Formation of In Situ Stellar Haloes in Milky Way-Mass Galaxies

16.6 MB·English

by  Andrew P. Cooper

Mon.Not.R.Astron.Soc.000,1–17(2013) Printed6October2015 (MNLATEXstylefilev2.2)
Formation of In Situ Stellar Haloes in Milky Way-Mass
Galaxies
Andrew P. Cooper1(cid:63), Owen H. Parry2, Ben Lowing1, Shaun Cole1 and Carlos Frenk1
5 1Institute for Computational Cosmology, Department of Physics, University of Durham, South Road, Durham, DH1 3LE, UK
1 2Department of Astronomy, University of Maryland, College Park, MD 20742, USA
0
2

t Accepted2015September03.Received2015August11;inoriginalform2015January21
c
O

4 ABSTRACT
We study the formation of stellar haloes in three Milky Way-mass galaxies using

] cosmological smoothed particle hydrodynamics simulations, focusing on the subset
A
of halo stars that form in situ, as opposed to those accreted from satellites. In situ
G stars in our simulations dominate the stellar halo out to 20 kpc and account for 30-40
. per cent of its total mass. We separate in situ halo stars into three straightforward,
h
physically distinct categories according to their origin: stars scattered from the disc
p
of the main galaxy (‘heated disc’), stars formed from gas smoothly accreted on to
-
o the halo (‘smooth’ gas) and stars formed in streams of gas stripped from infalling
r satellites (‘stripped’ gas). We find that most belong to the stripped gas category.
t
s Those originating in smooth gas outside the disc tend to form at the same time and
a placeasthestripped-gaspopulation,suggestingthattheirformationisassociatedwith
[
the same gas-rich accretion events. The scattered disc star contribution is negligible
2 overall but significant in the Solar neighbourhood, where (cid:38) 90 per cent of stars on
v eccentric orbits once belonged to the disc. However, the distinction between halo and
0 thickdiscinthisregionishighlyambiguous.Thechemicalandkinematicpropertiesof
3 thedifferentcomponentsareverysimilaratthepresentday,buttheglobalproperties
6 of the in situ halo differ substantially between the three galaxies in our study. In our
4
simulations, the hierarchical buildup of structure is the driving force behind not only
0
the accreted stellar halo, but also those halo stars formed in situ.
.
1
0 Key words: methods: numerical – galaxies:formation – galaxies: haloes– galaxies:
5 structure
1
:
v
i
X
1 INTRODUCTION adistinct‘insitu’halocomponent,defined(loosely)ashav-
r ing formed bound to the Milky Way itself rather than to
a FollowingSearle&Zinn(1978),muchobservationalandthe-
anyofitshierarchicalprogenitors(Abadietal.2003;Brook
oreticalworkontheMilkyWay’sstellarhalohasfocusedon
et al. 2004; Zolotov et al. 2009; Font et al. 2011; Tissera
the tidal stripping and disruption of satellite galaxies. The
et al. 2013; Pillepich et al. 2015). Such haloes are a natu-
idea that galactic stellar haloes are built mainly by accre-
ral outcome of the ΛCDM model, which predicts that the
tioniswellsupportedbytheoreticalpredictionsofthestan-
vast majority of stars in a galaxy like the Milky Way form
dard dark energy/cold DM (ΛCDM) cosmogony (White &
from the cooling of gas trapped by the galaxy’s own DM
Frenk 1991; Bullock & Johnston 2005; Cooper et al. 2010)
(DM)potential(White&Rees1978;White&Frenk1991).
anddirectevidenceoftidalstreamsaroundnearbygalaxies
The bulk of these in situ stars can be identified with the
(Belokurov et al. 2006; McConnachie et al. 2009; Mart´ınez-
kinematically cold, rapidly rotating Galactic disc, but the
Delgado et al. 2010). However, recent work has shown that
proto-Milky Way may also have suffered strong perturba-
someaspectsoftheMilkyWay’sstellarhalomaybedifficult
tions from satellites and quasi-secular rearrangement (e.g.
toexplainbyaccretionalone,notablyitscentralconcentra-
‘disc flips’; Bett & Frenk 2012), or even wholesale destruc-
tionanduniformityacrossthesky(Carolloetal.2007;Bell
tion and regrowth before the majority of present-day disc
etal.2008;Cooperetal.2011;?;Deasonetal.2011;Helmi
stars were formed (e.g. Sales et al. 2012; Aumer & White
et al. 2011; Xue et al. 2011).
2013;Aumeretal.2013).Ifrealgalaxiespassthroughsuch
Meanwhile,hydrodynamicalsimulationshavepredicted
messy stages of formation, it seems likely that a significant
fractionofstarsformedintheearlyGalaxywouldnowhave
highly eccentric orbits.
(cid:63) E-mail:[email protected]
c 2013RAS
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2 Cooper et al.
Recentsimulationsfindthattheseinsituprocessescre-
Table 1. Numerical parameters adopted for the three simula-
atehaloesthataremoreconcentrated,metal-richandoblate tions: DM and gas particle masses and the maximum gravita-
thanthoseformedbyaccretedstars(McCarthyetal.2012). tionalsofteninglengthinphysicalunits(definedasthescaleofa
This supports the hypothesis of a transition between an in Plummerkernelequivalenttotheactualsplinekernelusedinthe
situ and an accreted halo as an explanation for the appar- simulation).
ently‘bimodal’propertiesofhalostarsobservedintheMilky
MDM(M ) Mgas(M ) (cid:15)phys[pc]
Way (Carollo et al. 2010; Beers et al. 2012; Tissera et al. (cid:12) (cid:12)
2014). Aq-C 2.6 105 5.8 104 257
× ×
Aq-D 2.2 105 4.8 104 257
× ×
Aq-E 2.1 105 4.7 104 257
However, quantitative results concerning the origin of × ×
in situ halo stars and their importance relative to accreted
stars are still very uncertain. Where they rely on simula- 2 SIMULATIONS
tions, such conclusions can be particularly sensitive to the
numericalmethodsused.Startingfromidenticalinitialcon- We examine the stellar haloes that form in three smoothed
ditions,currentstate-of-the-artsimulationspredictsubstan- particle hydrodynamics (SPH) simulations of Milky Way-
tially different properties for the bulk of the in situ stellar mass galaxies. Dark-matter-only versions of these simula-
mass in Milky Way-like DM haloes (e.g. Scannapieco et al. tions formed part of the Aquarius project (Springel et al.
