Properties of simulated Milky Way-mass galaxies in loose group and field environments
C. G. Few, B. K. Gibson, S. Courty, L. Michel-Dansac, C. B. Brook, G. S. Stinson
aa r X i v : . [ a s t r o - ph . C O ] O c t Astronomy&Astrophysicsmanuscript no. rades c (cid:13)
ESO 2018February 25, 2018
Properties of simulated Milky Way-mass galaxies in loose groupand field environments
C. G. Few , B. K. Gibson , , , S. Courty , L. Michel-Dansac , C. B. Brook , and G. S. Stinson Jeremiah Horrocks Institute, University of Central Lancashire, Preston, PR1 2HE, UKe-mail: [email protected] Department of Astronomy & Physics, Saint Mary’s University, Halifax, Nova Scotia, B3H 3C3, Canada Monash Centre for Astrophysics, Monash University, Victoria, 3800, Australia Universit´e de Lyon; Universit´e Lyon 1, Observatoire de Lyon, 9 avenue Charles Andr´e, Saint-Genis Laval, F-69230, France; CNRS,UMR 5574, Centre de Recherche Astrophysique de Lyon; Ecole Normale Sup´erieure de Lyon Grupo de Astrof´ısica, Departamento de Fisica Teorica, Modulo C-15, Universidad Aut´onoma de Madrid, 28049 Cantoblanco, Spain Max-Planck-Institut f¨ur Astronomie, K¨onigstuhl 17, 69117 Heidelberg, GermanyReceived May 22, 2012
ABSTRACT
Aims.
We test the validity of comparing simulated field disk galaxies with the empirical properties of systems situated within envi-ronments more comparable to loose groups, including the Milky Way’s Local Group.
Methods.
Cosmological simulations of Milky Way-mass galaxies have been realised in two di ff erent environment samples: in thefield and in loose groups environments with similar properties to the Local Group. Apart from the di ff ering environments of thegalaxies, the samples are kept as homogeneous as possible with equivalent ranges in last major merger time, halo mass and halo spin.Comparison of these two samples allow for systematic di ff erences in the simulations to be identified. A kinematic decomposition isemployed to objectively quantify the spheroid-to-disk ratio and to isolate the disk-star population. Metallicity gradients, disk scalelengths, colours, magnitudes and age-velocity dispersion relations are studied for each galaxy in the suite and the strength of the linkbetween these and environment of the galaxies is studied. Results.
Metallicity gradients are consistent with observations of HII regions in spiral galaxies and, in agreement with observations,correlate with total galaxy mass. The bulge-to-disk ratio of the galaxies show that these galaxies are less spheroid dominated thanmany other simulated galaxies in literature with the majority of both samples being disk dominated. We find that secular evolutionand mergers dominate the spread of morphologies and metallicity gradients with no visible di ff erences between the two environmentsamples. In contrast with this consistency in the two samples there is tentative evidence for a systematic di ff erence in the velocitydispersion-age relations of galaxies in the di ff erent environments. Loose group galaxies appear to have more discrete steps in theirvelocity dispersion-age relations, if this is true it suggests that impulsive heating is more e ffi cient in the stars of galaxies in denser en-vironment than in the field. We conclude that at the current resolution of cosmological galaxy simulations field environment galaxiesare su ffi ciently similar to those in loose groups to be acceptable proxies for comparison with the Milky Way provided that a similarassembly history is considered. Key words.
Galaxies: Local Group, formation, evolution – methods: numerical
1. Introduction
It is well established that galaxy interactions and merg-ers result in significant changes in a system’s star for-mation rate (Barton et al. 2000; Lambas et al. 2003;Nikolic et al. 2004; Ellison et al. 2008) and its chemicalproperties (Donzelli & Pastoriza 2000; M´arquez et al. 2002;Fabbiano et al. 2004; Kewley et al. 2006; Michel-Dansac et al.2008; Rupke et al. 2008; Kewley et al. 2010; Sol Alonso et al.2010). Studies have shown that in denser large scale environ-ments the star formation rate of galaxies tends to be lower(G´omez et al. 2003). It is often suggested that galaxies inclusters are older and have therefore consumed the limited gasavailable for star formation (Lilly et al. 1996), or that proximityto other galaxies means that the reservoir of infalling gas mustbe shared (Lewis et al. 2002). It is also thought that a dominantmethod of reducing the star formation rate in dense environmentis through ram pressure stripping that removes the gas envelopefrom field galaxies as they are accreted to groups and clusters(Balogh et al. 2004b). Proximity to a cluster centre is also known to impact themorphology of galaxies and clusters have a greater fraction ofearly type galaxies; i.e. the so-called morphology-density rela-tion (Dressler et al. 1997). While the accretion of field galax-ies into denser environments may strip gas from the galaxy andleave a slowly reddening S0 galaxy, it will do little else to al-ter the morphology. Morphological transformations are thereforeattributed to gravitational interactions with other group mem-bers (Moore et al. 1996; Weinmann et al. 2006). Denser envi-ronments also increase the likelihood of galaxy mergers. Thisis supported by the findings of McGee et al. (2008) where an en-hancement in the number of asymmetric disks is found in groupenvironments (these groups typically have velocity dispersionsless than 700 km s − , smaller than the larger clusters consideredin many other works). The authors also put forward the intrigu-ing conclusion that while the groups exhibit a larger fraction ofgalaxies that are bulge dominated, no evidence is found that thegroup environment has any e ff ect on the bulk properties of thedisk galaxy population .
