Simulating high-redshift galaxies

0.85 MB·

by  R. Salvaterra

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed13January2011 (MNLATEXstylefilev2.2)
Simulating high-redshift galaxies
Ruben Salvaterra1, Andrea Ferrara2 & Pratika Dayal3
1 Dipartimento di Fisica e Matematica, Universita´ dell’Insubria, Via Valleggio7, 22100 Como, Italy
2 Scuola Normale Superiore, Piazza dei Cavalieri 11, 56126 Pisa, Italy
3 SISSA/International School forAdvanced Studies, Via Beirut 2-4 Trieste,Italy, 34014
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ABSTRACT
a
J Recent observations have gathered a considerable sample of high redshift galaxy can-
didates and determined the evolution of their luminosity function (LF). To interpret
2
thesefindings,weusecosmologicalSPHsimulationsincluding,inadditiontostandard
1
physical processes, a detailed treatment of the Pop III−Pop II transition in early ob-
] jects. The simulated high-z galaxies match remarkably well the amplitude and slope
O ofthe observedLFin the redshift range 5<z <10.The LF shifts towardsfainter lu-
C minosities with increasing redshift, while its faint-end slope keeps an almost constant
. value,α≈−2.Thestellarpopulationsofhigh-z galaxieshaveagesof100-300(40-130)
h Myr at z = 5 (z = 7−8), implying an early (z > 9.4) start of their star formation
p
activity;thespecificstarformationrateisalmostindependentofgalacticstellarmass.
-
o TheseobjectsareenrichedrapidlywithmetalsandgalaxiesidentifiedbyHST/WFC3
r (MUV < −18) show metallicities ≈ 0.1Z⊙ even at z = 7−8. Most of the simulated
st galaxies at z ≈ 7 (noticeably the smallest ones) are virtually dust-free, and none of
a them has an extinction larger than E(B−V)=0.01. The bulk (50%) of the ionizing
[ photons is produced by objects populating the faint-end of the LF (MUV < −16),
3 which JWST will resolve up to z = 7.3. PopIII stars continue to form essentially at
v all redshifts; however, at z =6 (z =10) the contribution of Pop III stars to the total
3 galacticluminosityisalwayslessthan5%forMUV <−17(MUV <−16).Thetypical
7 high-z galaxies closely resemble the GRB host galaxy population observed at lower
8 redshifts, strongly encouraging the use of GRBs to detect the first galaxies.
3
. Key words: methods: numerical - galaxies:high redshift - luminosity function -
3
cosmology:theory
0
0
1
:
v
i 1 INTRODUCTION = 28.8 in the above bands) galaxies as remote as z = 10.
X
In addition, the WFC3 crafted filters have considerably al-
r leviated the contamination problem due to interlopers and
a The search for themost distant galaxies, located at thebe-
provided more precise photometric redshift estimates. The
ginning of the cosmic dawn, is now entering its maturity.
standardselectionmethodappliedtothesesurveydatasets
Thelast few yearshavewitnessed a tremendousincrease in
is based on the dropout technique introduced by Steidel
the data available, and the number of candidates at red-
et al. (1996) and later constantly refined and improved by
shiftsashighasz =10,correspondingtoonlyhalfabillion
several authors (e.g. Giavalisco et al. 2004, Bouwens et al.
yearsaftertheBigBang. Thishasbeen madepossiblebya
2007). Though this method has proved to be very solid in
combinationofnewtechnologiesandrefinedselectionmeth-
identifying high-redshift sources, it has the drawback that
ods. In the first class of triggers, it is easy to acknowledge
the exact source redshift cannot be determined with com-
the role of the Hubble Space Telescope (HST). Thanks to
plete confidence. This uncertainty can be partly overcome
dedicated surveys including the Hubble Ultra Deep Field
by also using the longer wavelength infrared data, such as
and its predecessor, the Hubble Deep Field, we have been
that provided by the Spitzer satellite; by building a more
able to collect information on the luminosities and num-
complete Spectral Energy Distribution (SED), the stellar
bercountsof galaxies located at theendofthereionization
mass, age and redshift of a given source can be constrained
epoch. Immediately after, follow-up experiments performed
further. Other complementary techniques to search for dis-
withthenewlyinstalledWideFieldCamera(WFC3),yield-
tant(z>5)galaxiesarealsowidelyused,amongwhichthe
ingskyimagesintheF105W(Y-band,1.05µm),F125W(J-
narrow-bandspectroscopy(Malhotraetal.2005;Shimasaku
band, 1.25µm) and F160W bands (H-band, 1.60µm), have
et al. 2006; Taniguchi et al. 2005; Kashikawa et al. 2006)
allowed to push the exploration to very faint (e.g. AB mag
(cid:13)c 0000RAS
2 Salvaterra, Ferrara & Dayal
aimedatdetectingtheLyαline,carryingalargefraction of AB mag), wide-area (∼ 40 arcmin2) WFC3 Early Release
thebolometric luminosity,isdefinitelythemost established Science reveals 66 and 47 candidate galaxies at z = 7 and
one. Such narrow-band searches have yielded the record- z = 8, respectively (Bouwens et al. 2010b). After carefully
holding most distant galaxy at z = 6.96 (Iye et al. 2006). modelling theselection volumeof each field and of thepos-
Finally, another series of experiments involve searching for sible contamination by spurious sources, the LF obtained
remotegalaxies behindforegroundgalaxy clustersactingas from these data, while consistent with previous derivations
magnification lenses (Schaerer & Pello´ 2005; Richard et al. ofM∗ andofthenormalization, showsasteeperfaint-end
UV
2008;Bradleyetal.2008).Althoughthesesearchesresultin slope with α=−1.94±0.24 and α=−2.00±0.33 at z=7
deepermagnitudes, theirinterpretation is hampered bythe and z=8, respectively.