2012; Aumer et al. 2013), not just the few per cent that 2008)andweretaintheAquariusnomenclatureforourthree
mightbeidentifiedwithaninsituhalo.Moreover,theprop- sets of initial conditions, labelling them Aq-C, Aq-D and
ertiesofinsituhaloesmaybemuchmoresensitivetocertain Aq-E. The DM resolution (particle mass) in our SPH sim-
modellingchoicesthanthoseofmassivestellardiscs,includ- ulations is similar to that of the ‘level 4’ simulation set in
ingprescriptionsforstarformationandthetreatmentofthe Aquarius.
multi-phaseinterstellarmedium(ISM;forexample,themix- The Aquarius DM haloes were themselves extracted
ingofhotandcoldingalacticwinds,tidalstreamsandcold from a cosmological simulation in a cube of comoving vol-
clumps of free-falling gas). ume 1003Mpc3. They were chosen to have masses close to
that of the Milky Way (∼1012M(cid:12)) and to avoid dense en-
vironments (no neighbour exceeding half the mass of the
Here we analyse the origin of in situ halo stars using
target halo within 1h 1Mpc; Navarro et al. 2010). Ini-
−
three Milky Way-scale simulations run with the code de-
tial conditions for a resimulation of each halo were cre-
scribedinParryetal.(2012),oneoftheparticipantsinthe
ated with a ‘zoom’ technique, with higher mass bound-
Aquila comparison project (Scannapieco et al. 2012). Two
ary particles used to model the large scale potential and
of the three DM haloes we simulate have also been simu-
lower mass particles in an ∼ 5h 1Mpc region surround-
−
lated by Tissera et al. (2012, hearafter T12) and Tissera
ing the target halo. Extra power was added to the initial
et al. (2013, 2014, hearafter T13, T14) using different ‘sub-
particle distribution on small scales in the high resolution
grid’ recipes for star formation and feedback but an other-
region, as described by Frenk et al. (1996). The numeri-
wise similar hydrodynamic solver and identical initial con-
cal parameters for each simulation, including the particle
ditions. We define what we mean by in situ halo stars in
massesandgravitationalsofteninglengths,arelistedinTa-
a straightforward and easily reproducible way. Careful defi-
ble 1. We assume a ΛCDM cosmology, with parameters
nitions are particularly important for this problem because
Ω = 0.25, Ω = 0.75, Ω = 0.045, σ = 0.9, n = 1
the concept of an in situ halo straddles an extremely fuzzy m Λ b 8 s
and H =100hkms 1Mpc 1 =73kms 1Mpc 1.
boundarybetweenalltheconventionalGalacticcomponents 0 − − − −
Oursimulationcodeisbasedonanearlyversionofthe
–disc,thickdisc,bulgeandhalo.Basedonthesedefinitions, PM-Tree-SPH code gadget-3. Baryon processes are mod-
we discuss physical mechanisms by which in situ haloes are
elledasdescribedinOkamotoetal.(2010)andParryetal.
generatedinoursimulations,motivatedbythefactthatthe
(2012). Briefly, each gas particle represents an ISM with
mechanisms we identify are somewhat different from those
separate ‘hot’ and ‘cold’ (star-forming) phases. Gas parti-
previously discussed in the literature. In particular, we find
cles above a critical density (n >0.1cm 3) are assigned a
thatthegrowthofthein situhaloisverycloselyrelatedto H −
coldphasemassaccordingtotheirthermalenergyandalo-
the accretion of satellites responsible for the growth of the
calpressureaccordingtoapolytropicequationofstate.Gas
canonical ‘ex situ’ halo.
in the cold phase is converted to stars at a rate inversely
proportional to a local dynamical time, which in turn de-
We proceed as follows. We describe our simulations in pends on analytic approximations for the effective pressure
Section 2. In Section 3 we explain how we identify in situ anddistributionofcoldcloudsizes.Ourcodefollowsthenu-
halo stars and in Section 4 we examine their origins. Sec- cleosynthetic production of individual elements separately,
tion 5 describes the present-day properties of our in situ in particular the iron yields of Types II and I SNe. Mass,
halo.Section6investigatesthesatelliteprogenitorofinsitu metals and energy returned by evolved stars and their SNe
starsformedfromstrippedgas.InSection7weinterpretour are smoothly distributed over 40 near neighbour gas parti-
results, discuss the limitations of in situ halo models based cles.Theeffectivemetallicityusedtocalculatetheradiative
on hydrodynamical simulations and compare with similar cooling rate of a given particle is also a smoothed average.
studies.AsummaryofourconclusionsisgiveninSection8. Kinetic energy is imparted directly to particles subject to
AdetailedcomparisonwiththeresultsofT12andT13isin- SNe feedback, in proportion to the local velocity dispersion
cludedinAppendicesAandB,alongwithashortdiscussion ofDM.ParticlesareentrainedinSNwindsonaprobabilis-
of numerical convergence. tic basis and launched perpendicular to the plane of the
c 2013RAS,MNRAS000,1–17
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In Situ Stellar Haloes 3
galactic disc. Wind particles are decoupled from the hydro-
Table 2.Totalmassinthe(outer)disc,‘bulge’andstellarhalo
dynamical calculation until they reach an ambient density
nH < 0.01cm−3 or the time they have been decoupled ex- rgeivgeiosntshoefftrhacet(iro,nEoEf)mplaasnseinactchoerdstinelglatrohoaulrocrreigteiorina.thTahteifisnfoarlmroewd
ceedsalimitingtime.Parryetal.(2012)improvethetreat- insitu.OurgalaxiesareroughlyhalfthemassoftheMilkyWay;
ment of fluid instabilities in the hydrodynamic scheme of note that the disc mass quoted is only for stars with r >5 kpc.
