On the Evolution of the Star Formation Rate Function of Massive Galaxies. Constraints at 0.4

0.51 MB·English

by  Fabio Fontanot

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed11January2012 (MNLATEXstylefilev2.2)
On the Evolution of the SFR Function of Massive
Galaxies. Constraints at 0.4 < z < 1.8 from the
GOODS-MUSIC Catalogue
Fabio Fontanot1,2, Stefano Cristiani1, Paola Santini3, Adriano Fontana3, Andrea
2 Grazian3 and Rachel S. Somerville4,5
1
1INAF-Osservatorio Astronomico, Via Tiepolo 11, I-34131 Trieste,Italy
0
2HITS-HeidelbergerInstitut fu¨rTheoretische Studien, Schloss-Wolfsbrunnenweg 35, 69118 Heidelberg, Germany
2
3INAF-Osservatorio Astronomico di Roma, via Frascati 33, I-00040, Monteporzio, Italy

n 4Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218
a 5Department of Physics and Astronomy, Johns Hopkins University,Baltimore, MD 21218, USA
J email: [email protected]

0
1

Accepted ...Received...
]
O
C ABSTRACT
. We study the evolution of the Star Formation Rate Function (SFRF) of massive
h
p (M⋆ > 1010M⊙) galaxies over the 0.4 < z < 1.8 redshift range and its implications
- for our understanding of the physical processes responsible for galaxy evolution. We
o use multiwavelength observations included in the GOODS-MUSIC catalogue, which
r providesasuitablecoverageofthespectralregionfrom0.3to24µmandeitherspectro-
t
s scopic or photometric redshifts for each object. Individual SFRs have been obtained
a
by combining UV and 24 µm observations, when the latter were available. For all
[
other sources an “SED fitting” SFR estimate has been considered. We then define

2 a stellar mass limited sample, complete in the M⋆ > 1010M⊙ range and determine
v the SFRF using the 1/Vmax algorithm. We thus define simulated galaxy catalogues
9
based on the predictions of three different state-of-the-art semi-analytical models of
2
galaxyformationandevolution,andcomparethemwiththeobservedSFRF.Weshow
0
that the theoretical SFRFs are well described by a double power law functional form
0
and its redshift evolution is approximated with high accuracy by a pure evolution of
.
2 the typical SFR (SFR⋆). We find good agreementbetween model predictions and the
1 high-SFR end of the SFRF, when the observationalerrors on the SFR are taken into
1
account.However,the observationalSFRF is characterisedby a double peaked struc-
1
ture, which is absent in its theoretical counterparts. At z > 1.0 the observed SFRF
:
v showsa relevantdensity evolution,whichis notreproducedby SAMs, due to the well
i known overprediction of intermediate mass galaxies at z ∼2. Semi-analytical models
X
are thus able to reproduce the most intense SFR events observed in the GOODS-
r
MUSIC sample and their redshift distribution. At the same time, the agreement at
a
the low-SFR end is poor: all models overpredict the space density of SFR ∼1M⊙/yr
and no model reproduces the double peaked shape ofthe observationalSFRF. If con-
firmed by deeper IR observations, this discrepancy will provide a key constraint on
theoretical modelling of star formation and stellar feedback.
Key words: galaxies: evolution - galaxies: fundamental parameters - cosmology:
observations
1 INTRODUCTION galaxies is a complex task, owing to the uncertainties in-
volved in the reconstruction of this quantity from obser-
vational data. It is widely accepted that dusty molecular
The evolution of the star formation rate (SFR) over the
clouds are the main sites for star formation: this implies
cosmic time is a fundamental constraint for every theory
that newly born stars are subject to significant dust atten-
of galaxy formation and evolution (see e.g. Hopkins 2004;
uation,untiltheyare ableto escape ordisrupt theirparent
Hopkins& Beacom 2006). Estimating SFRs for individual
(cid:13)c 0000RAS
2 Fontanot et al.
cloud.YoungOBstarsemitaconsiderableamountofenergy comparing the observed evolutionary trends with the pre-
intherestframeultraviolet(UV)band,whichhasthusbeen dictionsoftheoreticalmodels.Inparticular,Fontanot et al.
consideredakeywavebandforrecoveringtheinstantaneous (2009b)concludedthatthediscrepanciesseenbetweenmod-
SFR in external galaxies. However, dust absorbs UV pho- elsanddataformassivegalaxiesarenotsignificant,ifmodel
tons,heatsupandre-emitsthisenergyasthermalradiation predictions are convolved with typical observational errors,
in the Infrared (IR) bands. For this reason, SFR estimates while the strongest discrepancies between model and data
based on UV luminosity include correction factors to ac- are seen for low-to-intermediate mass galaxies.
count for dust attenuation and re-emission (Calzetti et al. Theimportanceofthestudyoftheredshiftevolutionof
1994; Kennicutt 1998; Bell et al. 2003). Dust attenuation thecosmic SFRforgalaxies atagivenmassrangehasbeen
is particularly relevant for star forming galaxies, where the widely recognised by a number of authors (Noeske et al.
dustemissionpeakisthedominantcomponentofthegalac- 2007;Elbaz et al.2007;Zheng et al. 2007;Drory & Alvarez
ticspectralenergydistribution(SED,seee.g.Calzetti et al. 2008; Dunneet al. 2009; Santini et al. 2009; Gilbank et al.