lens modelling and by the extremely narrow field of views, Besides the LF, tentative information on the physical
rendering it difficult to keep cosmic variance undercontrol. propertiesofthesesourcescanbeextractedfromtheirSED,
As a final remark, we note that the most distant, spectro- exploiting available Spitzer data (Eyles et al. 2005; Yan et
scopically confirmed, cosmic object is a Gamma Ray Burst al. 2006; Stark et al. 2009). In a recent study Labb´e et al
(GRB090423atz=8.2,Salvaterraetal2009b;Tanviretal. (2010b),basedonfollow-upSpitzer/IRACobservations,an-
2009). Althoughnotagalaxy,thepresenceofthisindicator alyzedtheSEDof12z-dropoutand4Y-dropoutcandidates.
implies that star formation was already well under way at NoneofthemisdetectedintheSpitzer/IRAC 3.6µm band
those early epochs, thus further encouraging deeper galaxy toamagnitudelimitofAB=26.9(2σ),butastackinganaly-
searches. Inaddition,theGRBcan beseen as asignpost of sisrevealsarobustdetectionforthez-dropoutsampleanda
the underlying galaxy which could possibly be detected in strongupperlimitfortheY-dropoutone.ThestackedSEDs
thefuture knowing its exact position. Such a findingwould are consistent with a stellar mass of about 109M⊙, no dust
beoftheutmostimportanceasGRBsaremostlyassociated reddening, sub-solar metallicity, and best-fit ages of about
withstarformingdwarfgalaxies(Savaglio,Glazebrook&Le 300 Myr, implying a formation epoch z ≈10. These results
Borgne2009) whicharenowconsidered tobethedominant for the stacked sample should be compared with those ob-
sourcesof(re)ionizingphotonsathighredshifts(Choudhury tainedbyFinkelsteinetal(2010)whoperformedanobject-
& Ferrara 2007; Choudhury,Ferrara & Gallerani 2008). by-objectanalysisandfoundsimilaragesbutwithaconsid-
What have we learned from this wealth of experimen- erable spread, allowing ages as low as a few Myr.
tal results ? The most solid piece of information that can Oneofthemajortriggerstolookforveryhigh-z galax-
be determined from the data appears to be the luminos- ies is the quest for the reionization sources. The ionizing
ity function (LF) and, less robustly, its evolution. It is photon budget provided by the candidate high-z galaxies
useful to briefly recap the present observational situation is often estimated by extrapolating their LF to lower lumi-
marching towards increasing redshift. Bouwens et al (2007) nosities, a step that introduces a considerable uncertainty
presentacomprehensiveviewofgalaxycandidatesfromthe inthefinaldetermination.Havingthisinmind,itisstillin-
UDF/ACS/GOODS fields using NICMOS in the redshift terestingtonotethatmoststudiestendtoagreeonthefact
range z = 4−6. They identify 1416 (627) V-dropouts (i- that the integrated UV specific luminosity for the detected
dropouts) corresponding to z ≈ 5 (z ≈ 6) down to an galaxies at z = 7−8 falls short of accounting for the ion-
absolute UV magnitude of M ≈ −17 with a LF de- izing power required to reionize the intergalactic medium.
UV
scribedbyaSchechterfunctionwithcharacteristicluminos- Of course, this conclusion is subject to at least two major
ity and faint-end slope given by M∗ =−20.64±0.13 and unknown factors, these being the gas clumping factor (af-
UV
α=−1.66±0.09(M∗ =−20.24±0.19,α=−1.74±0.16) fecting its ability to recombine), and the escape fraction of
UV
respectively. Thesame group (Bouwens et al. 2008) has ex- ionizingphotons(affectedbydustandneutralhydrogenab-
tendedthedataanalysistoincludez≈7z-dropouts(8can- sorption within galaxies). Additionally, the effect of poorly
didatesatz=7.3)andJ-dropouts(nocandidatesatz≈9). constrained ages and metallicities (including the presence
More recently, the installation of WFC3 on board the HST ofmetal-free, massivePopIIIstars),furthercomplicate the
has triggered a new series of searches. Oesch et al. (2010) calculation.
used data collected during the first-epoch WFC3/IR pro- Inspiteofthelargeexperimentaleffort,surprisinglylit-
gram(60orbits)intheY,J,Hbandsreachingamagnitude tleattentionhasbeendevotedbymodelerstotheveryhigh
limit of AB≈ 29(5σ). They identify 16 z-dropouts in the redshift universe. Most of the work has so far concentrated
redshift rangez =6.5−7.5 from which they obtained aLF on a semi-analytical approach (Stiavelli, Fall & Panagia
with (M∗ =−19.91±0.09,α=−1.77±0.20), essentially 2004;Schneideretal.2006;Bolton&Haehnelt2007;Maoet
UV
confirmingthepreviousfindingswhileextendingittofainter al. 2007; Samui, Subramanian, Srianand 2009; Trenti et al.
luminosities (M ≈ −18). Bouwens et al. (2010a) pushed 2010) to compute the luminosity function, number counts
UV
the investigation to z = 8.0−8.5 by using 5 Y-dropouts. andemissivityevolutionofhigh-z galaxies.Albeitquitefast
Finally,Bouwensetal. (2009) wereabletoidentifythreeJ- and versatile, these methods cannot provide detailed infor-
dropouts.Ifconfirmed,thesesourceswouldbethemostdis- mation on the properties of the galaxies, often being based
tant objects detected so far. Similar studies using the same onsimplifiedassumptions.Numericaldedicatedsimulations
data has been performed by Bunker et al. (2010), who find attempting to model galaxy populations beyond z = 5−6
acomparablenumberofz−andY−dropouts.McLureetal. arealsoveryscarce,with thepartialexceptionsconstituted
(2010) did not apply specific color cuts as in the previous bytheworksby Nagamine et al. (2006) and Finlator, Dav´e
works,thusfindingalargernumberofcandidates;however, & Oppenheimer(2007).