Okamotoetal.(2010)byincorporatingartificialconductiv- Our‘bulge’definitionincludesallstarswithr<5kpc,regardless
ity (Price 2008) and a time-step limiter (Saitoh & Makino oftheirkinematics(itdoesnotcorrespondtoaspecifickinematic
2009); they also adjust the treatment of SN winds to re- orphotometriccomponentinoursimulationsorinrealgalaxies).
ducetheresolutiondependenceofmassloadinganddeposit
thermal rather than kinetic energy from Type Ia SNe. The
Aq-C Aq-D Aq-E
most relevant effect of these improvements is to suppress
the formation of stars in cooling instabilities in diffuse cir- Mass Disc(r>5kpc,EE>0.8) 3.0 4.3 4.3
cumgalactic gas (e.g. Kaufmann et al. 2006; Kereˇs et al. Bulge(r<5kpc) 34.5 21.9 25.2
(109M )
2012; Hobbs et al. 2013). In the results we present below, (cid:12) Halo(r>5kpc,EE<0.8) 4.6 8.4 6.8
weexplicitlyidentifystarsformedthroughsuchinstabilities
In situ halofraction 37% 33% 41%
and find that they contribute (cid:46) 20 per cent of the mass
of the in situ stellar halo in our simulations. This fraction
depends somewhat on resolution (becoming larger at lower
ofastarwiththesamebindingenergyonacircularorbit.All
resolution) as we discuss in Appendix B. Other modelling
stars with E > 0.8 are identified with the central galactic
uncertainties are also discussed in Section 7 and Appendix E
disc and excluded from our halo star sample.
B.
Fig. 1 shows the distribution of stellar circularity as a
Detailsoftwoofourthreehydrodynamicalsimulations
function of radius in our three simulations. A concentra-
(Aq-CandAq-D)havebeenpresentedpreviouslyinstudies
tion of corotating stars on near-circular orbits extending to
that focused on satellite galaxies (Parry et al. 2012) and
∼30 kpc is obvious in all cases, which we identify with the
pseudo-bulge formation (Okamoto 2013). The luminosity
thindisc.Anumberofstreamsonpro-andretrogradeorbits
functionandluminosity–metallicityrelationofthesimulated
are also visible at large radii.
satellites are comparable to those of dwarf galaxies in the Atr(cid:46)5kpcthedensityofstarsonnon-circularorbits
Local Group. All three simulations result in galaxies with
is comparable to the density of stars in the disc. We iden-
massive centrifugally supported discs as well as dispersion
tify this complex region with a galactic ‘bulge’ (using the
supported spheroids.
termloosely,sincethisregionissubstantiallymoreextended
than the bulge of the Milky Way). To simplify our defini-
tionofthestellarhalo,weexcludeall starswithr<5kpc,
3 SAMPLE DEFINITION
regardless of circularity. This cut is easy to apply to both
The first step in defining our stellar halo sample is to iden- modelsanddata.Italsofollowsthelooseconventionofmost
tifyallstarsbelongingtothecentral(MilkyWay-analogue) MilkyWaystellarhalowork,inwhichstarsmorethanafew
galaxy at the present day (redshift z = 0). We choose kiloparsecsinteriortothesolarneighbourhoodareexcluded
stars that lie within a radius r which encloses a sphere (the exception being those high above the disc plane) even
200
of mean density 200 times the critical value for closure though the inward extrapolation of a canonical r−3 density
(r = 227 kpc for Aq-C and Aq-D, 202 kpc for Aq-E). profile would predict a substantial mass of halo stars in the
200
From this sample, we isolate the halo by excluding stars centreoftheGalaxy(seealsothediscussioninCooperetal.
that belong to satellite galaxies within r and stars that 2010).
200
belongtothemaingalaxydiscoraninnerspheroid(‘bulge’), Fig. 1 further separates star particles into accreted
as follows. (middlerow)andinsitu(bottomrow)accordingtowhether
Satellite DM haloes and their galaxies are isolated us- ornottheyareboundtothemainbranchprogenitorofeach
ingaversionofthesubfindalgorithm(Springeletal.2001) DMhaloatthefirstsnapshotaftertheirformation.Starpar-
adapted by Dolag et al. (2009) to identify self-bound sub- ticlesthatarefirstboundtoaDMhalootherthanthemain
structures,takingintoaccounttheinternalenergyofthegas progenitor are considered as accreted, even if they form in
whencomputingparticlebindingenergies.Allstarparticles asubhaloofthemainbranch(i.e.iftheyforminasatellite
boundtoDMsubhaloesatz=0areexcludedfromourhalo galaxy of the Milky Way analogue) and are subsequently
star sample. stripped1. Table3summarizesthetotalmassofthestellar
Thecentralgalacticdiscisidentifiedbyfindingstarson halo and the relative proportion of in situ stars.
orbits that are approximately circular and that lie close to Fig. 2 shows the mean density of accreted and in situ
a plane normal to the net angular momentum vector of the halostarsinsphericalshellscentredonthegalaxy.Thepro-
wholestellarcomponent.Acoordinatesystemischosensuch file of the in situ halo has a similar shape and amplitude
that the net angular momentum vector of all stars within in all three simulations, with a slight steepening evident in
0.2r points in the positive z-direction. The circularity of the ‘bulge’ region of Aq-C. In both Aq-C and Aq-D, the
200
each star’s orbit is then defined as accreted halo stars are less centrally concentrated than the
J
E = z , (1)
E J (E)
circ 1 ThisisanimportantdifferencewiththeworkofT13,whoin-
where Jz is the z component of the star’s specific angular cludedstarsformedinboundsatelliteswithinr200 inthein situ
momentum and Jcirc(E) is the specific angular momentum haloaspartoftheir‘endodebris’category.
