Confronting predictions of the galaxy stellar mass function with observations at high-redshift

0.49 MB·English

by  Stephen M. Wilkins

Confronting predictions of the galaxy stellar mass function
with observations at high-redshift
Stephen M. Wilkins1(cid:63), Tiziana Di Matteo1,2, Rupert Croft1,2, Nishikanta Khandai2,3,
Yu Feng2, Andrew Bunker1, William Coulton1
1University of Oxford, Department of Physics, Denys Wilkinson Building, Keble Road, OX1 3RH, U.K.
2McWilliams Center for Cosmology, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, U.S.A.
3 3Brookhaven National Laboratory, Department of Physics, Upton, NY 11973, U.S.A.
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15January2013

n
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J ABSTRACT

2 Weinvestigatetheevolutionofthegalaxystellarmassfunctionathigh-redshift(z ≥5)
1 using a pair of large cosmological hydrodynamical simulations: MassiveBlack and
MassiveBlack-II.Bycombiningthesesimulationswecanstudythepropertiesofgalax-

] ies with stellar masses greater than 108M h−1 and (co-moving) number densities of
O (cid:12)
log (φ[Mpc−3dex−1h3]) > −8. Observational determinations of the galaxy stellar
10
C mass function at very-high redshift typically assume a relation between the observed
. UVluminosityandstellarmass-to-lightratiowhichisappliedtohigh-redshiftsamples
h
in order to estimate stellar masses. This relation can also be measured from the sim-
p
- ulations. We do this, finding two significant differences with the usual observational
o assumption: it evolves strongly with redshift and has a different shape. Using this
r relation to make a consistent comparison between galaxy stellar mass functions we
t
s find that at z = 6 and above the simulation predictions are in good agreement with
a
observed data over the whole mass range. Without using the correct UV luminosity
[
and stellar mass-to-light ratio, the discrepancy would be up to two orders of magni-

1 tudeforlargegalaxies>1010M h−1.Atz =5,howeverthestellarmassfunctionfor
(cid:12)
v low mass < 109M h−1 galaxies is overpredicted by factors of a few, consistent with
(cid:12)
5 the behaviour of the UV luminosity function, and perhaps a sign that feedback in the
8
simulation is not efficient enough for these galaxies.
6
2 Key words: galaxies: evolution - galaxies: formation - galaxies: starburst - galaxies:
1. high-redshift - ultraviolet: galaxies
0
3
1
:
v 1 INTRODUCTION identification of star forming galaxies to z = 7 − 8 (e.g.
i Bouwens et al. 2010, Oesch et al. 2010, Bunker et al. 2010,
X The observational exploration of the high-redshift (z > 2)
Wilkins et al. 2010, Wilkins et al. 2011a, Lorenzoni et al.
r Universehasbeendriven,overthepast10-15years,predom-
2011, Bouwens et al. 2011b) and potentially even to z∼10
a inantlybydeepHubbleSpaceTelescope(HST)surveys.Deep
(Bouwens et al. 2011a, Oesch et al. 2012).
AdvancedCameraforSurveys(ACS)observationsalone(of
theHUDFforexample)permittedtheidentificationoflarge
By combining ACS optical and NICMOS or WFC3
numbers of galaxies at z = 2−6 (e.g. Bunker et al. 2004,
near-IRimagingwithSpitzerIRACobservationsitbecomes
Beckwith et al. 2006, Bouwens et al. 2007). While some
possibletoprobetherest-frameUV-opticalspectralenergy
galaxies at z > 7 were identified using ACS and near-IR
distributionsofgalaxiesatz=4−8(e.g.Eylesetal.2005,
Camera and Multi-Object Spectrometer (NICMOS) obser-
Gonzalezetal.2012).Rest-frameopticalphotometryiscru-
vations (e.g. Bouwens et al. 2008) or ground based imaging
cial to accurately determine stellar masses (e.g. Eyles et
(e.g. Bouwens et al. 2008, Ouchi et al. 2009, Hickey et al.
