A Deep Probe of the Galaxy Stellar Mass Functions at z~1-3 with the GOODS NICMOS Survey

1.2 MB·English

by  Alice Mortlock

Mon.Not.R.Astron.Soc.000,1–16(2002) Printed18January2011 (MNLATEXstylefilev2.2)
A Deep Probe of the Galaxy Stellar Mass Functions at
z ∼ 1 − 3
with the GOODS NICMOS Survey
1
1 Alice Mortlock1, Christopher J. Conselice1, Asa F. L. Bluck1,2, Amanda E. Bauer1,3,
0
Ruth Gru¨tzbauch1, Fernando Buitrago1, Jamie Ownsworth1
2
1Universityof Nottingham, School of Physics and Astronomy, Nottingham, NG7 2RD UK
n
2 Gemini Observatory, Hilo, Hawaii 96720, USA
a
3Anglo-Australian Observatory, PO Box 296, Epping, NSW2111, Australia
J

7
1
Accepted ??.Received??;inoriginalform??

]
A
G ABSTRACT
We use a sample of 8298 galaxies observed as part of the HST H160-band GOODS
.
h NICMOS Survey (GNS) to construct the galaxystellar mass function both as a func-
p tion of redshift and stellar mass up to z = 3.5. Our mass functions are constructed
- within the redshift range z = 1−3.5 and consist of galaxies with stellar masses of
ro M∗ = 1012M⊙ down to nearly dwarf galaxy masses of M∗ = 108.5M⊙ in the low-
t est redshift bin. We discover that a significant fraction of all massive M∗ > 1011M⊙
s
a galaxiesareinplaceuptothehighestredshiftsweprobe,withadecreasingfractionof
[ lowermass galaxiespresentat allredshifts. This is an example of ‘galaxymass down-

sizing’, and is the result of massive galaxies forming before lower mass ones, and not
2
just simply ending their star formation earlier as in traditional downsizing scenarios,
v
whose effect is seen at z < 1.5. By fitting Schechter functions to our mass functions
7
wefindthatthefaintendsloperangesfromα=−1.36to−1.73,whichissignificantly
6
8 steeperthanwhatisfoundinpreviousinvestigationsofthemassfunctionathighred-
2 shift.We demonstratethatthis steeper massfunctionbetter matches the stellarmass
. added due to star formation,thereby alleviating some of the mismatch between these
1
two measures of the evolution of galaxy mass. We furthermore examine the stellar
0
mass function divided into blue/red systems, as well as for star forming and non-star
1
1 forming galaxies. We find a similar mass downsizing present for both blue/red and
: star-forming/non-star forming galaxies, and further find that red galaxies dominate
v
at the high mass end of the mass function, but that the low mass galaxies are mostly
i
X all blue, and therefore blue galaxies are creating the steep mass functions observed
at z > 2. We furthermore show that, although there is a downsizing such that high
r
a mass galaxies are nearer their z =0 values at high redshift, this turns over at masses
M∗ ∼1010M⊙, such that the lowestmass galaxies are more commonthan galaxiesat
slight higher masses, creating a ‘dip’ in the observed galaxy mass function. We argue
that the galaxy assembly process may be driven by different mechanisms at low and
highmasses,andthattheefficiencyofthegalaxyformationprocessislowestatmasses
M∗ ∼ 1010M⊙ at 1 < z < 3. Finally, we calculate the integrated stellar mass density
for the total, blue and red populations. We find the integratedstellar mass density of
the totaland blue galaxypopulation is consistentwith being constantoverz =1−2,
while the redpopulation showsan increasein integratedstellar massdensity overthe
same redshift range.
Key words: galaxies:evolution–galaxies:general–galaxies:luminosityfunction,mass
function
1 INTRODUCTION With the continued development of instrumentation and of
new analysis techniques our knowledge of the high redshift
A deep understanding of the high redshift universe is vi- universe is increasing rapidly. Thanks to new deep imag-
talinordertocompleteourknowledgeofgalaxy formation, ing and multiobject spectroscopy we now have the power
and hence uncover the history of the universe as a whole. to routinely look back at the universe over cosmic time
2 Mortlock et al.
to witness step by step evolution. The result of this has lar mass galaxies have their star formation truncated, or
been a wealth of observations of large samples of galax- gas depleted, earlier than lower mass galaxies. This for-
ies over a large redshift range in various surveys, such as mation scenario was first observed by Cowie et al. (1996)
within GOODS (Giavalisco et al. 2004), COSMOS and z- and subsequently observed in various studies including
COSMOS (Scoville et al. 2007a and Lilly et al. 2007) and e.g.Bauer et al. (2005),Feulneret al. (2005),Bundy et al.
AEGIS (Daviset al. 2007).These large samples give usthe (2006), and Vergani et al. (2008). Downsizing is now ac-
power toachieve statistically meaningful results concerning cepted as part of the formation scenario of galaxies, but is
theevolution of galaxy properties. not yetfully understood.What is also not fully understood
As a result a detailed picture is beginning to iswhethertherelated,butdifferentprocessofmassdownsiz-
form regarding when galaxy stellar mass is built up ing,isoccurringintandem,suchthatthehighmassgalaxies
over cosmic time. Various studies (Dickinson et al. 2003, formtheirstellarmassearlierthanlowermassgalaxies,and
Drory et al. 2005, Conselice et al. 2007, Elsner et al. 2008, when this stellar mass differentiated galaxy formation pro-
P´erez-Gonz´alez et al. 2008) have focused on the change of cess first reveals itself.