2000),nottomentiontheextremecasesofsub-mmgalaxies 2011). These results and the evolution of the stellar mass
(see e.g. Chapman et al. 2004). The study of thecosmic IR density provide fundamental information about the evolu-
backgroundshowsthattheglobalenergyemittedbygalaxies tion of the global process of galaxy formation. The latter
in theIRis comparable tothedirect starlight emission, de- approach is best complemented by the analysis of the stel-
tectableintheoptical (seee.g. Lagache et al.2005),clearly lar mass function (i.e. the volume density of galaxies as a
showingthatasignificantfractionofstarformationactivity function of stellar mass), which allows us to characterise
is expected to be heavily extinguished and detectable only galaxy evolution as a function of both redshift and stel-
in theIR. lar mass. Despite the wealth of information already avail-
These uncertainties become more relevant, when SFR able in the literature about the stellar mass function and
estimates for galaxies covering a wide redshift range are its redshift evolution, very little is known about the corre-
considered, since both galaxy physical properties and sponding Star Formation Rate Function (SFRF hereafter)
dust properties are expected to evolve with cosmic time and its evolution: Bell et al. (2007) studied its evolution in
(Maiolino et al.2004;Fontanot et al.2009a;Gallerani et al. the 0.2 < z < 1.0 redshift range in the COMBO-17 sur-
2010;Fontanot & Somerville2011).CombiningUVinforma- vey,Schiminovich et al.(2007)presentedthedistributionof
tion with supplementary information from direct observa- SFRs in the SDSS survey and Bothwell et al. (2011) con-
tions in the IR region has thus been proposed as the best sidered the distribution of SFRs in the Local Volume (de-
tooltoaccountforthetotalSFR(Kennicutt1998;Bell et al. finedasan11MpcradiusaroundtheMilkyWay)combining
2007).Inparticular,observationsat24µmhaveshowntobe GALEXandSpitzerobservations.Thisismainlyduetothe
extremelyusefulforestimatingtheglobalIRluminosityand uncertainties involved in the SFR estimate, but also to the
the instantaneous SFR (Papovich et al. 2007; Santini et al. difficultiesincorrectly accountingforthecompletenesscor-
2009). Thanks to the advent of the Herschel Space Obser- rection needed,especially at the low-SFR end.
vatory,wewillbeabletoconstraintotalIRluminosities,by In this paper, we focus on a new treatment of the
directly sampling thepeakof thethermalemission. Infact, GOODS-MUSICdata,byfocusingonamasscompletesam-
ithasbeenrecentlyshownbyRodighiero et al.(2010),that pleof galaxies. Inthisway,weareabletofully characterise
the combination of 24µm data with Herschel observations thevariouslevels ofstarformation intheseobjects andfol-
atlongerwavelengthsrepresentsaverypromisingtoolfora low their redshift evolution. Moreover, since the strongest
moreaccurate determination of SFRsof individualgalaxies starbursts are hosted by galaxies above the chosen mass
up to z∼3. limit,thehigh-SFRendoftheresultingSFRFprovidesfun-
Nowadays, our view of the evolution of galaxy prop- damental information about the redshift evolution of this
erties has substantially changed thanks to the advent of particular galaxy class. Therefore, this paper represents a
multiwavelength surveys. If the spectral sampling is fine complementary study of the evolution of SFRs in galaxies
enough, these catalogues can be used to infer the physical ofdifferentstellarmasswithrespecttoSantini et al.(2009),
properties also in the absence of spectroscopic information. towhichwereferthereaderfortheanalysisoftheevolution
In recent years several groups (see e.g. Fontanaet al. 2004; ofthecosmicSFRandspecificSFR.Adetailedcomparison
Panter et al.2007)developedanumberof“SEDfitting”al- ofthesamecataloguewithotherestimatesfortheevolution
gorithms:thesecodescomparetheavailablephotometryfor of SFR as a function of redshift and stellar mass has been
individualsourceswithsyntheticSEDlibrariesandthebest- presentedinFontanot et al.(2009b)(seereferencesherein).
fitmodeltemplateischosenbymeansofaχ2 minimisation. In the present paper we focus on the determination of the
Theresultingestimate for redshift (theso-called photomet- SFRF and compare results with the predictions of state-
ricredshift),stellarmass(M⋆),dustextinctionandSFRare of-the-art semi-analytical models of galaxy formation and
themostwidelyusedresultsofthisprocedureandhavebeen evolution.
of fundamentalimportancefor ourunderstandingof galaxy This paper is organised as follows. We present the
evolution. GOODS-MUSICcatalogueinsec.2andthetheoreticalpre-
Thecommoninterpretationoftheseresultsisconnected dictionsinsec.3;wepresentourresultsinsec. 4;finallywe
totheso-called“downsizing”scenario,inwhichthestarfor- discuss our conclusions in sec. 5. In the original GOODS-
mationshiftsfromhighmasstolowmassgalaxiesasredshift MUSIC papers a Salpeter initial mass function (IMF) is
decreases (first introduced by Cowie et al. 1996). This pic- mostly used; throughout this work, we assume a Chabrier
turehasbeenrecentlyrevisedbyFontanot et al.(2009b)by IMF and we rescale all stellar mass and SFR estimates, ac-
showingthatthetypicalerrorsassociatedwiththeestimate cordingly.WealsoadopttheΛCDMconcordancecosmolog-
ofthephysicalquantitieshastobetakenintoaccount,when ical model (H0=70km/s/Mpc, Ωm =0.3 and Ωλ =0.7).