theypointedoutthatabout75%ofthecandidatesatz>6.3 Our approach is novel and different in spirit from all
(100% at z > 7.5) allow a z < 2 interloper solution. A re- the previous theoretical ones. As our main aim is to model
cent analysis of the three HUDF and of the deep (∼ 27.5 veryhighredshiftreionizationsources,wecanaffordsmaller
(cid:13)c 0000RAS,MNRAS000,000–000
Simulating high-redshift galaxies 3
simulation boxes, thereby reaching the high resolutions re- Supernova winds are treated as in the original model
quired to resolve the dominant reionization sources - dwarf bySpringel&Hernquist(2003);however,forsimplicityand
galaxies.Most importantly,though,wehaveimplementeda because the mass load and kinetic energy fraction are un-
careful treatment of metalenrichment andof thetransition knownparameters,wehavegiventhewindsfrombothpopu-
from PopIIItoPop IIstars,alongwith acarefulmodelling lationsaninitialvelocityv =500kms−1,whichappearsto
w
of supernova feedback. Here we are interested in deriving be consistent with that derived from observations of high-z
the LF plus other observables from the simulations and to starburstgalaxies.Windparticlesaretemporarilyhydrody-
casttheminaformthatcanbecompareddirectlywiththe namically decoupled until either (i) they have moved by a
availabledataorusedtomakenewpredictionsfortheJames travelinglengthλ=2kpc,or(ii)theirdensityhasdecreased
Webb SpaceTelescope (JWST). below 0.5 times the star formation density threshold. The
metals are donated bystar particles tothesurroundinggas
ones using a SPH kernelas described in TFS07.
The gas photo-ionization and heating rates are calcu-
2 NUMERICAL SIMULATIONS
lated at equilibrium with a background ionizing radiation
For the present study we have performed a set of cosmo- due to the combined contribution of galaxies and quasars,
logical1 simulations usingthepubliclyavailable codeGAD- taken from Haardt & Madau (1996), shifted so that the in-
GET2 (Springel2005)withanimprovedtreatmentofchem- tensity at 1 Ryd is J = 0.3 × 10−21 erg s−1 Hz−1, in
ν
ical enrichment as detailed in Tornatore, Ferrara & Schnei- agreement with Bolton et al. (2005). Gas cooling and wind
der (2007, TFS07). A unique feature of the computation treatment details are thesame as in TFS07.
concerns the Initial Mass Function (IMF) of stars, which
is taken to be different for Pop III and Pop II stars and
depends on gas metallicity, Z. In brief, if Z < Zcr, the 3 LUMINOSITY FUNCTION
adopted IMF is a Salpeter law with lower (upper) limit
of 100M⊙ (500M⊙) and only pair-instability supernovae Asafirstcheckofthesimulationresultswewillcomputethe
(140M⊙ < M < 260M⊙) contribute to metal enrichment evolution of the LF of the simulated galaxies and compare
(Heger & Woosley 2002). If Z > Zcr, the above limits are it with available data. To this end we make a number of
shifted to 0.1M⊙ (100M⊙), respectively; stars above 40M⊙ physical assumptions that are discussed in the following.
For each galaxy at a redshift z, the luminosity at rest-
end their lives as black holes swallowing their metals. Ac-
cordingtothecanonicalchoice,wefixZcr =10−4Z⊙.These frame wavelength, λ, is the sum of the contribution of its
two populations, to which we will refer to as Pop III and Pop II and Pop III stars. The SED of Pop II stars is com-
puted by running the Starburst99 code (Leitherer et al.
PopIIstarsrespectively,differalsofortheirmetalyieldand
explosion energy.Complete details of thesimulation can be 1999,Vazquez&Leitherer2005) usingthemetallicities and
foundinTFS07.Thesimulation follows theproductionand stellar ages appropriate for the galaxy under consideration
as obtained from the cosmological simulation. The SEDsof
transport of six different metal species, namely: C, O, Mg,
Si, S,Fe,based on which thelocally appropriate IMF isse- massive (metal-free) Pop III stars have been computed by
lected. The simulated volume has a linear (comoving) size Schaerer(2002)includingtheeffectofnebularemission.For
L = 10h−1 Mpc with N = 2×2563 (dark+baryonic) par- both populations the IMF is taken according to the same
p
ticles, corresponding to a dark matter (baryonic) particle prescription used in thesimulation and described in Sec. 2.
mass of Mp = 3.62×106h−1M⊙ (6.83×105h−1M⊙); the The total luminosity of a galaxy is then given by
cnoortreaslploownduinsgtfoortcreacrkesotlhuetiofonrmisa2tikonpco.fOmurinrie-shoalluotsi,onwdhoosees Lλ =LIλI+LIλII=lλII(τII,Z)M˙∗II+lλIIIM˙∗IIIτIII (1)
stellar contribution remainsveryuncertain duetoradiative where lII(τII,Z) is the SED template for Pop II stars with
λ
feedback effects (Haiman & Bryan 2006; Susa & Umemura mean age τII and metallicity Z corresponding to acontinu-
2006; Ahn & Shapiro 2007, Salvadori & Ferrara 2009). The ousstarformationrateof1M⊙ yr−1;M˙∗IIisthePopIIstar
computation is initialized at z = 99 and carried on until formation rate. The SED template of Pop III stars, whose
z = 2.5. Star formation is treated as a stochastic process, starformation rateisM˙∗III,islλIII;τIII=2.5×106 yristhe
following Springel & Hernquist (2003) Basically, at a given mean lifetime of massive Pop III stars (Schaerer 2002). We
timethestar formation rateof a (multi–phase) gas particle haveimplicitlyassumedthattheemissionpropertiesofPop
is computed using a Schmidt-type law m˙ = xm/t∗, where IIIstarsareconstantduringtheshortlifetimeofthesemas-
xm is the mass of cold clouds providing the reservoir for sive metal-free stars. Next, the luminosity is converted into
starformation.Withintheeffectivestarformationmodelby absolute AB magnitudes, M , where the suffix UV refers
UV
Springel & Hernquist (2003), thestar formation time-scale, to the wavelength λ = (1600,1350,1500,1700,1500,1600)
is computed as t∗(ρ) = t0∗(n/n∗)−1/2, where t0∗ = 1.5 Gyr ˚A for z = (5,6,7,8,9,10), respectively. Though this wave-
andthedensitythresholdforstarformation,n∗ =0.1cm−3, length choice is chosen to be consistent with the observa-
are free parameters of the model chosen so as to reproduce tional data we compare with, a different value would not
theobserved Kennicutrelation within uncertainties. affect the results in any sensible way, given the flatness of
thespectrum in this short wavelength range.