stellarmassdensitywithtime,andhaveseengenerallycon- Despite the considerable work done investigating the
sistentresults.Thesestudiesfindthattheintegratedstellar high mass end of the stellar mass function, there are still
mass density decreases at higher redshift, as expected since many issues that are not yet fully understood. Firstly, the
the ongoing process of star formation increases the amount generally shape of the high redshift stellar mass function is
of stellar mass in theuniverseovertime. These studiesalso not well described. Nearby stellar mass functions are well
show that roughly 50% of the mass density of the universe fit by a form of the Schechter function, and there are vari-
is in place by z ∼ 1. This implies prior to this redshift the ous investigations regarding how the parameters of this fit
comoving stellar mass density has a more rapid evolution. change with redshift. Secondly, difficulties with obtaining
This ties in with studies that show that the star formation deep data at high redshifts mean that the low mass end of
ratepeakisat z>1−2(Madau et al.1996,Hopkins2004, thestellarmassfunctionhasnotbeenexploredasfully,orto
Hopkins& Beacom 2006). as high a redshift. More recent work has started to uncover
Whilestudiesofthestarformationhistoryhasbeenthe a possible steepening with redshift of the low stellar mass
traditional way to examine and probe galaxy evolution, a end,anda“dip”intheintermediatestellarmassrange(e.g.
greatdealofresearchhasbeencarriedoutinvestigatingthe Kajisawa 2009). It has been suggested that this is a result
evolution ofgalaxies usingthegalaxy stellarmass function. of evolution of different galaxy populations driven by their
Earlyexamplesofthemeasurementofthelocalgalaxymass mass (Bolzonella et al. 2009, Drory et al. 2009, Ilbert et al.
function at z ∼ 0 have been carried out by e.g. Cole et al. 2009b, Pozzetti et al. 2009). The exact nature and reasons
(2001)andBell et al.(2003),usingsurveyssuchas2MASS, behind such features of the stellar mass function are not
2dF, and the Sloan Digital Sky Survey. data. These and well understood, and this can only be improved upon with
otherinvestigationsconstructthestellarmassfunction,and deeper,morerobustdata.Thiswillthenleadtoabetterun-
integratedstellarmassdensitywithinthelocaluniverse,and derstanding of how the populations of galaxies, as defined
henceprovideavitalbenchmarkforcomparisonwithhigher bystellar mass, change and evolve overtime.
redshifts. In this paper we use data from the GOODS NICMOS
It is important to understand the stellar mass func- survey (GNS) to investigate how the stellar mass function
tion of the local universe in itself as this traces the inte- evolves from z = 1 to z ∼ 3.5. By examining the stel-
grated star formation and mass assembly history over the lar mass functions of galaxies ranging in stellar mass from
entire universe. However, by extending similar studies to M∗ = 1012M⊙ to as low as M∗ = 108.5M⊙ we investigate
higher redshift we can investigate not only galaxy growth when, and which galaxies are forming at various epochs in
as a function of stellar mass, but also the growth of inte- theuniverse.ThedepthoftheGNSdataissuchthatweare
grated galaxy stellar mass with time. That is, we can trace abletoprobeoverafactor of103 thestellar mass evolution
the evolution of stellar mass for galaxies of different stellar up to z ∼3.5 and importantly trace how galaxies of differ-
masses, i.e., very massive galaxies vs. lower mass galaxies, ent masses are evolving with time. Wefindthroughout this
over time. This gives us insights into the growth of galax- paper a differential in the stellar mass function and how it
iesofdifferentstellarmassesduetostarformation,mergers evolves, revealing a strong stellar mass dependence in the
and other assembly processes. Many studies have investi- galaxy formation process. We describe this and give some
gated the stellar mass function up to z =2 using relatively general explanations for how this differential evolution can
large area surveys (Fontana et al. 2004, Bundy et al. 2006, occur dueto different physical processes.
Borch et al. 2006, Franceschini et al. 2006 Bell et al. 2007, The paper is set out as follows: Section 2 discusses the
Bolzonella et al. 2009). This has been further extended to GOODS-NICMOS Survey, the galaxy sample and how the
evenhigherredshiftsusingdeepersurveys,generally within data used in this paper was obtained. Section 3.1 examines
a much smaller area (Conselice et al. 2005, Fontanaet al thegalaxystellarmassfunctionsofallthegalaxiesinvarious
2006,P´erez-Gonz´alez et al. 2008, Kajisawa 2009). redshift bins. In Sections 3.2 and 3.3 we split the galaxies
These studies of the stellar mass function at high red- into blue and red and star forming and non-star forming
shifts allows us to form a picture of the high mass end respectively.Section4describesthecalculationofthestellar
of the stellar mass function as a function of redshift. It is massdensitiesforthetotalsampleandfortheredandblue
widely agreed that the dominance of star formation within populations. Sections 5 and 6 contain the discussion and
massive galaxies ends much earlier than within low stel- summaryofourfindingsrespectively.Throughoutthispaper
lar mass galaxies by z ∼ 1 (Bundyet al. 2006). This is weassumeΩ =0.3,Ω =0.7andH =70kms−1Mpc−1.
M Λ 0
one form of galaxy downsizing, whereby the higher stel- ABmagnitudes and a Salpeter IMFare used throughout.