c 2013RAS,MNRAS000,1–17
(cid:13)
4 Cooper et al.
Aq-C Aq-D Aq-E
1.0
0.5
)
E 0.0
( All
(cid:15)
0.5
−
4.0
1.0
− 3.5
0.5 3.0
) 2.5
E 0.0 Accreted N
(
(cid:15) 10
2.0 g
o
0.5 l
−
1.5
1.0
− 1.0
0.5 0.5
E) 0.0 InSitu 0.0
(
(cid:15)
0.5
−
1.0
− 0 20 40 60 80 0 20 40 60 80 0 20 40 60 80 100
r(kpc) r(kpc) r(kpc)
Figure 1.Thedistributionofstarsinradius-circularityspaceforAq-C(leftcolumn),Aq-D(centrecolumn)andAq-E(rightcolumn).
PanelsinthetoprowincludeallstarsboundtothemainDMhalo(r<90kpc),whilethemiddleandbottomrowsincludeonlyaccreted
andinsitustarsrespectively.Dashedhorizontallinesindicatethecircularitycutusedtodefinediscstars.Dashedverticallinesmarkthe
5kpccutinradiususedtodefine‘bulge’stars.Allstarsoutsidetheseregionsareclassifiedashalostars.Thecolourscalecorresponds
tothelogarithmofthenumberofstarparticles.
in situ component, with a mild break due to accreted stars respect,inlinewithearlierstudiesoftheoriginandstructure
aloneat70<r<90kpc,whileinAq-Ethetwocomponents of thick discs in simulations (e.g. Sales et al. 2009). Fig. 1
arealmostindistinguishable.Theaccreted–insitutransition showsthataccretedstarscanmakeasignificantcontribution
in these profiles at ∼ 20 kpc is consistent with the average to the ‘disc’. In Aq-D, they contribute mainly to the ‘thin’
for Milky Way analogues in the GIMIC simulation (Font disc–thethickdiscisformedinsitu.InAq-E,accretedand
et al. 2011). in situ ‘disc’ stars contribute at a similar ratio over a wide
Aq-DandAq-Ehave‘thick’discswithahighdegreeof range of circularity and radius.
non-circular motion, apparent in the top row of Fig. 1 as a In the context of observations of the Milky Way, a ge-
high density of stars at 0.5<E <0.8 and 5<r<20 kpc. ometrically oblate stellar component, intermediate between
E
According to the aformentioned cuts on circularity and ra- discandhalo,wasidentifiedbyYoshii(1982)andGilmore&
dius,weclassifytheseashalostars.However,examiningthe Reid(1983),butoptimalandobjectivewaystoclassifythis
variationofthecircularitydistributionwithheightabovethe component are still under debate (see, for example, recent
disc plane reveals that these stars simply make up the low- reviews by Ivezi´c et al. 2012; Rix & Bovy 2013). Classifi-
circularity tail of a continuous distribution. The fraction of cations have been suggested based on metallicity and kine-
stars on circular orbits is highest close to the plane. matics that imply different distinctions between thick disc
Themostimportantquestionfromthepointofviewof and halo stars (Ivezi´c et al. 2008; Bovy et al. 2012; Rix &
this paper is not the origin of thick disc stars, but whether Bovy 2013; Schlesinger et al. 2014; Ruchti et al. 2015). The
or not they can, or should, be distinguished as a separate chemodynamicaldistributionfunctionsofourthreegalaxies
galactic component. Our simulations differ greatly in this are different from one another, and almost certainly differ-
c 2013RAS,MNRAS000,1–17
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In Situ Stellar Haloes 5
10 Table3.Breakdownofallinsituhalostarsintothreesubtypes,
accordingtotheirformationmechanism.
Aq-C
8
Aq-C Aq-D Aq-E
3
−
c Heateddisc 2.8% 26.0% 31.0%
p
k 6 Strippedgas 59.8% 56.7% 56.9%
(cid:12)
M Smoothlyaccretedgas 37.3% 17.3% 12.1%
/
ρ 4
0 Disc
1 bekeptinmindwhencomparingourresultstoobservations
g Allhalo
o of the Milky Way.
l 2
Insituhalo
Accretedhalo
100
4 THE ORIGIN OF IN SITU STARS
Aq-D
Inthissectionwelookinmoredepthattheoriginofthein
8
3 situcomponentofthestellarhalo.Thedensityofthiscom-
−
c ponentexceedsthatofaccretedhalostarsintheinner∼20
p
k 6 kpcofourgalaxies.Itmaythusbeveryimportantforspec-
(cid:12)
troscopic observations of halo stars in the solar neighbour-
M
/ hoodandinsurveysofmain-sequenceturnoffstarswithina
ρ 4 few kiloparsecs of the Milky Way disc plane.
0
1 In order to trace how in situ stars formed in our simu-
g
o lations, we separate them into three disjoint subcategories:
l 2
(i) ‘heateddisc’stars,whichmetthethindisccircularity
criterion when they were formed, but are not in the disc at
100
z=0;
Aq-E (ii) stars formed from ‘stripped gas’, brought into the
8 main DM halo bound to a subhalo and subsequently
3
− stripped by tidal forces or ram pressure;
c
p (iii) stars from ‘smoothly accreted gas’, which enters the
k 6
(cid:12) main DM halo through direct (smooth) accretion.