1. G. Few et al.: Properties of simulated Milky Way-mass galaxies
Mergers have a direct impact on both the star formation his-tory of the galaxies and the metal distribution. Hydrodynamicalsimulations by Hernquist (1989) and Barnes & Hernquist (1996)show that mergers funnel gas into the central regions of galax-ies. This would tend to dilute the gas phase metallicity atsmall radii and trigger centrally concentrated star formation(Rupke et al. 2010; Montuori et al. 2010; Perez et al. 2011). Thistrend is consistent with observations of flattened metallicitygradients in luminous and ultraluminous infrared galaxies thatare identified as merged systems (Rupke et al. 2008) and in in-teracting galaxy pairs (Ellison et al. 2008; Michel-Dansac et al.2008; Kewley et al. 2010) where the influence on star forma-tion rates extends to projected separations of up to 40 h − kpc(Ellison et al. 2008).Interactions are far more common in denser environmentsand one would expect to see the e ff ect of these interactions im-printed on the metallicity of cluster and group galaxies whencompared with those in the field. Cooper et al. (2008) observethat not only do members of clusters have greater metallicitiesbut also that on average galaxies that are closer to other clus-ter members have greater oxygen abundances (an e ff ect of order0.05 dex). The conclusion of the work is that metallicity e ff ectsare not driven by the cluster as a whole but only by the spe-cific proximity of each galaxy to others; consistent with pastfindings (Balogh et al. 2004a; Mart´ınez et al. 2008). The inde-pendence of metallicity on large-scale environment is perhapsrefuted by the findings of Ellison et al. (2009) where a resid-ual metallicity-environment e ff ect is found observationally evenafter the dependence on luminosity and colour have been ac-counted for, however these two results are not entirely irreconcil-able. Martinez-Vaquero et al. (2009) select simulated dark mat-ter systems based on the mass and circular velocity of haloes, themutual proximity of the haloes and the distance to a halo withthe same mass as the Virgo cluster. These simulations explorethe properties of the haloes while relaxing these criteria and findthat the nearness of massive external haloes is the most signifi-cant factor determining the dispersion of Local Group systems:the coldness of the Local Group can be attributed mostly to itsisolation from clusters.Recent simulations have employed higher resolutionand more advanced supernova feedback prescriptionswhich ameliorate the traditional failings of galaxy sim-ulations (Robertson et al. 2004; Governato et al. 2007;Scannapieco et al. 2009; S´anchez-Bl´azquez et al. 2009;Stinson et al. 2010; Rahimi et al. 2010; Brooks et al. 2011).It is now possible (and prudent) to examine the more subtlefactors that influence galaxy properties. Given the demonstrabledi ff erence between galaxies in di ff erent (albeit extremely so)environments it is reasonable to expect that galaxies in loosegroups such as our own Local Group may di ff er from those infield.At present the majority of literature on this topic focusseson constrained simulations based upon cosmological initial con-ditions that will purposefully give rise to systems with theproperties of the Local Group (Gottloeber et al. 2010; Peirani2010; Libeskind et al. 2011; Peirani et al. 2012) or the use of ex-tremely large simulation volumes to search for analogous sys-tems (Snaith et al. 2011, and references therein). Here we pro-vide a complementary approach by identifying Local Group ana-logues in a suite of hydrodynamical simulations. In what fol-lows, we will explore the hypothesis that simulated isolated fieldgalaxies can be considered suitable proxies for Local Group ana-logues. The purpose of this work is not to reproduce artificial clonesof the Local Group but rather to gauge the systematic o ff set inproperties between field galaxies and those with a similar de-gree of interaction with neighbours such as is encountered be-tween the Milky Way and Andromeda. These groups are hence-forth termed as “loose groups” to be clear that the systems inthe loose group sample are not Local Group clones from initialconditions designed to reproduce the exact layout of the localuniverse but are chosen from cosmological simulations basedon certain similarities to the Local Group. In doing so we findgalaxies with a range of merger histories that nonetheless pro-duce disk galaxies. It is hoped that the discrepancy between theproperties of these two samples will place constraints on futuresimulations and present insight into the failings of field galaxysimulations when attempting to recover the properties of LocalGroup galaxies. The method employed in producing this sampleand the properties of the simulation code are described in §
2. In § §
2. Method
The galaxies presented here were simulated using the adaptivemesh refinement code ramses (v3.01) (Teyssier 2002). ramses isa three-dimensional Eulerian hydrodynamical code with an N-body particle-mesh scheme to compute self-gravity. The meshautomatically refines according to the local particle density inaddition to a static refinement of nested regions that reduces therun-time while maintaining high resolution around the galaxyof interest. Details of the refinement scheme are describedby Teyssier (2002). ramses includes density- and metallicity-dependent radiative cooling rates, using an ionisation equilib-rium with an ultra-violet radiative background (Haardt & Madau1996). Gas cells with a density ρ exceeding a star formationthreshold of ρ = − form stars at a rate of ˙ ρ = − ρ/ t ⋆ .The star formation timescale t ⋆ is itself a function of the den-sity and the free-fall time through the free parameter, t , as fol-lows: t ⋆ = t ( ρ/ρ ) − / (Dubois & Teyssier 2008). We use t = ffi ciency for ρ = − . We use the kinetic feedback mode of ramses that aimsto reproduce the energetic and chemical enrichment of SNeIIexplosions: After 10 years, star particles release some mass,momentum and energy into a 2-cell radius feedback-sphere cen-tred on the star particle. We characterise the initial mass fractionof the star particles with the parameter η SN =
10% (which cor-responds to the mass fraction of stars contributing supernovaefeedback) and we do not use any mass loading factor. The en-ergy injected into the gas phase is in the form of kinetic energywith 100% e ffi ciency (i.e. 10 erg SN − ). Chemical enrichmentof the gas is followed through the global metallicity Z using ayield of 10%. ramses includes a polytropic equation of state withan index of 5 / T th = K andin the analysis and Table 2 in particular, we will set the temper-ature of the high-density gas cells to 10 K to account for unre-solved cold gas. A detailed description of the star formation andfeedback treatments may be found in Dubois & Teyssier (2008),though the v3.01 ramses has a di ff erent technical implementa-tion of the kinetic feedback.