The LF of galaxies at any redshift z is obtained by
1 Throughoutthepaper,weadoptaΛCDMcosmologicalmodel
counting the galaxies with a given absolute magnitude in
with parameters ΩM = 0.26, ΩΛ = 0.74, h = 0.73, Ωb = 0.041,
n=1 and σ8 =0.8, in agreement with the 3-yr WMAP results each magnitude bin and dividing the final result by the
(Spergeletal.2007). total volume of the simulation and bin size (0.5 mag).
2 www.mpa-garching.mpg.de/galform/gadget/ We perform this procedure for the following six redshifts
(cid:13)c 0000RAS,MNRAS000,000–000
4 Salvaterra, Ferrara & Dayal
Figure 1.TheUVLFofgalaxiesatthedifferentredshiftsshownineachpanel.Observationaldata(andupperlimits)fromHUDFare
taken from Bouwens et al. (2007) for z =5,6; Oesch et al. (2010; squares), McLureet al. (2010; triangles) and Bouwens et al. (2010b;
circles) for z = 7; Bouwens et al. (2010a; squares), McLure et al. (2010; triangles) and Bouwens et al (2010b; circles) for z = 8 and
Bouwensetal.(2009)forz=10;theyareshownascircles(arrows).ThehistogramsshowthesimulatedLFwitherrorbarsrepresenting
Poissonerrors.Dotted linesaretheSchechter functionfits to theLF;the vertical short(long)-dashed linesmarkthe sensitivitylimitof
JWST(HST/WFC3).
Figure2.MapsshowingthedistributionofgalaxieswithanobservedfluxlargerthantheJWSTsensitivitylimitof1nJyintheJ-band
(leftpanel)andH-band(right).Themapsarea2Dcutofa3Dimageproducedbystackingsimulationsnapshotsbetweenz∼7.6−11.6.
Theverticalcolorbargivestheredshiftoftheobject,thesizeofthegalaxiesscaleswiththeirfluxintherange1nJy<F <24.4nJy.
(cid:13)c 0000RAS,MNRAS000,000–000
Simulating high-redshift galaxies 5
slightly larger than the one derived from the data (see Sec.
1) at z =5−6 but perfectly consistent with the recent de-
termination ofαforthez =7−8LFobtained byBouwens
et al. (2010b). This behavior is most likely produced by a
combination of the halo mass function evolution, feedback
effects and evolving stellar populations.
Clearlythefaint-endslopewillbebetterconstrainedby
forthcomingfacilities suchastheJWST;theabovesuccess-
ful test of our model allows us to make reliable predictions
for surveys that will be performed with such instruments.
For a deep exposure of 106 s, JWST is expected to reach
a photometric sensitivity of about 1 nJy (10σ) allowing an
investigation of the faint-end of the LF predicted by our
simulations at least up to z = 9 (see Fig. 1). This will be
particularly exciting because it will very likely unveil the
physical properties of these objects which are now thought
to be the main reionization sources, as we will discuss in
detail in Sec. 5. We want to stress here that our simula-
tion allow us to resolve properly (i.e. with more than 200
DM particles) the galaxy population that will be observed
by JWST, being their total halo masses > 109 M⊙. This,
toghetherwiththecarefullthreatmentofthechemicalfeed-
back,makes our predictions particularly robust.
Figure3.thecolorexcess,E(B−V),asafunctionofthestellar To give a visual idea of the high-z (z > 7.5) galaxy
mass for z ≈ 7 galaxies obtained from the simulation snapshot. population in a typical JWST field (of size 5.3 arcmin) we
The dark (light) regionshows the color excess for 65% (95%) of haveproducedthemapsshowninFig.2whichdemonstrate
thegalaxies. the wealth of objects that JWST will be able to detect up
to z ∼>11. The maps are a 2D cut of a 3D image produced
by stacking all the available simulation snapshots between
z=(5,6,7,8,9,10).TheresultsareshowninFig.1assolid z ∼ 7.6−11.6, and filling in the gaps between snapshots
histograms, where the error bars represent the Poisson er- by randomly rotating the orientation axes in all the three-
roronthenumberofgalaxiesineachmagnitudebin.These dimensions simultaneously.
theoreticalLFsarethencomparedtotheexperimentalones As it has emerged from the overview of the observa-
collectedfromthevariousanalysesoftheHUDF.Forz =10 tional results given in the Introduction, dust seems to have
weshowtheupperlimitsontheLFobtainedfromthethree onlyaminoreffectonshapingtheSEDoffainthigh-redshift
available candidates identified byBouwens et al. (2009). galaxies.Thisiseasilyunderstood,aswewillseelateron,as
Let usnowanalyze theresults shown in Fig. 1 in more aresult oftherelatively lowstellarmasses andmetallicities
detail. It is clear that the luminosity range sampled by the characterizingtheseobjects.Dustcanhoweverbecomemore
observations and our predictions is only partially overlap- important in luminous Lyman Break Galaxies (LBGs) and
ping.Thisis becauseon onehand,eventheexquisitesensi- LymanAlphaEmitters(LAEs)asmanystudieshaveshown
tivityofWFC3isnotsufficienttoproperlysamplethefaint- (Laietal.2007;Ateketal.2008;Nagamine,Zhang&Hern-
endoftheLF(MUV ∼>−18);ontheotherhand,oursimula- quist 2008; Dayal et al. 2008, 2009, 2010, 2011; Finkelstein
tions,whicharespecificallydesignedtoproperlyresolvethe et al. 2009).
