σ scatter. Second panel : Hot gas fraction.
Third panel : Stellar mass fraction. The simulation results include stars in the galaxies as well as those comprising the diffuseintragroup stars [IGS]) component. Of the observational estimates, only the golden circles (Gonzalez et al. 2013) account for the IGS.
Bottom panel : Cold gasfraction ( i.e. diffuse gas with
T < × K and the galactic ISM). Right column: The same mass fractions for simulated groups at z = 0 (black), z = 0 . (blue), z = 1 (red), z = 1 . (magenta), z = 2 (green) and z = 3 (cyan) computed within R to facilitate comparison with observations. Triangles, circlesand squares are observational results from Mok et al. (2013), van der Burg et al. (2014) and Connelly et al. (2012), respectively. Data for z < ∼ . groups arein black, . < z < ∼ . in red, and . < z < ∼ . groups in blue. These do not account for the IGS. tively. Of these, only Gonzalez et al. (2013) (golden circles) explic-itly account for the extended, diffuse intragroup stellar component(hereafter referred to as the intragroup stars or IGS). The simula-tion results include all stars, those in the galaxies as well as thosethat belong to the extended population. In spite of the large scatterin the observed values, the total baryon fraction within R in oursimulated present-day groups is generally greater than that in realgroups by approximately − .This is the first indication that powerful stellar-powered galac-tic outflows, in and of themselves, are not capable of preventing theover-concentration of baryons within R in the simulated groups,in comparison to the observations. This is not to say that the out- flows have no impact on the galaxy groups. The baryon fraction ofour simulated groups is comparable to that seen in non-radiativesimulations (see for instance Crain et al. 2007) – i.e., simulationsthat do not allow for cooling. It is most definitely lower than the val-ues seen in the Cool+SF simulations (Lewis et al. 2000; Kravtsovet al. 2005, DOS08), where the baryon fraction within R is typi-cally equal to or even slightly larger than the universal value. Belowwe try to understand precisely how the galactic outflows affect thebaryon fraction in our simulated groups.Examining the simulation results more closely, we note thatthe median value of the baryon fractions within R in the z = 0 groups exhibits a gradual rise with increasing halo mass, going MNRAS000
T < × K and the galactic ISM). Right column: The same mass fractions for simulated groups at z = 0 (black), z = 0 . (blue), z = 1 (red), z = 1 . (magenta), z = 2 (green) and z = 3 (cyan) computed within R to facilitate comparison with observations. Triangles, circlesand squares are observational results from Mok et al. (2013), van der Burg et al. (2014) and Connelly et al. (2012), respectively. Data for z < ∼ . groups arein black, . < z < ∼ . in red, and . < z < ∼ . groups in blue. These do not account for the IGS. tively. Of these, only Gonzalez et al. (2013) (golden circles) explic-itly account for the extended, diffuse intragroup stellar component(hereafter referred to as the intragroup stars or IGS). The simula-tion results include all stars, those in the galaxies as well as thosethat belong to the extended population. In spite of the large scatterin the observed values, the total baryon fraction within R in oursimulated present-day groups is generally greater than that in realgroups by approximately − .This is the first indication that powerful stellar-powered galac-tic outflows, in and of themselves, are not capable of preventing theover-concentration of baryons within R in the simulated groups,in comparison to the observations. This is not to say that the out- flows have no impact on the galaxy groups. The baryon fraction ofour simulated groups is comparable to that seen in non-radiativesimulations (see for instance Crain et al. 2007) – i.e., simulationsthat do not allow for cooling. It is most definitely lower than the val-ues seen in the Cool+SF simulations (Lewis et al. 2000; Kravtsovet al. 2005, DOS08), where the baryon fraction within R is typi-cally equal to or even slightly larger than the universal value. Belowwe try to understand precisely how the galactic outflows affect thebaryon fraction in our simulated groups.Examining the simulation results more closely, we note thatthe median value of the baryon fractions within R in the z = 0 groups exhibits a gradual rise with increasing halo mass, going MNRAS000 , 1–26 (2015) he Growth and Enrichment of Intragroup Gas [ M b a r ( < R ) / M t o t ( < R ) ] / [ Ω b / Ω m ] . ≤ log M vir E(z) < R / R ≤ log M vir E(z) < . . ≤ log M vir E(z) <
14z = 0z = 0.5z = 1z = 2z = 3Cool+SF
Figure 9.
The mean baryon fraction within radius
R/R in simulated groups at z = 0 groups (black curve), z = 0 . (blue), z = 1 (red), z = 1 . (magenta), z = 2 (green) and z = 3 (cyan), normalized to the cosmic baryon fraction Ω b / Ω m = 0 . for the simulation. We have sorted the groupsinto three bins according to the depth of their potential wells: In each panel, the dashed black curve shows the z = 0 mean baryon fraction profile for the Cool+SF simulation from Lewis et al. (2000), which had no galactic winds. from ∼ of the universal cosmological value in the least mas-sive groups to ∼ of the universal value in the most massivegroups. Comparing these results against those for the OWLS-starsgroups (in this case “ZCOOL+SF+SN” simulation; McCarthy et al.2011), we find good agreement. The median baryon fractions inthe latter groups range from of the cosmological value in thelower mass groups to in the high mass systems. The medianbaryon fractions within R of the z = 0 groups also increasesgradually with halo mass, from ∼ of the universal value inour lowest mass groups to ∼ in the high mass groups. Thebaryon fractions within R are slightly but systematically lowerthan within R because, in our simulated groups, the principalsource of outflows is the dominant central galaxy and as notedwhile discussing the IGrM entropy, these preferentially heat the gasin the central regions.The trend highlighted above, of lower mass systems beingmore baryon depleted, is a common feature of the strong stellarfeedback models. In the case of the momentum-driven wind model,Dav´e (2009) has shown that the baryon fraction in present-dayMilky Way-sized halos ( ∼ M (cid:12) ) drops to of the cos-mic value and decreases further to below of the cosmologicalvalue in lower mass galactic halos ( ∼ M (cid:12) ). On these galacticscales, the reason is fairly clear. The winds physically carry awaya large fraction of the baryons from such systems and in fact, candrive down the baryon fraction over regions that extend well be-yond the virial radius of the galactic halos. Similar results are alsoseen in other “no AGN” simulations where stellar feedback is im-plemented via a thermal prescription (see Sokołowska et al. 2015,and references therein).As one moves up in halo mass, the deepening gravitationalpotential wells engender a transition from a state where the bulkof the baryonic matter within a halo is in the form of stars andcold gas localized in the galaxy (or galaxies), to one where thehot diffuse gas component that suffuses the entire halo eventuallydominates the baryon budget. This transition has been discussed indetail by Kereˇs et al. (2009) and Gabor & Dav´e (2015), and ref-erences therein. Following Gabor & Dav´e (2015), we define thetransition point between these two states as one where the hot gasmass exceeds 50% of the total gas mass. In our simulations, thischangeover group mass occurs at M ≈ . × M (cid:12) at z = 0 , M ≈ × M (cid:12) at z = 1 and M ≈ . × M (cid:12) at z = 2 . These masses are comparable to the transition mass cited inGabor & Dav´e (2015) although in detail our transition masses areslightly larger because we impose an additional constraint that thehalos must host at least three luminous galaxies. The presence ofa pervasive IGrM alters the wind dynamics: Galactic winds flow-ing through such a medium are subject to hydrodynamic drag, therelative importance of which grows as the density of the mediumincreases. In the case of our group halos, the combination of thedeeper gravitational potential wells and the higher likelihood ofstrong hydrodynamic interactions results in the winds being almostcompletely confined within the halos. So the reduced baryon frac-tion, relative to the cosmic mean, is not due to the outflow of thebaryons.Instead, the reduced baryon fraction in the group halos is theresult of the following two effects. First, groups typically formin regions that have been rendered somewhat baryon deficient bywinds from their member galaxies at earlier times. Consequently,when the groups first form, their baryon fraction can be as low as ∼ of the cosmic mean, as illustrated by the baryon fractioncurve for z = 3 groups in the top right panel of Figure 8. This“baryon depletion” is illustrated much more clearly in Figure 9. At z ≈ , for example, the baryon fraction within R is − of the mean value for the simulation, and one would have to goout to ∼ R before the fraction returns to the cosmic mean.(For comparison, we also show the baryon fraction profile for a Cool+SF simulation from Lewis et al. (2000); the baryon fractionnever really drops below the mean value and converges to the meanvalue by R .) This depletion is slightly less pronounced in themore massive groups and diminishes towards the present.Returning to the top right panel of Figure 8, we have noted pre-viously that individual groups, once formed, tend to grow in mass.And as the halos grow, their physical reach extends further out. Asa result, in addition to the inflow of the usual baryonic complementof the accreting dark matter, they are also able to recapture an in-creasing fraction of the expelled gas previously associated with thegroup galaxies ( c.f., Ford et al. 2014, for a discussion of a simi-lar phenomenon in galactic halos.), and the overall baryon fractionincreases with halo mass.This, however, is not all. There is a second effect at play, oth-