Galaxy Stellar Mass Functions in the GNS 3
2 DATA REDUCTION AND THE GNS Therefore in this case, not only does the code find the best
fitredshiftsolutionandspectraltype,italsoconsidereshow
2.1 The GOODS-NICMOS Survey
likely it is to find a galaxy of that type and magnitude at
The galaxy sample used in this work is taken from and that redshift.
imaged as part of the GOODS-NICMOS Survey (GNS) A total of 906 spectroscopic redshifts are avali-
(Conselice et al.2011).TheGNSconsists of60pointingsof able for comparison with our photometric redshifts from
the HST NICMOS-3 camera utilising a total of 180 orbits. the GOODS-N (Barger, Cowie, & Wang 2008) and the
The field of view of NICMOS-3 is 51.2 arcsec x 51.2 arcsec GOODS-S(Wuytset al.2008)fields.Thereliabilityofpho-
with a pixelscale of 0.203 arcsec/pixel. Each NIC3 tile was tometric redshifts is defined as ∆z/(1 + z) = (zspec −
observedinsixexposures,whichcombinedgiveapixelscale zphot)/(1+zspec), themedian error (h∆z/(1+z)i) and the
of 0.1 arcsec/pixel with apoint spread function (PSF) of ∼ r.m.s(σ)areasfollows. ForHYPERZ,theGOODS-Ngives
0.3 arcsec full width half maximum (FWHM). Within the h∆z/(1+z)i = 0.027 with σ=0.04, and for the GOODS-S
GNS we find8298 galaxies in the H band (F160W), and h∆z/(1+z)i = 0.043 with σ=0.04. For BPZ, the GOODS-
160
the 60 pointings are designed to contain as many massive N h∆z/(1+z)i = 0.07 with σ=0.05 and for the GOODS-S
galaxies(M∗ >1011M⊙)aspossible.Thesemassivegalaxies h∆z/(1+z)i=0.07withσ=0.06.Inbothcodestheextreme
areintheredshiftrangez =1.7−2.9andatadepthofthree catastrophic outliers, as defined by |∆z/(1+z)| > 0.5, are
orbits. The galaxies are redshift selected based on their op- around ∼6%. The dependence of the redshift on the H160
tical to infrared colour described in Conselice et al. (2011). magnitudeshows thereliability ofredshift within ourselec-
Details on the data reduction pipeline are described in tionmethodsandinthiscaseHYPERZshowsaslightlybet-
Magee, Bouwens & Illingworth (2007). The detections and ter performance (Gru¨tzbauch et al. 2011). Our work shows
photometry were doneusingSExtractor (Bertin & Arnouts good agreement with photometric redshifts from past sur-
1996).At5σthelimitingmagnitudeisH =26.8,amarked veys (e.g. FIREWORKS), although our sample is bright,
160
improvementontheGOODSgroundbaseddataatK =24.5 and it is unclear if this would be the case for fainter galax-
(Retzlaff et al. 2009). Further description of the GNS, the ies.
pointingsandthetargetselectionisgiveninConselice et al. Wefurtherinvestigatetheperformance ofHYPERZat
(2011). Other analysis of the GNS data set can be found different redshifts, at low redshift (z <1.5) and in the red-
in Buitrago et al. (2008), Bluck et al. (2009), Bauer et al. shift range of 1.5 6 z 6 3, which is the redshift range of
(2010, submitted), Bluck et al. (2010), Gru¨tzbauch et al. thegalaxysampleweuseinthisstudy.Forthehighredshift
(2011). sampleweobtainanaverageoffseth∆z/(1+z)i=0.06 and
a RMS of σ =0.10, with a fraction of catastrophic
∆z/(1+z)
outliers of 20%. Here catastrophic outliers are defined as
2.2 Photometric Redshifts
galaxies with |∆z/(1+z)| > 0.3, which corresponds to ∼
Thanks to the large amount of optical data covering the 3 times the RMS scatter. Galaxies below z = 1.5 show a
GOODS fields, the H160 band sources are matched to a slightly lower, but still comparable scatter of σ∆z/(1+z) =
catalogue of B,V,i and z band data. This photometry is 0.08, however the outlier fraction decreases dramatically to
avaliable down to a limiting magnitude of B∼28.2, and the only∼2%.Furthermore,wesimulatetheeffectsofthepho-
matching is done within a radius of 2′′. However the mean tometricredshifterrorsonourresultsthroughoutthispaper.
separation between the optical and H band coordinates
160
is markedly better than this with hri ∼0.28±0.4”, which
is roughly the resolution of NICMOS. With this multiband 2.3 Stellar Masses and Colours
datatemplatespectrawefittotheBVizHphotometricdata
The stellar masses we use are obtained from the same
points. This was handled in two different ways to overcome
BVizH catalogue as used to measure the photometric red-
thedegeneracy in colour-redshift space.
shifts described previously, using a standard multicolour
The first uses HYPERZ (Bolzonella et al. 2009) which
is the standard χ2 minimisation technique. HYPERZ uses stellar population fitting technique (e.g., Conselice et al.
2008 and Conselice et al. 2011). The photometry is fit to
model spectra which were constructed using the evolution-
different star formation histories, based on the redshift of
arycodesofBruzual & Charlot(1993).Hereweusefiveevo-
thegalaxy,withspectroscopicredshiftsusedwhenavaliable.
lutionary types, E, Sa, Sc, Im and a single burst scenario.
This produces a distribution of likely stellar masses, rest
ThereddeninglawisthatofCalzetti et al.(2000).Themost
frame optical colours and various other parameters based
likely redshift is then computed in the age, metalicity, red-
on a Baysian approach. The model SEDs are constructed
dening parameter space, giving the best fit redshift, corre-
fromBruzual & Charlot(2003)models,andthestarforma-
spondingprobabilityandseveralotherbestfitparameteres.
tion history is characterised by an exponentially declining
Thesecondmethodusedtoobtainourphotometricred-
model with various ages, metalicities and dust extinctions.
