The earliest stars and their relics in the Milky Way

0.49 MB·English

by  L. Gao

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed14January2010 (MNLATEXstylefilev2.2)
The earliest stars and their relics in the Milky Way
L. Gao1,2⋆, Tom Theuns2,3, C. S. Frenk2, A. Jenkins2, J. C. Helly2, J. Navarro4,
0 V. Springel5 and S. D. M. White5
1
0 1National Astronomical Observationaries, Chinese Academy of Science,Beijing, 100012, China
2 2Institute of Computational Cosmology, Department of Physics, University of Durham,

n Science Laboratories, South Road, Durham DH1 3LE
a 3 UniversiteitAntwerpen, Campus Groenenborger, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium
J 4 Department of Physics and Astronomy, Universityof Victoria, PO Box 3055 STN CSC, BC V8W 3P6, Canada
5Max-Planck Institute for Astrophysics, Karl-Schwarzschild Str. 1, D-85748, Garching, Germany
4
1

]
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14January2010
C
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h ABSTRACT
p
We have implemented a simple model to identify the likely sites of the first stars and
-
o galaxies in the high-resolution simulations of the formation of galactic dark matter
r halos of the Aquarius Project. The first star in a galaxy like the Milky Way formed
st around redshift z = 35; by z = 10, the young galaxy contained up to ∼ 3 × 104
a dark matter haloes capable of forming stars by molecular hydrogen cooling. These
[ minihaloes were strongly clustered andfeedback may have severelylimited the actual

number of Population III stars that formed. By the present day, the remnants of the
2
v first stars would be strongly concentrated to the centre of the main halo. If a second
3 generation of long-lived stars formed near the first (the first star relics), we would
9 expect to find half of them within 30h−1kpc of the galactic centre and a significant
5 fraction in satellites where they may be singled out by their anomalous metallicity
1 patterns. The first halo in which gas could cool by atomic hydrogen line radiation
9. formed at z = 25; by z = 10, the number of such ‘first galaxies’ had increased to
0 ∼ 300. Feedback might have decreased the number of first galaxies at the time they
9 undergo significant star formation, but not the number that survive to the present
0 becausenearneighboursmerge.Halfofallthe“firstgalaxies”thatformbeforez =10
: merge with the main halo before z ∼ 3 and most lose a significant fraction of their
v
mass.However,todaythereshouldstillbemorethan20remnantsorbitingwithinthe
i
X central ∼ 30h−1kpc of the Milky Way. These satellites have circular velocities of a
r few kilometers per second or more, comparable to those of known Milky Way dwarfs.
a
They are a promising hunting ground for the remnants of the earliest epoch of star
formation.
Key words: methods: N-body simulations – methods: numerical –dark matter –
galaxies: haloes – galaxies: structure, formation
1 INTRODUCTION Such stars were very massive, M ∼ 102M⊙ (Abel, Bryan
&Norman 2000; Bromm, Coppi&Larson 2002; Yoshidaet
Thefirststarsprobablyformedthroughmolecularhydrogen
al. 2007; Gao et al. 2007) and, depending on their initial
cooling of gas compressed in dark matter potential wells
mass, would have ended their short lives as supernovae or
(Couchman & Rees 1986; Tegmark et al. 1997; see Bromm
by collapsing directly into a black hole (Heger et al. 2003).
&Larson2004 forarecentreview).Thetemperatureofthe
In neithercase can theremnantsbe identified today.
gas needs to be ≥ 103K for H2 formation to be efficient;
in a ΛCDM universe dark matter haloes with deep enough
Very massive first stars (‘Population III’ or ‘Pop. III’
potential wells to heat the gas to this temperature form as
stars)emitcopiousamountsofUVphotons(Schaerer2002)
early as redshift z∼50 (Gao et al. 2004, Reed et al. 2005).
which may affect star formation in nearby haloes through
photoevaporation (Shapiro, Iliev & Raga 2004; Whalen
et al. 2008) and/or destruction of molecular hydrogen
⋆ Email:[email protected] by photons in the Lyman-Werner bands (Haiman, Rees
2 Gao et al.
& Loeb 1997). These photons could contribute to the earliest star formation? Helmi et al. (2006) argued that the
reionization of the Universe (e.g. Sokasian et al. 2004). remnants of early star formation in the Milky Way differ
Elements synthesised during stellar evolution may pollute from those in dwarf galaxies because thelatter had already
thesurroundings,affecting thecooling rate of gas (Bromm, been polluted with metals. However, Kirby et al. (2008)
Yoshida & Hernquist 2003). The combined ‘feedback’ of drew the opposite conclusion from more detailed modelling
photoionisation, energy injection and changes in com- of stellar metallicities.