MNRAS , 1–26 (2015) L. Liang et al. erwise we would expect the baryon fraction to continue rising withdecreasing redshift and approach the mean cosmological value. In-stead, we observe a sharp increase in the halo baryon fraction be-tween z = 3 and z = 2 , a much more tempered rise from z = 2 to z = 1 , and very little change, if any, thereafter. This second effectis the result of the winds ejected from the group galaxies interactingwith and heating the hot halo gas, which not only reduces the rateat which the halo gas cools and accumulates in the group centralgalaxies but also causes its distribution to remain more extended.In the preceding discussion, we use the word “extended” de-liberately. Hot gaseous halos generally extend beyond the virial ra-dius ( c.f., Bah´e et al. 2013; Gabor & Dav´e 2015) but in simulationswithout winds, radiative cooling inside the halos leads to the lossof pressure support, which then results in a denser, more compactbaryon distribution. In the case of our wind model, the hot halo gasdensity starts out lower than usual and it is easier for heating bythe winds to compensate for a significant fraction of the radiativecooling losses and drastically slow down its collapse. As indicatedin the top right panel, halos with gravitational potential wells ofa given depth ( i.e., at a fixed M E ( z ) ) establish an equilibriumdistribution by z = 1 , and the baryon fraction remains essentiallyconstant from z = 1 to the present.However, the efficacy of the galactic winds to maintain an ex-tended hot gas distribution via heating drops with deepening po-tential wells because the characteristic temperature ( T wind ) corre-sponding to the complete thermalization of the kinetic energy in theoutflows from any one galaxy in a group halo, even the dominantgalaxy, does not grow as quickly as the group halo’s virial tem-perature ( T vir ). The reason for this is that T wind scales as M / ,where M gal is the mass of individual galaxies, whereas T vir growsas M / and as we explain below, the fraction of the baryons con-densing into the cold gas + stars phase decreases with increasinggroup halo mass. Moreover, by virtue of being multi-galaxy sys-tems, even the baryons that have condensed out are distributed over3 or more “luminous” galaxies. In the end, the IGrM is not able towithstand gravitational compression despite being heated.The second set of panels in Figure 8 show the diffuse hot ( T > × K ) IGrM gas fraction in the simulated groups. The IGrMfraction within R (left column) nearly doubles, from ∼ . to . , in going from M ≈ × M (cid:12) to M ≈ M (cid:12) .This increase with group mass is the result of the larger mass sys-tems having deeper potential wells and higher virial temperatures.As a result, more of the diffuse gas is shock-heated to constitute theIGrM. Additionally, the deeper potential wells are also better ableto compress and confine this gas.Comparing our results against Figure 4 of McCarthy et al.(2010), we find that the IGrM gas fraction within R of com-parable groups at the low mass end of the group distribution inour simulation is about lower ( i.e., . for our groups ver-sus . for the OWLS-stars groups) and about lower for thegroups at the high mass end. The lower IGrM fraction is a key rea-son why our simulated groups are less X-ray luminous than theOWLS-stars groups. We do note that McCarthy et al. (2010) definethe IGrM using the temperature cut of T > × K instead of T > × K , as we have. However, we have recomputed theIGrM fraction for our groups using this lower threshold and findnegligible changes to our results.Comparing the simulation results for the z = 0 IGrM frac-tion within R (left panel) against observations (red triangles,open magenta squares, green stars , filled blue squares, golden cir-cles, and orange stars are data from Lin et al. (2003), Sun et al. (2009), Sanderson et al. (2009), Giodini et al. (2009), Gonzalezet al. (2013), and Lagan´a et al. (2013), respectively), we find thatthe two are in reasonable agreement. In detail, there is a hint that theIGrM fraction in the simulated groups is rising slightly faster withincreasing group mass but it is difficult to be more definite giventhe large scatter in the observations. Such a trend would, however,be consistent with our previous finding that the most massive sim-ulated groups are slightly more X-ray luminous than real systemsand that the stellar-powered winds are unable to keep the baryonfraction from creeping upwards. Together, all of these suggest theneed for another gas heating/redistribution mechanism.The right panel in the second row of Figure 8 shows the IGrMfraction in the groups at different redshift. Like the results for thebaryon fraction (top right panel), the IGrM fraction in halos withcomparable potential wells increases between z ≈ and z ≈ and then, stabilizes. Since most of the freshly accreted baryons di-rectly contribute to the IGrM over the epochs and in the halo massregime being considered, that the total baryon and the IGrM frac-tions behave similarly is not surprising.To investigate the make-up of the present-day IGrM within R in detail, we have tracked all the IGrM gas particles back intime and tagged all those that, at any point in the past, were boundto a galaxy and enriched while bound. We refer to this componentof the present-day IGrM as “processed” and the rest of the gas as“unprocessed.” We find that the fraction of the present-day IGrMthat is “processed” gas ranges from ∼ in the highest massgroups to − in the lowest mass groups. (We relaxed the “en-riched while bound” condition and repeated the analysis, and gotidentical results.) This increase in the fraction of “processed” IGrMor equivalently, the decrease in the fraction of “unprocessed” IGrM,with increasing halo mass is the continuation of the trend observedby Ford et al. (2014). On galactic scales ( M ∼ M (cid:12) ), Fordet al. (2014) find that the “unprocessed” component, which theycall “ambient gas”, makes up nearly all of the hot gas. That thefraction of processed gas in the IGrM is relatively small even in themost massive groups may seem surprising but only a small fractionof the metal-rich wind material ejected from central galaxies, forexample, thermalizes at T > × K and remains in the IGrM.Acting more like a galactic fountain, the most of the wind lifts offfrom the galaxy, transfers its kinetic energy to the ambient gas, andfalls back into the galaxy. This behaviour has been discussed indetail in Oppenheimer et al. (2010) and Ford et al. (2014)The fraction of the gas that is heated to T > × K and is lost to cooling is relatively small. Over a Hubble time,it ranges from ∼
10% at M = 3 × M (cid:12) , to ∼ M = 3 × M (cid:12) , to ∼ M = 3 × M (cid:12) .Most of the gas that drops out of the IGrM is initially heated onlyto × K < T < × K . Metal-enriched IGrM in this tem-perature range sits on the broad peak of the cooling curve and issubject to efficient cooling, which even heating by stellar-poweredgalactic winds/fountains cannot fully offset.The third set of panels in Figure 8 show the stellar mass frac-tion in our simulated groups. We include both stars in the galax-ies as well as stars belonging to the diffuse intragroup component(IGS) when we compute the stellar mass. Comparing the stellar “Unprocessed” material is essentially gas that has never passed througha galaxy and has entered the group halos via diffuse accretion directly fromthe intergalactic medium. We emphasize that “unprocessed” should not beinterpreted as un-enriched. A significant fraction of the present-day “unpro-cessed” IGrM has non-primordial metallicity owing to enrichment by thediffuse IGS component. MNRAS000
10% at M = 3 × M (cid:12) , to ∼ M = 3 × M (cid:12) , to ∼ M = 3 × M (cid:12) .Most of the gas that drops out of the IGrM is initially heated onlyto × K < T < × K . Metal-enriched IGrM in this tem-perature range sits on the broad peak of the cooling curve and issubject to efficient cooling, which even heating by stellar-poweredgalactic winds/fountains cannot fully offset.The third set of panels in Figure 8 show the stellar mass frac-tion in our simulated groups. We include both stars in the galax-ies as well as stars belonging to the diffuse intragroup component(IGS) when we compute the stellar mass. Comparing the stellar “Unprocessed” material is essentially gas that has never passed througha galaxy and has entered the group halos via diffuse accretion directly fromthe intergalactic medium. We emphasize that “unprocessed” should not beinterpreted as un-enriched. A significant fraction of the present-day “unpro-cessed” IGrM has non-primordial metallicity owing to enrichment by thediffuse IGS component. MNRAS000 , 1–26 (2015) he Growth and Enrichment of Intragroup Gas fraction within R in our z = 0 simulated groups to the samefrom the OWLS-stars simulation (McCarthy et al. 2011), we findthat the two are similar, ranging from . in the low mass groupsto . in the high mass groups. Additionally, this stellar fraction,like the baryon fraction, is a significant improvement over thoseseen in simulations of Lewis et al. (2000) and Nagai et al. (2007),which do not include this type of stellar feedback, confirming thatgalaxy-wide outflows indeed do suppress excessive star formation.This improvement, however, is not sufficient to bring the simula-tion results into agreement with the observations. The red triangles,blue squares, green diamonds, orange stars, and golden circles inthe left panel show results from Lin et al. (2003), Giodini et al.