shiftsistheBayesianapproachusingBPZ.Thisisasimilar
The star formation rate is parameterised by an e-folding
fitting method to HYPERZ but employs empirical SEDs
time and an age such that,
ratherthanmodelones.Aswellasthis,BPZ usesthemax-
imum likelihood in the same parameter space as HYPERZ, SFR(t)∼SFR ×e−τt. (1)
0
butwiththeadditionofempiricalinformationregardingthe
likelihood of a certain combination of parameters. This is The parameters in Equation 1 are varied randomly within
knownaspriorinformation,orpriors.Here,weusedthedis- the ranges; τ=0.01 to 10 Gyrs, t=0 to 10 Gyrs, metallic-
tribution of magnitudes of different galaxy types as a func- ity= 0.0001 to 0.05 and the dust content is parameterised
tion of redshift as the priors (from HDF-N, Ben´ıtez 2000). by τ =0.0, 0.5, 1, 2. These model SEDs are then fit to the
v
4 Mortlock et al.
observedphotometricdatapointsusingaBayesianapproach near-ultraviolet band and z ∼2 galaxies show that the UV
resultinginalikelihooddistributionofstellarmass,ageand slope from the local starburst relation can be used to re-
absolutemagnitudeforeachpossiblestarformationhistory. coverthedustattenuation ofavast majority of moderately
The stellar mass is determined based on this distribution, luminous galaxies at z ∼ 2 (Buat et al. 2005, Seibert et al.
where the most likely stellar mass produces a peak in the 2005, Reddyet al. 2010).
distribution, and theuncertainty isthewidth. Thefinal er- To determine the UV slope, we use the SED-fitting
rorsproducedarearesultofthemodelsusedandarefound procedure. We fit a spectral energy distribution (SED) to
tobein therange0.2 to0.3dex.Whileseveral oftheother multi-wavelengthobservationsfromopticaltomid-infrared,
parameters produced by this method are not reliable, the following the procedure described in P´erez-Gonz´alez et al.
stellarmassesandcoloursarerobust(seeBundyet al.2006 (2008) and Bauer et al. (2011). Briefly, the UV through
andConselice et al.2007forfurtherexplanation.).Itisalso MIR SEDs obtained for all sources in the GOODS fields
possible that the stellar masses are an overestimate dueto were fitted with stellar population synthesis models. Then,
the poor treatment of the TP-AGB phase in a star’s life. thebest-fittingtemplateswereusedtogetsyntheticestima-
Theeffectsofthisaremuchlessimportantattherestframe tionsoftheUVemissionat1600˚Aand2800˚A.Fromthesyn-
wavelengthsusedinthisstudy,especially intheinfraredH- thetic,model-derivedUVluminositiesat1600˚Aand2800˚A,
band. By using the newer models of Bruzual and Charlot wecalculatethespectralslope,β.WeusetheCalzetti et al.
(2010) which include a more proper treatment of TP-AGB (2000) law to derive A from the UV spectral slope,
2800
starswefinditonlylowersthemassesinourmassivegalaxy whichwethenapplytotheUV-derivedstarformationrates.
sample by <0.07 dex. This effect is much smaller than the Using this method we find an average extinction value of
stellar mass error and the effects of cosmic variance and it A = 1.6 ± 1.2 mag. We find that all galaxies in the
2800
is therefore considered negligible in this work. GNS exhibit a range in SFRUV,corr between 0.2 M⊙yr−1
and∼2000M⊙yr−1.Afulldescriptionofourstarformation
measure is provided in Bauer et al. (2011).
2.4 Star Formation Rates
Toobtainstarformationrates(SFRs)forourGNSgalaxies
weusetherest-frameultraviolet(UV)luminosity,whichwe 3 THE STELLAR MASS FUNCTIONS
derive from observed rest frame optical light following the
3.1 Total Stellar Mass Function
procedure described in Bauer et al. (2010, submitted). The
UVluminosity is closely related tothelevel of ongoing star Toconstructgalaxystellarmassfunctionsourdatahasbeen
formation because it is mainly produced by short-lived O splitintofiveredshiftbinsbetweenz=1andz=3.5.These
and B stars. An advantage of using UV light to estimate arechosentohaveroughlythesamecomovingvolumetore-
star formation is that it remains largely unaffected by the ducefluctuationsinthetotalnumberofgalaxies. Thehigh-
age-metallicity degeneracy (Worthey 1994), but as is well est redshift bin, z =3 to 3.5, contains around 300 galaxies,
known,starformation rateestimatesderivedfromUVlight thus we maintain a good sample size throughout. However,
are strongly affected by dust extinction. we exclude the final redshift bin from much of our analysis
The2800˚Arest-frameluminosityiscalculatedfromthe as,in thatredshift range, theH-bandisnolongersampling
observed optical Hubble/ACS z-band flux density, which primarily optical lightand no longer provides a good mea-
corresponds to rest-frame wavelengths of 3400 - 2125˚A for sure of the balmer break, thus we find larger errors in the
z = 1.5 −3 galaxies. To derive SFRUV we apply a sim- measurement of stellar masses.
ple K-correction derived from the redshift of each object as We calculate the number densities, i.e. the number of
log(1+z) (Kim et al. 1996, Daddiet al. 2004) and use the galaxies per co-moving volume per mass interval, and plot
Kennicutt (1998) conversion from 2800˚A luminosity to star the stellar mass functions for each redshift bin in Figure 1.
formation rate assuming a Salpeter IMF: PlottedforcomparisoninFigure1,asasolidblackcurve,is
SFRUV(M⊙yr−1)=1.4×10−28Lν(ergs s−1Hz−1). (2) thelocal stellar mass function from Cole et al. (2001). Also
plottedistheverticallinethatindicatesthemasslimitofthe
Beforedustextinctionistakenintoaccount(Section2.5),we surveyineachredshiftbin(explanationofthecalculationfor
findatz=1.5alimitingSFRUV =0.28±0.1M⊙yr−1andat thiscanbefoundinSection3.1.1).Theselowerlimitsareat
z=3.0,wefindalimitofSFRUV =0.98±0.3M⊙yr−1.The a very low stellar mass compared with other work such as
errorstakeintoaccountphotometricerrorsandtheerrorin Marchesini et al. (2009), P´erez-Gonz´alez et al. (2008) and
the conversion from a luminosity to a star formation rate Fontanaet al (2006), who do not probe stellar masses as
(see also Bauer et al. (2011, in prep.). low as we do(see Section 5 for discussion of this).