(cid:13)c 0000RAS,MNRAS000,000–000
SFR function from GOODS-MUSIC 3
2 DATASET In order to provide a reliable estimate of statistical
quantities like the stellar mass function and the SFR func-
Our dataset is based on the updated version of GOOD-
tion, acareful analysis of observational biases and selection
MUSICcatalogue(Grazian et al.2006;Santiniet al.2009).
effects is of fundamental importance for a complete census
GOODS-MUSICis a multiwavelength catalogue, with pho-
of all galaxies. Those corrections are critical for the SFRF,
tometry in 15 bands, from 0.35 to 24 µm, covering an area
giventhecomplexcombinationofmultiwavelengthinforma-
of∼143.2arcmin2 oftheGOODS-Southfieldandlisting∼
tion needed, including both the selection of galaxies in the
15000 sources. Main source detection has been performed
K-band, fundamental for the definition of a mass-limited
on the z image, but faint z-band objects detected either
sample, and the SFR estimate from 24µm for direct de-
on the K image or at 4.5 µm have also been included in
tection (if available) or UV and optical data for the SED
thecatalogue.TheGOODS-MUSICcataloguehasbeenalso
fitting procedure. In order to reduce the uncertainties in-
cross-correlatedwithavailablespectroscopiccatalogues,and
volvedinouranalysis,wedecidetofocusonasubsampleof
a spectroscopic redshift has been assigned to ∼ 12% of
the GOOD-MUSIC catalogue, defined by considering only
sources.Foreachsourceinthecatalogue,itsphysicalparam- sources with a stellar mass estimate M⋆ > 1010M⊙. The
eters, such as M⋆, SFR and the photometric redshift, have GOODS-MUSIC catalogue is expected to be highly com-
been estimated through a “SED fitting” algorithm (see e.g.
plete in this mass range over the whole 0.4 < z < 1.8 red-
Santiniet al.2009andreferenceherein);forthepurposesof
shiftinterval,correspondingtoK-bandmagnitudesbrighter
χ2 minimisation, the available broad band photometry up than ∼23 (Fontanaet al. 2006). Moreover, for these ob-
torest-frameλ<5.5µm hasbeenconsidered.Thereference
jects, either 24µm fluxes or detailed multiwavelength pho-
synthetic SED library is defined using Bruzual & Charlot
tometry are available, and provide reliable estimates for
(2003)syntheticmodelsandassumingexponentiallydeclin-
SFR>0.01M /yr (Santiniet al. 2009).Objectswith docu-
⊙
ing star formation histories. The relevant parameters for
mented AGN activity (i.e. spectroscopically determined or
the SED synthesis (such as dust content, metalicity, age,
X-ray sources) have been removed from the final sample.
timescale for star formation histories, etc) are defined on
Comptonthickcandidates,selectedonthebasisoftheirvery
a grid in order to cover a wide range of possible values
red spectra (Fiore et al. 2008), have been removed as well.
and combinations. The discreteness of SED generation im-
Intheredshiftrangeofourinterestthereareonly4removed
pliesthatthefinalestimatesforthephysicalparametersare
objects with 1.4<z<1.8(0.5% of theconsidered sample).
subject to relevant degeneracies (see e.g. Marchesini et al.
Wetestthatourconclusionsarerobustagainsttheinclusion
2009 for a discussion focused on the effect of changing the
of these objects. Ourfinal sample consists of 740 sources.
physical ingredients in theadopted stellar population mod-
It is also worth mentioning the known overdensities
els).Inparticular,theoreticalmodelspredictstarformation at z ∼ 0.7 and z ∼ 1.6 in the GOODS fields, as well
histories for individual galaxies, which grossly differ from as the known underdensity at z ∼ 0.9 (Gilli et al. 2003;
any assumed smooth analytical shape: this has important
Castellano et al. 2007; Salimbeni et al. 2009). Ongoing sur-
implications for the M⋆ estimate (Stringer et al. 2009). By veys like COSMOS (Scoville et al. 2007) and CANDELS
comparing theavailable spectroscopic redshifts (z ) with
spec (Grogin et al. 2011; Koekemoer et al. 2011), will be able to
thecorrespondingestimatesfromtheSEDfittingalgorithm
reduce the effect of cosmic variance on the SFRF determi-
(z ), Santini et al. (2009) computed the average abso-
phot nation, and study its environmental dependencies.
lutescatterbetweenspectroscopicandphotometricredshift
∆z = |zspec−zphot|. They found σ(∆z)=0.06 for the whole
1+zspec
sampleandσ(∆z)=0.043 whenonlythebrightestgalaxies
3 MODELS
(z<23.5) are considered.
A parallel estimate of the star formation rate is pro- In order to understand the physical implications of our re-
vided by the combination of IR and UV luminosities. For sults, we consider the prediction of the recent implementa-
sourcesintheGOODS-MUSICsample,Santiniet al.(2009) tions of 3 state-of-the-art semi-analytical models, namely,
combined the rest-frame UV luminosity derived from the the Wang et al. (2008) model, the Somerville et al. (2008)
SED fitting and the integrated luminosity between 8 and and morgana (Monaco et al. 2007). The predictions of
1000 micron, obtained by fitting 24 micron fluxes with these3modelshavebeenextensivelycomparedinanumber
Dale & Helou(2002)templates.Thecorrectionprovidedby of recent papers (Kimm et al. 2009; Fontanot et al. 2009b,
Papovich et al. (2007) has been applied on the resulting 2011) and we refer thereader to thesepublications and the
SFRs in order to account for the overestimation of the to- original papers for all the details of the galaxy formation
tal IR luminosity at high redshifts/IR luminosities when and evolution modelling. In these models, the evolution of
extrapolating from 24 µm fluxes (e.g. Elbaz et al. 2010). thebaryoniccomponent isfollowed bymeansof anapprox-
Santiniet al. (2009) explicitly compared these SFR esti- imate description of the physical processes at play (such
mates with the SED fitting results, for sources with both as gas cooling, star formation, stellar feedback, Black Hole
estimates available. They found an overall good agreement, growthandAGNfeedback)andoftheirinterplaywithgrav-
but also a systematic trend at all redshift, with IR-based itational processes (i.e. dynamical friction, tidal stripping
estimates exceeding the fit-based ones as the star forma- andtwo-bodymergers),linkedtotheassemblyofthelarge-
tionrateincreases,andviceversaforlowvaluesofSFR(see scale structure of the Universe. These “recipes” include a
alsoPapovich et al.2007;Nordon et al.2010).Inthefollow- numberofparameterswhichareusuallyfixedbycomparing
ingof thispaper,unlessexplicitly stated,for each object in model predictions with a set of low-redshift observations.