position may allow the formation of lower mass stars
(M ∼ 40M⊙, Yoshida et al. 2007) and their feedback In this paper we address some of these questions using
may eventually allow the formation of even lower mass a suite of ultra-high resolution cosmological dark matter
stars, some of which could still be present today. These simulations of galactic haloes – the Aquarius Project. The
very old stars could provide ‘archaeological’ evidence six dark matter haloes data from the Aquarius Project
for early star formation through, for example, unusual picked from a large cosmological simulation to be similar
element abundance patterns (e.g. Iwamoto et al. 2005). in mass to that of theMilky Way,and they were simulated
As structure formation progresses, more massive dark at a variety of numerical resolutions. This enables us to
matter haloes form in which gas can now cool by radiation investigate halo-to-halo variations, and establish the limi-
from atomic hydrogen. This can occur as early as redshift tationsimposed byresolution. Weemploysimplemodelsto
z ∼ 40 (Reed et al. 2005). Star formation in such ‘first identify the sites of first star or first galaxy formation and
galaxies’ may be very different from that in the first haloes follow a suitable selection of dark matter particles to track
(see e.g. Wise & Abel 2008) because of more efficient cool- where their progenitors are today, yielding generic cold
ingbyHIandthemetalsreleasedbypreviousPop.IIIstars. dark matter predictions for early star formation in galaxies
like theMilky Way.
There are currently no direct observational constraints
on this scenario and so many uncertainties remain. For The outline of the paper is as follows. In Sections 2, 3
example, first star formation in a Universe where structure and 4 respectively we describe the simulations, our models
on small-scales is suppressed due to free-streaming of the foridentifyingfirststarandfirstgalaxy haloes,andinvesti-
dark matter (as in Warm Dark Matter models) is very gatetheclusteringofthesehaloes.InSection5wetracethe
different (Gao & Theuns 2007); annihilating dark matter, early objects to z =0 and discuss their properties and spa-
not fusion, may power the first stars if the dark matter tialdistribution.Finally,inSection6wepresentasummary
consists of Majorana particles (Freese et al. 2008). Whilst and discussion of our results.
the initial stages of cloud collapse can be understood in
termsofthepropertiesoftheH2 molecule(Abeletal.2002;
Yoshida et al. 2006), uncertainties from the modelling of 2 SIMULATIONS
radiative feedback of the proto-star make the final stellar
massuncertain (McKee&Tam 2008), although thegeneral The dark matter simulations analyzed in this study come
view is that these stars are massive. The second generation fromtheAquariusProject2(Springeletal.2008a,b;Navarro
stars may, in fact, have relatively high metallicity if metal et al. 2009): a set of six haloes similar to that of the
mixing is inefficient. Ionisation front instabilities (Whalen Milky Way (virial mass M200 ∼ 1012h−1M⊙, circular ve-
andNorman2008)andtheexplosivegrowthofH2 following locity V200 ∼ 180 km s−1, where the subcript 200 refers to
photoionizationmayalsostronglyaffectthenextgeneration the region within which the density is 200 times the cos-
of stars (Whalen et al. 2008). mic critical density; see Table 1). The halos were identi-
fied in a larger cosmological simulation, the hMS simula-
A number of important questions remain unanswered. tion (Gao et al. 2008), which follows the growth of struc-
Did star formation in the Milky Way galaxy start with ture in a periodic box of comoving length 100h−1Mpc with
a display of fireworks? If so, where should we look for 9003 particles, assuming the same cosmological parameters
archaeological evidence? Will most very old stars be in as in the Millennium simulation3 (Springel et al. 2005):
the bulge (White & Springel 2000) or will some be found Ωm =0.25,ΩΛ =0.75,h=0.73,σ8 =0.9. The hMS is itself
in the halo? Two recently discovered ‘hyper metal poor’ alowerresolution version oftheMillennium-IIsimulations4
stars ([Fe/H] < −5) have peculiar element abundances. (Boylan-Kolchin et al. 2009), so that the Aquarius haloes
Were these second-generation stars enriched by the first are alos present in theMillennium-II simulation.
stars1 (seethereviewbyBeers&Christlieb 2005)?Finding Resimulating the formation of haloes in such a large
more such unusual stars in the Milky Way is a key science box correctly accounts for tidal forces and yields realistic
driver for new surveys such as SEGUE, and LAMOST. formation times. The ‘zoom’ technique for resimulating
Did any of the first galaxies survive to the present day? haloes represents the mass which ends up inside or near
Where are their remnants? Are they related to the newly the chosen halo with many low mass particles and a small
discovered dwarfs (Willman et al. 2005; Belokurov et al. gravitational softening; the mass in more distant regions
2006), as discussed in a number of recent papers (Madau, is represented with increasingly more massive particles
Diemand & Kuhlen 2008; Bovill & Ricotti 2009; Koposov with larger gravitational softening. Appropriate small-scale
et al. 2009). If so, what constraints do these place on the power is added in the initial conditions to perturb the
2 http://www.mpa-garching.mpg.de/aquarius/
1 We willrefer to nearly primordialstars contaminated only by 3 http://www.mpa-garching.mpg.de/galform/virgo/millennium/
metalsfromthefirststarsas‘firststarrelics’. 4 http://www.mpa-garching.mpg.de/galform/millennium-II/
The earliest stars and their relics in the Milky Way 3
high-resolution particles. The haloes, labelled Aq-A to
Aq-F, are simulated with up to 109 particles within the
virial radius (particle mass ∼ 103−4h−1M⊙), using the
Gadget-3 simulation code which is an updated version of
Gadget-2 (Springel 2005). The Aq-A halo has been resim-
ulated at different resolutions in order to study numerical
convergence.