2. G. Few et al.: Properties of simulated Milky Way-mass galaxies
Candidate haloes for this work were identified from darkmatter simulations and then resimulated with baryonic physicsand a more refined grid around regions of interest, usingthe same technique as in S´anchez-Bl´azquez et al. (2009). Thesimulations are conducted in a cosmological framework with H =
70 km s − Mpc − , Ω m = Ω Λ = Ω b = σ = h − Mpc and24 h − Mpc and the maximum refinement achieved (16 levels)corresponds to 436 pc and 523 pc respectively. The dark mattermass resolution is 5.5 × M ⊙ and 9.5 × M ⊙ respectively. Wenow describe the selection of our candidate haloes. A rich literature exists comparing simulated field disk galax-ies with observations of the Milky Way (e.g. Brook et al.2004; Scannapieco et al. 2005; S´anchez-Bl´azquez et al. 2009;Kobayashi & Nakasato 2011; House et al. 2011; Guedes et al.2011). The purpose of our work here is to determine whether ornot environments comparable to those of the Local Group - thetrue environment of the Milky Way - result in any measurablecharacteristics which would call into question this fundamentaltenet of simulation vs observation comparison.The dark matter haloes of the galaxies presented here arechosen as follows. Dark matter haloes with virial mass (M vir ) inthe range 5 × –10 M ⊙ are considered as loose group candi-date haloes. Further selection criteria for the loose group sampleare such that large groups are excluded; each halo must haveat least one companion with a comparable virial mass at a dis-tance of 500–700 kpc but have no haloes more massive than5 × M ⊙ within 5 Mpc. Please note that the loose groups arenot specifically constrained to be pairs, rather they may includeup to four haloes each with M vir > M ⊙ .The field sample consists of galaxies that have no other darkmatter haloes of mass M vir > × M ⊙ within a 3 Mpc radius.These field environment galaxies are far more common than theloose groups and those presented here were chosen based uponproperties such as mass, spin factor and number of mergers suchthat a similar range in each of these can be found in both theloose group and field samples. The spin factors of the dark mat-ter haloes range from 0.007 to 0.08, this range encompasses themajority of dark matter halos and is simply used to exclude out-liers. The merger trees of the galaxies are used to select loosegroup and isolated haloes to avoid galaxies (in both loose groupand field samples) that have any significant mergers after z = ff erences. The full sample ofgalaxies covers a range in virial mass from 10 –10 M ⊙ andincludes the field galaxies and all the group galaxies in this massrange, i.e. massive satellites in addition to the dominant groupmembers.There are ten loose group galaxies (taken from three groups)and nine field galaxies. The dark matter distributions of a fieldgalaxy and a loose group are shown in Figure 1. Each sample isroughly divided into two di ff erent resolutions corresponding tothe di ff erent cosmological volumes. None of the galaxies havepassed pericenter with one another as of z = ff ects. Two of the galax-ies do have recent mergers, but for the analysis presented hereare studied at an earlier timestep (that is una ff ected by the z = Fig. 1.
Examples of the di ff erent environments considered in thiswork. The dark matter haloes of the field galaxy Selene (top)and the loose group galaxies
Castor , Pollux , Tyndareus and
Zeus (bottom) are shown as blue particles (lighter colours correspondto denser regions). Images are 4 × in size and have a depthof 4 Mpc.populations. This is true of the galaxies presented here (stellarmasses are stated in Table 1) with the stellar-to-total mass frac-tion a factor of 2–3 times too high when counting all mass inthe virial radius (Mandelbaum et al. 2006; Moster et al. 2010;Leauthaud et al. 2012). We do not believe that this has a dras-tic impact on this analysis. Firstly, the issue a ff ects galaxies in-dependent of environment, so comparisons of the loose groupand field samples are not systematically o ff set by this e ff ect.Secondly, the early formation of stars would lead to an overly
3. G. Few et al.: Properties of simulated Milky Way-mass galaxies
Fig. 2.
Major mergers distributions, the top two rows are loosegroup galaxies and the bottom two rows are field galaxies, a con-vention that is followed throughout this work. The magnitude ofthe merger is represented by the virial mass of the host halo di-vided by the virial mass of the merging body. As stated in thetext, mass ratios are calculated at the time the haloes first comeinto contact as the mass associated with merging structures is of-ten greatly diminished by the time the disk is disrupted. The ma-jority of mergers take place at early times when the galaxy halostill has a low mass and assembly is mostly hierarchical. Wefind that only mergers shown above to occur further back than4 Gyr have any significant influence on the disk structure andthat mergers can take several Gyr before they have descended farenough into the halo to disrupt the disk. A dashed line shows thelower bound of the commonly used definition of major mergers.massive spheroid. We will show later that the spheroid mass is not extreme, although admittedly the disk stars are too concen-trated, i.e. disk scale lengths are too short (see § § The predominant strength of using cosmological simulations todevelop this suite of galaxies is that a self-consistent merger treeprovides the basis of the evolution for each galaxy. This ensuresthe conditions in the environments selected here are consistentwith the current understanding of cosmology and not biased byartificial initial conditions that may a ff ect the results. We begin by demonstrating that there is at least a superficial similarity be-tween the merger histories of the two samples in spite of theenvironmental di ff erences.At each timestep a catalogue of haloes and subhaloes is cre-ated using the Adaptahop algorithm (Aubert et al. 2004). Thehalo catalogues are then linked into merger trees for the selectedhaloes using the “most massive substructure method” detailed inTweed et al. (2009). Under this formalism, at any given branchin the tree the most massive progenitor is considered the parenthalo.It is not however a trivial exercise to define mergers in thiscontext, and the following definition of a merger is adopted: amerger occurs when an object is identified as a subhalo in agiven output but not in the previous output. In practice, the sub-halo continues to exist as an identifiable structure orbiting thehost halo for several Gyr. Due to dynamical friction, the subhalogradually sinks into the potential well of the host halo and isslowly stripped of mass before dissolving completely, at whichpoint all particles are attributed to the host halo. We found thatin general with the merger time definition above there is a delayof up to 4 Gyr between the merger time and any real interactionwith the disk, i.e., there is a delay time between the dark mat-ter merger and the galaxy disk merger. The definition above isused because the amount of mass loss before the subhalo dis-solves is unpredictable and the mass ratio of subhalo to host isa more useful quantity for the purpose of evaluating the mag-nitude of the merger. The magnitude and timing of mergers foreach galaxy are shown in Figure 2. This figure shows that mostmergers a galaxy experiences occur at early times and that theseearly mergers tend to have mass ratios closer to unity. This ispartly due to universal expansion reducing the merger likelihoodand partly to the limited size of haloes at early times limiting themass range and making equal mass mergers more likely.The traditional definition of a major-merger, M host / M sub ≤ M host / M sub ≤ ff ects,these galaxies are chosen from dark matter haloes based partlyon the merger trees and haloes with many mergers were dis-counted as unsuitable for hosting disk galaxies. A commonlyused metric of the merger history is the time at which the lastmajor-merger took place. At this point we note that two of thegalaxies (identified by the names, Castor and
Eos ) show obvioussigns of disturbance at z = ffi cult to identify. The presence of merg-ers may at first be considered counter to the previously men-tioned constraint that the galaxies have no recent major mergers,in both cases the merger did not appear in the dark matter-onlysimulation and only became apparent following the inclusion ofbaryons. We remedy this in both cases by analysing the galaxydisk at a timestep immediately preceding the disturbance. Whilethese galaxies appears in the analysis as a low redshift (z ≃ = ff ect of mergers on disk galaxies but to examine what e ff ect theenvironment might have (i.e. via ambient e ff ects) when the in-creased instance of mergers is discounted. As such we point toFigure 2 as evidence that the loose group galaxies have the samediversity of merger history as do the field galaxies.