thesample we consider IR-basedSFRs when available, and Despitetheirsimplified approach,SAMshaveturnedintoa
“SED fitting”estimates elsewhere. flexibleandwidelyusedtooltoexploreabroadrangeofspe-
(cid:13)c 0000RAS,MNRAS000,000–000
4 Fontanot et al.
cific physical assumptions, as well as the interplay between
0.0<z<0.2 0.2<z<0.4 0.4<z<0.6 different physical processes. All models we consider resolve
galaxies with M⋆ >109M⊙, and they reproduce fairly well
a number of observational constraints on the evolution of
theSFR,bothasaglobal quantity(i.e.thecosmic starfor-
mationrate),andforindividualgalacticpopulation(i.e.the
fraction of passive galaxies in the local Universe, see e.g.
0.6<z<0.8 0.8<z<1.0 1.0<z<1.4
Kimm et al. 2009).
Also for the theoretical predictions, we consider purely
stellarmassselectedsamples(M⋆ >1010M⊙)and,asforthe
GOOD-MUSICcatalogue,weexcludedfromtheanalysisall
objects with SFR< 0.01M /yr. After the selection proce-
⊙
1.4<z<1.8 1.8<z<2.5
durewearethusleftwith385187galaxiesfortheWang et al.
(2008)model,342795 fortheSomerville et al.(2008)model
and 249823 galaxies for morgana. In fig. 1, we show the
binnedSFRFsforeachmodel(crosses).Inordertoquantita-
tivelyestimatetheredshiftevolutionofthepredictedSFRF
we apply to model predictions a fitting procedure similar
to Fontanot et al. (2007a). We determined best fit analyt-
ical solutions to the theoretical predictions assuming both
0.0<z<0.2 0.2<z<0.4 0.4<z<0.6 a Schechter and a double power law shape for the SFRF.
Weusethecorresponding numberdensities toMonteCarlo
generateindependentdatapointsinthez-SFRspaceandwe
calibratethebestfitparametersfortheSFRFanditsevolu-
tion by means of a χ2 binning procedure. Our results show
that thedoublepower law shape systematically scored bet-
0.6<z<0.8 0.8<z<1.0 1.0<z<1.4
terresults thantheSchechterfunction in terms of χ2 (with
typical values χ2 < 1.0). This is mainly due to the extra
degreeoffreedom inthehigh-SFR-endslope, with provides
abetterdescription ofthisregion with respect totheexpo-
nential cut-off of the Schechter function, even if it is worth
1.4<z<1.8 1.8<z<2.5
stressing that theSchechtershapeis not formally ruled out
byouranalysis. Anyhow,inthefollowing wethusassumea
SFRFin the form of a doublepower-law:
Φ⋆(SFR⋆)
Φ(SFR)= (1)
(SFR/SFR⋆)−α+(SFR/SFR⋆)−β
whereΦ⋆,SFR⋆,α,βarefreeparameters.Inordertomodel
the redshift evolution of the SFRF we fix the values of the
0.0<z<0.2 0.2<z<0.4 0.4<z<0.6 4parametersattheirz=0valuesandweconsiderdifferent
combinations for their redshift evolution. We consider both
a pureevolution in SFR⋆ (PSE) of theform:
SFR⋆ =SFR⋆ (1+z)kSFR (2)
z=0
0.6<z<0.8 0.8<z<1.0 1.0<z<1.4 and a puredensity evolution (PDE) of theform:
Φ⋆ =Φ⋆ ekΦ(1+z) (3)
z=0
wherek andk representstheevolutionary parameters.
SFR Φ
Ourresultspointout thattheredshift evolutionof thethe-
1.4<z<1.8 1.8<z<2.5 oretical SFRF is in general well described by a pure evo-
lution in SFR⋆. In fig. 1, we show the best fit results for
the Wanget al. (2008) model as a solid red line, while the
dashed magenta line represents the corresponding z = 0.1
best fit SFRF. As for morgana and the Somerville et al.
(2008) model, the fit at the low-SFR end is improved (by
a factor of 2 in terms of χ2) if the pure SFR⋆ evolution
(which is still statistically acceptable) is combined with an
Figure1.TheredshiftevolutionoftheSFRFinsemi-analytical evolution of theslope α of theform:
models. Crosses refer to the intrinsic predictions of the models,
whilesolidlinesshowtheanalyticfit(pureSFR⋆evolution)ofthe α=α0+kαz (4)
theoreticalSFRF.Ineachpanel,dashedlinereportstheposition
whereα0 =α(z =0) and kα is theevolutionary parameter.
ofthez=0SFRF.
We conclude that a double power law is a good represen-
(cid:13)c 0000RAS,MNRAS000,000–000
SFR function from GOODS-MUSIC 5
Table 1.BestfitparametersfortheevolutionoftheSFRfunctionaspredictedbysemi-analyticalmodels.