M
/ Categories(ii)and(iii)areeasilydistinguishedbytrac-
ρ 4 ingtheDMhalomembershiphistoryoftheparentgaspar-
0
g1 ticle for each star particle. The gas from which heated disc
o
l 2 stars form must originally have either been stripped from
a subhalo or smoothly accreted, so these stars could also
be classified into the second or third categories. However,
0 in this case it is the fact that they formed in the thin disc
0.0 0.5 1.0 1.5 2.0
and were scattered out of it, rather than how their parent
log10r/kpc gasparticlearrivedinthedisc,thatweconsidertobemost
important.
The fraction of in situ halo stars in each category is
Figure 2. Spherically averaged stellar density profiles for Aq-
shown in Table 3. It is clear that there is a large variation
C(top),Aq-D(centre)andAq-E(bottom).Thereddashedand
between the three simulations, although the in situ stars
greendot–dashedlinescorrespondtotheaccretedandinsituhalo
componentsrespectively.Thesolidblacklineisthesumofthese forming from gas stripped from satellites dominate in all
andcanbecomparedtomeasurementsfortheMilkyWay(black cases. In the next section we discuss each category in more
star; Fuchs & Jahreiß 1998; Gould et al. 1998). The blue dotted detail and compare their properties.
linecorrespondstodiscstars,selectedbytheirorbitalcircularity.
Theminimumextentoftheradialaxisissetbythegravitational
softeninglengthforstarparticles.Agreydashedverticallineat 4.1 Heated disc stars
5kpcmarksthe‘bulge’regionthatweexcludefromouranalysis
ofthestellarhalo. Thecentralgalaxiesinourthreesimulationsundergoseveral
episodesofdiscdestructionandregrowthatz>3.Overthe
redshift range 3 > z > 2, a stable disc is established. This
entfromtheMilkyWaydistributionfunctiononwhichthese disc continues to grow until z = 0, although its angular
observationaldefinitionsarebased.Therefore,wedonotbe- momentumaxismayprecess.Ourheateddisccategoryonly
lievethatadditionalcutstoseparateathickdisccomponent includes stars that once belonged to this stable disc. Stars
from the thin disc and halo (for example, using a threshold onhighlycircularorbitsmaybescatteredtomoreeccentric
metallicity,alimitingrotationvelocityorverticalextent)are orbitsbysecularevolutionandsatelliteimpacts(e.g.Purcell
helpfulfortheinterpretationofoursimulations.Thisshould et al. 2010). We refer to this loosely as ‘heating’, in the
c 2013RAS,MNRAS000,1–17
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6 Cooper et al.
Table 4. Properties of the present-day thin stellar discs in our
tlehfrteetosimriguhlattigoinvse,fdoerfimnaetdiobnyrceirdcsuhliaftr,itymEaEss>fr0a.c8t.ioCnoliunmpnlascferoamt Aq-C
0.8
formation redshift, and redshift at which half the z =0 mass is
inplace.
r]
/y 0.6
zform fform z1/2 M(cid:12)
[
Aq-C 2.54 12% 0.92 R 0.4
Aq-D 2.32 8% 0.83 F
S
Aq-E 2.20 16% 0.76 Heateddisc
0.2 Strippedgas
Smoothlyaccretedgas
senseofanincreaseinnon-circularmotion.Theseperturbed
0.0
disc stars are likely to have a clear kinematic and chemical
relationship to those in the present-day thin disc. Aq-D
0.8
Weidentifyallstarparticlesinthez=0disc,asdefined
in Section 3, that exist in a given earlier snapshot and use r]
these to define Jz (assuming that the number of star parti- /y 0.6
clesscatteredinto thediscisnegligible).Wethenapplythe (cid:12)
M
circularity threshold EE > 0.8 to identify all newly formed [
starparticlesinthediscatthatsnapshot.Anyofthesethat R 0.4
F
have E < 0.8 at z = 0 are assigned to our heated disc S
E
category. 0.2
Beyond a certain redshift, z , we can no longer reli-
form
ablyidentifyastableprogenitorofthez=0disc,andhence
we cannot define J . This limit is due to the small number 0.0
z
(<100)ofancientdiscstarsandincreasingfrequencyoffluc-
Aq-E
tuationsinthecentralpotentialthatdestabilizeprotodiscs. 0.8
Table 4 gives z for each of our simulations, along with
form
z ,theredshiftbywhichthez=0dischasassembledhalf r]
it1s/2finalmass. Table4alsogivesf ,themassfractionof /y 0.6
form (cid:12)
z=0discstarsthatformearlierthanz .Thisfractionis M
form
[
no more than 16 per cent (Aq-E). Stars scattered from this R 0.4
unidentifiedprotodisc(andanyothersdiscsthatwerecom- F
S
pletelydestroyedbeforez )areconsideredtofallintoone
form
0.2
of the other two in situ categories, according to the origin
of their parent gas particle.
0.0
0 2 4 6 8 10 12
4.2 Stars from stripped gas and smoothly Time[Gyr]
accreted gas
Halo stars can form directly in the circumgalactic medium, Figure 3. Formation history for in situ halo stars assigned to
either in quasi-free-falling cold gas clouds (not associated eachofourthreeinsituformationmechanisms.Timeismeasured
with DM clumps) or the gaseous tidal or ram pressure fromtheoriginoftheuniverse.Peaksintheformationofstarsin
smoothlyaccretedgasareclearlycorrelatedwiththoseinstripped
stripped streams of satellite galaxies. We distinguish be-
tween these two possibilities based on whether or not the gas at t < 4 Gyr. Vertical dotted lines mark zform and z1/2 as
givenin Table4.