al. 2007, Stark et al. 2009, Labb´e et al. 2010, Gonzalez et
2010)thevery-highredshiftUniversewasonlytrulyopened
al. 2011). With a sufficiently large, well defined sample of
up by the installation of Wide Field Camera 3 (WFC3) in
galaxiesitispossibletostudythegalaxystellarmassdemo-
2009. WFC3 near-IR (1.0−1.6µm) observations allow the
graphics, and in particular the galaxy stellar mass function
(e.g.Gonzalezetal.2011).Thegalaxystellarmassfunction
(GSMF) is a fundamental description of the galaxy popu-
(cid:63) E-mail:[email protected] lation and is defined as the number density of galaxies per
2 Stephen M. Wilkins et al.
Table1.MaincharactericsofMassiveBlackandMassiveBlack- majorimprovementoverpreviousversionsofGADGETisin
II simulations. Both simulations included dark matter, SPH, a the use of threads in both the gravity and SPH part of the
multiphasemodelforstarformation,andamodelforblackhole code which allows the effective use of multi core processors
accretion and feedback. The number of particles Npart is given, combined with an optimum number of MPI task per node.
the size of the simulation box Lbox, the gravitational softening The MassiveBlack simulation contains Npart =2×32003 =
length (cid:15), the number of cores used Ncores and the final redshift 65.5 billion particles in a volume of 533Mpc/h on a side
zf. Both runs were started at z =159 and used 6 threads/MPI with a gravitational smoothing length (cid:15) = 5.0kpc/h in co-
task. For MassiveBlack-II the number of cores and threads used
moving units. The gas and dark matter particle masses are
was optimized as it progressed.
m = 5.7×107M and m = 2.8×108M respectively.
g (cid:12) DM (cid:12)
The simulation has currently been run from z = 159 to
z =4.75 (beyond our original target redshift of z =6). For
Run Npart Lbox (cid:15) zf this massive calculation it is currently prohibitive to push
(Mpc/h) (kpc/h)
it to z = 0 as this would require an unreasonable amount
of computational time on the world’s current fastest super-
MassiveBlack 2×32003 533 5.0 4.75 computers.Thesimulatedredshiftrangeprobesearlystruc-
MassiveBlack-II 2×17923 100 1.85 0 ture formation and the emergence of the first galaxies and
quasars.
MassiveBlack-II (see Khandai et al. in-prep for an
overview) is a smaller volume but the mass and spatial res-
olution are better than MassiveBlack by a factor of 25 and
logarithmicstellarmassbin.ThefirstmomentoftheGSMF
2.7 respectively. The smaller volume means that a smaller
corresponds to the cosmic stellar mass density.
part of the high mass function can be sampled and that in
Hereweusestate-of-the-artcosmologicalhydrodynam-
the mass range where it overlaps with MassiveBlack it can
ical simulations of structure formation (MassiveBlack and
be used to check for convergence as well as to extend our
MassiveBlack-II) to investigate their predictions of the
predictions towards the low mass end. This is the largest
GSMFandcompareitwithcurrentconstraints.Theseruns
volume ever run at this resolution with a final redshift of
are large, high resolution simulations, with more than 65.5
z=0.
billion resolution elements used in a box of roughly cu-
These runs contain gravity and hydrodynamics but
bic gigaparsec scales (for MassiveBlack), making it by far
also extra physics (subgrid modeling) for star formation
the largest cosmological Smooth Particle Hydrodynamics
(Springel & Hernquist 2003), black holes and associated
(SPH) simulation to date with full physics of galaxy for-
feedback processes (Di Matteo et al. 2008, Di Matteo et
mation (meaning here an inclusion of radiative cooling,
al. 2012). The cosmological parameters used were: the am-
star formation, black hole growth and associated feedback
plitude of mass fluctuations, σ = 0.8, spectral index,
physics) ever carried out. The combination of the two sim- 8
n = 0.96, cosmological constant parameter Ω = 0.74,
ulations allows us to probe galaxies with stellar masses s Λ
greater than 108M h−1 and (co-moving) number densities mass density parameter Ωm = 0.26 , baryon density pa-
(cid:12)
of log (φ[Mpc−3dex−1h3]) > −8, a range well matched rameter Ωb = 0.044 and h = 0.72 (Hubble’s constant in
10 units of 100kms−1Mpc−1; WMAP5) for MassiveBlack. For
with current observations at high-redshift.