2.5 Dust Correction 3.1.1 High Mass Bias and Completeness
To obtain reliable star formation rates from the rest-frame The GNS is specifically intended to maximise the popula-
ultraviolet, we need to account for the amount of light ob- tionofhighmassgalaxies,andhencethegalaxysamplewill
scuredbydust,whichisanon-trivialproblem.Meurer et al. containmoregalaxieswithM∗ >1011M⊙ thanexpectedfor
(1999) demonstrated a correlation between dust attenua- arandomlypositionedsurvey.Thehighmassendofthestel-
tion and rest-frame UV slope, β, for a sample of nearby larmassfunctioniscorrectedforthisbycomputingtheratio
starburst galaxies (where F ∼ λβ). Updated studies of lo- ofhighmassgalaxiesintheGNSpointingstothenumberof
λ
cal galaxies using the Galaxy Evolution Explorer (GALEX) highmassgalaxiesinthetotalGOODSfields.Bycomparing
Galaxy Stellar Mass Functions in the GNS 5
Figure 1. The galaxy stellar mass function between redshifts z =1−3.5 in the GNS. The dashed green curve is the Schechter fit to
the data. The black points are the data that has been fitted, and the red points are the data that has been left out of the fit due to
incompleteness.ThefinalredshiftbinisrepresentedbyopencirclesasitisnotincludedinthebulkofouranalysisasdiscussedinSection
3.1.Thesolidpinkverticallinesshow thetheoretical masslimitsofthe GNSsurvey(seeSection 3.1.1).Alsoincludedforcomparionis
thesolidblacklinewhichrepresents the localgalaxy stellarmassfunctionofColeetal.(2001).Thedata usedtoconstruct thesemass
functionscanbefoundinTable1
Figure2.TheparameterresultsoftheSchechterfits.Left:TheresultsofthefittingforM∗withallparametersfree,Middle:Theresult
of the fitting for α with M∗ held constant (see Table 2), and Right: The results of the fitting for φ∗ with M∗ held constant. For each
paneltheblackcirclesaretheresultsfromthiswork,theredtrianglesareP´erez-Gonz´alez etal.(2008)results,thegreensquaresarethe
Kajisawa (2009) results (from three different SED models) and the pink stars (pink line for middle panel) are the Elsneretal. (2008)
results.Foreachpanel thefinal redshiftpointisplotted asanopencircleas itisnot consideredintheanalysis.Theparameters ofthe
finalredshiftbinarerepresentedbyopencirclesastheyarenotincludedinthebulkofouranalysisasdiscussedinSection3.1.
6 Mortlock et al.
RedshiftRange M∗ φ(×10−4) α
1.0to1.5 11.43 6.01±1.05 -1.36±0.05
1.5to2.0 11.43 7.53±1.23 -1.19±0.06
2.0to2.5 11.43 3.52±0.89 -1.50±0.08
2.5to3.0 11.43 1.11±0.36 -1.89±0.11
3.0to3.5 11.43 0.89±0.22 -1.73±0.09
Table 2.ThevaluesoftheparametersfromtheSchechter fit.M∗ isthemeanvaluefromfittingwithallparametersfree.φ∗ andαare
theresultoftheSchechter fitwithM∗ heldconstant.
this to the fraction of the area that the pointings covered, P´erez-Gonz´alez et al. (2008) andElsner et al. (2008)(these
weobtain acorrection factor for theoverdensityof galaxies points can also be seen in the left hand panel of Figure 2).
withM∗ >1011M⊙,findingavalueof3.05.Thehighstellar WethenrepeatthefittingholdingM∗ constantatitsmean
mass galaxies (M∗ > 1011M⊙) in the redshift bins 2.0 to value (see Table 2) over the whole redshift range, which al-
2.5 and 2.5 to 3.0 were thus divided by 3.05 before fitting lowsforabetterconstraintonαandφ∗.Somepreviouswork
(Conselice et al. 2011). havefoundaconstantαuptoz∼2(e.g.Fontana et al.2004
Anotherproblem in constructingthestellar mass func- and Borch et al. 2006). In this work we find no evidence of
tions is incompleteness at the low mass end. As mentioned this, hencewe only use a constant M∗ for investigating the
previously,Figure1showsthemasslimitofthesurvey.This evolutionofαandφ∗ at1<z<3.Thevaluesofthefitting
isapurelytheoreticalmasslimitcalculatedfromthecentral parametersareshown in Table2andalso compared topre-
wavelengthoftheNICMOScamera.Weusethistocalculate vious work in Figure 2. For this repeated fitting we do not
therest frame band observed byNICMOS for each redshift combine the high mass points as before, as the high mass
bin.Fromthiswecalculatethemasstolightratiosofamax- end of the stellar mass function is already well constrained
imally old stellar population, again for each redshift range. byM∗.
Wecombinedthiswiththeluminositylimitcalculated from
thelimitingmagnitudeofthesurveyandtheluminositydis-
tance for each redshift bin. This gave us the mass limit of
3.1.3 Errors and Simulations
thesurveyrepresentedbythepinkverticallinein Figure1.