(2009) , Balogh et al. (2011), Lagan´a et al. (2013), and Gonza-lez et al. (2013), respectively. Of these, only the latter account forthe IGS component. Compared to the observations, the simulatedgroups have, on the whole, a factor of ∼ R .In the right panel, we show how the group stellar fractionwithin R changes with redshift. We also plot the observationalestimates of the stellar fraction in groups at z ∼ . and z ∼ as blue and red symbols, respectively. These data points should becompared to curves of the same colour. These observational resultsare among the first estimates of the stellar fraction in groups athigher redshifts and are subject to considerable uncertainty ( c.f., discussion in Leauthaud et al. 2012; Gonzalez et al. 2013, for ex-ample). This renders a detailed comparison between the simula-tions and the observations difficult. Nonetheless, the general trendseen in the left panel ( i.e. at z = 0 ) — that the stellar fraction in thesimulated groups is generally higher than in the observed groups –seems to hold out to z = 1 .Examining the z = 0 simulated groups in a bit more de-tail, we note that the ‘super-sized’ galaxies ( i.e., the galaxies with M ∗ > M (cid:12) that we mentioned when discussing Figure 2)contain ∼ of the stellar mass within R in the lowest massgroups, and the fraction drops with group halo mass to ∼ inthe most massive groups. The average stellar mass of these galaxiesranges from × M (cid:12) in the lowest mass groups to × M (cid:12) in the most massive groups. Artificially reducing the stellar mass ofjust these super-sized systems by a factor of 3 resolves the discrep-ancy between the observed and model stellar mass fractions acrossthe entire mass range over which this fraction has been observa-tionally determined. It also goes a long way towards improving theagreement with observed galaxy stellar mass function ( c.f., bottompanel of Figure 2).In all our groups, the group central galaxy is always a “super-sized” galaxy. In the lowest mass groups, ∼ of the starswithin R reside in the central galaxy. Examining the stellarbuild-up in these central galaxies, we find that about of thestars formed elsewhere and were subsequently incorporated intothe central galaxies through galaxy-galaxy mergers; of thestars formed in-situ from cooled IGrM; and the balance (approxi-mately of the total stellar mass at z = 0 ) formed in-situ eitherfrom T < × K gas that was either originally funnelled ontothe central galaxies via cold mode accretion (Kereˇs et al. 2009), or The results for Giodini et al. (2009) shown in Figure 8 differ from thosein their paper because they have been revised as suggested by Leauthaudet al. (2012) – see also discussion in Giodini et al. (2012). We show thecorrected results based on the Chabrier IMF. We remind the reader that “cooled IGrM” refers to gas in the MMP thatis heated to
T > × K at some point in the past and cools directlyonto the central galaxy. from cold gas that was deposited in the central galaxies by mergers.The bulk of the mergers affecting the central galaxies in low massgroups occur either before or just after the groups – that is, systemswith at least three “luminous” galaxies – formed.In the most massive groups, the contribution of the centralgalaxy to the total stellar mass within R drops to about and as for the stars that comprise these central galaxies, about were brought in by mergers, formed in-situ from cold gas, andonly about formed out of cooled down IGrM. These percent-ages are important in two respects. First, the fraction of the stellarmass in the central galaxies that is deposited by mergers increaseswith overall halo mass. This trend has been noted previously byHirschmann et al. (2013) in their study of galaxy-scale halos. Ourresults show that the trend continues on the group-scale. Second,and perhaps much more importantly, these results show that theoverabundance of stars in our simulated groups is not primarily dueto the cooling of the hot diffuse IGrM despite the fact that we donot have AGNs in our simulation. Unchecked cooling of the IGrMcontributes only a small fraction of the excess.The plots showing the stellar fraction in groups at differentepochs offer some idea of what is going on. We have previouslynoted that once individual groups form, they slide to the right alongthe x -axis in this plot because the stellar mass in fact grows fasterthan the actual mass of the group halos in all except the most mas-sive groups. This star formation is fuelled by an excess of cold gasthat has accumulated in the group galaxies while these galaxies areat the centres of their own halos either before the groups form, inthe case of the central galaxies, or before they are incorporated intothe groups, in the case of the satellite galaxies.We can see evidence for the presence of significant cold gas inthe group galaxies in the bottom two panels of Figure 8. The pan-els show the total mass fraction of “cold” gas in the groups, where“cold gas” includes both the diffuse gas with T < × K as wellas the dense gas that comprises the ISM in group galaxies. In prac-tice, the former is negligible because diffuse gas with temperatures T < × K lies on the broad peak of the cooling curve, expe-riences very efficient cooling and ends up flowing into the centralgalaxy. The gas in groups is typically either hot and diffuse or coldand dense. At any redshift, the lowest mass groups, which are alsotypically the youngest within the population, have the most amountof cold gas. In the same vein, the earliest groups have the highestcold gas fraction. Taken jointly, these results show that the galax-ies, especially the more massive galaxies, that first come togetherto form the groups contain a significant cold gas reservoir. As thegroups grow and age, the cold gas reservoir is not replenished asrapidly as it is consumed by star formation, and the cold gas frac-tion drops. We note that there is also considerable merger activity,especially early in the history of the groups, during which some ofthe massive satellites sink to the centre and are cannibalized by thegroup central galaxies, and while this impacts the distribution ofthe stars and the gas within the groups, it does not affect the curvesin Figure 8 because we are considering the total stellar and cold gasfractions within R .Demonstrating that the group galaxies host a significant frac-tion of cold gas is not the same as asserting that the group galaxieshave an excess of cold gas. We therefore turn to two recent studiesto compare the cold gas content of the most massive of our z = 0 group galaxies to real galaxies: (1) The Saintonge et al. (2011)sample that comprises 350 nearby massive ( M ∗ > M (cid:12) ), ofwhich 222 have both CO and HI measurements. We focus on thelatter subset and compute the “cold gas” mass of each galaxy as M coldgas = ( M HI + M H ) /X , where the division by X = 0 . , MNRAS , 1–26 (2015) L. Liang et al. the hydrogen mass fraction, corrects for the helium mass. (2) TheCatinella et al. (2013) study that lists HI measurements for 800galaxies with stellar masses < ∼ M ∗ < ∼ . M (cid:12) and red-shifts . ≤ z ≤ . . We convert the HI masses to total coldgas mass using a constant ratio of M H /M HI = 0 . , based onthe results of Saintonge et al. (2011), and X = 0 . .Both studies yield a mean cold gas mass of approximately × M (cid:12) for galaxies with M ∗ > M (cid:12) . We specificallyrestrict ourselves to such massive galaxies because the vast major-ity of the galaxies that populate the two most massive bins in M ∗ in the Catinella and Saintonge samples are, in fact, group galax-ies. For the simulated galaxies, we follow Dav´e et al. (2011) anddefine “cold star-forming gas” as gas within the galaxies whosedensity exceeds the star formation threshold of n H > . cm − ( c.f., Section 2.1). The resulting cold gas mass in our simulated M ∗ > M (cid:12) group galaxies is 5-6 times larger.Further investigation indicates that our hierarchical structureformation model, in which feedback is entirely due to stellar-powered galactic outflows, first breaks down not on the group scalebut rather in the giant galaxies (with stellar mass > ∼ × M (cid:12) )that precede the formation of the groups. These are the first sys-tems in the hierarchy where the deepening gravitational potentialwells and a higher cross-section for hydrodynamic interactions be-tween the galactic outflows and the shock-heated halo gas compo-nent, once the latter starts to form, are able to confine the outflow-ing gas within the circumgalactic region around the galaxies. Mostof this material, being extremely metal-rich, cools down and fallsback into the galaxy. This is discussed at length in Oppenheimeret al. (2010) and their Figure 2 shows that in galaxies with stel-lar mass > ∼ × M (cid:12) , the median time between the launchingof a wind particle, and it falling back into the galaxy and is eitherconverted into a star or launched for a second time is < ∼ Gyr. Ineffect, the winds power galactic fountain flows rather than galacticoutflows and consequently, the ≥ L ∗ galaxies can no longer mod-erate their star formation rates by depleting their cold gas mass viaexpulsion. The high cold gas mass in our group central galaxies is aconsequence of this, and the overproduction of stars is a byproduct.This is nicely illustrated in Figure 4 of Oppenheimer et al. (2010),which shows that > ∼ of the stars in massive galaxies at z = 0 have formed out of re-accreted wind material.There are two potential ways of resolving the above problem:(1) Increase the wind launch velocities so that even in the giantgalaxies, the winds are not confined within the circumgalactic re-gions and when they thermalize, the ejected material heats up toIGrM temperatures. This may help reduce both the cold gas and thestellar masses of the massive galaxies in our simulated groups but ata cost of making the IGrM mass fractions in these groups, and theircorresponding X-ray properties, potentially discrepant with the ob-servations, and it will not improve our baryon fraction results. Or,(2) M ∗ ≈ × M (cid:12) is the transition mass scale where an al-ternate feedback mechanism, like AGN feedback, must come intoplay. The main requirement of this alternate feedback mechanism isthat it must be sufficiently potent that it, either by itself or in com-bination with the galaxy-wide stellar powered outflows, can drivedown the total baryon fractions and the cold gas mass fractions ingiant galaxy or group halos with M < × M (cid:12) . Having discussed the evolution of various baryonic componentscomprising the groups in some detail above, we conclude our dis-cussion of the group baryonic properties by considering the five redshifts that encapsulate the key features of the groups’ formationhistories. To determine these, we reconstructed each present-daygroup’s merger history by stepping back in time from the presentand identifying, at each epoch, all the individual halos that are thepresent-day group’s ancestors. We label the largest of these themost massive progenitor (MMP). Our five redshifts are based onthe properties of the MMP. These redshifts are: Z . : The redshift at which the total mass of a present-daygroup’s MMP is half of the group’s final mass; i.e., M MMP , ( z ) = M ( z ) | z =0 . Z . : The redshift at which the hot (