MassiveBlack-II we instead used Ω = 0.725, and Ω =
This article is organised as follows: in Section 2 we in- Λ m
0.275 (according to WMPA7).
troduce the MassiveBlack and MassiveBlack-II simulations.
InSection3weexplorethepredictedevolutionofthegalaxy Catalogues of galaxies are made from the simulation
stellar mass function, how both the intrinsic and observed outputs by first using a friends-of-friends groupfinder and
luminositiescorrelatewiththestellarmass-to-lightratioand then applying the SUBFIND algorithm (Springel 2001) to
in §3.5 compare galaxy stellar mass functions to recent ob- find gravitationally bound subhalos. The stellar component
servations. Finally, in Section 4 we present our conclusions. of each subhalo consists of a number of star particles, each
Throughout this work magnitudes are calculated using labelledwithamassandtheredshiftatwhichthestarpar-
the AB system (Oke & Gunn 1983). We assume Salpeter ticle was created.
(1955) stellar initial mass function (IMF), i.e.: ξ(m) = To generate the spectral energy distribution (SED),
dN/dm∝m−2.35. and thus broad-band photometry, of each galaxy we sum
the SEDs of each star particle (weighted by the particle
mass).TheSEDofeachstarparticleisgeneratedusingthe
Pegase.2 stellar population synthesis (SPS) code (Fioc &
2 MASSIVEBLACK AND MASSIVEBLACK-II Rocca-Volmerange 1997,1999) taking account of their ages
and metallicities. Nebula (continuum and line) emission is
2.1 Simulation runs: Massive Black and Massive
alsoaddedtoeachstarparticleSED,thoughthishasaneg-
Black-II
ligibleeffectontheUVphotometryconsideredinthiswork.
Our new simulations (see Table 1 for the parameters of In addition we apply a correction for absorption in the in-
the simulation) have been performed with the cosmological tergalactic medium (IGM) using the standard Madau et al.
TreePM-SmoothParticleHydrodynamicscodeP-GADGET, (1995)prescription(thoughagainthishasanegligibleeffect
a hybrid version of the parallel code GADGET2 (Springel onthiswork).Throughoutthisworkwemeasurethebroad-
2005)whichhasbeenextensivelymodifiedandupgradedto band UV luminosity using an idealised rest-frame top-hat
runonthenewgenerationofPetaflopscalesupercomputers filter at λ = 1500±200˚A. A rest-frame filter is chosen to
(e.g.machinesliketheupcomingBlueWatersatNCSA).The allow a consistent comparison between samples at different
Confronting predictions of the GSMF 3
redshifts.Theshapeofthisfilterisselectedforconvenience,
but closely reflects the profile of near-IR bandpasses which
are available to measure the rest-frame UV flux at high-
redshift.
We note that our work is complementary to the recent
simulation predictions of the galaxy stellar mass functions
of Jaacks et al. (2012), who compare results for a suite of
smaller simulations to the Gonzalez et al. (2011, hereafter
G11)observationaldata.Ourworkdiffersinextendingtoa
lower redshift, correcting for the effect of an evolving ratio
of UV luminosity to mass to light ratio, and also for the
inclusionofsupermassiveblackholeformationandfeedback
inoursimulations.WediscusstheJaacksetal.(2012)results
further below.
3 THE GALAXY STELLAR MASS FUNCTION
MeasuringtheGSMFfromoutputsoftheMassiveBlackand
MassiveBlack-II simulations is straightforward, given that
the total masses of star particles in each galaxy are known.
Beforemakingacomparisontoobservationaldata,however,
wemustrememberthatobservedUVluminositieswereused
(e.g.byGonzalezetal.2011,hereafterG11)tocomputethe
published observed GSMFs. This means examining the re-
lationship between UV luminosity and stellar mass to light
Figure 1. The galaxy stellar mass function measured from the
ratio in the simulation and using this information in our MassiveBlack (dashed lines) and MassiveBlack-II (solid lines)
comparison to observations. In this section, we do this, af- simulationsforz∈{5,6,7,8,9,10}.Thetworighthandaxesshow
ter first presenting the GSMF measured directly from the thenumberofgalaxiesintheMassiveBlackandMassiveBlack-II
simulations. volumes.