Snapshots are stored at 128 output times equally
spaced in log(a), where a = 1/(1 + z) is the expansion
factor, between redshifts z = 127 and z = 0. Dark matter
haloes and their substructure are identified using a combi-
nationofthefriends-of-friendsalgorithm(Davisetal.1985)
and SUBFIND (Springel et al. 2001). SUBFIND groups
particles into substructures based on their density and
binding energy. Haloes and their substructure are traced
throughthesnapshotsandlinkedtogetherinamergertree,
as in Cole et al. (2008).
Although the Aquarius haloes range in mass only from
0.6×1012h−1M⊙ to1.3×1012h−1M⊙,theirmassaccretion
histories, plotted in Fig. 1,differsignificantly. Forexample,
the mass of the main progenitor of the Aq-F halo is nearly
an order of magnitude lower than that of Aq-C as late as
z ∼1, and similarly large differences occur for other haloes
at higher z. The thick dashed line is the extended Press-
Schechter(Press&Schechter1974; Bondet al. 1991; Lacey
&Cole1993)predictionforahaloofthemedianmass,M = Figure 1. Mass of the most massive progenitor of each of the
1.3×1012h−1M⊙, computed following Gao et al. (2004a). six Aquarius haloes as a function of redshift (M(z), coloured
Apart from a systematic overestimate of the mass at high lines), compared to the extended Press-Schechter (ePS) the-
redshift (z>20), theprediction works well. ory for a halo of mass equal to the median for the six halos,
M = 1.3×1012h−1M⊙ (dashed line). There is over an order of
magnitude variation in M(z) between the haloes at certain red-
shifts,eventhoughthez=0massesareallwithinafactoroftwo
3 IDENTIFYING SITES OF HIGH-REDSHIFT (Thenumberinbrackets sortshaloesbytheirz=0mass.).The
STAR FORMATION ePS prediction works well, but systematically overestimates the
massabovez∼20.
In this section, we describe a simple model for identifying
those haloes in the simulations which are likely to be the
sites of early star formation.
star.Thedurationofthisprocessscaleswiththedynamical
time of the halo and is typically ∆z ∼ 3−4; during this
3.1 Sites of Pop. III star formation time, a halo may increase its mass significantly through
mergersandaccretions.Thereforeneithertheinstantaneous
Our model is based on the results of a suite of hydrody- halo mass, nor the virial temperature, are sufficient to
namical simulations of the formation of early structures in describe the star forming properties of a halo; its merger
aΛCDMcosmology,carriedoutbyGaoetal.(2007),which history needs to betaken into account.
included nine-species, non-equilibrium gas-phase chemistry
ofH2production.Thesimulationsusedzoomedinitialcondi- Gao et al. (2007) developed a simple model of Pop. III
tiontofollowthecollapsetohighdensities(nH ∼1010cm−3) starformation,basedonthemergertreesoftheparenthalos,
of gas in haloes with a wide range of formation redshifts which quite accurately matches the Pop. III star formation
(50 > z > 10) and masses (105h−1M⊙ < M < a few× propertiesofall8individualobjectssimulatedinthatstudy.
106h−1M⊙), and investigated how this depends on the as- Define the virial temperature Tvir of a halo in terms of its
sumedcosmologicalparameters.Inagreementwithprevious circular velocity, V200, at a radius R200 (within which the
studies (e.g. Abel et al. 2002; Bromm et al. 2002; Yoshida mean density equals200 times thecritical density) as
et al. 2006), these authors found that the virial tempera-
1
ture,Tvir,oftheparentdarkmatterhaloisthekeyphysical kBTvir ≡ 2µmpV2200, (1)
parameter that regulates how efficiently gas collapses and
cools. wherekB is Boltzmann’s constant,µ is themean molecular
Once Tvir ≥ 103 K, the formation of molecular hydro- weight (µ = 1.22 for neutral H-He admixture), and mp is
genbecomesveryefficient,asignificantmolecularhydrogen the hydrogen mass (e.g. White & Frenk 1991). Once the
abundance(fH2 ∼10−4)buildsupandthegascoolsrapidly, virial temperature reaches Tmin =1100 K (or, equivalently,
becomes self-gravitating and collapses to higher and higher the circular velocity exceeds V200,min = 4kms−1), a star is
densities, presumably culminating in the formation of a assumed to form after a redshift delay of ∆z ∼ 3−4. We