veryfirstgalacticunitsinarelativelysmallvolume,lackthe The dust enrichment of galaxies can be followed self-
mostmassive,rareobjectswhichcomprisethebrightendof consistently by post-processing our simulation through the
the LF. In spite of these shortcomings, we consider it a re- modelintroducedbyDayaletal.(2010),usingwhich,wecan
warding success that the amplitudes of the theoretical and quantitatively check the previous statement. In brief, the
experimental LFs match almost perfectly, and at the same modelassumesthatdustisproducedbysupernovae(wene-
time,havequitesimilarslopesatallredshiftsforwhichdata glectherethecontributionofAGBstars,thoughseeValiante
areavailable.Thisisevenmorestrikingasnoattemptshave etal.(2009)whofoundasignificantcontributionfromthese
been made to fit or adjust the theoretical curves to the ob- objectsforpopulationages>150−200Myr)andtakinginto
served LF, i.e. they have been computed directly from the account three processes: (a) dust forms in the expanding
simulation outputwith no free extra parameters. ejecta with a yield per SNII of 0.54M⊙ (Todini & Ferrara
Ourresultssuggesttwocleartrends.First,theLFsshift 2001; Nozawa et al. 2003; Bianchi & Schneider 2007), (b)
towards fainter luminosities with increasing redshift, mim- SNIIdestroydustintheISMtheyshocktovelocities>100
icking a pure luminosity or density evolution. This is quite km s−1, with an efficiency of 0.12 (McKee 1989), and (c)
consistent with the trend of an increasing M∗ with red- a homogeneous mixture of gas and dust is assimilated into
UV
shift, foundin thedatabyseveral groups(seetheextended starformation(astration).Oncethedustmassiscalculated
discussioninOuchietal.2009),preferringapureluminosity for each galaxy in the simulation, we translate this into a
evolution. Second, the faint-end slope of the simulated LF valueofE(B−V)usingtheappropriateSNdustextinction
does not vary (within errors) from z = 5 to z = 10, main- curve given by Bianchi & Schneider (2007) as explained in
taining an almost constant valueof α=−2.0. This value is Dayal et al. (2010). The resulting values of E(B−V) for
(cid:13)c 0000RAS,MNRAS000,000–000
6 Salvaterra, Ferrara & Dayal
galaxies at z ≈ 7 are shown in Fig. 3 as a function of the lower mass galaxies the efficiency of star formation is also
stellarmass.Manygalaxies,especiallythesmallestones,are depressed and the amount of time required, once scaled by
almost dust-free, and none of them shows a dust reddening the baryonic mass of the system, is not dramatically differ-
value larger than E(B−V) = 0.009. This evidence allows ent from that of larger systems.
usto safely neglect the effects of dust on theUV LF. Taken together, Fig. 4 and 5 provide a first guess of
thepropertiesofatypicalhigh-zgalaxywithgivenabsolute
UV magnitude M . This can be useful when comparing
UV
theobserved photometric data with syntheticSEDs.
4 PROPERTIES OF FIRST GALAXIES
Fig. 6 shows the relation between the SFR and stellar
In addition to predicting the global evolution of the LF, a massofgalaxiesatz =7.Simulatedobjectsfollowanalmost
major strength of ourstudyis that it makespossible toex- linear relation with significant spread, i.e. an almost con-
tractthephysicalpropertiesofthehigh-zgalaxieswhichare stantspecificstarformationrate.Thistrendcloselymatches
apartofthefaint-endoftheLF.Westartbyconcentrating the one found in the analysis of stacked SEDs of WFC3 z-
on the stellar ages, reported in Fig. 4 as a function of the dropout by Labb´e et al. (2010b), although a single object
UV magnitude, from which the following main conclusions analysis reveals large errors in the determination of both
can be drawn. On average, fainter (and less massive) ob- thestellar massandtheSFRfortheseobjects(Gonzalezet
jects tend to be younger at all redshifts, with typical ages al. 2010). We note that simulated galaxies tend to have a
for observable objects in the range 200-300 Myr at z = 5 slightly higherSFR (forafixedstellar mass) than expected
and80-130Myratz=7−8,withthecaveatthataconsid- bytheextrapolationoftherelationtosmallerobjects.How-
erableagespreadexistsatallluminosities.Theseagesimply ever,inare-analysisoftheobservedz=7sampleincluding
thatthesegalaxies startedtoformstarsasearlyasz=9.4, theeffectofnebularcontinuumandlineemissionalongwith
clearlysuggestingthattheirUVlightmighthaveinfluenced that of dust absorption, Schaerer & de Barros (2010) find
thecosmicreionizationhistory.Fromadifferentperspective, smallerstellarmassesandlargerSFRwithrespecttoprevi-
we note that stellar ages of ∼ 100−150 Myr are expected ous works. Oursimulated galaxies lie somewhat in between
for galaxies at the sensitivity limit of WFC3 for z =7−8, thesetwo observational estimates.
in agreement with the observational estimates obtained by Fig.7showstheevolutionofthegalaxypropertiesasa
Labb´eet al. (2010a) and Finkelstein et al. (2010). functionofredshiftforgalaxieswithdifferentstellarmasses.