4. G. Few et al.: Properties of simulated Milky Way-mass galaxies
Table 1.
List of the disk galaxies simulated for this work, with their total, dark matter, baryonic, stellar and gaseous masses. Thespatial resolution of the simulation they originate from and their host environment is also quoted. The properties are calculated atz = Castor and
Eos as described in § Name Environment Resolution M tot M DM M baryon M stellar M gas (pc) (M ⊙ ) (M ⊙ ) (M ⊙ ) (M ⊙ ) (M ⊙ )Castor loose group 436. 1.05 × × × × × Pollux loose group 436. 4.23 × × × × × Zeus loose group 436. 2.33 × × × × × Tyndareus loose group 436. 3.30 × × × × × Apollo loose group 523. 8.94 × × × × × Artemis loose group 523. 7.45 × × × × × Daphne loose group 523. 3.09 × × × × × Leto loose group 523. 2.49 × × × × × Luke loose group 523. 1.13 × × × × × Leia loose group 523. 3.93 × × × × × Ben field 523. 7.74 × × × × × Tethys field 523. 7.21 × × × × × Krios field 523. 5.68 × × × × × Atlas field 523. 6.48 × × × × × Hyperion field 523. 1.03 × × × × × Eos field 436. 4.64 × × × × × Helios field 436. 1.05 × × × × × Selene field 436. 6.07 × × × × × Oceanus field 436. 1.12 × × × × × We now separate the stellar particles into spheroidal and diskpopulations using a kinematic decomposition similar to thatof Abadi et al. (2003). Details on the decomposition for eachgalaxy can be found in the appendix where the orbital circular-ity distributions are presented. In short, stars are assumed to be-long to either a spheroidal or a rotating disk component throughanalysis of the orbital circularity, i.e. the ratio of their angularmomentum, J z to the circular orbit angular momentum J circ fora given particle energy. The successes of this method are shownin Figure A.2. It should be noted that while the J z / J circ distri-bution has two components, in the intermediate region, particlesare stochastically attributed to each component. Thus it is notnecessarily true that stars identified as belonging to the spheroiddid not form as disk stars. As such the spheroidal component willcontain disturbed disk stars (which is arguably appropriate) andmore critically, circularly rotating bulge stars will be attributedto the inner regions of the decomposed disk. This does not skewthe spheroid-to-disk mass ratio as the vast majority of star parti-cles have equal mass, furthermore the order of this e ff ect shouldbe small as shown in Figure A.1 which plots the star formationhistory for the entire galaxy (solid line) and the disk (dashedline) and demonstrates that the selected disk stars well representthe stars formed at late times.In the analysis that follows we define a disk annulus to ex-clude contamination by bulge stars and avoid halo stars at thedisk edge. Figure 3 shows the rotation curves for the galaxies(and circular velocities for each phase of matter) and choice ofdisk annulus (indicated by diamond symbols at an arbitrary ver-tical position). The outer extent of the stellar disk region is firstconstrained by examination of the rotation curve of the youngstars (less than 100 Myr old), the departure of the young starsrotation curve (solid red line) from the gaseous rotation curve(solid blue line) is a useful indicator of the stellar disk edge.Consideration is also given to the stellar density profiles andmetallicity gradients of each galaxy, in several cases the den-sity profile or metallicity gradient extends beyond or falls short of the young disk edge. The final disk annulus is conservativeto allow for gradients to be measured for each property overa consistent region while avoiding bias from unusual features.Despite this there are cases where the region over which gradi-ents and scale-length are determined has been changed to reflectthe characteristics of the galaxy in question. A summary of thegalaxy properties can be found in Table 2 and star formation his-tories for each galaxy are plotted in Figure A.1. The galaxy’s stellar and gaseous distributions, ages and metallic-ities have been used by the ray tracing program S unrise (Jonsson2006) to produce mock images. The
Starburst99 stellar popula-tion models (Leitherer et al. 1999) define the colour and magni-tude of stellar particles. Scattering and extinction are determinedby assuming that dust follows the gas phase metallicity distribu-tion. Mock images of the galaxies may be found in Figure 4,each image being 50 ×
50 kpc in size and produced using SDSSg, r and i filters. We draw the reader’s attention to the asymme-try of the more extended disks of Luke and
Oceanus , the warpeddisks of
Castor , Tyndareus , Krios and
Hyperion and to the red,spheroid-dominated
Helios .
3. Results
One of the potential di ff erences that may be seen between thegalaxies in di ff erent environments is the bulge-to-disk ratio.There is a body of evidence suggesting that a morphology-density relation exists (Dressler 1980; Giuricin et al. 1995;Bamford et al. 2009) due to harassment by neighbours andthe increased likelihood of mergers. The spheroid-to-disk stel-lar mass ratios for the sample are shown in Figure 5 and itis immediately apparent that the majority are disk dominated(spheroid / total <
1) in spite of the spheroid containing the net
5. G. Few et al.: Properties of simulated Milky Way-mass galaxies
Fig. 3.