4 Gao et al.
Name mp[h−1M⊙] ǫ[h−1pc] M200[h−1M⊙] r200[h−1kpc] Vmax[s−1km] V200[s−1km]
Aq-A-1 1.25×103 15.0 1.34×1012 179.40 208.8 179.2
Aq-A-2 1.00×104 48.0 1.34×1012 179.40 208.5 179.2
Aq-B-2 4.70×103 48.0 0.60×1012 136.51 157.7 137.5
Aq-C-2 1.02×104 48.0 1.30×1012 177.26 222.4 177.6
Aq-D-2 1.02×104 48.0 1.30×1012 177.26 203.2 177.6
Aq-E-2 7.00×103 48.0 0.87×1012 155.00 179.0 155.4
Aq-F-2 4.95×103 48.0 0.83×1012 152.72 169.1 153.2
Table1.PropertiesofthesixAquariushaloes,Aq-A–Aq-F.TheAq-Ahalohasbeenresimulatedatavarietyofnumericalresolutions,
labelledAq-A-1–Aq-A-5.(Inthispaper,weanalyzeonlyAq-A-1andAq-A-2.)Fromlefttorightthecolumnsgive:thehaloidentifier,
particlemass,(comoving)forcesofteninglengthinthehigh-resolutionregion,virialmass,virialradius,andmaximumandvirialcircular
velocity,allatredshiftz=0(M200,r200,Vmax andV200,respectively).
apply this model to identify which haloes form Pop. III 4 FORMATION HISTORY AND CLUSTERING
stars, and when. OF STAR FORMING HALOES
The general picture of early star formation sketched above
The first star may suppress or enhance star formation
changes dramatically as soon as the star-forming gas be-
in neighbouring halos through the combined effect of
comes ionised, either through photons emitted by nearby
its ionising and Lyman-Werner radiation (e.g. Haaiman,
stars, or because the universe as a whole becomes ionised.
Rees & Loeb 1996; Machacek et al. 2003; Yoshida et al.
Thephoto-heatingofthegas andthesuppressionofatomic
2003, Wise & Abel 2008; Whalen et al. 2008). The net
coolingquenchesstarformationindwarfgalaxieswithcircu-
effect is still unclearand sowe introducebelow asimplified
feedbackmodelbasedonthespatialclusteringofthehaloes. lar velocity,Vmax ≤25 km s−1 (e.g. Efstathiou 1992; Thoul
&Weinberg1996;Gnedin2000;Hoeftetal.2006;Okamoto,
Gao&Theuns2008).TheThomsonscatteringopticaldepth
towards the last scattering surface, as determined from the
WMAP data (Komatsu et al. 2008), suggests that the uni-
verse was reionized at a redshift, z ∼10. We will consider
r
earlier times, z > z , when the Universe was still mainly
r
neutral, and star formation could take place in haloes with
circular velocity as small as a few kilometers per second.
3.2 Sites of the first galaxies
4.1 The first stars in galaxies like the Milky Way
Once the virial temperature of the halo is high enough for
atomic line cooling of gas to become important, Tvir ∼ Figure 2 shows the evolution in the number of Aquarius
6000 K, we assume that the nature of star formation progenitor dark matter haloes that, in the absence of feed-
changes. Rather than a single, massive primordial star per back, would be able to form Pop. III stars. The numbers
halo, the cooling of the metal-enriched gas is assumed to are calculated either using a simple virial temperature
lead to the formation of a normal stellar population with criterion (full lines) or the more detailed model of Gao
a range of masses. The depth of the potential well of these et al. (2007; dashed lines). Star formation begins around
‘first galaxy’ haloes is still so shallow that even a single su- z ∼ 40 (z ∼ 35 in the Gao et al. 2007 model), and the
pernovaexplosioncanproducestrongwinds,asintheclassic number of star-forming progenitor haloes increases very
White & Rees (1978) picture, leading to bursty behaviour rapidlytoreach 103 atz∼30 and104 at z∼15;thereafter
which is difficult to model; see e.g. Mori, Ferrara & Madau the numbers decrease as the haloes begin to merge. The
(2002); Yoshida et al. (2007); Wise & Abel (2008); Greif et halo-to-halo variation remains relatively small up toz∼20
al. (2008); Bromm et al. (2009). Whether it is simply the but, by z ∼ 10, it has increased to about a factor of five,
contributionofatomiclinestocoolingthatleadstothefor- with more massive Aquarius haloes tending to have more
mation of lower mass stars alongside massive ones, or that star forming progenitors at z ∼10.
of metals or dust (Schneider et al 2006), or the change in
theturbulentpropertiesofthestar-forminggas(Krumholtz The difference in the number of star-forming haloes
& McKee 2005), or all of the above, is presently unclear. predicted by the simple, Tvir = 1100 K, cut and the Gao
Given these uncertainties, we adopt the simple criterion, et al. (2007) model is large, of order a factor 10 or more
Tvir ≥ 104 K, to separate haloes that form Pop. III stars at z ≥ 15. The reason for this difference is the delay (by
from‘firstgalaxy’halosthatformstarswithabroaderIMF. ∆z ≈ 3) in the onset of star formation in the Gao et al.