parentgasparticleofagivenstarparticlewasboundtoan-
other DM halo before being bound to the main halo. Stars
forming from stripped satellite gas particles may be chemi- stars.InAq-DandAq-E,therearealso∼2Gyr-longbursts
callyandkinematicallysimilartostarsintheaccretedstellar ofin situstarformationstartingatt≈4and6Gyrrespec-
halo.Incontrast,starsformingingascondensingoutofthe tively.Interestingly,thesealsocorrespondtoepisodesoffor-
hot hydrostatic gas halo, or other ‘smoothly’ accreted cold mationforscattereddiscstars(blue)andthindiscstars(not
clumps,mayhavepropertiesmoresimilartothoseexpected shown).Theseepisodescorrespondtotherapidinfallofcold
of an in situ halo formed by monolithic collapse. gasontothediscduringperiodsinwhichseveralrelatively
Fig. 3 shows the absolute star formation rate of each massive satellites are being disrupted simultaneously.
in situ category as a function of time elapsed since the big AnothernotablefeatureofFig.3isthatthestarforma-
bang.Thesestarformationratesarelowcomparedtothose tionrateinsmoothlyaccretedgas(red)isclearlycorrelated
typical of the stable disc and the progenitors of accreted with that in stripped gas (green), especially in the domi-
stars (∼ 1M(cid:12)yr−1). The majority of halo stars that form nant early epoch of in situ halo formation (ages > 9 Gyr).
in stripped or smoothly accreted gas are more than 9 Gyr Thiscorrelationpersistsevenifweselectonlystarsforming
old,onlymarginallyyoungerthanthetypicalageofaccreted at r > 30 kpc, far away from the disc, suggesting that the
c 2013RAS,MNRAS000,1–17
(cid:13)
In Situ Stellar Haloes 7
conditions under which most in situ halo stars form are in
fact related to the accretion and stripping of gas-rich satel-
lites.Itappearsthatstarformationmaybetriggeredbythe 5 Aq-C
mixing of free-floating gas from the hydrostatic halo with
3
star-forming stripped gas. We also see corresponding peaks −
c 4
intheaccretedhalostarformationrate,suggestingthatstar p
k
formation is triggered in the infalling satellites as well. (cid:12)
M 3
Theseeffectsmustarisefromthesubgridmodelofstar
/
formation. They may therefore occur, to a greater or lesser ρ
extent, with other similar star formation prescriptions used 10 2
g
in the literature. Since there are no unambiguous observa- lo
tional tests of the predictions of models for star formation 1
inthediffusecircumgalacticgas,itisverydifficulttojudge
whether or not the behaviour of a particular simulation is
physicallyplausible(seealsothediscussioninAppendixB).
Isolating dependencies on modelling uncertainties such as 5 Aq-D
theseisoneofourmotivationsforseparatingsimulatedhalo
3
stars into categories based on their physical origin. c− 4
Regardlessofhowtheyactuallyform,theclassification p
k
of gas particles as ‘smoothly’ accreted is resolution depen- (cid:12)
M 3
dent: gas bound to a low-mass infalling DM halo, and so
/
classifiedas‘stripped’athighresolution,wouldbeclassified ρ
as ‘smoothly accreted’ in a lower resolution simulation that g10 2
o
does not resolve the parent halo. In Appendix B we con- l
clude that, in our simulations, the uncertainty in the total 1
massofthesmoothlyaccretedhalocomponentisdominated
bythisclassificationuncertainty,ratherthantheresolution
dependence of star formation efficiency.
5 Aq-E
3
−
5 IN SITU HALOES AT z=0 c 4
p
k
Inthissection,weexaminetheobservablecharacteristicsof (cid:12)
M 3
insituhalostarsatthepresentday,startingwithasummary
/
ofhalopropertiesandthenlookinginmoredetailatregions ρ
analogous to the solar neighbourhood. og10 2 AHcecarteetdedDisc
l
Strippedgas
1
5.1 Whole halo Smoothlyaccretedgas
Fig. 4 compares the spherically averaged density profiles of
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
our three in situ halo categories and accreted halo stars.
log r/kpc
In the r <20 kpc region where in situ halo stars dominate 10
overaccretedstars,theycontributeroughlyequalmassfrac-
tions;theexactproportionsvaryfromhalotohalo.Weseea
Figure 4. Spherically averaged density profiles of halo stars in
strong correspondence between stars formed from stripped theaccretedandthreein situcomponentsforAq-C(top),Aq-D
andsmoothlyaccretedgasatallradii,which,incombination (centre)andAq-E(bottom).
withFig.3,suggeststhattheyformwithasimilardistribu-
tion in both space and time. As expected, heated disc stars
haveasteeperprofile,withmostconcentratedatr<20kpc. dynamics of the two components. In the Toomre diagram
Fig.5showsToomrediagrams(Sandage&Fouts1987) they resemble the classical Milky Way halo, with zero net
that compare the amplitude of circular and radial motion rotation and high radial velocity dispersion. Accreted halo
for different components. A galactocentric UVW velocity stars show a similar distribution overall, but with notable
frame(e.g.Binney&Merrifield1998,p.627)isdefinedwith overdensitiesduetoindividualstreams,someofwhichhave
respect to the thin disc in each simulation. a net retrograde motion.
Of the three simulations, the stellar halo in Aq-C has The heated disc stars in Aq-D and Aq-E have similar
kinematic properties most similar to those measured for kinematics to those in Aq-C, but the stripped/smooth in
the Milky Way. The peak rotational velocity of the disc situ haloes have a greater net rotation. In Aq-E, all three
is ∼ 220kms 1. The heated disc stars (blue) rotate in components once again resemble one another, although the
−
the same sense as those on circular orbits, with a lag of stripped- and smooth-gas halo stars have a greater velocity
∼40–180kms 1.Starsformedfromstrippedandsmoothly dispersion.Anunderlyingstripped/smoothinsituhalomay
−
accreted gas are kinematically indistinguishable from each still be present, but the bulk of in situ halo stars are more
other,onceagainpointingtoaclosecorrelationbetweenthe similar kinematically to the Milky Way thick disc. The be-
c 2013RAS,MNRAS000,1–17
(cid:13)
8 Cooper et al.
Aq-C). Both in situ and accreted halo stars are systemati-
400
cally more metal poor than heated disc stars.