Rotation curves showing the circular velocity for stars (red), gas (blue) and dark matter (black) as dashed lines and rotationvelocities (solid lines) of young stars (age <
100 Myr at z =
0) and gas as a function of radius. Two blue diamonds denote the inner andouter “disk radii” at an arbitrary vertical position. These values are chosen from inspection of the rotation curve of the gas, surfacedensity maps, stellar surface density profiles and metallicity profiles. The most conservative choice is made to avoid spurious fitsbut to maintain consistency throughout the analysis.mass of the halo in addition to the bulge. Only the smallestgroup members are spheroid dominated (
Leto , Tyndareus and
Zeus ) with many of the larger galaxies having disk masses ex-ceeding spheroid masses by a factor of 2–4. There is no no-ticeable tendency for the galaxies with more disturbed disksand smaller galaxies to be spheroid dominated;
Artemis has adisturbed disk and yet still exhibits a spheroid-to-disk ratio of0.326, likewise the low mass galaxies
Daphne , Pollux and
Eos have quite strong disk components in contrast with the similarlyless massive (M vir < × M ⊙ ) galaxies Zeus , Tyndareus and
Leto . Given the typical problem of forming too many stars, par-ticularly at early times, in simulated galaxies one might expectthe spheroid mass to dominate over disk mass but this does notappear to be the case; although admittedly the spheroid-to-diskmass ratios of these galaxies are still not as low as typical brightspiral galaxies (Weinzirl et al. 2009). Also note from Figure 3that although the characteristic central peak in the rotation curve(associated with excessive concentrations of mass) is present,the decline of the rotation curve has more to do with the concen-tration of the disk. This issue a ff ects all galaxies irrespective of
6. G. Few et al.: Properties of simulated Milky Way-mass galaxies
Fig. 4.
Mock images of the galaxies. Face- and edge-on views are separated by dashed lines, images are created by combining SDSSg, r and i filters and are each 50 ×
50 kpc in size. Simulation outputs at z = Castor and
Eos wherethe galaxies are shown at z ≃ . 7. G. Few et al.: Properties of simulated Milky Way-mass galaxies environment and thus biases in the star formation history do notrender comparison of the two environment samples unreliable.The lack of a clear separation in the loose group and fieldpopulations in the spheroid-to-disk plot may point to the fact thatthe environments here are not su ffi ciently di ff erent to allow thegalaxies to manifest di ff erent disk properties and that galaxiesdi ff er significantly only if they inhabit more extreme overdensi-ties. It also reflects the dynamics of these groups. None of thegalaxies have undergone much interaction with any other mas-sive group member, having not passed pericenter with one an-other at z =
0. This removes harassment by massive galaxies asa possible source of disruption and leaves only the possibilityof complete mergers with smaller satellite galaxies than thoseshown in Figure 2 as a possible explanation.
Fig. 5.
Spheroid and disk masses as determined by kinematic de-composition of the z ∼ We now examine the metallicity gradients of the galaxies for evi-dence of environmental influences. Metallicity gradients of inter-acting and merged galaxies are known to be flatter (Ellison et al.2008; Rupke et al. 2008; Kewley et al. 2010; Perez et al. 2011)and as such, abundance gradients provide a probe of the dy-namical mixing. To make comparisons with observed HII gra-dients we select stars that are younger than 100 Myr from thekinematic decomposition and also employing the spatial con-straints described in § − .
07 to − .
02 dex kpc − , consistent with observations by Zaritsky et al.(1994) of spiral galaxies in the field ( − .
231 to 0 .
021 dex kpc − ).Gradients are also calculated for spiral galaxies in van Zee et al.(1998) spanning − .
07 to − .
04 dex kpc − and Garnett et al. (1997) with a range of − .
083 to − .
020 dex kpc − , the RaDESgalaxies are remarkably close to these values.Metallicity gradients are thought to be flatter for galaxies indenser environments and has been demonstrated to be true forclose interacting binaries by Kewley et al. (2010) where HII re-gion metallicity gradients are found between − .
040 to − . − . While there is no obvious distinction between thetwo samples presented here it is worth bearing in mind that theRaDES loose group galaxies are an order of magnitude moredistant from each other than the galaxy pairs in Kewley et al.(2010). Furthermore the simulated gradients are not dramati-cally inconsistent with those measured for interacting binaries.We note that the simulated loose group galaxies do not haveappreciably flatter young stellar gradients (with the exceptionof Leia ), however they likewise do not have steeper gradients,which leaves the possibility that the statistical sizes of the sam-ples here may be too small to probe such a slight e ff ect. Fig. 6.
Metallicity gradients of the disk stars at z ∼ ff set to flatter gradients for the loosegroup galaxies.Another feature of Figure 6 is the trend for less massivegalaxies to have steeper gradients. Leia is a notable outlier fromthis trend, having a particularly flat metallicity distribution, how-ever when the gradient is calculated on stars of all ages the trendremains and
Leia does not appear to be peculiar. This is counterto what might be expected since these galaxies have less massivedark matter haloes and therefore may be more easily perturbedand have flattened metallicity gradients. In Prantzos & Boissier(2000), cosmologically motivated scaling relations are used todemonstrate that the metallicity gradients of spiral galaxies aresteeper in less massive galaxies when expressed in dex kpc − but not so when expressed in dex R − where R d is the disk scalelength. This is a consequence of the shorter scale-length of theless massive disks arising from a steeper star formation rate pro-
8. G. Few et al.: Properties of simulated Milky Way-mass galaxies
Table 2.
Galaxy properties of the simulated disks at z ∼
0: scale length, metallicity gradient (for stars with age less than 100 Myr),cold gas mass-weighted metallicity average (T < × K), stellar mass (kinematically defined disk stars), cold gas mass, andmagnitudes (b and r SDSS filters). Note that for the gas mass and metallicity determinations, spatial cuts are used to excludesatellites.
Name Environment scale length d[Z] dR − mean [Z] stellar disk mass gas disk mass M b M r (kpc) (dex kpc − ) (M ⊙ ) (M ⊙ )Castor loose group 3.88 − . − .
194 7.19 × × − . − . − . − .
139 3.45 × × − . − . − . − .
159 1.03 × × − . − . − . − .
086 1.32 × × − . − . − . − .
269 6.30 × × − . − . − . − .
239 3.24 × × − . − . − . − .
139 2.14 × × − . − . − . − .
207 1.19 × × − . − . − . − .
164 6.61 × × − . − . − . − .