3.1 Galaxy Stellar Mass Function from
simulations spectralenergydistributionsofhigh-redshiftgalaxies.Rest-
frameopticalphotometryisvitaltodetermineaccuratestel-
Theevolutionofthe>108M h−1galaxystellarmassfunc-
(cid:12) larmasses.Severalstudieshaverecentlyattemptedtomea-
tion from z = 10 → 5 predicted by MassiveBlack and
surethestellarmassesofhigh-redshiftLyman-breakselected
MassiveBlack-II is shown in Fig. 1. The shape of the sim-
galaxies(e.g.Eylesetal.2007,Starketal.2009,Labb´eetal.
ulated GSMF is a declining distribution with mass and, at
2010,Gonzalezetal.2011).Withasufficientlylargesample
least at z =5, exhibits a sharp cut off at high-masses. Val-
andahandleontheincompletenessissuesitisalsopossible
uesofthenumberdensityφarealsotabulatedinTable2in
to study the galaxy stellar mass function (e.g. Stark et al.
various logarithmic mass intervals.
2009, Labb´e et al. 2010, Gonzalez et al. 2011).
Figure1alsodemonstratestheevolutioninthenormal-
To understand how to make simulation predictions
isationoftheGSMF.Atz=10thereareonly∼500galax-
it is useful to examine exactly how the G11 GSMF is
ies with stellar masses > 108M h−1 in the MassiveBlack-
(cid:12) constructed. The G11 study draws a sample of galaxies
II volume (106Mpc3h−3), while at z = 5 this has in-
from the observed UV luminosity functions (LFs) at z ∈
creased to ∼135,000 (×270). The shape of the GSMF also
{3.8,5.0,5.9,6.8} (using Bouwens et al. 2007, 2011). These
evolves strongly; while the number of galaxies with masses
UV luminosities are converted into stellar masses using
>108M h−1increasesbyafactorof×270fromz=10→5
(cid:12) the observed UV Luminosity (L ) - stellar mass-to-
thenumberofgalaxieswithmasses>1010M h−1increases 1500,obs
(cid:12) light ratio (M/L ) distribution measured at z ∼ 4.
by a factor of ×5000. 1500,obs
This relation is fairly well fit by a power law1, such that
Theevolutionofthesimulatedgalaxystellarmassfunc-
M/L ∝ L0.7 (i.e. the stellar mass-to-light ratio in-
tion is stronger than that exhibited by the UV luminosity 1500,obs
creaseswithobservedUVluminosity).Whilethisrelationis
function.ThisreflectsthefacttheaverageUVmass-to-light
calibrated at z =4 G11 note that that it appears to fit ob-
ratioofgalaxiesalsoincreasesz=10→5(asdemonstrated
servationsof stellarmassesand luminosities atz∈{5,5.9}.
in Section 3.3).
However at these redshifts the sample sizes are small (78
and 28 galaxies at z ∼5 and z ∼6 respectively) and there
3.2 Observational Estimation of the Galaxy is a large degree of scatter.
Stellar Mass Function
By combining HST optical and near-IR observations (from
ACS and NICMOS or WFC3) with Spitzer IRAC photom-
etry it is possible to measure the rest-frame UV-optical 1 ThoughthepowerlawfitisnotusedtodeterminetheGSMF.
4 Stephen M. Wilkins et al.
Table 2. The number density (in units of Mpc−3dex−1h3) of galaxies in various logarithmic mass intervals ([9.5,10.0) ≡ 9.5 ≤
log10(M)<10.0,whereM hasunitsM(cid:12)h−1)forz∈{5,6,7,8,9,10}.Wheretherearenoobjectswithinthemassintervalthenumber
densityisreplacedbyanupperlimitcorrespondington<1(i.e.φ<1/V).