SAM Φ⋆(×10−2) SFR⋆ kSFR α β α0 kα χ2
Wangetal.(2008) 0.47±0.04 0.29±0.14 2.10±0.64 0.84±0.10 −2.03±0.27 — — 0.32
Somervilleetal.(2008) 0.46±0.05 0.39±0.12 1.99±0.72 — −1.84±0.24 0.29±0.07 0.23±0.11 0.44
morgana 0.41±0.03 0.70±0.17 1.23±0.42 — −1.95±0.22 0.26±0.03 0.15±0.04 0.29
tation of the SFRF as predicted by the theoretical models Table 2.SFRFunctionintheGOODS-MUSICCatalogue.
at z<2 and for SFR>0.01M /yr. Wepresent thebest fit
⊙
parameters corresponding to the above equations in tab. 1.
log(SFR) Log(Φ(SFR))
It is worth stressing that we obtain very low χ2 value even
if our fits tend to break down at the highest redshift and 0.4<z<0.6 −1.75±0.25 −3.23+−00..2358
lowest SFRs. This is due to the high number of object in −1.25±0.25 −3.09+−00..1148
the model samples, which thus provide a very accurate fit −0.75±0.25 −3.53+−00..2321
of the kneeof the SFRFand its evolution. −0.25±0.25 −4.14+−00..2498
Inordertocomparethetheoreticalpredictionswiththe +0.25±0.25 −3.09+−00..1136
results from the GOODS-MUSIC catalogue, we repeat the +0.75±0.25 −2.81+−00..0190
fittingprocedureafterconvolvingthetheoreticalpredictions +1.25±0.25 −3.14+−00..1136
withanestimateofthesystematicerrorontheSFRdetermi- +1.75±0.25 −3.69+−00..2334
nation,tofullyaccountforthetypicalobservationalerrorin 0.6<z<0.8 −1.75±0.25 −3.64+0.23
thecatalogue(Santiniet al.2009).Weassumealog-normal −1.25±0.25 −2.99+−00..1333
errordistribution fortheSFRwithan amplitudeof 0.3dex −0.75±0.25 −3.04+−00..1125
(seealsoFontanot et al.2009b).Werepeattheaboveanaly- −0.25±0.25 −3.39+−00..1175
sisandwedeterminethatapureSFR⋆evolutionofadouble +0.25±0.25 −3.14+−00..1222
power law is still a good description (i.e. consistent χ2 val- +0.75±0.25 −2.88+−00..0195
ues)oftheoverallredshiftevolutionofthepredictedSFRFs. +1.25±0.25 −2.77+−00..0170
The most noticeable difference in the best fit parameters is +1.75±0.25 −3.50+−00..1058
the systematic increase of the β parameter by as much as −0.19
20%. 0.8<z<1.0 −1.75±0.25 −3.99+0.27
−0.42
−1.25±0.25 −3.63+0.18
−0.24
−0.75±0.25 −3.99+0.20
−0.28
−0.25±0.25 −3.99+0.25
−0.38
4 RESULTS & DISCUSSION +0.25±0.25 −3.87+0.23
−0.34
+0.75±0.25 −3.30+0.12
We first compute the binned SFRF for massive galaxies by +1.25±0.25 −3.07+−00..1104
means of the standard 1/Vmax formalism, and we show the +1.75±0.25 −3.47+−00..1131
resulting SFRF in fig. 2 as open circles (cyan circles mark −0.16
the bin with less than 5 sources). In order to take into ac- 1.0<z<1.2 −1.75±0.25 −3.99+0.21
−0.30
count the observational uncertainties, we repeat the anal- −1.25±0.25 −3.51+0.12
−0.15
ysis 10000 times after convolving every individual SFR es- −0.75±0.25 −3.61+0.13
−0.16
timate with the corresponding error on SFR and redshift −0.25±0.25 −3.81+0.14
−0.17
(see Santini et al. 2009 for more details on the error es- +0.25±0.25 −3.68+0.14
−0.17
timate). Errorbars in fig. 2 refer to the 1-σ variance over +0.75±0.25 −3.31+0.08
−0.10
these10000realisations.Wecollectourfinalestimateofthe +1.25±0.25 −2.99+0.05
−0.06
SFRF and associated errors in tab.2. In the fig. 2 we also +1.75±0.25 −3.06+0.05
−0.06
include the previous estimate for the SFRF at z > 0 from +2.25±0.25 −4.29+0.19
−0.25
the COMBO-17 survey (Bell et al. 2007). It is worth not- +2.75±0.25 −4.59+0.29
−0.49
ingthattheCOMBO-17resultsareobtainedbyconsidering
1.2<z<1.8 −1.75±0.25 −4.49+0.31
all galaxies in their sample, with no cut in stellar mass. −0.54
−1.25±0.25 −4.37+0.22
Our estimates for the SFRF are in good agreement with −0.32
−0.75±0.25 −3.72+0.14
the Bell et al. (2007) result at the high-SFR end, where we −0.18
−0.25±0.25 −3.83+0.17
expect themassive galaxies to dominate the space density. −0.21
+0.25±0.25 −4.13+0.16
Fig. 2 clearly show that the COMBO-17 data are not −0.21
+0.75±0.25 −3.80+0.14
deep enough to explorethelow-SFR endwith thesame ex- −0.18
+1.25±0.25 −3.47+0.09
tent as in the GOOD-MUSIC catalogue, moreover the low- −0.10
+1.75±0.25 −3.40+0.07
SFR end of the SFRF shows a very peculiar feature, i.e. −0.07
+2.25±0.25 −3.45+0.07
a double peaked shape. It is really tempting to interpret −0.08
+2.75±0.25 −4.37+0.22
this feature in terms of the well known bimodality in the −0.31
colour (SFR)-mass diagram, and/or connect those galaxies
withtheintermediatesourcespopulatingtheso-calledgreen
valley. It is also worth noting that a populations of rela-
(cid:13)c 0000RAS,MNRAS000,000–000
6 Fontanot et al.
Figure2.TheevolutionoftheSFRFforM >1010M⊙ galaxiesintheGOOD-MUSICsample.Ineachpanel,thehorizontalcyanlong-
dashedlinerepresentsthespacedensitycorrespondingtooneobjectintheGOODS-MUSICvolume,whiletheyellowshadinghighlights
thetheSFRrangecoveredby24µmobservationsineachredshiftbin.OpencirclesrefertoourSFRFestimatefromtheGOODS-MUSIC
survey:ineachsubpanel,cyansolidcirclesmarkthebinswithlessthan5galaxies;errorbarsrepresentthe1-σconfidencelevels(seetext
formoredetails).LightgreyfilledcirclesrefertotheSFRFderivedonlyfromtheresultsoftheSEDfittingalgorithm.Purplediamonds
refertotheSFRFestimatefromtheCOMBO-17(Belletal.2007)survey.Inallpanels,dashedred,dot-dashedgreenandsolidbluelines
refertotheWangetal.(2008),Somervilleetal.(2008)andmorganapredictions,respectively.SAMpredictionsareconvolvedwithan
GaussianerrorontheSFR(width0.3dex,seetext).