130 3.03 × × − . − . − . − .
272 4.17 × × − . − . − . − .
231 5.12 × × − . − . − . − .
204 3.99 × × − . − . − . − .
170 4.38 × × − . − . − . − .
199 7.66 × × − . − . − . − .
279 2.51 × × − . − . − . − .
069 6.57 × × − . − . − . − .
244 5.20 × × − . − . − . − .
103 1.00 × × − . − . file which results in a greater metal production rate in the innerdisk compared with the disk periphery. This behaviour is sup-ported by observations (Garnett et al. 1997; van Zee et al. 1998)where it is shown that less luminous spiral galaxies have steepergradients than brighter galaxies when the absolute gradient ismeasured. When observed gradients are normalised to the diskscale-length however no significant variation with luminosity isapparent. Another finding of Garnett et al. (1997) is that the dis-persion of absolute gradients is larger for less luminous galaxiesbut when normalised the dispersion is consistent with brightergalaxies pointing to the existence of some degree of co-evolutionof metallicity and density profiles. The scale length normalisedmetallicity gradients of young stars are shown in Figure 7 andconfirm that metallicity gradients likely have a common originwith the stellar density profile. This is explored in more depthin Pilkington et al. (2012) where clear links are made betweenthe star formation profile and metallicity gradients. The abso-lute metallicity gradients of the RaDES galaxies are consistentwith values found in literature (Garnett et al. 1997) however thenormalised gradients are around an order of magnitude flattersuggesting that the measured density profiles are too steep, afeature that is consistent with the known issue of excess starformation at early times and peaked rotation curves in simula-tions (Navarro & Benz 1991; Governato et al. 2004; Guo et al.2010; Sawala et al. 2011). A result that is relevant to this work isthat of Dutil & Roy (1999). Here the authors find that HII metal-licity gradients are flatter for earlier morphological types, butcritically, that the trend is weaker when the gradients are nor-malised to some isophotal or e ff ective radius. While we do notshow the correlation between gradient and morphology (indeedno attempt is made to identify the classical morphology of thesegalaxies) it is clear that the metal gradient has some degree ofco-evolution with the scale length. Fig. 7.
Young stellar metallicity gradients at z ∼ We use S unrise to produce seven di ff erent projections rang-ing from face-on to edge-on and display the values in acolour-magnitude diagram (Figure 8) that overplots the ob-served (uncorrected) colour-magnitude diagram from SDSS data(Bailin & Harris 2008). We represent the change in magnitudeand colour as a function of projection angle for each galaxy in
9. G. Few et al.: Properties of simulated Milky Way-mass galaxies
Figure 8 with an arc that starts with a symbol denoting the face-on projection (symbol type follows paper conventions), the endof the arc denotes an edge on projection. Face-on magnitudesfor each galaxy are given in Table 2. Almost all the galaxiespopulate the blue cloud with only
Helios appearing within thered sequence. Much as expected, as the galaxies becomes moreinclined they appear to dim and redden; many of the galaxiestherefore have edge-on projections that stray into the dimmestend of the red sequence. There is a selection e ff ect at work hereas the galaxies are a priori chosen to be disk galaxies with on-going star formation and that only Helios is particularly red isreassuring. The colour of the galaxies reflects that while the diskstars are too concentrated there is no critical over production ofstars at high redshift which would bias the galaxies to the redregions of Figure 8.There is no apparent separation of the two samples once theobvious outlier of
Helios has been discounted. There is someobservational evidence that the colour distribution of late-typegalaxies is only weakly dependent on environment and that itis more strongly influenced by the luminosity or mass throughintrinsic evolution (Balogh et al. 2004b). The distribution in r-band magnitude is consistent with the mass of each galaxy andthe colour of galaxies can be considered a probe of their star for-mation history (Figure A.1). Taking
Helios as an example, wesee an initially prolonged star formation phase in comparisonwith other galaxies that have star formation rates that are less dis-parate throughout time. We examine the impulsive interactionsof the disk with respect to kinematics in the next subsection.
Fig. 8.
Colour-magnitude diagram. The background data areSDSS galaxies with no inclination correction. Symbols followthe paper convention and denote the face-on values. The tailstraces the change in orientation from face- to edge-on.
We now move away from morphology and chemistry to examinekinematics and use the temporal behaviour of the stellar velocity dispersion ( σ ) for this purpose. The velocity dispersion of a re-gion analogous to the “solar neighbourhood” is used to quantifythe influence that external interactions have on the kinematics ofthe disk. To remove the bias that arises from the velocity disper-sion gradient as a function of disk radius we select stars froman annulus of thickness 2 kpc, centred on 3 times the disk scalelength and a height of less than 3 kpc above and below the equa-torial plane. Figure 9 shows the velocity dispersion of stars, σ , asa function of their age at z =
0. While many of the RaDES galax-ies attain the observed velocity dispersion of the Milky Way (10–20 km s − found by Soubiran & Girard (2005); Soubiran et al.(2008); Holmberg et al. (2007)) when the youngest stars are con-sidered, the older populations have far greater dispersions thanobserved. The σ - age dispersion relations shown in Figure 9 ex-hibit a greater increase in dispersion as a function of age and theappearance of more discrete steps than are apparent in observa-tions. Greater velocity dispersions are to be expected in simula-tions as less than ten resolution elements are found in the would-be thin-disk (if such a structure were resolvable). The high earlyvelocity dispersions found even in field galaxies with the fewestmergers (e.g. Krios or Selene ) may indicate that these galaxiesexperience excess kinematic heating from mergers. Another pos-sibility is that very early in the galaxies formation cold flows(rather than discrete mergers) are responsible for forming themajority of stars. As it is well known that cosmologically sim-ulated galaxies form too many stars at early times (see Table 1for the stellar mass fractions) it is possible that the high velocitydispersion of old stars is simply reflecting this shortcoming. Wenote however that maps of the gas distribution at high redshiftclearly show discrete gaseous objects merging and no evidenceis found for cold streams after z = σ - age relations do not at first display any obvious dis-tinction between field and loose group environments, so a morerigorous analysis is called for. We have attempted to quantifythe di ff erence between a “stepped” and a smooth σ - age rela-tion by looking for spikes in the age-derivative of σ ( age ). If theage-derivative of σ ( age ) exhibits spikes above some significancelevel (the step-threshold) it will betray the existence of steps inthe velocity dispersion. Galaxies that have steps with magnitudeexceeding a threshold (the step-threshold) that is a factor of β greater than the average of the age-derivative of σ are definedas having a “stepped profile”. The value of β is chosen in therange 4–7 as values that are too low will not discriminate smallvariations in the age-derivative from larger steps and a value thatis too large will classify all steps as being normal. This test isrepeated for di ff erent spatial selections in each galaxy (annuliwith 2-4 × R d in radius with a width of ± ff erent values of beta in therange 4–7. In each case the field sample has approximately halfthe number of galaxies with step features than does the loosegroup sample. An example is shown in Figure 9 for β = × R d and aheight of 3 kpc above and below the equatorial plane) in whichseven out of ten loose group galaxies have stepped profiles whileonly three of the nine field galaxies do. The binning in age usu-ally places at least several hundred stars in each age bin makingthe uncertainty in the velocity dispersion (and propagated uncer-tainty in the discrete age-derivative) very small, these are plottedas 2 sigma error bars in Figure 9. In the extreme case of taking β = β results in the loosegroup sample having a greater fraction of galaxies with stepped
10. G. Few et al.: Properties of simulated Milky Way-mass galaxies
Fig. 9.