MassInterval log (φ[Mpc−3dex−1h3])
10
log10([M(cid:12)h−1]) z=5 z=6 z=7 z=8 z=9 z=10
MassiveBlack Volume=(533Mpch−1)3
[9.5,10.0) −2.85 −3.50 −4.25 −5.13 −6.07 −7.88
[10.0,10.5) −3.69 −4.46 −5.35 −6.43 −7.88 <−8.18
[10.5,11.0) −4.55 −5.46 −6.80 −7.88 <−8.18 <−8.18
[11.0,11.5) −6.23 −7.88 <−8.18 <−8.18 <−8.18 <−8.18
[11.5,12.0) <−8.18 <−8.18 <−8.18 <−8.18 <−8.18 <−8.18
MassiveBlack-II Volume=(100Mpch−1)3
[8.0,8.5) −0.70 −1.06 −1.46 −1.92 −2.44 −3.03
[8.5,9.0) −1.27 −1.69 −2.15 −2.69 −3.31 −4.06
[9.0,9.5) −1.95 −2.42 −3.01 −3.71 −4.47 −5.10
[9.5,10.0) −2.76 −3.37 −4.12 −4.80 −5.70 <−6.00
[10.0,10.5) −3.57 −4.27 −4.74 −5.70 <−6.00 <−6.00
[10.5,11.0) −4.40 <−6.00 <−6.00 <−6.00 <−6.00 <−6.00
3.3 The relation between UV luminosity and the nosities (as used in Fig. 2). Attenuation due to dust both
stellar mass-to-light ratio in simulations decreases the UV luminosity (i.e. L < L ) and
1500,obs 1500
increases the stellar mass-to-light ratio (i.e. M/L >
Asnotedabove,theG11studyusesthedistributionofstel- 1500,obs
M/L )relativetotheirintrinsicvalues.Apositivecorre-
lar masses and UV luminosities measured at z∼4 to effec- 1500
lation between luminosity and dust attenuation would then
tively convert the observed UV luminosity function into a
introduce a positive correlation between M/L and
galaxy stellar mass function. To make a proper simulation 1500,obs
the observed UV luminosity.
predictionwemusttakeintoaccountanydifferencebetween
Themeasurementofdustattenuationathigh-redshiftis
therelationbetweenUVluminosityandthestellarmass-to-
challenging.Far-IRobservations,andopticalemissionlines,
light ratio used by G11 and that in the simulations.
are generally inaccesible for the bulk of the galaxy popula-
Figure 2 shows the relationship between the intrinsic
tionathigh-redshiftleavingonlytheUVcontinuumslopeβ
UV luminosity (L ) and mass-to-light ratio (M/L )
1500 1500 asadiagnostic(e.g.Meureretal.1999,Wilkinsetal.2012a,
at z ∈ {5,6,7,8,9,10} predicted by MassiveBlack-II. This
Wilkins et al. submitted). A number of recent studies have
relationshipis(overthefullmassrange)approximatelyflat
attempted to constrain the relationship between β and the
(i.e.theintrinsicstellarmass-to-lightratioisconstant)and
observed UV luminosity at high-redshift though with some
issignificantlydifferentfromtheM/L ∝L0.7relation
1500,obs conflictingresults(e.g.Stanway,McMahon,&Bunker2005,
found by G11. Jaacks et al. (2012) plotted the rest frame
Bouwensetal.2009,Wilkinsetal.2011b,Dunlopetal.2012,
UVmagnitudeagainststellarmassintheirsimulations,also
Bouwensetal.2012,Finkelsteinetal.2012).Bouwensetal.
finding a flatter relationship that than used by G11. The
(2009),Wilkinsetal.(2011b)andBouwensetal.(2012)an
lower-panel of Fig. 2 shows that the relationship between
increaseinβ withobservedluminosity.Dunlopetal.(2012)
the intrinsic UV luminosity and stellar mass-to-light ratio
and Finkelstein et al. (2012) on the other hand found little
alsovariesstronglywithredshift,increasingby0.6dexfrom
evidenceofvariationofβ withluminosity(seeWilkinsetal.
z=10→5.
submitted for a detailed comparison).