T > × K) gasmass in the MMP is half of the group’s final IGrM mass; i.e., M MMP , IGrM , ( z ) = M IGrM , ( z ) | z =0 . Z . : The redshift at which the total stellar mass in theMMP is half of the group’s z = 0 total stellar mass; i.e., M MMP , star , ( z ) = M star , ( z ) | z =0 . Z group : The highest redshift at which the MMP hosts at leastthree luminous galaxies and can be considered a group. i.e., N MMP , gal ( z ) ≥ Z . gas , IGrM : the highest redshift at which the hot dif-fuse IGrM mass in the MMP exceeds 50% of the totalgas mass. i.e., M MMP , IGrM , ( z ) /M MMP , allgas , ( z ) > . .In Figure 10, we show the individual distribution of these red-shifts as well as the relationship between them. We have chosen Z . , the redshift commonly referred to as the “formation red-shift” of the present-day groups, as the common reference for fourcross plots. To start with, we consider this redshift by itself first.The bottom panel in each of column of plots shows the normalizeddistribution of the formation epoch.The distribution of formation times for groups in all threemass bins are similar and the median formation epoch is z ≈ . .If the halos populating each of the mass bins were a represen-tative ( i.e., unbiased) subset of all the dark matter halos in thesimulation volume with masses . < log M vir ≤ . (cid:12) (low), . < log M vir ≤ . (cid:12) (intermediate), and . < log M vir ≤ . (cid:12) (high), we would expect the “low masshalos” to be slightly older than the “intermediate mass halos” andthe “high mass halos” to be younger. The groups in the intermediate(median formation redshift is indicated by the blue dashed line) andthe high mass bins (median formation redshift is indicated by thered dashed line) conform to these expectations. This is perhaps notsurprising. As shown in Figure 1, nearly all dark matter halos withmasses M vir > M (cid:12) are groups and, therefore the group ha-los in the intermediate and the high mass bins form a representativesample. The median formation redshift of the groups in the lowestmass bin (median formation redshift is indicated by the magentadashed line), however, breaks the expected trend: Their median for-mation redshift is lower than that of the intermediate mass halos.This is because the group halos that populate the low mass bins are not an unbiased sample of all dark matter halos with masses in therange . < log M vir ≤ . (cid:12) . Rather, these groups forma very special subset with at least three luminous galaxies and asdiscussed by Zhu et al. (2006), this type of constraint on the galaxyoccupation number results in the selection of a relatively youngersubset of halos, which is indeed what we find.The y -axis of the top left panel of Figure 10 shows the distri-bution of Z . , the epoch when the hot diffuse IGrM mass inthe MMP exceeds 50% of the IGrM mass in the final group halo.The redshift distributions for the groups in the three mass bins arevery similar. Much more interestingly, the halo formation time and MNRAS000
T > × K) gasmass in the MMP is half of the group’s final IGrM mass; i.e., M MMP , IGrM , ( z ) = M IGrM , ( z ) | z =0 . Z . : The redshift at which the total stellar mass in theMMP is half of the group’s z = 0 total stellar mass; i.e., M MMP , star , ( z ) = M star , ( z ) | z =0 . Z group : The highest redshift at which the MMP hosts at leastthree luminous galaxies and can be considered a group. i.e., N MMP , gal ( z ) ≥ Z . gas , IGrM : the highest redshift at which the hot dif-fuse IGrM mass in the MMP exceeds 50% of the totalgas mass. i.e., M MMP , IGrM , ( z ) /M MMP , allgas , ( z ) > . .In Figure 10, we show the individual distribution of these red-shifts as well as the relationship between them. We have chosen Z . , the redshift commonly referred to as the “formation red-shift” of the present-day groups, as the common reference for fourcross plots. To start with, we consider this redshift by itself first.The bottom panel in each of column of plots shows the normalizeddistribution of the formation epoch.The distribution of formation times for groups in all threemass bins are similar and the median formation epoch is z ≈ . .If the halos populating each of the mass bins were a represen-tative ( i.e., unbiased) subset of all the dark matter halos in thesimulation volume with masses . < log M vir ≤ . (cid:12) (low), . < log M vir ≤ . (cid:12) (intermediate), and . < log M vir ≤ . (cid:12) (high), we would expect the “low masshalos” to be slightly older than the “intermediate mass halos” andthe “high mass halos” to be younger. The groups in the intermediate(median formation redshift is indicated by the blue dashed line) andthe high mass bins (median formation redshift is indicated by thered dashed line) conform to these expectations. This is perhaps notsurprising. As shown in Figure 1, nearly all dark matter halos withmasses M vir > M (cid:12) are groups and, therefore the group ha-los in the intermediate and the high mass bins form a representativesample. The median formation redshift of the groups in the lowestmass bin (median formation redshift is indicated by the magentadashed line), however, breaks the expected trend: Their median for-mation redshift is lower than that of the intermediate mass halos.This is because the group halos that populate the low mass bins are not an unbiased sample of all dark matter halos with masses in therange . < log M vir ≤ . (cid:12) . Rather, these groups forma very special subset with at least three luminous galaxies and asdiscussed by Zhu et al. (2006), this type of constraint on the galaxyoccupation number results in the selection of a relatively youngersubset of halos, which is indeed what we find.The y -axis of the top left panel of Figure 10 shows the distri-bution of Z . , the epoch when the hot diffuse IGrM mass inthe MMP exceeds 50% of the IGrM mass in the final group halo.The redshift distributions for the groups in the three mass bins arevery similar. Much more interestingly, the halo formation time and MNRAS000 , 1–26 (2015) he Growth and Enrichment of Intragroup Gas Figure 10.
A set of four plots showing the distribution of the five key redshifts that summarize the groups’ formation histories, defined in Section 4.2, andthe relationships between them: Z . vs. Z . (top left); Z . gas , IGrM vs. Z . (top right); Z . vs. Z . (bottom left); and Z group vs. Z . (bottom right). In the main plot of each set, the different colored regions show the 2D distribution of the redshifts for the low, intermediateand high mass groups – i.e., . < log M vir ≤ . (cid:12) (magenta), . < log M vir ≤ . (cid:12) (blue), and . < log M vir ≤ . (cid:12) (red)– separately. The inner and the outer contours of the shaded regions of each colour correspond to 1- σ and 2- σ , while the × marks the median for all thegalaxies within each mass bin. The panels to the left and below the main plots show the normalized marginalized distributions of y -axis redshift (left) and x -axis redshift (below): P ( z ) = ( dN/dz ) /N tot . The different coloured curves show the redshift distributions for the three mass bins and the dashed linesindicate their median: Z . are very tightly correlated. This suggests that the MMPsof the present-day groups have already built up a substantial reser-voir of hot diffuse gas by the time the group halos form at Z . .These results are consistent with the trends seen in Figure 8, whichshow that post-formation, the growth of dark matter mass and IGrMmass proceeds in lock-step.In the top right panel of Figure 10, we show the joint andthe marginal distributions of Z . gas , IGrM , the redshift whenthe hot diffuse IGrM begins to dominate the total gas mass in theMMP, and Z . . The plot suggests little or no correlation be-tween these two redshifts. However, the normalized distribution of Z . gas , IGrM confirms our earlier assertion that the progen-itors of the most massive z = 0 groups (red curve) build up asubstantial reservoir of hot diffuse X-ray emitting gas fairly earlyon; the median value of Z . gas , IGrM for these systems is z = 2 . . The distribution for the intermediate mass halos is shiftedto lower redshifts, with a median of z = 2 , and the distribution ofthe lowest mass groups is shifted to lower redshifts, with a median of z = 1 . . For the majority of the groups, the gas content of theMMPs is dominated by hot gas well before the MMP mass reaches50% of the corresponding present-day group’s final mass.In the bottom left panel, we show the joint and the marginaldistributions