Present day (z = § × R d and a height of 3 kpc above and below the equatorial plane. The lower line is the age-derivative of this function,d σ/ d age . Horizontal dotted lines define the zero point and a step-threshold that is 5 × h d σ/ d age i .profiles than the field sample, the number of galaxies studiedhere is not enough for this result to be conclusive and a morecomplete sample would be required to make it so. Neverthelesswe now discuss the implications of the trend if it is real. Thephysical mechanism shaping the σ - age relation can be simplythought of as stars being heated to greater dispersion by allmergers subsequent to their formation and to an extent that de-pends on the severity of the merger (Villalobos & Helmi 2008;Di Matteo et al. 2011). A series of gentle mergers therefore re-sults in a smoother decline in dispersion towards younger stars(Kazantzidis et al. 2008) while a large and disruptive merger ex-cites all stars formed previously to a plateau that gives a more step-like appearance to the σ - age relation (Brook et al. 2004).This contrasts with the conclusions of House et al. (2011) wherestars are found to form with a velocity dispersion and retain itas a signature of the gas state at that time, however in eitherscenario the analysis performed in this work is a valid measureof the e ff ect of disk disruption on stellar dynamics. The resultsshown in this work tentatively suggest that in spite of a super-ficially similar major-merger history, there may be some dif-ferences in the mergers experienced by the galaxy disk or theinteraction histories. Firstly galaxy disk major mergers couldimpact the galaxies di ff erentially depending on the gas fraction(Cox et al. 2006; Hopkins et al. 2009; Lotz et al. 2010), the or-
11. G. Few et al.: Properties of simulated Milky Way-mass galaxies bital configuration (Barnes 2002; Robertson et al. 2006) and thelarge-scale tidal field (Martig & Bournaud 2008). Secondly, thenumber of minor mergers or interactions with orbiting satellitescould have an impact in shaping the σ - age relation (Quinn et al.1993; Abadi et al. 2003; Bournaud et al. 2005). Third, the inter-action of the galaxy with the intragroup medium may have animpact as found by Bekki & Couch (2011) wherein the authorsfind that repetitive harassment in groups can lead to star forma-tion bursts and disk heating.
4. Conclusions
We present a suite of cosmological simulations with the inten-tion of comparing field galaxies with galaxies in Local Groupenvironments. The galaxies are taken from cosmological simu-lations where a zoom method is used to allow sub-kpc resolutionwhile simultaneously accounting for large scale structure forma-tion. A kinematic decomposition has been performed to separatedisk stars from spheroid stars and we have analysed the morphol-ogy of the galaxies. While all galaxies studied here have largerstellar mass fractions than observations dictate they should, thisissue is uniform and does not a ff ect comparisons between thetwo environments. We have also examined the metallicity gra-dients finding trends with mass but a very weak or non-existentcorrelation with environment. Finally the stellar velocity disper-sion is studied and evidence of a dependence on environment isfound in the signature of impulsive heating in group galaxies.The results of this work are pertinent to the comparison of sim-ulated field galaxies with observations of the Milky Way. Theconclusions of this work are summarised here:1. No distinction between loose group and field galaxies is seenwhen considering the spheroid-to-disk ratio although exami-nation of galaxies with greater spheroidal components showsthat they all have interactions that disturb their disk ratherthan forming from kinematically hotter gas. However this isfar from conclusive as there are only four galaxies with sig-nificantly higher spheroidal components of the total 19.2. Metallicity gradients of loose group galaxies are very simi-lar to those of field galaxies with the same disk mass, a resultthat is still consistent with observations of strongly interact-ing galaxies (Kewley et al. 2010) though non conclusive ev-idence is seen that loose group galaxies should have signif-icantly flatter gradients compared with their counterparts inthe field. The absolute gradients are consistent with observa-tions (Zaritsky et al. 1994; Garnett et al. 1997; van Zee et al.1998) yet when normalised by disk scale-length gradientsare an order of magnitude flatter than observed suggestingthat density profiles are too concentrated. Observations alsoshow that more massive spiral galaxies have flatter gradients,this has previously been matched by semi-analytical mod-els (Prantzos & Boissier 2000) using scaling relations but thetrend has now also been shown to exist for our numericallysimulated galaxies. We also find a link between metallic-ity gradients and stellar density gradients that suggests thatgalaxies in the mass range studied here have similar metalgradients when expressed in dex / R d and that variance in thisvalue may be attributable to radial migration or disruptivemergers.3. Examination of the age-velocity dispersion relation revealsthat as expected the velocity dispersion of old stars in thesimulated galaxies is greater than observed for the MilkyWay disk. Loose group galaxies exhibit more stepped rela-tions that suggest mergers / harassment do have a greater im- pact on the loose group galaxies than field galaxies. This isat odds with the apparent similarities in the major mergerfrequency of the two samples and suggests that the majormerger history of dark matter haloes may not be an accu-rate probe of the galaxy disk merger history. We note how-ever that the relatively small sample size means that it is notconclusive whether or not this is a real e ff ect depending onenvironment or simply because the loose group galaxies hap-pen to have more turbulent formation histories independentof environment; certainly the individual formation history ofeach galaxy will impact on its velocity dispersion evolutionand this would be consistent with the other findings of thiswork.The main conclusion to come from this work is that in suchsparse environments where the galaxies are not directly interact-ing galaxies exhibit di ff erent properties depending on individualmerger histories and infall rates but that loose groups environ-ments are only very weakly di ff erent to the field. It has beensuggested for cluster galaxies that it is likely that galaxies areshaped more by direct mergers and their own secular behaviourrather than the large-scale environment that impacts the afore-mentioned only indirectly (McGee et al. 2008). Structures fur-ther than ∼ ffi cient to link mergers to the signatures of the impact theyhave on the disk properties and a future study to follow thisshould develop a larger suite using only dark matter simulationsto quantify the satellite distribution and minor merger rates witha greater statistical significance. Simulations at higher resolutionshould also be employed to determine conclusively if any sys-tematic di ff erence in metallicity gradients exists. We finish bystating that at the resolutions considered here simulated galax-ies may be safely compared with Milky Way properties whetherthey inhabit loose group or field environments, however atten-tion must be given to the aggregated merger properties, massand internal structure for such comparisons to be meaningful. Acknowledgements.