It is also interesting to note from Figure 2 that it ap-
Adoptingtherelationship(s)2betweenβandluminosity
pears the intrinsic UV luminosity of galaxies with L >
1500 found by Bouwens et al. (2012) and utilising the Meurer et
1028ergs−1h−1 can alone be used to estimate the stellar
al.(1999)calibration(betweentheobservedUVcontinuum
mass with an accuracy of ≈ 50%. This contrasts sharply
slopeβ andUVattenuation)wecandeterminetherelation-
withthelow-redshiftUniversewherestarformationhaster-
ships between the observed UV luminosity (L ) and
minated in many systems (particularly massive ellipticals) 1500,obs
observed mass-to-light ratio at z ∈{5,6,7} as predicted by
rendering the UV luminosity to be negligible. The strong
MassiveBlackandMassiveBlack-II.TheseareshowninFig.
correlationbetweenUVluminosityandstellarmassreflects
3.Themostsignificantchange(relativetothatfoundforthe
the fact that virtually all galaxies at high-redshift (in the
intrinsicluminositiesandmass-to-lightratios)isthatthere-
MassiveBlack and MassiveBlack-II simulations) continue to
lationshipbetweenL andM/L isnolongerap-
actively form stars. 1500,obs 1500,obs
3.4 The effect of dust attenuation 2 Ifaluminosityinvariantdustcorrectionwasassumedtheshape
oftheobservedUVluminosity-mass-to-lightratiorelationwould
TheG11relationishoweverbasedontheobserved(i.e.dust remainthesame(thoughtheaverageobservedmass-to-lightratio
attenuated luminosities) as opposed to the intrinsic lumi- wouldincrease).
Confronting predictions of the GSMF 5
Figure 3. The relationship between the dust attenuated (ob-
served) UV luminosity and stellar mass-to-light ratio at z ∈
{5,6,7}predictedfromMassiveBlack-IIandusingBouwensetal.
(2012)torelatedustattenuationtotheobservedUVluminosity.
Thepointsdenotethemedianvalueofthemass-to-lightratioin
eachbinwhiletheverticalerrorbars(atz=5)denotethe68.2%
confidenceinterval.ThediagonallinesdenoteM/L ∝Lγ
1500,obs
forγ={0.1,0.2,...,1.0}.Thedashedlinedenotesγ=0.7.
UV luminosity and mass-to-light ratio. We construct a vol-
ume limited sample (referred to below as “B07/B11+MB
MTOL”) of galaxy UV luminosities using the Bouwens
Figure 2.TherelationshipbetweentheintrinsicUVluminosity et al. (2007, 2011) observed UV luminosity functions. We
and stellar mass-to-light ratio at z ∈ {5,6,7,8,9,10} predicted then convert the observed UV luminosity of each galaxy to
from MassiveBlack-II. In both panels the points denote the me- a stellar mass using the relation between luminosity and
dianvalueofthemass-to-lightratioineachluminositybin.Inthe
stellar mass-to-light ratio (M/L ) predicted by the
upper-panelthe2-dhistogramshowsthedensityofsourcesona 1500,obs
MassiveBlack-II simulation (combined with the empirical
linearscaleandtheerrorbarsshowtherangeencompassingthe
dust correction described above) and construct a galaxy
central68.2%ofgalaxies.Thearrowintheupper-panelshowsthe
stellar mass function. These galaxy stellar mass functions
effectofdustattenuation(thelabelsdenotevaluesofA1500).The
dashedlineinbothpanelsshowsM/L1500∝L0.7whichprovides are shown at z ∈{5,6,7} in Fig. 4. We also show in Fig. 4
a good fit to the distribution used by Gonzalez et al. (2011) to theGSMFspredictedbyMassiveBlack/MassiveBlack-IIand
determinestellarmassesfromobservedUVluminosities. those determined by Gonzalez et al. (2011, hereafter G11)
at z ∈ {5,6,7} (the z ∼ 7 GSMF comes from Labb´e et al.