Of course, if feedback from one halo strongly affects star modelatatimewhenthenumberofstar-formingobjectsis
formation in its surroundings, this distinction may be too rising extremely rapidly. Once the number of star-forming
simplistic. haloes reaches its maximum, the two models agree to
The earliest stars and their relics in the Milky Way 5
Figure 2. Pop. III star formation in galaxy halo progenitors as a function of redshift. Left panel: cumulative number of progenitor
haloes withvirialtemperature above 1100 K foreachof the sixAquarius haloes (colour solidlines).The blackdots show the extended
Press-Schechter prediction which works well, but increasingly overestimates the number of halos after z ∼ 15. Gas in such haloes is
hot enough for significant H2 formation. The dashed lines show the cumulative number of independent sites of Pop. III star formation
according to the model of Gao et al. (2007) which, in addition to a virial temperature criterion, takes the merger history of the halo
into account. This more stringent criterion reduces the number of formingstars; yet a MilkyWay-type halo still had several hundreds
ofPop. IIIstar-formingprogenitors atredshiftz=25and∼104 at z=10. Thehalo-to-halovariationislarge,afactor∼5atz=10.
Thecumulative number of haloes drops after z ∼10as haloes begin tomerge. Right panel: the star formationrate. Therate increases
fromafewstarformingevents perMyratz=30,toseveraltens atz=20andchanges littlethereafter.
Figure3.ClusteringofPop.IIIstar-formingprogenitorhaloes.Leftpanel:meannumberofprogenitorhalopairsinAq-A,asafunction
of proper separation at the three redshifts indicated in the panel. Right panel: mean separation of progenitor haloes in each of the six
Aquariushaloes.Eachhalohasoneneighbourwithinthedistancegivenbythesolidline,and10neighbourswithinthedistancegivenby
the dashed lines.Star-forminghalos have relatively nearby companions, indicating that feedback effects could be important (see text).
Thelinearriseinseparationbetweensubstructuresbelowz∼20isbecausetheproto-haloregionisstillexpandingwiththeHubbleflow
atthisearlytime.
6 Gao et al.
within afactor of a few. The star formation rate is of order
N˙ ≈ 1Myr−1 at z = 30, increasing rapidly to reach a
⋆
broad peak of N˙ ≈ 102Myr−1 at z ∼ 15. According to
⋆
the Gao et al. model, the first stars in a Milky Way sized
halo appear around z ∼ 35, later than in a proto-cluster
wherestarformationstartsaroundz ∼47(Gaoetal.2007).
So far we have neglected potential feedback effects,
arising from star formation, on neighbouring haloes which
could, in fact, be quite severe. UV photons with energy,
hν > 13.6 eV, emitted by massive stars may ionise and
heat the gas in a neighbouring halo. Star formation may
thus be quenched due to the suppression of atomic cooling
andphoto-heating,oraltogetherpreventedasthehaloloses
gas through photo-evaporation (e.g. Shapiro, Iliev & Raga
2004;Whalenetal.2008,Okamotoetal.2009).Ontheother
hand, H2 formation may be enhanced in photo-ionised gas,
oncethesourceofionisingphotonshasfaded(Haiman,Rees
&Loeb 1996). Theseeffectswill bemostly restricted tothe
HII region surrounding the star because of the high optical
depth of ionising radiation, except for the high-energy tail
of the photon energy distribution.
Lyman-Werner photons with 11.2 ≤ hν/eV ≤ 13.6
may destroy the H2 coolant, also quenching or suppressing Figure4.Theabundanceofhaloeshosting‘firstgalaxies’(virial
star formation. Most of the gas is optically thin to Lyman- temperature Tvir > 104 K) as a function of redshift for the six
Wernerphotonsandsothis‘sphereofinfluence’extendsbe- Aquarius haloes (colours are the same as in Fig. 1). Dashed
yondtheedgeoftheHIIregion.However,somestar-forming lines are the prediction from extended Press-Schechter theory.
haloes may become dense enough to self-shield, even in the Thesehaloesstarttoappeararoundz∼25andtheirabundance
Lyman-Werner bands. Kinematical feedback from the star risesrapidlyto reacha broadpeak of 200-300 haloes by z ∼10.
in the form of a stellar wind or supernova explosion, may Progenitorsofhaloesmoremassiveatz=0tendtohaveahigher
abundance offirstgalaxyhaloesatallz.
also affect its surroundings.