of Z . , the redshift at which half of the total z = 0 stellar mass within R is in place within the MMP, and Z . . The main plot shows that these two redshifts are stronglycorrelated. During the early phases of group formation, the MMPgrows principally via mergers, which add to both the dark mattermass as well as the stellar mass of the system. However, if the twogrow in perfect lock-step, we would expect their joint distributionto define a narrow ellipse whose major axis lies along the line, but they don’t and even the median Z . is slightly lowerthan Z . , with ∆ z ≈ . . . As discussed previously, themergers not only contribute stars and dark matter, they also bringin cold gas. In Figure 8, we discussed the conversion of this coldgas into stars, especially at late ( z < ) times. This in-situ starformation breaks the 1-to-1 mapping between halo assembly and MNRAS , 1–26 (2015) L. Liang et al. the establishment of the stellar mass. As we have noted previously,any additional feedback mechanism that is added to these simula-tions must be able to prevent the build-up of cold gas in the smallersystems because once this cold gas reservoir is established, it is un-likely that any mechanism acting solely on group or cluster scalescan prevent this gas from being delivered to the central galaxies.An additional point of interest is that the median value of Z . indicates that half of the stellar component of today’s galaxy groupswas already in place about 6 billion years ago.Finally, the bottom right panel shows the joint and themarginal distributions of Z . and Z group , the highest redshiftat which the MMP first incorporates three or more luminous galax-ies and meets our definition of a group. There are two featuresworth noting. First, the distribution of redshifts at which the MMPsof the present-day groups first qualify as groups is fairly broad,much broader than the distribution of group halo formation times.Second, the MMPs of the present-day high and intermediate massgroups generally acquire a third luminous galaxy well before halfof the groups’ final mass is assembled and hence, there isn’t a clearrelationship between Z group and Z . of these systems. Onlyin the case of the lowest mass groups do a significant fraction ofthe halos form first and then become groups, and the two epochs, Z group and Z . , appear linked. The median Z group for thehigh, intermediate and low mass systems are z = 2 . , 2.0 and1.2, respectively, as compared to the median formation epoch of z ≈ . for the same three categories of groups.To better understand the behaviour of Z group , we plot in Fig-ure 11 the distribution of the number of luminous galaxies in theMMPs of the present-day groups at several different redshifts. Theresults show that the MMPs of the most massive systems todayqualify as groups in their own right (by acquiring three luminousgalaxies) much earlier than the MMPs of the lowest mass groups.Moreover, in keeping with the “downsizing” picture usually dis-cussed in the context of galaxy formation (Neistein et al. 2006;Fontanot et al. 2009), the most massive groups also grow the fastest,with the number of luminous galaxies in these systems increasingfive-fold from z = 4 to z = 0 . In contrast, nearly two-thirds of theMMPs of the present-day groups in our lowest mass bin host onlyone or two luminous galaxies even at redshifts as low as z = 0 . .We note that the number of luminous galaxies in the groupsdoes not grow monotonically with time. The satellite galaxies cansink down to the group centre due to dynamical friction and mergewith the central galaxies, resulting in a decline in the number ofgroup galaxies. This is illustrated in Figure 12, where we plot thefraction of MMPs of the z = 0 groups that host at least 3 luminousgalaxies at the redshifts under consideration (solid curves), and thefraction of MMPs that qualified as groups at some earlier redshift(dashed curves). In terms of Z group , the latter corresponds to thefraction present-day groups with Z group > z .Focusing first on the dashed curves in Figure 12, we see that of the MMPs of the present-day low ( i.e., . < log M vir ≤ . (cid:12) ), intermediate ( i.e., < log M vir ≤ . (cid:12) ) andhigh ( i.e., . < log M vir ≤ . (cid:12) ) mass groups first crossedthe “group threshold” by z ≈ (red), z ≈ (green) and z ≈ (cyan), respectively. These values are consistent with the results for Z group shown in Figure 10. However, achieving group status andmaintaining that status at subsequent times are two different con-cerns and this is illustrated by the differences between the dashedand the solid curves of the same colour in Figure 12. This differ-ence equals the fraction of MMPs that after achieving group statusat some earlier epoch by virtue of accreting one or two luminousgalaxies and just meeting the threshold criterion of three galaxies, N MM P N MM P N luminous N MM P z = 0 z = 0 . z = 1 z = 2 z = 3 z = 4 . < log M vi r ≤
14 M ⊙ < log M vi r ≤ . ⊙ . < log M vi r ≤
13 M ⊙ Figure 11.
Histograms showing the number of “luminous” galaxies( i.e., M ∗ ≥ . × M (cid:12) ) in the z = 0 groups (black), as well as in theirMMPs at z = 0 . (blue), z = 1 (red), z = 2 (green), z = 3 (cyan) and z = 4 (magenta). The top, middle and bottom panels show the results forthe present-day low, intermediate and high mass groups, respectively. Thevertical dashed line corresponds to N luminous = 3 , the threshold abovewhich a halo is defined as a ‘group’. lose one of them to a merger. Group halos are most susceptible tosuch fluctuations in status while the number of hosted luminousgalaxies is small. The MMPs of the present-day high mass groupsexperience such fluctuations at relatively high ( z ≈ − ) redshifts.At that time, the fraction of MMPs (of high mass groups) that qual-ify as groups is small, ∼ , but this fraction rises steeply and by z = 1 , nearly all the groups are well established and the fractionexceeds . In contrast, the fraction of MMPs of the our low masspresent-day groups that qualify as groups at z = 4 is , and evenat redshifts as low as z = 0 . , the fraction is only ∼ . Most ofthe present-day low mass systems qualified (or re-qualified) as bonafide groups at the present as a result of late-time ( z < . ) mergers.These mergers not only inject additional luminous galaxies into theMMPs but also contribute a significant fraction of MMPs final to- MNRAS000
Histograms showing the number of “luminous” galaxies( i.e., M ∗ ≥ . × M (cid:12) ) in the z = 0 groups (black), as well as in theirMMPs at z = 0 . (blue), z = 1 (red), z = 2 (green), z = 3 (cyan) and z = 4 (magenta). The top, middle and bottom panels show the results forthe present-day low, intermediate and high mass groups, respectively. Thevertical dashed line corresponds to N luminous = 3 , the threshold abovewhich a halo is defined as a ‘group’. lose one of them to a merger. Group halos are most susceptible tosuch fluctuations in status while the number of hosted luminousgalaxies is small. The MMPs of the present-day high mass groupsexperience such fluctuations at relatively high ( z ≈ − ) redshifts.At that time, the fraction of MMPs (of high mass groups) that qual-ify as groups is small, ∼ , but this fraction rises steeply and by z = 1 , nearly all the groups are well established and the fractionexceeds . In contrast, the fraction of MMPs of the our low masspresent-day groups that qualify as groups at z = 4 is , and evenat redshifts as low as z = 0 . , the fraction is only ∼ . Most ofthe present-day low mass systems qualified (or re-qualified) as bonafide groups at the present as a result of late-time ( z < . ) mergers.These mergers not only inject additional luminous galaxies into theMMPs but also contribute a significant fraction of MMPs final to- MNRAS000 , 1–26 (2015) he Growth and Enrichment of Intragroup Gas
12 12.5 13 13.5 1400.20.40.60.81 log M vir (M ⊙ ) N g r o up ( z ) / N MM P ( z ) z = 0 . z = 2 z = 1 z = 4 z = 3 Figure 12.
The solid curves show the fraction of the MMPs of the selected z = 0 groups that qualify as groups at various redshifts as labelled, againsttheir present-day virial mass. The corresponding dashed curves show thefraction of their MMPs that had once qualified as group before a given red-shift, regardless of the number of “luminous” groups in the MMP at thatredshift. tal masses, both biasing the groups’ formation epochs towards thepresent (Zhu et al. 2006) and also providing a direct physical con-nection between Z group and Z . , which in turn accounts for atighter relationship ( c.f., Figure 10) between the two in the case oflow mass groups.
In addition to altering the thermal and baryonic properties of galaxygroups, large-scale galactic outflows also transport metals from thegalaxies to the intergalactic space. Such outflows are key to ex-plaining the widespread enrichment of the intergalactic medium(IGM) as early at z ∼ (Oppenheimer & Dav´e 2006; Oppenheimeret al. 2009) and the observed mass-metallicity relation in galaxies,both today and at higher redshifts (Finlator & Dav´e 2008; Dav´eet al. 2011; Hirschmann et al. 2013; Somerville & Dav´e 2014). Inthis section, we focus specifically on the hot, diffuse, X-ray emit-ting, intragroup medium. The observed iron and silicon abundancesranging from ∼ . to ∼ . solar offers clear evidence that a sig-nificant fraction of the metals produced in galaxies escapes fromthese systems. We determine the level of iron, oxygen and siliconenrichment in the IGrM that can be attained via our momentum-driven outflows model and assess how these compare with the latestobservations. We also show how the abundances and abundance ra-tios evolve with time. And, we discuss how our metal abundanceswould change if the global stellar mass in our simulated groupswere to be reduced by a factor of ∼ to reconcile the model resultswith the observations ( c.f., Figure 8).