2010 but is also presented in G11).
proximately constant but is instead strongly positively cor-
From an examination of Fig. 4 it is clear that the
related,atleastatM <−19.5.AtM <−19.5
1500,obs 1500,obs B07/B11+MB MTOL sample shows a much closer corre-
theslopeofthisrelationisγ =0.5−0.8(whereγ isdefined
spondence to the simulations compared to G11. This es-
such that M/L ∝Lγ) (c.f. γ =0.7 found by G11 at
1500,obs sentially reflects the good overall agreement between the
z = 4). This suggests the physical cause of the strong ob-
simulated UV LF and the observations, at least at high-
servedcorrelationbetweenUVluminosityandmass-to-light
luminosities.TheflatteningoftherelationbetweenL
ratio is caused almost solely by the correlation of dust at- 1500,obs
andthemass-to-lightratioatlow-luminositiesdoesgosome
tenuationwithluminosity.Atlower-luminositiestherelation
way to explaining the difference in the shape of the sim-
flattens (γ <0.2). This arises due to the diminishing effect
ulated and observed galaxy stellar mass functions. More
ofdustatlower-luminosities,i.e.theL -M/L
1500,obs 1500,obs importantly however is the strong redshift evolution: from
begins to reflect the (virtually flat) intrinsic relation.
z =5→7 the calibration relating the the observed UV lu-
minositytothemass-to-lightratiodecreasesby0.3−0.5dex
(depending on the luminosity). Because the G11 study as-
3.5 Comparison with observations
sumed no redshift evolution (instead utilising a calibration
We are now in position to compare the MassiveBlack and based on observations at z ∼ 4 to convert UV luminosities
MassiveBlack-II results to observations. We follow a proce- to stellar masses at z = 4−7) this would cause the stellar
duresimilartoG11butusingthesimulatedrelationbetween masses to be overestimated. Because the GSMF declines to
6 Stephen M. Wilkins et al.
ever recent simulations of isolated galaxies (e.g. Hopkins,
Quataert&Murray2012)haveshownthat,inthepresence
of feedback, restricting star formation to molecular gas or
modifying the cooling function has very little effects on the
starformationrates.Bycontrastchangingfeedbackmecha-
nism or associated efficiencies translates in large differences
in final stellar mass densities. Based on these recent results
(albeit on idealized simulations) we are prone to interpret
our discrepancy at the low mass end to details in the stel-
larfeedbackmodel(andinparticulartoitsefficiencywhich
may be too low).
Comparing to the simulation results of Jaacks et al.
(2012) (which do not include AGN modelling), we see that
a similar sign to the disagreement with observations at low
mass.Atthehighmassend,wehaveshownthatcorrecting
for the UV luminosity-mass to light ratio assumed brings
the observations and simulations into agreement, and this
would also be likely to work for the Jaacks et al. results.
Finally, it is also worth noting that the G11 GSMF evolves
only very mildly from z = 5 → 7. Indeed, the stellar mass
density(whichisthefirstmomentoftheGSMF)ofgalaxies
with > 108M is virtually flat z = 5 → 7. This is surpris-
(cid:12)
inggiventhatallthegalaxiescontributingtotheGSMFat
these redshifts/masses are likely actively forming stars (by
virtue of being UV selected) and suggests either the high-
redshiftGSMFisoverestimatedorthelower-redshiftGSMF
underestimated.
4 CONCLUSIONS
Wehaveinvestigatedthehigh-redshift(z=5−10)evolution
Figure4.ThegalaxystellarmassfunctionpredictedbyMassive-
of the galaxy stellar mass function (GSMF) using a pair of
Black (dashed lines)and MassiveBlack-II (solid lines)compared
large cosmological hydrodynamic simulations MassiveBlack
withobservationsatz∈{5,6,7}(top,middle,andbottompanels
respectively). The open symbols in each panel show the predic- andMassiveBlack-II.Overtheredshiftrangez=10→5we
tionfortheGSMFusingtheBouwensetal.(2007,2011)observed findboththenormalisationandshapeoftheGSMFevolves
UV LF and a relationship between stellar mass and luminosity strongly with the number density of massive galaxies (>
derived from MassiveBlack-II. The filled grey points show the 108M ) increasing by a factor of around ×300.