tivelymassivegalaxieswithverylowlevelsofstarformation peaked behaviour persists. Ourmain conclusions are there-
hasbeen already reported at lower redshifts (Wilman et al. fore insensitive tothe origin of SFR estimate, in agreement
2008;Schawinski et al. 2010). with Santiniet al. (2009) results (i.e. the 24µm-based SFR
estimates are in reasonable agreement with SED fitting re-
However, a word of caution is necessary. We have lim-
sults for sources with both estimates available).
ited information about individual 24µm fluxes for galax-
ies in our mass-selected sample, and typically only for Nonetheless,wecannotcompletelyexcludethehypoth-
SFR> 1M /yr. This implies that the secondary peak at esis that the gap between the two peaks is an artifact of
⊙
SFR< 1M /yr is populated by galaxies whose SFR esti- the SED fitting procedure (i.e. piling up of low-SFR galax-
⊙
matecomesfromtheSEDfittingalgorithm.Inordertotest ies in the secondary peak, due to the coarse grid-sampled
the robustness of our result, we repeat our analysis consid- properties of the synthetic SED library). We plan to study
ering only SFR estimates coming from theSED fitting. We theefficiencyoftheSEDfittingalgorithmintheestimateof
findnosignificantchangeintheshapeoftheresultingSFRF SFRsintherange0.1M /yr<SFR<10M /yrasapartof
⊙ ⊙
(light grey filled circles in fig. 2): in particular, the double a larger programme, comparing the global performances of
(cid:13)c 0000RAS,MNRAS000,000–000
SFR function from GOODS-MUSIC 7
ouralgorithminrecoveringthephysicalpropertiesofmodel
galaxieswithcomplexstarformationhistories,startingfrom
synthetic photometry extracted from SAM simulated cata-
logues. A similar procedure has been recently employed by
Lee et al. (2009) to a sample of high-redshift model galax-
ies:theyfoundthatSEDfittingunderestimatesSFRintheir
sampleandattributedthisbehaviourtotothedifferentstar
formationhistoriespredictedbySAMswithrespecttothose
assumed in thereference syntheticSED libraries.
As a preliminary test we consider a small sample of
5000modelgalaxieswith0.4<z <1.8takenfromthesame
morganarealisationanduniformlydistributedinSFR.For
the purpose of this test we do not limit the sample to
M⋆ >1010M⊙ modelgalaxies. Foreachobject,wecompute
a synthetic SED using the Radiative-Transfer code grasil
(Silvaet al. 1998, see also Fontanot et al. 2007b). We then
apply the SED fitting algorithm to the corresponding syn-
thetic photometry. In fig. 3 (upper panel) we compare the
original, flat, distribution of SFR in our sample (black his-
togram) with the distribution of reconstructed SFRs (blue
Figure3.TestontheSEDfittingalgorithm.Upper panel:com-
shaded histograms). This test suggests that some depletion
parison of the SFR distribution in a sample of 0.4 < z < 1.8
effects in SFR distribution may be effective at SFR below morganamodelgalaxies(solidblackhistogram),withthecorre-
our fiducial limit (SFR ∼ 0.01M⊙/yr); however, the SFR sponding distribution of reconstructed SFRs, obtained applying
distribution in the region corresponding to the secondary theSEDfittingalgorithmtosyntheticphotometry(bluehatched
peakandthevalley(roughlyidentifiedbythegreenarrows) histogram). Red line represents the limiting SFR considered in
does not seem to be affected by any obvious systematic ef- theSantinietal.(2009)paper,whilegreenarrowbracketthere-
fect. We also repeat the same analysis on a subsample of gion containing the main features of the observed SFRF. Lower
M⋆ > 1010M⊙ model galaxies, (lower panel), whose distri- Panel: same as upper panel, but for a sample of M⋆ >1010M⊙
modelgalaxies.