A second important key physical parameter of pristine The mean age of stellar population for all galaxies in the
galaxies is their stellar and gas metallicity. In the follow- simulation is found to decrease with redshift ∝ (1+z)−2;
ing we will only discuss the stellar metallicity, keeping in however,theagespreadincreasesforlessmassivegalaxiesat
mindthatthetwocloselymatcheachother.Somewhatsur- any redshift. The average stellar metallicity is also growing
prisingly (but not unexpectedly) even the faintest galaxies withtimeforM∗ >107M⊙,butshowamuchflatter(almost
appear to be already enriched to remarkable levels: at the constant)evolutioninthesmallestobjects,levelingatabout
JWST sensitivity threshold, we findZ >0.03Z⊙ at all red- 1/25Z⊙ forthetinieststar-forminggalaxies.However,even
shifts; galaxies identified by HST (MUV < −18) system- fordwarfgalaxieswithM∗ ≈105M⊙onecanfindindividual
atically show metallicities in excess of Z = 1/10Z⊙ even objects enriched up to 1/10 of solar metallicity already at
at z = 7 − 8. Thus we come to the interesting conclu- z=10.Thismass-dependentmetallicity evolutionisproba-
sion that even at these early epochs, the self-enrichment, blycausedbythedifferentabilitytoretainmetalsdeposited
due to the metals produced, following the first star forma- by supernova explosions of the massive and dwarf popula-
tion episodes is able to increase the metal abundances of tions. As thepotential wells of thelatter one are shallower,
suchsmallobjectstolevelscomparabletotheirpresent-day metalsescapeeasily intotheintergalactic mediumthusset-
counterparts(e.g.theMagellanicClouds).Inaddition,such ting an upper limit to the amount of metals than can be
high mean metallicites could in principle preclude the for- kept in their main body (Mac Low & Ferrara 1999). An
mation of Pop III stars according to the critical metallicity obvious implication is that IGM metals preferentially come
scenario (Schneider et al 2002, 2003; Schneider & Omukai fromsmallandcommonobjects,thusresultinginamoreho-
2010)whichpredictsZcr =10−5±1Z⊙ astheupperlimitfor mogeneousenrichment(Ferrara,Pettini&Shchekinov2000;
theformationofPopIIIstars.However,aswewilldiscussin Madau, Ferrara & Rees 2001).
moredetaillater,insidetheseearlystructures,smallpocket
of(quasi)pristinegasmaysurviveinwhicharelativelytiny
amount of Pop IIIstars continueto form as pointed out by 5 REIONIZATION SOURCES
TFS07andJimenez&Haiman(2006).Inbrief,thescenario
Having obtained the luminosity function and characterized
leads to the concept of a ”PopIII wave”, i.e. the physical
some of thephysical properties of thecurrent high-z candi-
phenomenonbywhichineachgalaxytheformation ofstars
dategalaxies,wenowturntoananalysisoftheirroleinthe
below the critical metallicity is progressively segregated to-
reionization process.
wards the external regions of the galaxy, where almost un-
The rate of ionizing photons from the j-th galaxy is
pollutedregionsarestillpresent.Untilthisprocesscomesto
given by
anend(whenmetalpocketsproducedaroundthefirststars
formingregionsreachaconsiderablevolumefillingfactorin n˙ =f QIIM˙II+QIIIM˙IIIτIII (2)
ion,j esc j j
the system), PopIII and PopII formation modes coexist in
(cid:2) (cid:3)
the same galaxy. One might naively think that this process whereQII (QIII)is theionizing photonfluxforPop II(Pop
can take longer in large galaxies than in small ones, but it III) stars, which of course is a function of the IMF, metal-
is (roughly) trueonly tozero-th order approximation, as in licity and stellar age of any given galaxy. Finally f is
esc
(cid:13)c 0000RAS,MNRAS000,000–000
Simulating high-redshift galaxies 7
Figure4.Meanstellarageofgalaxieslocatedatdifferentredshifts(seelabels)asafunctionoftheirabsoluteUVmagnitude.Thedark
(light) shaded area show 68% (95%) of the galaxies in the magnitude bin. The vertical short (long)-dashed lines mark the sensitivity
limitofJWST(HST/WFC3).
Figure5.Meanmetallicityofgalaxieslocatedatdifferentredshifts(seelabels)asafunctionoftheirabsoluteUVmagnitude.Thedark
(light) shaded area show 68% (95%) of the galaxies in the magnitude bin. The vertical short (long)-dashed lines mark the sensitivity
limitofJWST(HST/WFC3). ThefilledcirclerefertotheGRB050904hostgalaxyatz=6.3.
(cid:13)c 0000RAS,MNRAS000,000–000
8 Salvaterra, Ferrara & Dayal
Figure 7. Redshift evolution of the mean stellar age and metallicity for galaxies in given stellar mass ranges (see labels). The dark
(light)shadedareashow68%(95%)ofthegalaxiesintheredshiftbin.
the escape fraction of ionizing photons. For simplicity, we
assumearedshift-independentvalueoff forthetwostel-
esc
larpopulations. The ionization rateprovided bygalaxies in
thesimulation box per unit comoving volumeat redshift z,
N˙ (z), is then given by the sum over all galaxies at that
ion
redshift divided bythe volumeof thesimulation.
The actual ionization rate must also include galaxies
that are too rare to be caught in our relatively small sim-
ulation volume. To account for this correction, we add the
ionization rateduetobrightgalaxies byintegrating theob-
served LF (or the upper limits) from the luminosity of the
brightestgalaxyintheoutputdowntoverylowmagnitudes
(M =−25).Theionizingphotonfluxisobtainedusinga
UV
SEDderivedassumingthatraregalaxieshavethesamestel-
lar age and metallicity as the brightest simulated one. The
extracontribution of theunaccounted bright-end of theLF
is found to be at most 10% of the total ionizing photon
emission.
Theevolutionofthetotalspecificionizationrate,N˙ ,
ion
is plotted in the top panel of Fig. 8 (f =0.2) along with
esc
thesame rate dueto galaxies detected in the HUDF,N˙H ,
ion
or detectable by JWST, N˙J . The ratios between (N˙H ,
ion ion
N˙J ) and N˙ are also shown for clarity in the bottom
ion ion
Figure 6. Stellar mass–SFR relation for simulated galaxies at panelof thesame Figure. HSTis now resolving thesources
z = 7 (black points) compared with recent estimates for ob- that provide ≈ 1/3 of the ionizing photon budget at z = 5
served z-dropout as derived by different authors: triangles are
and ∼ 20% at z = 7−7.5. This results is consistent with
from Schaerer & de Barros (2010), open squares from Gonzales
the limits set by the observed very steep faint-end slope of
et al. (2009), and filled squares for the mean values derived by
the z = 7 − 8 LF (Bouwens et al. 2010b) and with the
Labb´eetal.(2010b).Thedottedlineshowstheempiricalrelation
estimateofrecentsemi-analyticalmodels(Choudhuryetal.
betweenthetwoquantities obtainedbyLabb´eetal.(2010a).