Clearly,thedetailsofthesefeedbackeffectsaredifficult
to model accurately, and so the degree of suppression of N˙ ∆t 100 1/3 10
starformationnearaPop.IIIstarremainshighlyuncertain R=1.3 γ kpc, (2)
(see Yoshida et al. 2003; O’Shea & Norman 2007 and 2008; (cid:18)1050s−1 3Myr 1+δ(cid:19) 1+z
Wise& Abel2008; Yoshidaet al.2008; Whalen et al. 2008;
around a source emitting ionising photons at a rate, N˙ ,
Ahn&Shaprio2006,forrecentdiscussions).Inviewofthis, γ
over a time interval, ∆t. The medium is at an overdensity,
we have developed a simple model for feedback that takes
δ, has the cosmological baryon fraction, Ω h2 = 0.045, and
into account the clustering of the halos. We consider only b
ahydrogen abundanceof 0.75 bymass. Fullnumerical sim-
radiative feedback and neglect external radiation from dis-
ulations find similar radii for the HII region (e.g. Abel et
tantstarsorgalaxies.Foreachprogenitorhalo,wecalculate
al. 2007, Yoshida et al. 2007). The fact that R is compa-
theaveragenumber,N(r),ofneighbouringpotentiallystar-
rable to the mean interhalo separation implies that feed-
forming haloes a function of separation, r. The number of
back from ionising photons could indeed be rather impor-
neighbours,showninFig.3,scalesroughlyasN(r)∼r2.At
tant in quenching first star formation. The formation rate
z=30,thetypicalpairseparationisr∼1h−1kpc(notethat
of first stars could then be significantly smaller than the
hereandbelowwegiveseperationsinproper,notcomoving
no-feedback case depicted in Fig. 2.
units).
Amoredirectmeasureoftheredshiftevolutionofclus-
tering is the mean separation of pairs, N(1), and the mean
4.2 The first galaxy haloes
distance to the 10th star-forming nearest neighbour halo,
N(9), as a function of redshift, also shown in Fig. 3. Both Progenitors ofAquariushaloesfirstachieveavirialtemper-
curves fall rapidly with decreasing redshift as haloes begin ature, Tvir >104 K, around z ∼25; the abundance of such
toforminprofusion,reachaminimumbetweenz=30−20 “first galaxy” halos rises rapidly to a few tens by z ∼ 18
and thereafter increasing slowly due to Hubble expansion and reaches a broad peak of ∼ 300 by z = 10, as shown
of the proto-galactic region. On average, each potentially in Fig. 4. The scatter amongst the six Aquarius haloes is
star-forming halo has another potentially star-forming halo large. The rise in abundance is reasonably well described
within 0.5h−1kpcat z =30, increasing slowly to0.6h−1kpc by the Press-Schechter formula, but this overestimates the
at z = 20, and ten others within 2h−1kpc over the same number at z = 10 by ∼ 50 percent. As was the case for
redshift range. Pop.IIIhaloes discussedearlier, thefirstgalaxy haloesina
To estimate the effect of feedback from ionising radia- proto-Milky Way object form at z ∼25, substantially later
tion,we compare thesenumberstotheradius, R,of an HII than in a proto-cluster region where they form at z ∼ 40
region in a uniform density medium, (Gaoetal.2004a).Themoremassivez=0Aquariushaloes
The earliest stars and their relics in the Milky Way 7
Figure 5.Clusteringof‘firstgalaxy’progenitorhaloes(virialtemperature,Tvir>104 K).LeftPanel:meannumberofprogenitorhalo
pairs in Aq-A, as a function of proper separation, at the redshifts indicated in the panel. Right Panel: redshift evolution of the mean
separation between pairs of haloes with Tvir >104 K. Byz =10, the mean separation between firstgalaxy haloes is ∼6h−1kpc and
eachhalohasonaverageanother10haloeswithin∼20h−1kpc.Thetypicaldistancetoaneighbouringhalohasalargescatteramongst
realizations,reflectingthefactthatthesehaloesonlyjustbegantoformattheseearlytimes.
tend to havemore first galaxy progenitors at z ∼10.
As before, we characterise the clustering of haloes
that can cool through atomic processes by the number of
neighbours,N(r),atdistancer.AsshowninFig.5,N(r)is
again approximately a power-law, N(r) ∝ r2. At z = 10, a
firstgalaxyhalohasaneighbouringfirstgalaxyhalowithin
∼6h−1kpcand∼10within∼25h−1kpc.Thehalo-to-halo
scatter in clustering properties is large at early redshift
z ∼ 20 (Fig. 5, right panel), but as more haloes form, it
decreases; the typical separation reaches r ∼ 6 h−1kpc at
z = 10. Consequently, the ionised regions formed by star
formation aroundsuchfirstgalaxies neednotbeverylarge,
oforderafewh−1kpc beforeHIIregionspercolate across a
proto-Milky Way galaxy byz =10.
Feedbackfrom starformation in afirstgalaxy may po-
tentially affect a neighbouring halo. Figure 6 displays the
fraction of halos that would be affected depending on the
value of the radius, R, of influence of the feedback, when
taking clustering into account. For R = 1h−1kpc, feedback
has no effect, but for R = 5 h−1kpc, 20-30 percent of po-
tential first galaxy halos could be affected, rising to 40-50
percent for R=10h−1kpc.