In Figure 13, we plot the global mass-weighted (left column) andemission-weighted (middle column) iron and silicon abundances in the IGrM within R of the simulated groups (top and bot-tom rows, respectively), as well as the global mass-weighted abun-dances of all the gas, including the cold gas within individual groupgalaxies (right column), as a function of core-corrected spectro-scopic temperature. The coloured lines show the abundances at dif-ferent epochs over the redshift range ≤ z ≤ . The fact thatwe have chosen to show both mass- and emission-weighted curvesmay seem a bit excessive. For the kind of comparisons we wish tocarry out, mass-weighted data is preferable. However, the availablegroup observations (for comparison) are limited because spatiallyresolved, X-ray spectroscopy of galaxy groups, which is a prereq-uisite for mass-weighted abundance measurements, involves longobservations and challenging analyses. On the other hand, therehas been a steady reporting of group abundance measurementsin the literature over the years but most of this data is emission-weighted. Given such circumstances, we have opted to leverageboth types of measurements: In the first column on the left, theblack open squares show the core-corrected data from Fukazawaet al. (1998) , the open black circles show the results from Ras-mussen & Ponman (2007), and the magenta filled squares show thelatest Suzaku results from Sasaki et al. (2014). We focus on mea-surements from “warm” groups, i.e., groups with T spec , corr > ∼ . keV or M > ∼ . × M (cid:12) , because this data range has beenstudied by several independent groups and collectively, the mea-surements are more likely to be representative. In the middle col-umn, we show as grey diamonds the data from Helsdon & Pon-man (2000) while the grey triangles show data from Peterson et al.(2003). To facilitate comparison, all metal abundances, whethertheoretical or observational, are normalized to the solar “photo-sphere abundances” level from Anders & Grevesse (1989) (see Sec-tion 2.3).Turning first to the mass-weighted IGrM abundance in warm z = 0 simulated groups, we find that [Fe / H] rises gently from − . to − . with temperature and then flattens, while [Si / H] risesfrom − . to − . and then flattens. The model results are invery good agreement with the observations although there is a hintthat the observed iron abundance measurements might be higher by . − . dex. This level of mismatch, if real (note that the latest Suzaku results are lower than the earlier
XMM-Newton or Chandra results and hence, much more compatible with the model results), isnot unexpected given the factor ∼ uncertainties in the adopted nu-cleosynthesis yields and supernovae rates. The emission-weightedobservations and the simulation results are also in agreement; how-ever, this is not surprising given the large scatter in the observa-tional measurements. Interestingly, the emission-weighted siliconand iron IGrM abundances of warm z = 0 groups overestimatethe “true”, i.e., mass-weighted, abundances by 0.6-0.7 dex. This isa consequence of emission-weighted results being biased towardsthe brighter (in X-ray) central cores of the groups, which – if recentobservations are a fair guide – are expected to be more metal-rich.We will be examining the metallicity profiles, and other related dis-tributions, of our simulated groups in a follow-up paper.In the cooler ( T spec , corr < ∼ . keV) simulated groups, the ironand silicon abundances drop with decreasing IGrM temperature.This trend is the consequence of the metal-rich diffuse gas in thesesystems dropping out of the IGrM more efficiently because, as we As discussed in Appendix A3 of Nagashima et al. (2005), the core-corrected abundance measurements of each group in Fukazawa et al. (1998)provide a reliable estimate of the global mass-weighted abundance of thegroups under consideration.MNRAS , 1–26 (2015) L. Liang et al. − − [ F e / H ] − − − − − − [ S i / H ] − − log T s pec , cor r (keV) − − z = 0z = 0 .
5z = 1z = 2z = 3
Mass − weighted (IGrM) Emission − weighted (IGrM) Mass − weighted (all gas) Figure 13.
Global iron (top row) and silicon (bottom row) abundances within R of the group centers. The left column shows the mass-weighted abundancesin the IGrM; the middle column shows the X-ray emission-weighted abundances in the IGrM; and the right column shows the global mass-weighted abundancesof all the gas, including the cold gas within individual group galaxies. The coloured lines and the corresponding error bars show the median values and the1- σ dispersion for group populations in the simulation volume at z = 0 (black), z = 0 . (blue), z = 1 (red), z = 2 (green) and z = 3 (cyan). The openblack circles, the open black squares, and the filled magenta squares in the left column show measurements from Rasmussen & Ponman (2009), Fukazawaet al. (1998) and Sasaki et al. (2014), respectively. The grey diamonds and triangles are results from Helsdon & Ponman (2000) and Peterson et al. (2003),respectively. − − − M x , F e , I G r M / M F e , I G r M ( < R ) − − − M x , O , I G r M / M O , I G r M ( < R ) − − − M x , S i , I G r M / M S i , I G r M ( < R ) log T spec , corr (keV) satelliteexternalIGScentral Figure 14.
The fraction of IGrM iron (left panel), silicon (middle panel) and oxygen (right panel) mass within R in z = 0 groups, characterized by their T spec , corr , contributed by the central galaxies (red curve), the group satellite galaxies (magenta curve), the non-group external galaxies (blue curve), and theintragroup stars (orange curve) over cosmic time. See § σ error. have mentioned previously, the gas sits closer to the broad peakin the cooling curve. The total iron and silicon abundances of allthe gas, including the cold gas inside group galaxies, within R are, however, broadly similar across both warm and cool groups(see the right column of Figure 13), and at z = 0 , perhaps evenshows evidence of a slight rise towards the coolest groups. Thislatter trend is not surprising given that the z = 0 stellar fraction isthe largest in the coolest groups. It is possible that the inclusion ofAGN heating as well as turbulent diffusion, which is not included inour present simulation but is expected to play a role in transportingthe chemical elements from regions of high metallicity within the IGrM to regions of low metallicity, may moderate the decline in theabundances towards lower temperatures.The coloured lines in Figure 13 show how the abundancesgrow with time. On the whole, the iron abundance within R increases by a factor of ∼ . − from z = 2 to z = 0 , and thesilicon abundance increases by a factor of ∼ . Both show a simi-lar growth pattern, growing gently between . < z < and thensomewhat more rapidly between < z < . , with the iron abun-dance growing a bit faster than silicon. This late growth is fuelledby the release of metals locked up in AGB stars (iron and silicon)as well as the injection of iron by delayed Type Ia SNe. We will re- MNRAS000
The fraction of IGrM iron (left panel), silicon (middle panel) and oxygen (right panel) mass within R in z = 0 groups, characterized by their T spec , corr , contributed by the central galaxies (red curve), the group satellite galaxies (magenta curve), the non-group external galaxies (blue curve), and theintragroup stars (orange curve) over cosmic time. See § σ error. have mentioned previously, the gas sits closer to the broad peakin the cooling curve. The total iron and silicon abundances of allthe gas, including the cold gas inside group galaxies, within R are, however, broadly similar across both warm and cool groups(see the right column of Figure 13), and at z = 0 , perhaps evenshows evidence of a slight rise towards the coolest groups. Thislatter trend is not surprising given that the z = 0 stellar fraction isthe largest in the coolest groups. It is possible that the inclusion ofAGN heating as well as turbulent diffusion, which is not included inour present simulation but is expected to play a role in transportingthe chemical elements from regions of high metallicity within the IGrM to regions of low metallicity, may moderate the decline in theabundances towards lower temperatures.The coloured lines in Figure 13 show how the abundancesgrow with time. On the whole, the iron abundance within R increases by a factor of ∼ . − from z = 2 to z = 0 , and thesilicon abundance increases by a factor of ∼ . Both show a simi-lar growth pattern, growing gently between . < z < and thensomewhat more rapidly between < z < . , with the iron abun-dance growing a bit faster than silicon. This late growth is fuelledby the release of metals locked up in AGB stars (iron and silicon)as well as the injection of iron by delayed Type Ia SNe. We will re- MNRAS000 , 1–26 (2015) he Growth and Enrichment of Intragroup Gas turn to this issue when we consider the evolution of the abundanceratios in Section 5.3. Having compared the metallicity of the IGrM in present-day sim-ulated galaxy groups with available observations, we now examinewhere the metals in the IGrM originated. We focus on the IGrMwithin R and label the potential sites of metal production basedon their status at the time of enrichment as follows: Central:
The central galaxy of the present-day group or thecentral galaxy of the group’s MMP at an earlierepoch.
Satellite:
A non-central galaxy that is contained within the z =0 group halo or within the group’s MMP. External:
A galaxy that is neither a central nor a satellite at thetime of enrichment.
IGS:
Direct enrichment of the IGrM by intragroup stars, i.e., stars in the present-day group or any of its pro-genitor subhalos that are not bound to any of the skid-identified galaxiesThe left, middle and right panels of Figure 14 show the contribu-tion of each of these to the total iron, silicon and oxygen mass,respectively, in the IGrM within R of the present-day simulatedgroups. The figure shows the results for the full sample of simulatedgroups: warm and cool. In the following, we will only discuss thewarm ( i.e., T spec , corr > ∼ . keV) simulated groups whose metal-licity we are able to compare directly with observations.As illustrated in Figure 14, the central galaxy is an importantsource of all three metal species in the warm groups. This compo-nent contributes ∼ of the iron mass, ∼ of the siliconmass, and ∼ of the oxygen mass. In the case of oxygen, theexternal galaxies contribute about the same fraction, followed bythe satellite galaxies, which contribute about . The IGS con-tribution is approximately and the balance ( ∼ ) comesfrom ‘unresolved’ galaxies ( i.e. SKID-identified galaxies with atotal mass in cold gas and stars < . × M (cid:12) ; c.f., § ∼ ) and again, the ‘un-resolved’ galaxies contribute < . Since silicon and oxygenare both α -elements, it may seem surprising that the relative con-tributions of the four categories to IGrM mass of these two ele-ments are not identical. However, as we elaborate in Section 5.3,while the two are produced via the same mechanisms, they are pro-cessed differently by AGB stars. For iron, the second most impor-tant source in the IGrM, after the central galaxy, is the IGS compo-nent. This component contributes the same amount of iron ( )as the central galaxy in groups with T spec , corr ≈ . keV but frac-tion drops with increasing IGrM temperature to in groups with T spec , corr ≈ keV. The satellites and the externals both contributethe same amount: − , with the unresolved systems makingup the rest ( < ). One important take-away is that the centraland the satellite galaxies within the group halo or its MMP ( i.e., in-situ wind enrichment) produce nearly half of the total mass of allthree metal species in the IGrM and are more important than thelow-mass galaxies responsible for the early enrichment of the in-tergalactic medium.Knowing where the metals are produced allows us to ascer-tain the extent to which the estimates of [Fe/H] and [Si/H] that wecompare with the observations in Figure 13 are affected by the over-production of stars in the group galaxies. To do so, we have deter- [ S i / O ] − − − [ S i / F e ] log T sp ec , corr (keV) z = 0z = 0 .