2008, Trenti et al. 2010).
At the sensitivity limit of JWST, it will be possible to
detect the bulk of ionizing sources up to z ∼ 7.3, but at
(cid:13)c 0000RAS,MNRAS000,000–000
Simulating high-redshift galaxies 9
higher redshifts most of the ionizing photons will still be
produced by sources that are too faint to be detected even
by JWST.
ThetotalionizationratedensityN˙ (z)shouldthenbe
ion
compared with the recombination rate density of the IGM,
N˙ (z), given by (e.g. Madau, Haardt & Rees 1999)
rec
hn i 1+z 3
N˙ = H =1050.0C s−1Mpc−3, (3)
rec htreci HII(cid:16) 7 (cid:17)
where hn i is the mean comoving hydrogen density in the
H
Universe and ht i is the volume-averaged recombination
rec
timeforionizedhydrogenwithaneffectiveHIIclumpingfac-
torC =hn2 i/hn i2.Therecombinationratedensity
HII HII HII
isshown in thetoppanelof Fig.8with dotted linesfordif-
ferentvalueoftheclumpingfactorC .Forf =0.2and
HII esc
C =10, the balance between ionization and recombina-
HII
tion is obtained at z ∼ 6.8. For f = 0.1 N˙ = N˙ at
esc ion rec
z=6 assuming C =10.
HII
6 LIGHT FROM POP III STARS
Another piece of useful information than can be extracted Figure 8. Upper panel: Redshift evolution of the total specific
ionization rate (solid line). The short (long)-dashed line corre-
from the simulation outputs is the relative fraction of nor-
sponds to galaxies detectable by JWST(HST/WFC3); dotted
mal (Pop II) and massive, metal-free (Pop III)stars. There
lines show the specific IGM recombination ratefor different val-
are several questions to which we can provide quantitative
uesoftheclumpingfactorCHII.Bottompanel:Fractionofioniz-
answer:(i)dosomeofthecurrentcandidatescontainPopIII
ingphotonscomingfromgalaxiesidentifiedbyJWSTandinthe
stars?(ii)inthatcase,whatfractionoftheirUVluminosity HUDF.Anescapefractionfesc=0.2hasbeenassumed.
ispoweredbythem?(iii)howisthisfraction dependenton
their M luminosity ? (iv) is there a clear observational
UV
signature imprinted byPop III stars ?
luminosity) will be found, due to their extreme faintness
The answer to the first question is straightforward:
having analyzed the stellar populations of the simulated (MUV ∼> −14. at z = 6). However, some objects having
≈10% of their luminosity powered by Pop IIIs are present
galaxies present at four observationally relevant redshifts,
at z = 6 at the 1 nJy sensitivity level reachable by the
z=(5,6,8,10),wefindthatafraction0.07-0.19(depending
JWST.
onz)ofthegalaxiescontainatleastsomePopIIIstars.We
Recently, many authors (Shapley et al. 2003, Nagao et
should not emphasize too much on the exact values of this
al.2008,diSeregoAlighierietal.2008)havesearchedforthe
Pop III/Pop II galaxy ratio as fluctuations in galaxy mass
HeII1640˚A emissionlineinthespectraoftheso-calleddual
andstarformationratemightintroduceaverylargedisper-
emitters,i.e.high-zgalaxiesshowingstrongemissioninboth
sion. The most robust physical quantity to understand the
LyαandHeIIlines.TheHeIIlineisusuallytakenasawell-
relative importance of the two populations is the ratio of
definedsignatureofPopIIIstars.Uptonow,thesesearches
PopIII-to-PopIIstarformation rateswhichisadecreasing
functionoftime(seeFig.1ofTFS07)neverexceeding10−3 havegivennegativeresults.Motivatedbytheseattempts,we
have computed the rest-frame equivalent width of the HeII
below z=10.
line for the objects in our simulation box as EW(HeII) =
More relevant is question (ii) above, whose answer
L(HeII)/L whereL(HeII)=5.67×10−12Q(He+)isthe
can be obtained by inspecting Fig. 9, showing the ratio, 1460˚A
L /L ofUVluminositiescontributedbyPopIIIand luminosityoftheHeIIlineinergs−1,Q(He+)istherateof
UV,III UV
Pop IIstarsasafunctionof MUV.Light from Pop IIIstars He ionizing photons, and L1460˚A is the continuum luminos-
becomes progressively more important towards fainter ob- ity at λ = 1460˚A in erg s−1 ˚A−1. In particular, we focus
jects. This confirms previous findings (e.g. Schneider et al. here on z = 6 which might be more easily accessible to
2006) that Pop III stars preferentially form in low-σ peaks presentorfutureobservations.Regretfully,theperspectives
rather than in larger galaxies whose gas has already been ofdirectdetectionofPopIIIstarsthroughthistechniquedo
enriched by several stellar generations. At the same time, not appear as very promising. Forobjects detectable in the
we do not find galaxies containing only Pop III stars: this JWST (HUDF) deep field survey, the expected HeII rest-
occurrence is made unlikely by the short lifetimes of such frame equivalent width is < 0.5 ˚A (< 0.1 ˚A). Such small
very massive stars. At z = 6 (z = 10) the contribution of EWs will be very difficult to detect. The EW increases to
Pop III stars to the total luminosity is always less than 5% more accessible values of about 10 ˚A only if much fainter
for M <−17 (M <−16). objects (M = −13) could be observed. We have to un-
UV UV UV
Among the candidate galaxies detected so far, we find derlinethattheabovediscussion impliesthatwecannotset
that Pop III stars contribute less than a few percent to limits on the total cosmic SFR in Pop III stars using the
the total galaxy luminosity. Even at the detection limit results of dual emitters searches given that thebulk of Pop
of JWST, no Pop III-dominated galaxies (∼> 50% of total III stars may be ’hidden’ in galaxies much fainter than any
(cid:13)c 0000RAS,MNRAS000,000–000
10 Salvaterra, Ferrara & Dayal
that providethebulkof theionization photonsin theearly
Universe3
. Moreover, the study of their afterglows can provide
newhintsabout themetal(and dust)contentoftheparent
galaxy.Finally,ithasbeenproposedthatevenPopIIIstars
may eventually blow as powerful GRBs (Fryer, Woosley &
Heger 2001; Yoon, Langer & Norman 2006; Hirschi 2007;
Komissarov & Barkov 2010). The observation of these Pop
III-GRBs may provide a valuable way to detected the elu-
sive, short living first stars. We will discuss these points in
thefollowing.