350 Aq-C TheMDFofinsituhalostarsformedfromstrippedgas
1]− 300 idsiavnersyysstimemilaatrictaolltyhahtigohfearcbcyrenteodmsaotreelltihteanst0a.r1s,dwexit.hTahimseis-
s
m
k 250 tobeexpected,asthedensecoldgasstrippedfromsatellites
2[ willhavebeenenrichedbythesamestellarpopulationsthat
1/) 200 makeuptheaccretedhalo.Moreover,verysimilardistribu-
2
W tions will also result if prolonged star formation occurs in
150
+ satellitegalaxieswhiletheirgasisbeingstripped.Theover-
2U 100 all in situ MDF is close to that of the stripped-gas stars,
( since they dominate the in situ mass budget.
50
Looking in detail, the degree of similarity between the
0 MDFsofthevariouscomponentsvariesineachofourthree
simulations. This may depend on the extent to which the
350 Aq-D satellitegalaxiescontributingthebulkofstripped-gasstars
1]− 300 are the same as those that contribute the majority of ac-
s creted stars. Since gas can be more easily expelled from
m
k 250 shallower potentials, the most massive and metal-rich ac-
[
2 creted progenitor galaxies are likely to retain the most gas
1/ 200
) when they enter the main DM halo. Stars stripped from
2
W 150 these galaxies are expected to dominate the accreted halo,
+ particularlynearthecentre.Weinvestigatetherelativecon-
2U 100 tributionsofstar-formingstrippedgasanddirectlyaccreted
(
stars from different progenitors in Section 6 below.
50
Of the different in situ components, it is the stars that
0 formedfromsmoothlyaccretedgasthathavethelowestme-
dian metallicity and the broadest dispersion. This is con-
350 Aq-E
sistent with the expectation that the gas surrounding each
1]− 300 galaxywillbeamixofitsownmetal-richejectaandalarge
ms quantity of ‘pristine’, or only marginally enriched, gas from
k 250 directcosmologicalinfall(Crainetal.2010).Inoursimula-
[
1/2 200 tions,theMDFistheonlycleardistinctionbetween‘smooth
2) gas’ stars and ‘stripped gas’ halo stars.
W
150
+
2U 100 5.2 The Solar Neighbourhood
(
50 Asaroughanalogueofthesolarneighbourhoodregionmost
relevant to current observations, we examine the average
0
300 200 100 0 100 200 300 400 propertiesofhalostarsinatorusofcross-sectionaldiameter
− − − V [kms−1] 4 kpc and galactocentric radius r = 8 kpc in the plane of
the thin disc.
Table5summarizesthefractionofstarsineachcompo-
Figure 5. Toomre diagrams of the whole stellar halo. For
nent.Foramoredirectcomparisontotherealdata,wehave
stripped-gas,smooth-gasandheateddiscin situhalostars(red,
greenanddarkbluerespectively),contoursmarktheregionsen- grouped heated disc stars and stars that meet our thin disc
closing10,30,50,70and90percentofthestellarmass.Forthe circularitycutintoasingledisccomponent,becausethetyp-
accretedhalo(cyan)only10,50and90percentlevelsareshown. icallyhighcircularvelocitiesofheateddiscstarswouldmost
The dashed vertical line marks the rotation velocity of the disc likely result in them being classified as ‘thick disc’ rather
at8kpc. than halo stars in observations. Approximately 10 per cent
ofthestellarmassthenremainsinacomponentresembling
the‘classic’halo,ofwhichaccretedstarscontributebetween
haviourofaccretedstarsonceagainresemblesthatofthein 34 and 67 per cent.
situ component, even to the extent that they have a strong Toomre diagrams in this region are almost identical to
prograde rotation in Aq-E. Accreted halo components with thoseinFig.5.Thebiggestdifferencesincomparisontothe
prograderotationwerenotedbyAbadietal.(2003)andalso overall halo are found in the solar neighbourhood MDFs,
found in Milky Way-like systems in the GIMIC simulations which are shown in Fig. 7. Stars formed from smoothly ac-
(Font et al. 2011; McCarthy et al. 2012) cretedgasthatendupinthesolarneighbourhoodaremore
Finally,inFig.6,weexaminethenormalizedmetallicity metalrichonaverage,suchthattheirMDFhasaverysim-
distribution functions (MDFs) of each component of the in ilarshapeandamplitudetotheaccretedhalo.Thismaybe
situ halo. Heated disc stars have the highest median [Fe/H] becausethemetal-poorcontributionofthiscomponentseen
andnarrowestdispersion.TheirMDFresemblesthatofthe in Fig. 6 is dominated by stars forming at large radii from
thin disc, but is slightly more metal poor (by ∼ 0.5 dex in gas that has not been polluted by the galactic wind of the
c 2013RAS,MNRAS000,1–17
(cid:13)
In Situ Stellar Haloes 9
Table 5. Breakdown of all stars in the solar neighbourhood. Heated disc stars are grouped together with thin disc stars in this table.
Thetoptworowsgivefractionsoftotalstellarmass,whilethelowerthreerowsgivefractionsofstellarhalomass(secondrow)only.