Figure 1shows thatgalaxies appeartodrop outbefore WecalculateerrorsonournumberdensitiesusingtwoMonte
the calculated mass limit. This is due to the pipeline de- Carlosimulationstakingintoaccountthe1σGaussianmea-
tection being less sensitive to galaxies at the low mass end sured error on the stellar masses and accounting for errors
(Conselice et al. 2011), thuswe do not include these points on the redshifts. We first use the measured error on each
in our fits. To determine when this occurs we look at the stellar mass and compute a Gaussian distribution of simu-
residualsbetweenthelocalmassfunctionandthecalculated lated stellar masses, for each galaxy, between ±3σ of their
number densities. A change in trend of the residual repre- measured error. Then a new stellar mass was randomly se-
sents the loss of completeness and we do not fit below this lected from this Gaussian distribution, so that we obtain
partofthestellarmassfunction.Thepointsnotincludedin a simulated stellar mass for each galaxy. We then recalcu-
thefit are thered points in Figure 1 latethenumberdensitiesin thesamewayaswedidfor the
originalcatalogueofstellarmasses,andtheerrorduetothe
cataloguemasserror,isthedifferencebetweenthesimulated
3.1.2 Fitting the Schechter Function numberdensity and theoriginal catalogue numberdensity.
Forthephotometricredshifterrorsweconstructacata-
We fit our stellar mass functions, within the errors on
logueofsimulatedredshiftsusingthesameGaussianmethod
the number densities, with a Schechter function (Schechter
weusetoobtainthesimulatedstellarmassesdescribedpre-
1976) of the form
viously.WeassumeGaussianerrorsonthephotometricred-
φ(M)=φ∗·log(10)·[10(M−M∗)](1+α)·exp[−10(M−M∗)]. (3) shifts,anddonotconsiderthecatastrophicoutliers.Wethen
calculate the luminosity distance for both the original and
InthisequationtheparameterM∗isthecharacteristicmass thesimulatedredshiftsofeachgalaxy.Wecalculatetheratio
at which the stellar mass function turns over, α parame- of these two luminosity distances and assume this is equal
terises the slope of the faint end of the stellar mass func- to the ratio of stellar masses. By multiplying the original
tion,andφ∗ isthescalefactor.Thefirstfittingofthestellar galaxy stellar mass by the luminosity distance squared ra-
mass functionswe performed was donebyleaving all of the tio,weobtainanewsimulatedgalaxystellarmass.Asbefore
three parameters free. For the redshift bins z = 2 − 2.5 we then recalculated the number densities using this cata-
and z = 2.5 − 3 we find that the highest mass points logueofsimulated stellarmasses, thensubtract theoriginal
(M∗ > 1011M⊙) have extremely large errors. To help con- stellar mass from the simulated stellar mass to obtain the
strain the high mass end we combine the highmass points error. We then add the stellar mass and redshift errors in
into onepoint in theseredshift bins. quadrature,aswellastheerrorduetoPoisson statistics, to
The left hand panel of Figure 2 shows the results of obtainthetotalerroroneachnumberdensity.Thesearethe
M∗ for the first fitting, where we find there is very little errors shown on Figure 1.
change in M∗ over redshift (except at z = 3−3.5). This We also simulate independently the effects of the mea-
is in good agreement with various other studies such as surederrorsonthestellarmassfunctionbyrandomlyalter-
Galaxy Stellar Mass Functions in the GNS 7
ing each stellar mass by ±0.25 dex. We chose this number
RedshiftRange logM∗[h−702M⊙] logφ[h370Mpc−3/logM] toinvestigatetheextremesoftheeffectoflargeerrors.This
1.0to1.5 8.6 -1.79±0.12 showshowamassbincontaininglessgalaxieswillbeeffected
8.9 -1.83±0.12 bytheerrorsonthestellarmassmorethanafullermassbin.
9.1 -1.99±0.11 This is due to the Eddington bias, i.e. if a mass bin is rela-
9.4 -2.06±0.12 tively empty,galaxies from nearby fuller bins will spill over
9.6 -2.31±0.13
in to these bins more readily due to measurement errors.
9.9 -2.40±0.12
We reanalyse the altered masses and find that the largest
10.1 -2.48±0.13
10.4 -2.60±0.13 variationisintheemptier,highmassbins.Thesevariations
10.6 -2.67±0.13 liewithinthecalculatederrorsonthenumberdensitiesand
10.9 -2.55±0.14 thus we can still reconstruct the same Schechter function
11.1 -2.89±0.15 parameters.
11.4 -3.17±0.15
11.6 -3.47±0.18
11.9 -4.17±0.24 3.1.4 Inspection of the Mass Functions
1.5to2.0 9.4 -2.38±0.12
9.6 -2.37±0.13 There are several features that can be noted through in-
9.9 -2.54±0.12 spection of thestellar mass functions, and from thebest fit
10.1 -2.56±0.13 parameters. Firstly, the massive galaxies (M∗ > 1011M⊙)
10.4 -2.57±0.13 are present, with a similar number density as at z = 0, up
10.6 -2.64±0.13 to a redshift z = 3. The low mass galaxies do not reach
10.9 -2.68±0.13
thelocalvalueofthenumberdensityuntilafterthemassive
11.1 -3.02±0.14
galaxies. This is a downsizing in terms of stellar mass over
11.4 -3.04±0.15
11.6 -3.55±0.20 a large range. Wediscuss this furtherin Section 5.
11.9 -3.95±0.25 The intermediate stellar mass galaxies (M∗ ∼109.5M⊙
12.1 -4.25±0.27 to M∗ ∼1011M⊙) show a decreased rate of formation com-
2.0to2.5 9.4 -2.17±0.12 paredtothelowerstellarmassgalaxies.Thismanifestsitself
9.6 -2.15±0.12 mostclearlyinthelowestredshiftbinasadipinthegalaxy
9.9 -2.21±0.12 stellarmassfunctionintheintermediatestellarmassrange.