5z = 1z = 2z = 3
Figure 15.
Global silicon-to-oxygen (top panel) and silicon-to-iron (bot-tom panel) abundance ratio within R . The symbols show data fromRasmussen & Ponman (2009) (open black circles), Fukazawa et al. (1998)(open black squares), Sasaki et al. (2014) (filled magenta squares), and Pe-terson et al. (2003) (grey triangles). The coloured lines and the correspond-ing error bars show the median values and the 1- σ dispersion for grouppopulations in the simulation volume at z = 0 (black), z = 0 . (blue), z = 1 (red), z = 2 (green) and z = 3 (cyan). We point out that this y -axisscale is not the same as in Figure 13. We have deliberately zoomed in tohighlight the differences between the curves. mined how much of the iron and silicon mass in the warm groupsoriginates in galaxies whose stellar mass exceeds M (cid:12) at thetime of ejection. In the case of both iron and silicon, approximately of their IGrM mass is ejected from ‘super-sized’ galaxies. If,as an exercise in post-processing, we assume that some mechanism( e.g. AGN heating) quenches star formation in massive galaxies,limiting their stellar mass to a maximum of M (cid:12) , then the met-als that were ejected of the galaxies after they evolved into ‘super-sized’ galaxies would either have not been made or would have re-mained locked up in the galaxies. In this case, the [Fe/H] and [Si/H]of warm groups in Figure 13 would decrease by . , or less thanspace between consecutive tick marks in the plot. The [Si/H] wouldlie right on top of the Suzaku observations while the [Fe/H] woulddrop below the
Suzaku results, but still be consistent with the ob-servations given the factor ∼ uncertainties in the nucleosynthesisyields and supernovae rates. The main point of this exercise is todemonstrate that the metal abundance results shown in Figure 13,and by extension the abundance ratios that we will discuss next,are relatively insensitive to any suppression of star formation in themassive galaxies invoked to bring the overall stellar mass fractionin the groups in alignment with the observations ( c.f., Figure 8).
MNRAS , 1–26 (2015) L. Liang et al.
In Figure 15, we examine the IGrM silicon-to-oxygen (top panel)and silicon-to-iron (bottom panel) abundance ratios within R for the simulated groups at different epochs. Silicon and oxygenare both α -elements and are produced by core-collapse SNe. As aresult, in the absence of any other process, the silicon-to-oxygenabundance ratio would be expected to remain constant over time.The ratio in our simulation, however, increases with time. This is aconsequence of silicon and oxygen being processed differently byAGB stars (Oppenheimer & Dav´e 2008): When AGB stars form,the silicon and oxygen present in the ISM is locked up in thesestars. Over their lifetime, these stars burn some of the oxygen whilethe silicon remains unaffected. Consequently, when the AGB starsrelease their metals back into the ISM, the amount of silicon isnearly the same as that locked up in the first place but the amountof oxygen returned is reduced. The evolution in [Si/O] in Figure15 results from this differential evolution. As for the gentle rise in[Si/O] with increasing group temperature, this is a consequence ofthe four categories in Figure 14 not contributing identically to thesilicon and oxygen mass. We emphasize, however, that this increasewith group temperature amounts to maximum change of ∆ [Si/O] ≈ . , which is insignificant. For all intents and purposes, [Si/O] isindependent of group temperature or mass.In contrast, z = 0 [Si/Fe] curve (lower panel) not onlyincreases by ∆ [Si/Fe] ≈ . in going from the coolest to thewarmest groups in our simulation sample, this change evolves from ∆ [Si/Fe] ≈ at z = 3 to its present-day value while the valueof [Si/Fe] in the warmest group drops slightly. To zeroth order,the redshift evolution is due to delayed Type Ia SNe spewing newforged and winds from AGB stars spewing previously locked-upiron mass to their local environment. Generally, this environmentis the ISM within the group galaxies. However, transporting this‘late’ iron out of the galaxies and into the IGrM is not straight-forward. As we have noted previously, metal-rich winds from thecentral galaxies in cool groups tend to behave more like galacticfountains and therefore, very little of the ‘late’ iron production getsinto the IGrM. The central galaxies in the more massive groups areable to drive the iron into the IGrM but they are not outrightly dom-inant sources because they are running out of cold gas and hence,not forming stars as vigorously. Moreover, because of the size ofthe galaxies, the mass loading factor of the wind that is ejected isonly a fraction of the star formation rate ( c.f., Section 2.1) and evenin this case, the ejection of the ‘late’ iron is inefficient. However,winds are not the only way to enrich the IGrM. Direct enrichmentby the IGS component is another. And as illustrated in Figure 14,the latter is the dominant source of iron mass in the cool groupsand also the reason why [Si/Fe] in cool groups evolves much morerapidly than in warm groups.
We conclude our investigation of the metal enrichment of theIGrM by examining the redshifts by which half of the iron, sil-icon and oxygen mass in the z = 0 IGrM within R is pro-duced by the stars, regardless of whether the metals are initiallydeposited in the ISM or introduced directly into the IGrM. We re-fer to these characteristic redshifts as Z . , IGrM , Z . , IGrM and Z . , IGrM . We show their distributions in Figure 16, wherewe compare them to the redshifts by which half of the group’s z = 0 stellar mass has been assembled in its MMP ( Z . ). Figure 16.
The joint distribution of Z . , IGrM , the redshift by whichhalf of the metals of species XX= { Fe, O, Si } in a present-day group’s IGrMhas been forged by the stars/supernova, versus Z . , the distribution ofredshifts by which half of the present-day group’s stellar mass has beenassembled in its MMP. The contour plots show the 2D distribution of theredshifts for the low, intermediate and high mass groups – i.e., . < log M vir ≤ . (cid:12) (magenta), . < log M vir ≤ . (cid:12) (blue),and . < log M vir ≤ . (cid:12) (red) – separately. The inner andthe outer contours of the shaded regions of each colour correspond to 1- σ and 2- σ , while the × marks the median for the galaxies in each massbin. The panels to the left and below the contour plots show the normalizedmarginalized distributions of Z . , IGrM (left), and Z . (below).The different colour curves show the results for the low, intermediate andhigh mass groups, and the dashed lines indicate the median.MNRAS000
The joint distribution of Z . , IGrM , the redshift by whichhalf of the metals of species XX= { Fe, O, Si } in a present-day group’s IGrMhas been forged by the stars/supernova, versus Z . , the distribution ofredshifts by which half of the present-day group’s stellar mass has beenassembled in its MMP. The contour plots show the 2D distribution of theredshifts for the low, intermediate and high mass groups – i.e., . < log M vir ≤ . (cid:12) (magenta), . < log M vir ≤ . (cid:12) (blue),and . < log M vir ≤ . (cid:12) (red) – separately. The inner andthe outer contours of the shaded regions of each colour correspond to 1- σ and 2- σ , while the × marks the median for the galaxies in each massbin. The panels to the left and below the contour plots show the normalizedmarginalized distributions of Z . , IGrM (left), and Z . (below).The different colour curves show the results for the low, intermediate andhigh mass groups, and the dashed lines indicate the median.MNRAS000 , 1–26 (2015) he Growth and Enrichment of Intragroup Gas There are several other characteristic redshifts, such as the haloformation redshift ( Z . ) or the redshift at which the hot ( T > × K) gas mass in the MMP is half of the group’s final IGrMmass ( Z . ), that we have compared Z . , IGrM (whereXX= { Fe, O, Si } ) against; however, we do not show these becausethey do not offer any additional insights and Figure 10 offers astraightforward map between Z . and the other potential red-shifts of interest.Examining the timescales in detail, the most significant featureis that in all but the most recently formed groups, the characteristic‘metal production’ redshifts are lower than Z . or Z . .In other words, typically more than half of the iron, silicon andoxygen in the z = 0 IGrM was forged after half of the groups’IGrM was already in place within the nascent groups.The relationship between Z . , IGrM , where XX= { Fe, O,Si } and Z . is more nuanced. In the case of iron ( c.f., the toppanel of Figure 16), the major axis of the contours has a shallowerslope relative to the one-to-one line. Since Z . is a measure ofwhen stars first appear inside groups, the orientation of the contoursindicates that the iron in the z = 0 IGrM is typically made after halfof the groups’ final stellar mass is in place within the MMP. Thisis not surprising. As we have discussed previously, AGB stars anddelayed Type Ia SNe play a key role in the build-up of iron in theIGrM and there is a lag between the formation of a stellar popula-tion and the start of enrichment by Type Ia SNe and AGB stars asso-ciated with that population. However, if this was all, we would haveexpected the width of the contours at fixed Z . to be fairly nar-row. Instead, as suggested by the left panel of Figure 14, about 20%of the z = 0 IGrM iron is forged by the stars/supernovae beforethe source galaxies become incorporated into groups. In this case, Z . registers the stars in these external galaxies only after theyfall in; i.e., if they fall in before z = 0 , while the metal productionis registered whenever it happens.Turning to the second panel of Figure 16, we see that there ismore of a one-to-one relationship between the timescale for oxygenproduction and Z . . This alignment is the result of two effectsacting in concert: (i) Between 60-70% of the oxygen in the z = 0 IGrM is forged by stars that are already in the groups ( c.f., the rightpanel of Figure 14), and (ii) oxygen production by core-collapseType II SNe and transport into the IGrM (by winds) are both tieddirectly to star formation, with no significant built-in lag betweenthese events.Turning to the third panel of Figure 16, we find that the orien-tation of