Figure 6.Fractionoffirstgalaxiesnotaffectedbyneighbouring
firstgalaxiesasafunctionofredshift,iftheradiusofinfluenceof
thefeedbackisR=10,5or1h−1kpc(dashed, dotted, andsolid
5 RELICS OF EARLY STAR FORMATION lines,respectively).ForthesmallervalueofR,feedbackhaslittle
ornoeffect,butforlargerR,feedbackmaydecreasethenumber
5.1 Relics of the first stars offirstgalaxiesconsiderably,uptoafactor∼2.
If, as seems likely, the first stars that form in a CDM uni-
versearemassive,thenonlytheirdarkremnantswillremain makeuseofthemergerhistoryofthehaloeshostingprimor-
in the Milky Way today. However, evidence for their exis- dial stars which is readily available in thesimulations.
tence may be hidden in the anomalous abundance patterns It seems reasonable to assume that feedback from
oflong-lived second generation starsthatformed nearby,in Pop.III stars will havepreventedthegas enrichedby them
gas predominantly enriched by Pop. III stars (e.g. Beers & from forming further stars until it is accreted later into a
Christlieb 2005; Rollindeet al 2008); wewill call such stars first galaxy halo where it can cool by atomic processes (see
‘first star relics ’. Where are these fossils of primordial star e.g.thesimulationsofWise&Abel2008).Theearliestgen-
formation to be found today? To answer this question, we erationofstarsformedinsuchafirstgalaxymaythenhave
8 Gao et al.
thepeculiarabundancepatterncharacteristicofPop.IIInu-
cleosynthesis. Howeverstars that form later may havebeen
enriched by the elements produced by the previous gener-
ation of relatively metal rich stars, so that eventually the
net abundance pattern loses its characteristic Pop. III star
signature. To implement this idea we proceed as follows.
Weassumethateach firstgalaxy halocontainsafixedtotal
mass of ‘first star relics’ - stars that form in an envi-
ronment enriched solely by truly primordial stars –
independentofredshift.Totracethelocationofsuchstarsat
latertimes,wetagtheN =100mostboundparticlesatthe
time the virial temperature of the halo first exceeds
T = 104 K 5. This assumes that these second-generation
starsforminthecentresofsuchdark-matterhaloes.Oncea
halohasstartedformingstars,itwillgrowinmass,andmay
mergewithotherhaloes.Thenumberoffirststarrelicsina
halo will only change if it merges with a halo that contains
itsown population of first star relic stars. Wecontinuetag-
ging first star relics in haloes that reach the threshold Tvir
untilz=10, after which weassumethat reionisation of the
Universeevaporates all mini-haloes.
In summary, we identify the epoch when a halo is first
Figure 7. Projected distribution at z = 0 of first star relics
capableofsustaininggasthatcancool throughatomic pro-
(red), compared tothat of thedarkmatter forthe Aq-A-2halo.
A significant fraction of the stars lie in the central part of the cesses and tag its 100 most bound particles as thefirst star
maingalaxy,butsomeendupindarkmattersubhalos.Theimage relics, untilz=10. Wecan then investigate thespatial dis-
is 1080 kpc on a side, approximately twice the diameter of the tributionofthesefirststarfossilsatanylaterepochbytrac-
virialiseddarkmatterhalo. ing thetagged particles. The location of the first star relics
todayisillustratedinFig.7where,forclarity,weshowonly
a fraction of the stars. The image shows that most of the
firststarrelicsendupinthecentralregionsofthehalo,but
some surviveinside subhalos.
The visual impression gained from Fig. 7 is quantified
in Fig. 8 which shows that the distribution of the first star
relics today (which is similar in all six Aquarius halos) is
expected to be much more concentrated than that of the
darkmatter.Fiftypercentofthesefirststarrelicsliewithin
20h−1kpc of the centre and ∼ 10 per cent lie inside what
would be the galactic bulge, at r < 2h−1kpc. In contrast,
only ∼10 percent of thedark matter lies within 20h−1kpc,
andonlyabout0.1 percentisatr<1h−1kpc.Eventhough
the stars in our simulations are already very concentrated,
earlier models of the remnants of PoP-III stars (White &
Springel 2000; Diemand et al. 2005) suggested they should
beevenmoreconcentrated,withalmost allofthemlyingin
thebulge where they would bevery hard to detect.
Althoughmostofthefirststarrelicsresideinthecentral
partsofthemain halo, asignificant fraction endupin dark
mattersubhalos.Thisisinterestingbecauseitmaybeeasier
to detect such unusual stars in a nearby dwarf galaxy than
to hunt for them in the crowded surroundings of the Milky
Way bulge.
Figure8.Cumulativedistributionofsecondgeneration,firststar
relics, stars at redshift z = 0 for all six Aquarius haloes (colour 5.2 Relics of the first galaxies
lines), compared to the dark matter profile for the Aq-A halo
(dashedblackline). Inthissectionweinvestigatethefateoffirstgalaxyhalos.As
discussed in Section 4.2, these are dark matter halos which
formedbeforez=10andhaveTvir >104 K.Wearepartic-
ularlyinterestedindescendantswhichtodayaretobefound
5 Weverifiedthatourfinalresultsdonotdependstronglyonthe
arbitrarychoiceofN.