7.1 GRBs as metallicity probes
Fig. 5 shows the mean stellar metallicity of the simulated
sampleofhigh-z galaxiesasafunctionoftheirabsoluteUV
magnitude at different redshifts z > 5, i.e. the luminosity–
metallicity relation for such objects. Although the experi-
mentaldetermination ofsuch arelation would beof theut-
most importance in testing theoretical predictions, in prac-
ticesucheffortishamperedbytheextremedifficultytoinfer
Figure 9. Fraction of the total luminosity LUV due to Pop III Z fromlinesinthegalaxyspectrumwithavailablefacilities.
starsLUV,III asafunctionoftheabsoluteUVmagnitudeMUV. This problem can be considerably alleviated if a GRB
Theverticalshort(long)-dashedlinesmarkthesensitivitylimitof could be found inside of one of these remote galaxies. In
JWST(HST/WFC3).AbsoluteUVmagnitudesarecomputedas this case absorption features produced by heavy elements
inFig.1.
dispersed intheinterstellar medium(ISM)surroundingthe
GRB would leave a characteristic and recognizable imprint
on top of the GRB afterglow spectrum. Moreover, there is
present (and probably future) survey can detect (Scanna-
now a good agreement on that GRBs are usually hosted in
pieco, Schneider& Ferrara 2003).
relativelysmall,star-forminggalaxies(Savaglioetal.2009):
In conclusion, Pop III stars are found to form essen-
these requirements would make the dwarf high-z galaxies
tiallyatanyredshiftandin<20%ofthegalaxies.However,
which, according to our findings, are the dominant popula-
theircontributiontothetotalgalaxyluminosityisverylow,
tion during the first cosmic billion year, optimal candidate
apart from the very faint objects and their detection could
hosts.
beextremelydifficultevenwiththenextgenerationofspace
The only high-quality spectra burst at z > 6 available
telescopes.
so far, GBR 050904 at z = 6.3 (Kawai et al. 2006), shows
theexpectedmetalabsorptionfeatures,witnessingthepres-
ence of metals at the same redshift of the GRBs (Kawai et
7 EARLY GAMMA-RAY BURSTS al. 2006). From this data, and with the further assumption
thatthemeasuredsulfur([S/H]=−1.3±0.3)isagoodproxy
Long Gamma-Ray Burst (GRBs) are powerful flashes of γ-
for metallicity, one can determine the metal content of the
rays that are observed with a frequency of about one per
hostgalaxy.Bergeretal.(2007)attemptedadetectionofthe
dayoverthewholesky.Theγ−rayemissionisaccompanied
GRB host galaxy with HST and Spitzer, and were able to
byalong-lastingtail,calledafterglow,usuallydetectedover set an upper limit to the host luminosity of MUV ∼>−20.3,
tnheesswehaoslielyeloevcetrr-osmhiangensettihceslpuemctirnuomsit.yTohfeitrheexirtrhemosetbgrailgahxty- i.e. MUV ∼> MU∗V at z = 6. By combining the HST and
Spitzer upper limits, they set an upper limit to the stellar
and makes them detectable up to extreme high redshifts, mass of the galaxy, M∗ ∼<few×109 M⊙. This constraint is
as shown by the discovery of GRB 090423 at z = 8.2 (Sal-
consistent with the predictions presented in Fig. 5 (notice
vaterra et al. 2009b, Tanvir et al. 2009). Metal absorption
thedatapointcorrespondingtotheBergeretal.2007deter-
lines can often be identified in their afterglow spectra, al-
mination),whichmightindicatethatatz≈6agalaxywith
lowing a study of the metal (and dust) content of the en-
Z ≈ 0.05Z⊙ is on average 2-3 magnitudes fainter than the
vironment in which they blow. Finally, once the afterglow
detection limit of the experiment; in addition, such metal
has faded, follow-up searches of the GRB host galaxy be-
abundancelevel is quitetypical for galaxies located at that
come possible. At low redshifts, GRBs are typically found
epoch.
in blue, low-metallicity dwarf galaxies with stellar masses
M∗ ∼ 108−9 M⊙ and high specific star formation rates
(Savaglio et al. 2009). These objects closely resemble the
3 NotethatGRBsmaybebiasedtracersofthecosmicstarforma-
properties of high-z galaxies identified in our simulations,
tion rate (e.g. Daigne et al. 2006; Salvaterra & Chincarini 2007;
whosemeanspecificstarformationrates(SSFR)are≈8−10
Salvaterraetal.2009a).However,ifthisisrelatedtotheexistence
Gyr−1,albeit associated with alargespread (forM∗ >108, ofametallicitythresholdforGRBformationofZ<0.3Z⊙asre-
SSFR=1.5-7Gyr−1 atz=6−8).Thissuggeststhathigh-z quiredbythecollapsarmodel(e.g.MacFadyen&Woosley1999)
GRBs can be used as signposts of the same faint galaxies thenweexpect thathigh-z GRBscanbefaircosmictracers.
(cid:13)c 0000RAS,MNRAS000,000–000