10.1 -2.32±0.13 This feature is also possibly present between redshifts of
10.4 -2.62±0.13 z =2−3, although less obvious. We discuss this feature in
10.6 -2.70±0.13
Section 5
10.9 -2.89±0.13
As noted before we find a general trend for α is to
11.1 -3.45±0.42
11.4 -3.64±0.46 increase at higher redshift, as shown by the black line in
11.6 -3.98±0.54 the middle panel of Figure 2. We also find that our values
11.9 -4.75±1.81 of α are more negative (therefore steeper) than found in
2.5to3.0 9.6 -2.07±0.13 previous studies. The middel panel of Figure 2 shows that
9.9 -2.21±0.12 our results for α are steeper than Elsner et al. (2008) and
10.1 -2.31±0.13 P´erez-Gonz´alez et al. (2008). This is also thecase for other
10.4 -2.68±0.14 studies, including Fontanaet al. (2004) (held α constant at
10.6 -3.01±0.14 −1.27/ −1.36 from z = 1−2) and Fontanaet al (2006)
10.9 -3.09±0.14
(α= −1.27 to −1.47 from z = 1.15−3.5). We do however
11.1 -3.85±0.47
find a similarity between our results and Kajisawa (2009)
11.4 -3.98±0.49
11.6 -4.15±0.53 whoexplore a similar redshift range and stellar mass depth
11.9 -4.75±0.81 to us. We find that φ∗ is decreasing at higher redshift, as
3.0to3.5 9.6 -2.45±0.12 demonstrated by the straight line fit to the right panel of
9.9 -2.56±0.13 Figure 2. The overall decrease in φ∗ represents the overall
10.1 -2.62±0.13 decreaseinnumberdensity,asisexpectedathigherredshifts
10.4 -2.88±0.14 since fewer galaxies havehad time to form.
10.6 -2.98±0.14
10.9 -3.14±0.16
11.1 -3.96±0.20 3.2 Blue/Red Mass Functions
11.4 -3.78±0.17
11.6 -3.96±0.19 Toobtainthegalaxystellarmassfunctionsfortheblueand
11.9 -3.96±0.19 red galaxy populations we divided the galaxies by colour.
12.1 -3.96±0.22 Thiswasdonebydividingthesampleusingtheredsequence
equation,
Table 1. The total galaxy stellar mass functions seen inFigure
1 (U−B)=−0.032(MB+21.52)+1.284−0.25, (4)
from Willmer et al. (2006), modified for the AB magnitude
system.Theequationappliesatredshiftofz =1.0,hencewe
modified Equation 4 to account for redshift evolution. This
wasdonebyusingtheredshift evolution oftheluminosities
8 Mortlock et al.
Figure3.Thedivisionoftheredandbluegalaxypopulations.Thesolidblacklinerepresentsthecolourcutusedtodividethegalaxies
intotheirrespectivepopulations correctedforredshiftevolution.
RedshiftRange M∗ φ(×10−4) α
1.0to1.5 Blue 11.51±0.15 3.07±1.35 -1.48±0.06
Red 11.41±0.16 2.88±1.09 -0.60±0.19
1.5to2.0 Blue 11.06±0.14 6.94±3.23 -1.27±0.13
Red 11.13±0.12 8.42±1.69 0.03±0.30
2.0to2.5 Blue 10.68±0.21 14.19±10.16 -1.38±0.26
Red 10.58±0.24 4.79±1.75 0.82±0.63
2.5to3.0 Blue 10.67±0.24 10.21±9.40 -1.60±0.29
Red 11.11±0.29 1.92±0.85 -0.06±0.54
Table 3.Thevaluesoftheparameters fromtheSchechter fittotheblueandredgalaxypopulation.
and colours of galaxies from van Dokkum& Franx (2001). 3.1.3).Theresultingcolourstellarmassfunctionsareshown
This allowed us to obtain a change in M and (U − B) in Figure 4. Here the blue and red solid lines represent the
B
at higher redshifts due to passive evolution. The change is Schechter fits to the blue and red galaxy populations, and
thenincludedintheequationsothat theright handsideof thesolidblackcurveisthelocalgalaxystellarmassfunction
Equation 4 becomes ofCole et al.(2001).Thegreenpointsarethepointsthatare
not included in thefitting of the blue population. Both the
−0.032(MB−∆MB+21.52)+1.284−0.25+∆(U−B).(5) blueand red stellar mass functionsare fitusing equation 3.
InthiscaseweseenoevidenceforaconstantM∗,andthus
We then apply the cut so that if (U −B) is greater than
we leave all parameters free when fitting. This is discussed
Equation 5 the galaxy is red, and if (U −B) is less than
furtherin Section 5 in terms of implied evolution.
Equation5thegalaxyisblue.TheresultscanbeseeninFig-
ure3,wherethered/bluetriangles/squaresarethered/blue
galaxies and theblack line is thecolour cut.
3.2.1 Inspection of the Blue/Red Mass Functions
Afterapplyingthiscolourcutwesplittheblueandred
galaxy populations into the same redshift bins as before, The colour stellar mass functions in Figure 4, like the to-
andthenumberdensitiescomputedinthesamewayforeach talstellarmassfunctions,showstellarmassdownsizing.We
colour.Alsotheerrorsonthesemassfunctionsarecomputed see that even in the redshift range z = 2.5−3, red and
exactly as before using our Monte Carlo approach (Section blue galaxies at M∗ > 1011.5M⊙ are present with number
Galaxy Stellar Mass Functions in the GNS 9
Figure4.Thecolourdividedgalaxystellarmassfunctions.Theredandbluepointsrepresentstellarmassfunctionsoftheredandblue
galaxy populations as defined in Section 3.2. The green points are the points not included in the Schechter fit. The solidred and blue
curvesaretheSchechter fits.ThesolidblackcurveisthelocalgalaxystellarmassfunctionofColeetal.(2001).Thesolidpinkvertical
lineisthetheoretical masslimitofthissurvey(seeSection3.1.1).