Mass(108M ) Aq-C Aq-D Aq-E
(cid:12)
Discstars(thin+thick) 26.4(92.3%) 27.4(88.7%) 28.0(83.0%)
Halostars 2.21(7.7%) 3.49(11.3%) 5.72(17.0%)
Accreted 0.747(33.9%) 1.79(51.1%) 3.83(67.0%)
Strippedgas 0.837(37.9%) 1.23(35.3%) 1.53(26.7%)
Smoothlyaccretedgas 0.618(28.0%) 0.476(13.6%) 0.356(6.23%)
Aq-C Aq-C
1.0 1.0
0.8 0.8
) )
H] H]
e/ 0.6 e/ 0.6
F F
([ ([
P P
0.4 0.4
0.2 0.2
0.0 0.0
Aq-D Aq-D
1.0 1.0
0.8 0.8
) )
H] H]
e/ 0.6 e/ 0.6
F F
([ ([
P P
0.4 0.4
0.2 0.2
0.0 0.0
Disc Disc
Aq-E Aq-E
1.0 1.0
Accreted Accreted
HeatedDisc HeatedDisc
0.8 0.8
Strippedgas Strippedgas
) )
H] Smoothlyaccretedgas H] Smoothlyaccretedgas
e/ 0.6 e/ 0.6
F F
([ ([
P P
0.4 0.4
0.2 0.2
0.0 0.0
5 4 3 2 1 0 1 5 4 3 2 1 0 1
− − − − − − − − − −
[Fe/H] [Fe/H]
Figure 6. [Fe/H] distributions for the disc, accreted halo and Figure7.MDFs,asFig.6,buthereinthesolarneighbourhood.
three in situ halo components. Distributions are normalized by
thetotalmassofstarsineachcomponent.
c 2013RAS,MNRAS000,1–17
(cid:13)
10 Cooper et al.
central galaxy. Other components have the same relation-
100
ship to one another as those in Fig. 6. Hence, we find no
107 M
substantial differences between the properties of the in situ 108 MO •
halointhesolarneighbourhoodandtheinsituhalooverall. 109 MO •
10-1 1010 MO •
Thisisnotsurprisingbecausewehavealreadyseenthatthe 1011 MO •
bulk of the in situ halo is concentrated within r(cid:46)20 kpc. O •
10-2
6 SATELLITE PROGENITORS
10-3
We have shown that our simulated stellar haloes are dom-
inated by satellite accretion: the bulk of halo stars are
shtarlioppsetadrdsifroercmtlyfrforommgsaastesltlritipesp,eadndfrothmesmaatejollrititeys.oHf‘oiwnesviteur,’ uted 10-4 Aq-C
b 100
as Fig. 2 demonstrates, stars formed in situ from stripped ntri
gas have a more centrally concentrated spatial distribution o
c
at z =0 than directly accreted stars. In this section we ex- ars 10-1
amine the satellites which contribute to the halo, with the st
aimofdetermininghowtheirinfalltimes,massesandbary- s"
a
oniccontentaffectthespatialdistributionoftheinsituand g
d- 10-2
accreted components. e
p
We first ask whether the subset of satellite progenitors p
contributingthegasfromwhichaninsitustellarhaloforms stri
is the same subset contributing accreted stars. Fig. 8 com- of " 10-3
pares the mass fractions of stars formed from stripped gas on
and directly accreted stars associated with each progenitor cti
satellite. In all three simulations, satellites that contribute s fra 1100-04 Aq-D
significantlytoonecomponentalsotendtocontributesignif- s
a
M Surviving
icantly to the other. There is substantial variation in detail
Disrupted
betweenthethreehaloes,reflectingtheirdifferentaccretion
10-1
histories. A larger scatter is apparent in Aq-D, as well as a
noticeablefractionofgas-poorcontributors(lower-rightarea
of the plot) relative to Aq-C and Aq-E. A larger fraction of
10-2
thosesatellitesalsosurvivetoz=0withoutbeingdisrupted
(blue points). The smaller number of surviving satellites in
Aq-C reflects a quieter recent merger history.
10-3
InFig.9weisolatethetopthreesatelliteprogenitorsof
thestripped-gasinsitucomponentandplotthedensitypro-
files of the accreted and stripped-gas stars they contribute.
Aq-E
Aq-E stands out as having the most similar profiles for the 10-4
twocomponents,bothofwhichareslightlysteeperthanthe 10-4 10-3 10-2 10-1 100
total accreted profile. In this case, the satellites plotted ac- Mass fraction of accreted stars contributed
count for around 40 per cent of the total stripped-gas halo.
WiththepossibleexceptionofaccretedstarsinAq-C,both
accretedandstripped-gasstarsfromthetopthreesatellites Figure 8. Mass fraction of the accreted halo and stripped-gas
are distributed like the bulk of the stellar halo. halocontributedbydisrupted(red)andsurviving(blue)satellite
Fig.9suggeststhatthegreatercentralconcentrationof galaxies.Thesizesofthepointsareproportionaltothelogarithm
the stripped-gas halo profile is not simply because most of ofthesatellite’stotalmassatinfall,asshownbythelegendinthe
the progenitor gas particles originate in more massive pro- firstpanel.Thediagonaldashedlineindicatesanequalfractional
genitors, which sink more rapidly through the action of dy- contributiontotheaccretedandstripped-gascomponents.
namicalfriction.Ifthatwerethecase,wemightalsoexpect
stars accreted from the same progenitors to be more cen- gashaloisthereforeimprintedatthetimethosestarsform,
trally concentrated than the accreted halo overall. Instead, ratherthanthe time atwhich theirparentgas particles are
weseethatthedebrisprofilesofthethreemostmassivein- stripped.
dividualprogenitorsareverysimilartotheprofileoftheen-
tireaccretedhalo.Inoursimulations,atthepresentday,ac-
cretedstarsaredistributed(onaverage)overthesamerange
7 DISCUSSION
ofradiiatwhichtheywereliberatedfromtheirparentsatel-
lites. Conversely, we have confirmed that the stripped-gas Our finding of accretion-triggered star formation in
particles from which in situ halo stars form dissipate some smoothly accreted gas may be, at least in part, a conse-
of their orbital energy between the times of stripping and quence of our hydrodynamics scheme. In some hydrody-
starformation.Thepresent-daydistributionofthestripped namic models, cold clouds can condense independently of
c 2013RAS,MNRAS000,1–17
(cid:13)