(cid:12)
GSMF from Gonzalez et al. (2011), which was estimated using BycombiningHubbleSpaceTelescopeopticalandnear-
a non-evolving relationship between UV luminosities and stellar IR observations (from ACS, NICMOS and WFC3) with
mass to light ratios. Note that the units now implicitly assume
near-IRIRACphotometryfromtheSpitzerSpaceTelescope
h=0.7.
it is possible to identify and measure the stellar masses of
galaxiesatvery-highredshift,andthusconstraintheGSMF
(e.g. Gonzalez et al. 2011). While the simulated GSMF at
high-massesthiswouldcausethenumberdensityofsources z = 5 provides reasonable agreement with the Gonzalez et
at any mass to overestimated. al.(2011)observationsat>109.5M ,atlow-massesandat
(cid:12)
We also note from Fig. 4 that at z = 5 (and to a z>5 there is a significant discrepancy. The disagrement at
lesser extent at z = 6) this process does not fully reconcile low-masses at z = 5 is also reflected in the UV luminosity
the GSMF at low-masses. At z = 5 MassiveBlack-II over- function(LF)atlow-luminosities.However,atz>5thedis-
predicts the faint-end of the UV luminosity function rela- crepancyappearstoariseduetoadifferenceintheassumed
tive to the observations of Bouwens et al. (2007) by around relationshipbetweentheobservedUVluminosityandmass-
a factor ×5 at M = −18. This is difficult to reconcile to-light ratio. Gonzalez et al. (2011) applies a relationship
1500
observationallywithoutrequiringtheapplicationofamuch calibratedatz∼4,howeverwefindthattherelation,while
largercompletenesscorrection.Itthereforesuggeststhatthe havingasimilarform(i.e.thatthemass-to-lightratioispos-
discrepancy has its roots in the MB/MB-II modelling as- itivelycorrelatedwiththeobservedUVluminosity),evolves
sumptions. This disagreement occurs in low mass galaxies strongly with redshift. Applying a calibration based on the
which are much less affected by AGN feedback and hence simulateddistributionofUVluminositiesandstellarmasses
more sensitive to the details of the star formation model to the observed UV luminosity functions yields galaxy stel-
and stellar feedback. For example our model does not in- lar mass functions which closely reflect those predicted by
clude any treatment of the molecular gas component such thesimulations.Thissimplyreflectsthegoodagreementbe-
asine.g.KrumholtzandGnedin(2011)whichwouldtendto tween the observed and simulated intrinsic UV luminosity
suppress star formation rates in lower mass galaxies. How- functions.
Confronting predictions of the GSMF 7
Acknowledgements Salpeter,E.E.1955,ApJ,121,161
Springel,V.2005,MNRAS,364,1105
We would like to thanks Joseph Caruana and the anony-
Springel,V.,&Hernquist,L.2003,MNRAS,339,289
mous referee for useful discussions and suggestions. SMW Springel, V., White, S. D. M., Tormen, G., & Kauffmann, G.
andABacknowledgesupportfromtheScienceandTechnol- 2001,MNRAS,328,726
ogy Facilities Council. RACC thanks the Leverhulme Trust Stanway,E.R.,McMahon,R.G.,&Bunker,A.J.2005,MNRAS,
fortheirawardofaVisitingProfessorshipattheUniversity 359,1184
ofOxford.WRCacknowledgessupportfromanInstituteof Wilkins,S.M.,Gonzalez-Perez,V.,Lacey,C.G.,&Baugh,C.M.
Physics/Nuffield Foundation funded summer internship at 2012,MNRAS,424,1522
Wilkins,S.M.,Bunker,A.J.,Stanway,E.,Lorenzoni,S.,&Caru-
the University of Oxford. The simulations were run on the
ana,J.2011,MNRAS,417,717
Cray XT5 supercomputer Kraken at the National Institute
Wilkins,S.M.,Bunker,A.J.,Lorenzoni,S.,&Caruana,J.2011,
for Computational Sciences. This research has been funded
MNRAS,411,23
by the National Science Foundation (NSF) PetaApps pro-
Wilkins, S. M., Bunker, A. J., Ellis, R. S., Stark, D., Stanway,
gram, OCI-0749212 and by NSF AST-1009781. E.R.,Chiu,K.,Lorenzoni,S.,&Jarvis,M.J.2010,MNRAS,
403,938
Wilkins,S.M.,Hopkins,A.M.,Trentham,N.,&Tojeiro,R.2008,
MNRAS,391,363
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