the contours in the Z . , IGrM − Z . plot is midwaybetween that of iron and oxygen. As discussed in the previous sub-section, although silicon and oxygen are both produced in an iden-tical manner, there is one significant difference. AGB stars captureand retain a non-negligible amount of silicon present in the ISMat the time their progenitor stars form, and return it to their sur-roundings only after a lag time. In effect, this means that siliconenrichment of the IGrM can proceed via two channels: the galacticwind and, as is the case with iron, via direct enrichment by the AGBstars in the IGS. This late-time injection of silicon differentiates theevolution of silicon from that of oxygen and shifts the distributionof Z . , IGrM slightly towards lower redshifts with respect to thedistribution of Z . , IGrM . There is a growing consensus that models of galaxy evolution – orfor that matter, models describing the formation and evolution of galaxy groups and clusters – that do not allow for large-scale galac-tic outflows will fail to match the global evolutionary properties ofgalaxies. Observations of both local as well as high-redshift galax-ies indicate that not only are large-scale galactic outflows ubiqui-tous, but that they have a profound impact on the conditions in-side the galaxies as well as conditions in the wider environmentaround galaxies. For example, galactic outflows are thought to playa central role in establishing the observed mass-metallicity rela-tion in galaxies, in promoting widespread enrichment of the IGMas far back as z ∼ , and in accounting for the abundances andabundance ratios of α and iron-group elements observed in the hotdiffuse X-ray emitting gas in galaxy groups and clusters. Recentobservations as well as theoretical models indicate that AGNs andstars/SNe are both capable of driving powerful outflows and whiledefinitive observational evidence outrightly favouring one over theother remains elusive, we argue that only stellar processes are ca-pable of driving large-scale galactic outflows that can transport asignificant fraction of the metal-enriched ISM out of the galaxiesand into their halos and beyond.In this paper, we use cosmological SPH simulations to doc-ument the impact of a well-studied galaxy formation model thatincorporates stellar-powered, galaxy-scale winds with momentum-driven scalings (see Somerville & Dav´e 2014, and referencestherein) on the global properties of galaxy groups over the redshiftrange ≤ z ≤ . We look at some of the commonly constructed X-ray scaling relations, the evolution of the hot gas, the stellar and thetotal baryon fractions, as well as the growth of the iron, silicon andoxygen abundances within the intragroup medium. We examine thecharacteristic timescales for the emergence and the enrichment ofthis IGrM. Since the present model does not include AGN feed-back, we also take this opportunity to lay bare both the successesand the failings of stellar-powered winds so that we can identifyprecisely when, where and in what form AGN feedback is required,and we are using the resulting insights to guide the development ofour own model of AGN accretion and feedback. In this respect, thepresent study establishes a detailed baseline model of the galacticoutflows as a prelude to a similar study including AGN feedback,although we expect that many of the conclusions will be robust tothe inclusion of AGN feedback that quenches massive galaxies.Our main findings are as follows:(i) The distribution of the groups’ formation epochs can bereasonably approximated by a Gaussian with a median of z ∼ and σ = 0 . . Moreover, the epoch when half of a present-daygroup’s X-ray emitting, intragroup medium ( i.e. the diffuse halogas with T > × K) is in place is tightly correlated with thegroup’s formation epoch. Examining the emergence of the latter inmore detail, we find that in halos with gravitational potential wellsof a given depth, the median IGrM mass fraction increases withtime prior to z ≈ as the halos recapture the gas that was expelledout of the galaxy-scale halos at earlier epochs, (the ratio of baryons-to-dark matter of the infalling material is larger than the universalvalue) and most of these baryons are shock-heated to roughly thevirial temperature of the groups upon accretion. After z ≈ , theIGrM fractions within R cease to increase with time because theIGrM is sufficiently extended that the newly accreted (and thermal-ized) baryons primarily remain at r > R and become part ofthis extended halo gas distribution. Apart from this trend with time,the IGrM mass fractions within R also increase with halo massat all epochs. This increase is the result of the larger mass systemshaving deeper potential wells and higher virial temperatures. Con-sequently, more of the diffuse gas is shock-heated to constitute theIGrM and the deeper potentials confine this gas more effectively. MNRAS , 1–26 (2015) L. Liang et al. (ii) Our stellar-powered, momentum-driven wind modelyields X-ray scaling relations that are in excellent agreementwith observed scaling relations ( e.g.
X-ray luminosity-temperature,mass-temperature, entropy-temperature, etc.) over much of theregime associated with galaxy groups despite the fact that themodel does not include AGN feedback. These scaling rela-tions evolve self-similarly from z = 1 to the present, as does M IGrM , /M versus M . The hot, diffuse, X-ray emitting,intragroup gas is not subject to catastrophic cooling. Typically onlya percent or less of z = 0 IGrM mass is lost via cooling over a Hub-ble time. We do, however, see a tendency for the simulated galaxygroups to be slightly more X-ray luminous and/or have slightlycooler X-ray spectroscopic temperature than the observed groupson mass scales M E ( z ) > ∼ M (cid:12) . At face value, these resultscollectively suggest that AGN feedback is not necessary to under-stand the properties of the hot diffuse gas in the simulated groupsuntil the halos approach cluster-scale.(iii) Our simulation also successfully reproduces both the ob-served, spatially resolved, mass-weighted as well as the observed,unresolved, emission-weighted IGrM silicon and iron abundanceswithin R . This agreement also includes the observed trend of[Fe/H] and [Si/H] increasing with temperature until ∼ keV andthen flattening. Probing the origin of the metals in the IGrM in moredetails, we find that nearly of the IGrM silicon, oxygen andiron mass in our simulated groups are produced in the central andthe satellite galaxies of a present-day group or its MMP, and in-fused into the IGrM via galactic outflows, while between ∼ (oxygen) to ∼ (iron) is transferred to the IGrM via direct en-richment by the IGS.(iv) Turning our attention to the group galaxies, we find thatthe stellar-powered, momentum-driven wind model results in apresent-day stellar mass function for group galaxies that is in ex-cellent agreement with the observations for M ∗ < M (cid:12) ; how-ever, we also find galaxies – typically, one per group and invari-ably, the group central galaxy – that have much larger stellar massesthan any observed galaxy. These are the galaxies that are respon-sible for the elevated stellar and total baryonic mass fractions inour simulated groups. Artificially reducing the stellar mass in onlythese ‘large’ galaxies by a factor of ∼ reconciles the group stellarmass fractions with the observations across the entire mass range . ≤ log( M ∗ ) ≤ . .(v) The excess stellar mass in these ‘large’ group galaxies isdue to galaxies no longer being able to moderate their star forma-tion rates by depleting their cold gas mass via expulsion once theygrow larger than M ∗ ≈ × M (cid:12) . The deepening gravitationalpotential of these galaxies and a higher cross-section for hydro-dynamic interactions between the galactic outflows and the shock-heated halo gas component, once the latter starts to form, confinethe wind material within the circumgalactic region. Being metal-rich, most of this wind material cools down and falls back intothe galaxy in a manner more akin to galactic fountains rather thanoutflows ( c.f., Oppenheimer et al. 2010). The high cold gas massin our group central galaxies is largely a consequence of this, andthe overproduction of stars is a byproduct. The breakdown of thestellar-powered winds model in our giant group galaxies generallyoccurs before the galaxies are incorporated into bonafide groupsand is the earliest indication that another feedback mechanism, likeAGN feedback, is needed.(vi) We assert that in large galaxies, at least, AGN feedbackcannot simply act to heat the halo gas just enough to offset the ra-diative cooling losses. This maintenance-mode or hot halo quench-ing feedback may represent a reasonable description of how AGN feedback operates in galaxy clusters and may even result in ‘large’galaxies with realistic stellar properties ( c.f.,
Gabor & Dav´e 2012,2015, and references therein), but because this type of feedback is,in effect, only shifting baryons in our simulated groups from thegalaxies to the IGrM component, the total baryon fraction of thegroups will not change. Our simulated groups, however, alreadyhave too high a baryon fraction ( c.f.,
Figure 8). At the same time,the IGrM mass fractions will become more discrepant and a denserIGrM means that the simulated groups of a given mass will be moreX-ray luminous than their observed counterparts. To ensure thatboth the stellar masses of the ‘large’ galaxies and the hot gas prop-erties of the groups agree with observations, AGN feedback (or forthat matter, any new feedback mechanism or combination of mech-anisms) must step in when stellar feedback starts to fail and con-tinue to drive outflows beyond the galactic halos and perhaps even,beyond the low mass group halos.(vii) Finally, we emphasize that we do not expect the inclu-sion of AGN feedback, and the expected reduction in the stellarmass within the groups, to alter the agreement between our simu-lation results and the observed IGrM metal abundances (and abun-dance ratios) in galaxy groups. Even after discounting the metalsproduced by 2/3 of the stars in the ‘over-sized’ galaxies, the abso-lute abundances in the simulation are still consistent with the obser-vations, especially when one accounts for the factor ∼ ACKNOWLEDGMENTS
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