The earliest stars and their relics in the Milky Way 9
Figure 9. Left panel: Cumulative mass function at z = 0 of ‘first galaxy’ haloes (i.e. bound substructures which had a progenitor
at z > 10 with Tvir > 104 K), for the Aq-A-1 (solid line) and the 8× lower resolution Aq-A-2 (dashed line) simulations. Numerical
convergence is very good above 100 particles (corresponding to 106h−1M⊙ in Aq-A-2). For comparison, the dashed-dotted line is the
z = 0 mass function of all gravitationally bound substructures in Aq-A-1. Right panel: as the left panel, but for the maximum of the
circularvelocitycurve,Vmax.
within thevirial radius of theparent halo. To establish the
rangeofdescendantmasseswhicharereliablysimulated,we
begin by carryingout aconvergencetest of thepresent-day
mass function.
Wecompareresultsfromthe1.4billionparticleAq-A-1
simulationwiththosefromtheAq-A-2simulationwhichhas
8timespoorerresolution.(AllsixAquariushaloeshavebeen
simulatedattheresolutionoftheAq-A-2halo;seeTable1).
The cumulative mass function of first galaxy haloes that
survivetoz=0,showninFig.9,showsexcellentnumerical
convergence above a mass of 106h−1M⊙, corresponding to
100particlesinAq-A-2,andtoamaximumcircularvelocity
of Vmax ∼ 5kms−1. We therefore adopt Np = 100 as the
resolution limit of thesimulations.
Aq-A-2has 76 surviving first galaxy haloes with N >
p
100 (M >106h−1M⊙). Aq-A-1has 88 survivors with Np >
100,correspondingtoM >105h−1M⊙andVmax∼2kms−1.
Thus, Aq-A-1 resolves dark matter subhaloes with circular
velocities lower than the stellar velocity dispersions of the
smallest dwarf galaxy satellites of the Milk Way discovered
to date(e.g. Simon & Geha 2007).
5.2.1 Abundance of the first galaxies and their
Figure 11.Cumulative fractionoffirstgalaxy haloes that were
descendants
accretedbeforeagivenredshiftandsurviveuntilz=0.Thedif-
The mass function at z = 10 of those ‘first galaxy’ haloes ferentlinescorrespondtothe6Aquariushalos.Typically50per-
which ended up inside the virial radius (∼ 170h−1kpc see centofhaloesfellinbeforez=3.
Table1)ofthemainhalotoday,andthecorrespondingmax-
imum circular velocity function, are shown in the top two
panels of Fig. 10 for all Aquarius halos. The most mas- first galaxy descendants with mass M >106h−1M⊙ (corre-
sive of these subhaloes has M ∼ 1010h−1M⊙, and cir- sponding to Vmax > 5kms−1) that survived since z = 10.
cular velocity, Vmax ∼ 100 km s−1. There are typically Note that there is a large variation in the number of sur-
∼ 10 subhaloes with M > 109h−1M⊙ (corresponding to vivors in the different Aquarius simulations, with the more
Vmax > 40kms−1) and 100 with M > 108h−1M⊙ (corre- massive haloes harbouring more massive substructures on
sponding to Vmax>20kms−1). average.Themassofthemostmassivez=0remnantvaries
The lower panels of Fig. 10 give the present day mass from 3×109h−1M⊙ to nearly 1011h−1M⊙.
andVmax distributionsofthedescendantsofthefirstgalaxy ThelowerrightpanelinFig.10showsthat,atz=0,the
halosillustratedinthetoppanels.Everyhalocontains∼80 Aq-A-2halocontainsover60firstgalaxyremnantsubhaloes
10 Gao et al.
Figure 10. Statistics of firstgalaxy haloes in all sixAquarius haloes (the colour scheme is as inFig. 1) at z=10 (top), when they are
accreted bythe mainhalo(middle), andatz=0(bottom). Theleftpanels show cumulativemassfunctions andtherightpanels show
cumulativeVmax distributions.ThereisalargevariancebetweenthedifferentAquariushaloesatallredshifts.Forexample,themassof
themostmassivez=0remnantvariesbetween3×109h−1M⊙ tonearly1011h−1M⊙.ThemoremassiveAquarius haloes tendtohave
the more massive substructures. Comparing the z = 0 masses with those at infall or at z = 10 demonstrates that most substructures
loseaconsiderablefractionoftheirmassbythepresent.
with Vmax > 10kms−1inside its virial radius. This is a fac- lations of Aquarius halos, Okamoto & Frenk (2009) found
tor of a few larger than the numberof classical satellites of that all subhalos with Vmax = 23.5kms−1 host a satellite
theMilky Way.Howeverthetotal (i.e. not just descendants with V-band luminosity, LV > 2.5×105L⊙, whereas be-
of first galaxies) numberof subhalos with Vmax >10kms−1 lowthatvalueadiminishingfractionofsubhalosmanageto
at z = 0 is ∼ 400, as may be seen from the right panel make a visible satellite. It is therefore tempting to identify
of Fig. 9. By contrast, for Vmax >22kms−1 (corresponding these more massive first galaxy remnants with bright satel-
toM∼>3×108h−1M⊙),thenumberofsurvivingfirstgalaxy lite galaxies and to conclude that these must have formed
haloes equals the total number of haloes. From SPH simu- before z =10.