The authors would like to acknowledge Romain Teyssierfor both access to ramses and for helpful discussions regarding its use. Weare grateful to referee Sebastien Peirani for the many suggestions that havegreatly improved this manuscript. CGF acknowledges the support of STFCthrough its PhD Studentship programme (ST / F007701 / / F002432 / / H00260X / References
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13. G. Few et al.: Properties of simulated Milky Way-mass galaxies
Appendix A: Additional Galaxy Properties
Here we describe some properties of the galaxies that are not directly discussed in the main paper body but are still useful assupplementary material. We begin with some general comments on particular features of each galaxy that are of interest. – Castor is the only galaxy in the sample to exhibit a bar, perhaps reflecting the greater resolution or the more isotropic natureof its group (compared with, for example, the filamentary structure of the
Apollo group). It also presents the clearest exampleof spiral structure of the entire sample. The spiral structure presents challenges when quantifying the stellar scale length as thearms present a bump in the density profile. The young stars present in the arms mean that this is even more pronounced whenmeasuring the brightness profile.
Castor also has the most pronounced (and abrupt) disk warp, initially this was believed to beevidence of poor resolution at the disk edge but investigation has revealed no particularly favoured alignment of the disk warpsin this sample. Analysis of
Castor has been conducted on a snapshot slightly before z = – Artemis is unusual in that it has a relatively massive dark matter halo (7.45 × M ⊙ ), reasonably low spheroid-to-disk fraction(0.32) and flat metallicity profile (-0.0068 dex / kpc), yet its disk scale length is only 1.87 kpc and is truncated at a radius of 7 kpc.There exists a gaseous polar disk (not dense enough to form stars) and yet the vertical velocity dispersion changes very little asa function of age. This suggests that the last major merger experienced by Artemis left star-forming gas with a similar velocitydispersion to the older stars, an e ff ect not seen in the other galaxies. – Leto is the least massive galaxy within the
Apollo group and the most spheroid dominated of the galaxies. This spheroid isnot composed of older stars as in the other galaxies, there is a significant fraction of the spheroid stars that are young. This isthe result of a low star formation rate at early times compounded by a recent, disruptive event that is evident in the velocitydispersion-age relation. – Eos undergoes a merger at late times that leaves it with an extremely irregular morphology at the last time step, analysis of thisgalaxy is performed on a snapshot prior to this event. – Helios is the most early type galaxy of all. Despite its great mass it is the reddest galaxy and has young stars with around twicethe vertical velocity dispersion of much of the rest of the sample and a prolonged early star formation episode, this contrastswith the lack of an identifiable late merger to result in such a morphology. – Selene has few mergers in its history and is one of the most quiescent galaxies, forming the largest disk fraction of all thegalaxies and presenting definite spiral structure. – Oceanus has the greatest stellar mass in the sample (though it is among others with comparable halo masses) and has a rotatinggaseous disk that extends as far as 40 kpc from the centre. This disk is dense enough to form stars and hence this galaxy has anextremely long scale length (6.63 kpc) and one of the flattest metallicity gradients.One of the key ways of understanding the formation of galaxies is by examining the star formation history of the di ff erentcomponents. The distribution of star formation in time tells us a great deal about how the di ff erent components of a galaxyform. In the course of this work the signature of mergers were found to be identifiable in the bursts of star formation seen inFigure A.1. These bursts can in some cases be associated with steps in the velocity dispersion described in § ff ects of mergers is yetmore evidence that the signature of a merger depends on the gas fraction or phase space configuration of the merging bodies.Note the restrained recent star formation of the disrupted galaxy Artemis compared with the more disk dominated
Apollo or Oceanus .For the analysis of the simulated disk galaxies presented in this work to be as uniform as possible we performed a kinematicdecomposition to examine the disk stars with minimal contamination from halo and bulge stars. The decomposition employedfollows the Abadi et al. (2003) method of using the angular momentum of stars compared with the angular momentum expected forrotating stars. The distribution of the relative angular momentum is shown in Figure A.2 with blue and red lines highlighting thedistribution on disk and spheroid stars respectively.
14. G. Few et al.: Properties of simulated Milky Way-mass galaxies
Fig. A.1.
Star formation histories of the sample galaxies. The star formation rate of all stars within the virial radius at z = =
15. G. Few et al.: Properties of simulated Milky Way-mass galaxies
Fig. A.2. J z / J circ distribution of stars within the virial radius (black). Blue and red lines shows the distribution of the disk andspheroid components respectively. Note the existence of a third intermediate component included in the distribution that is associatedwith the disk in some of the galaxies.distribution of stars within the virial radius (black). Blue and red lines shows the distribution of the disk andspheroid components respectively. Note the existence of a third intermediate component included in the distribution that is associatedwith the disk in some of the galaxies.