bution is more similar to the theoretical SFRF. Again we
obtain no obvious systematic effect in SED fitting recon-
struction.Wealso checkthatsimilar results holdif wesplit derto get more insight on theevolution of the typical SFR
the sample in smaller redshift bins, but with less statistical of galaxies at different redshifts, we repeat on the data the
significance, due to the reduced dimensions of the subsam- samefittingproceduredescribedinsec.3.Giventhedouble
ples. peaked shape of the observed SFRF both a double power
Infig.2wealsoshowthepredictionsofourthreeSAMs lawandaSchechterfunctionarenolongeragoodrepresen-
ascolouredlines:thelevelofagreementbetweenthe3mod- tationoftheSFRFoverthewholeSFRrange.Therefore,we
els is striking, given the very different star formation and chose to repeat the fitting procedure both on the reference
stellar feedback schemes adopted. In particular we stress sample (SFR>0.01M /yr),and on a smaller sample con-
⊙
that the predicted redshift evolution of the typical SFR⋆ taining only sources with SFR>1M /yr (i.e. focusing on
⊙
isremarkablysimilarbetweenallmodels.Thisisduetothe the primary SFRF peak). This choice has no major impact
external constraints (i.e. the evolution of the cosmic SFR) onourconclusions;asexpectedonlythelow-SFR-endslope
usedtocalibratethemodels.Thestrongestdiscrepanciesare α show a relevant variation between the two samples. We
seen at the low-SFR end of the SFRFand clearly show the collect our final results in tab. 3. The results show that the
importance of using constraints based on the SFRF, in or- SFRF, as depicted by the GOODS-MUSICsurvey,shows a
der to disentangle between different theoretical approaches remarkable density evolution (PDE) in the 0.8 < z < 1.8
to star formation and stellar feedback. range, and a milder SFR⋆ evolution (PSE) over the whole
The comparison between theoretical predictions and redshift range. The theoretical SFRF is able to reproduce
the observational results from the GOODS-MUSIC survey the SFR⋆ evolution, although it peaks systematically at
shows a remarkably good agreement at the high-SFR end, lower typical SFR than the observational constraints, but
where the available 24µm observations are deep enough to itsdensityevolutionisnegligible.Thisrepresentsafirstrel-
constrain its shape and evolution out to z ∼ 1.8 (yellow evant discrepancy between models and data and it is due
shaded region in fig. 2). Therefore we conclude that SAMs to the well documented overprediction of the space density
provide a satisfactory description for the space density of of 1010M⊙ < M⋆ < 1011M⊙ galaxies at 1.0 < z < 1.8
galaxies with SFR> 10M⊙/yr at moderate redshifts. It seen in themodels and in thedata; Fontanot et al. (2009b)
worth stressing that accounting for observational errors is showedthatSAMspredictforthesegalaxiesspacedensities
essentialforthecorrectinterpretationofthecomparisonbe- very similar to the local value out to z ∼ 1.8, while their
tweenmodelanddata:theerror-freeintrinsicSFRFswould observed stellar mass function show a remarkable evolution
underpredict the space density of the strongest starbursts (their fig.1). This implies that the negligible density evolu-
by a factor of a few. tion predicted for theSFRFat z>1.0 isrelated to thetoo
Observations at 24µm are also able to constrain the efficient formation of intermediate mass galaxies in SAMs
position of the peak of the SFRF out to z ∼ 1 (and give (see also Lo Faro et al. 2009).
some indications for its position at higher redshifts). In or- Themostinterestingdiscrepanciesbetweenmodelsand
(cid:13)c 0000RAS,MNRAS000,000–000
8 Fontanot et al.
Figure 4. Upper panel: Specific SFR versus M⋆ Lower panel: Rest-Frame colour-magnitude diagrams. In each panel the yellow dots
refer to the K-limitedGOODS-MUSIC sample; red dots mark sources with M⋆ >1010M⊙ and SFR >0.01M⊙/yr; blue crosses refer
togalaxies belonging thesecondary peakonthe SFRFateach redshiftbin,whilegreencirclesrefertogalaxies withSFR intermediate
betweenthetwopeaks.Inthelowerpanel,darkredandbluelinesrefertothemeanU−V coloursalongtheredsequenceandtheblue
cloud, while the dark green solidline reproduces the divider between the blue and red populations (see Salimbenietal. 2008 for more
details).
(cid:13)c 0000RAS,MNRAS000,000–000
SFR function from GOODS-MUSIC 9
Table 3.BestfitparametersfortheevolutionoftheSFRfunctionintheGOODS-MUSICCatalogue.
Model Φ⋆(×10−2) SFR⋆ kSFR kΦ α β χ2
Log(SFR)>−2.0
PDE 0.37±0.11 1.13±0.13 0.70±0.58 — unconstr. −1.77±0.30 2.7
PSE 0.74±0.20 1.30±0.07 — −1.09±0.60 unconstr. −1.85±0.29 1.6
PDE+PSE 0.88±0.16 0.81±0.11 2.07±0.44 −1.22±0.22 unconstr. −1.43±0.31 1.2
Log(SFR)>0.0
PDE 0.30±0.05 1.02±0.19 0.93±0.35 — unconstr. −1.84±0.21 1.5
PSE 0.58±0.16 1.31±0.11 — −0.72±0.23 unconstr. −1.48±0.24 0.9
PDE+PSE 0.55±0.05 0.54±0.15 2.09±0.38 −0.56±0.11 unconstr. −1.43±0.24 0.6
dataareindeedseenatthelow-SFRend:allSAMspredicta bleorigin forsmallandlatestarformation episodesinmas-
featureless low-SFR end, whose slope (and its redshift evo- sive galaxies might be related to the duty cycles associated
lution) dependson thedetails of thetreatment of SFR and to the “radio-mode” AGN activity (Fontanot et al. 2011):
stellar feedback. The most relevant differencebetween data if the injection of energy from the central Black Hole into
andmodelprediction isthefact thatallmodelsoverpredict thesurroundingDarkMatterhaloisnotacontinuousevent,
theabundanceofSFR∼1M /yr sources.Itisalsointerest- some cold gas might still be allowed to infall onto massive
⊙
ing to notice that no model reproduces the double peaked galaxies.
feature of theobserved SFRF. Inordertogetmoreinsightinthepropertiesofgalaxies
Thereareatleasttwopossibleinterpretationsofourre- responsible for this feature, we consider the distribution of
sults. First (scenario A), as it has been suggested by many theGOODS-MUSICgalaxiesbothinthespecificSFRversus
authors (see e.g., De Lucia & Blaizot 2007; Wang et al. M⋆ and in rest-frame colour-magnitude diagram (as recon-
2007), SAMs predict too low SFRs for most of the galax- structed from the SED fitting algorithm) in fig 4. In both
ies in the mass range of our interest: they have SFRs well panels, we mark theM⋆ >1010M⊙ galaxies as red squares;
below the detection limit of our sample, and, overall, they bluecrossesandgreencirclesrefertothegalaxiesbelonging
are too passive at intermediate redshifts (Fontanot et al. to the secondary peak and lying between the two peaks re-
2009b). The three models indeed predict a secondary peak spectively.Darkred,greenandbluelinesinthelowerpanel
intheirSFRdistribution,anditconsistsofcompletely pas- reproduce the locus of red sequence, green valley and blue
sive galaxies (SFR= 0, see e.g. figure 4 in Fontanot et al. cloud as definedin Salimbeni et al. (2008).