Figure 5.The Schechter fit parameters of the blueand red galaxy stellar mass functions. Left: The results of the fitting for M∗. The
blue/redpoints areM∗ fortheblue/redgalaxypopulations whenalloftheparameters arefree.Middle:Theresultofthefittingforα.
The blue/red points are α for the blue/red galaxy populations when M∗ is held constant. Right: The result of the fitting for φ∗. The
blue/redpointsareαfortheblue/redgalaxypopulationswhenM∗ isheldconstant. Alltheredpointsareoffsetby0.05inredshiftfor
clarity.
10 Mortlock et al.
densities very close to the local value. In the redshift bin forming/non-star forminggalaxies matchtheblue/red pop-
z = 1−1.5 we see that both the red and the blue galaxies ulations within the errors plotted. However there is some
with M∗ > 1011.5M⊙ are nearly fully in place, whereas the slight disagreement at the high mass end of the mass func-
low stellar mass galaxies havenot formed as quickly. tionsin therangez=2−3.Thehighest mass starforming
ThelowstellarmassendshowninFigure4isdominated galaxies are better represented by the red Schechter func-
by blue galaxies at z < 3, and their number densities are tion, this is likely the result of the presence of dusty star
close to the local stellar mass function out to a redshift of formation (Bauer et al. (2011), Gru¨tzbauch et al. (2011).
z=3.Thismeansthatthesteepnessoftheslopeinthetotal
stellar mass function (Figure 1) is dominated by low mass
blue galaxies. For the blue galaxies themselves α remains
4 INTEGRATED STELLAR MASS DENSITIES
roughly constant and φ∗ is constant within the error bars.
This is shown in Figure 5. The parameter M∗ on the other
hand,showsageneraldeclineunlikewhatweseeinthetotal
stellar mass functions.
For the red population, the fitted value of α shows a
generalincrease(lesssteep)athigherredshifts,whichisalso
thecasefortheparameterM∗.Contrarytothis,theparam-
eterφ∗ showsverylittlevariation.Unfortunately,wedonot
havegoodnumberstatisticsforthestellarmassfunctionsof
theredpopulation(intherangez=2.5−3thereare26red
galaxiescomparedto639blue).Wealsohavelargeerrorson
the high mass galaxies over z =2−3, and hence the fit to
theredstellarmassfunctionsdonotproviderobustresults.
To this end, we cannot make any strong conclusions about
theevolution of the red galaxy population.
3.3 The Mass Functions of Star Forming and Non
Star Forming Galaxies
HavingpreviouslyexaminedthecoloursoftheGNSgalaxies
we next investigate the differences or similarities between
colour and star formation selected stellar mass functions.
We use the star formation rates calculated as described in
Section2.4forthesamplebetweenz =1.5−3andforM∗ >
109.5M⊙. To divide the galaxies into passive and evolving
populationsweusethestarformationratedividedbystellar
Figure 7. The integrated stellar mass density calculated for
mass of the galaxy to calculate the time it would take for each redshift bin using the integration of the Schechter func-
a galaxy to double in size, we call this tdouble. Using the tion. The black circles show the results of this work. The pink
Hubbletime (th) at theredshift of each galaxy weobtain a squares are from Dickinsonetal. (2003), the dark blue crosses
measureofhowfastagalaxyisformingbycalculatingt , arefromP´erez-Gonz´alezetal.(2008),thelightbluetrianglesare
form
where fromElsneretal.(2008)andthegreenandpurplediamondsare
fromDroryetal.(2005).Theblackdasheddotlineisaprediction
tform =tdouble/th. (6) of the stellar mass densities from the integrated star formation
rate (Wilkinsetal. 2008). The final redshift point is plotted as
We averaged over all the values of t to cut our sample
form
anopencircleasitisnotconsideredintheanalysisasdiscussed
into two distinct populations. Those above an average of
inSection3.1.
ht i=0.1areconsiderednon-starforming,thosebeloware
form
consideredstarforming.Theresultingstellarmassfunctions
can beseen in Figure 6. We integrate overthe Schechterfunction to get the in-
The general trend in Figure 6 shows an increase of tegrated stellar mass densitybetween z=1−3. Thisis the
both populations at high stellar mass. In this region M∗ > total amount of stellar mass contained within galaxies, in
1011M⊙ wefindthenon-starforminggalaxiesdominate.At a given redshift range, per comoving volume. The results
thelowstellarmassendweseethatthestarformingpopula- of this calculation are shown in Figure 7. To calculate this
tiondominatesoverthenon-starforminggalaxies.Theslope we perform a numerical integration between the limits of
of thelow stellar mass endis verysteep with thissteepness M∗ =1012M⊙ andM∗ =107M⊙.Weextendedtheintegra-
decreasing overtime, evenwithin the large error bars. tion beyond the lower mass limit of our survey by extrapo-
latingtheSchechterfunction tomasses beyondthosewhich
we fit.
3.3.1 Comparison Between the Blue/Red and the Star
Our stellar mass densities are generally higher than
Forming/Non Star Forming Mass Functions
what has been found in previous work, as shown in Fig-
Overplotted on Figure 6 are theSchechterfits for the blue ure7, dueto oursteeper values of α. The black dashed dot
andredgalaxy populations,shownastheblueandreddot- line shows the stellar mass density history obtained from
ted lines. We find that over all the redshift ranges the star the integration of the instantaneous cosmic star formation