2009b).Inthisscenario,wecouldinterprettheobservedsec- Weexpectthetwo scenarios wediscuss in theprevious
ondarypeak(atlow,butstilldetectableSFRs),ifconfirmed paragraph to predict a different colour evolution for galax-
by deeper observations, as an evidence that models are not ies.InscenarioA,weassumeacontinuitybetweenthecolour
able to reproduce the correct space density for galaxies mi- of galaxies belonging to the primary peak, valley and sec-
grating from the blue cloud to the red sequence (see also ondarypeak,intermsof bluecloud, “green valley”andred
Cassata et al. 2007),andwecould interpretit asanindica- sequence. Since scenario A assumes a continuous motion of
tion that galaxies in the GOODS-MUSIC sample move in galaxies from thebluecloud tothered sequence,weexpect
thecolour-magnitudediagramataslowerpacewithrespect galaxieswithdifferentSFRstopopulatewelldefinedregions
to theoretical expectations. This scenario is also consistent ofthecolour-magnitudediagram.Therelativeabundanceof
with the recent findings of Lagos et al. (2011): they revis- galaxies in thedifferentregions ofthediagram is anindica-
itedthedefinitionofthestarformationlawinthecontextof tion of thetime they spend in thedifferent phases.
the galform SAM (Baugh et al. 2005; Bower et al. 2006) On the other hand, in scenario B we expect a larger
taking into account recent results on the relation between spread of galaxies belonging to the secondary peak in the
starformation andtheatomicandmoleculargascontentof colourmagnitudediagram.Thephysicalprocessesresponsi-
galaxies (seee.g. Blitz & Rosolowsky 2006;Krumholz et al. ble for the retriggering have a strong dependence on the
2009).Theyshowedthatthepropertiesofgalaxieswithlow stellar mass and/or environment of galaxies, and are al-
SFRs (and their redshift evolution on the M⋆ versus SFR most insensitive totheposition of thegalaxy in thecolour-
plane)areparticularlysensitivetothedetailsoftheassumed magnitude diagram at the time of the retriggering. There-
star formation law, and suitable modifications to the stan- fore,therelativetightnessofthelocuswheresecondarypeak
dard prescriptions may indeed lead to bimodal SFR distri- objects are found in the rest-frame colour-magnitude dia-
butionsin thedirection needed toexplain our results. grams is in qualitative agreement with the former scenario.
An alternative scenario (scenario B) requires small Ontheotherhand,galaxieswithSFRintermediatebetween
SFR retriggering events in already red galaxies (see e.g. thetwo peaks show a much wider distribution in fig. 4. We
Treu et al. 2005): these events might be linked to the dy- warn the reader that these are qualitative conclusions that
namical evolution of galaxies in dense environments(merg- relyontheassumptionthattheU−V colourisafairtracer
ers, interactions). Therefore this also implies a dependence of the SFR activity, and that this colour is also sensitive
of these secondary SFR events on the environment, which enoughtothelow-levelsofSFRforgalaxiesinthesecondary
in principle could be accessible by larger surveys (see e.g. peak.ThefactthatmostofSFRestimatesforsourcesbelow
Cucciati et al. 2010 and references herein). Another possi- theSFRFpeakhavebeenderivedfromSEDfittingalsopre-
(cid:13)c 0000RAS,MNRAS000,000–000
10 Fontanot et al.
vents firm conclusions on this issue from GOODS-MUSIC put strong constraint on this relevant discrepancy seen be-
data alone. A more quantitative analysis will require bet- tweendataandmodels.Unfortunately,forlowerSFRlevels
terestimatesforSFRlevelsingalaxypopulationandbetter this information is not currently available, and we have to
tracersofphysicalstateofgalaxiesbelongingtothedifferent relyentirelyontheresultsofSEDfitting.Ourtestssuggest
regions of the colour-magnitude diagram, and it is beyond that the use of SED fitting results does not introduce any
theaims of the present work. obvious distortion in the SFR distribution at intermediate
SFR values, but we could not completely exclude the dou-
blepeaked feature in theSFRFto beduetosystematics in
5 CONCLUSIONS theSEDfittingalgorithm.Fromopticalphotometryaloneis
not possible to uniquely associate SFR ∼1M /yr galaxies
⊙
In this paper we consider the GOODS-MUSIC sample to (the region were models and data differ most and roughly
study the SFR function and its redshift evolution in the corresponding to the region between the two peaks of the
redshift range 0.4<z <1.8, just after the peak in the cos- SFRF)withknownpopulationsinthecolour-magnitudedi-
mic SFR, a fundamental epoch to understand the physical agram,i.e.thegreenvalleyorthebluecloud.TheredU−V
processesresponsibleforthedeclineofstarformingactivity colours, with a relatively small scatter, of galaxies belong-
as a function of galaxy stellar mass. In order to reduce the ing to the putative secondary peak provide only a qualita-
effect of completeness corrections, we restrict our analysis tive support to a scenario where star formation in massive
togalaxieswithM⋆ >1010M⊙,sinceatthesestellarmasses galaxies decrease at a slower pace with respect to theoreti-
the GOODS-MUSIC is expected to be a complete sample. cal expectations. If confirmed, this double peaked shape of
We thus compute the SFRF using SFR estimates coming the SFRF would thus represent a critical discrepancy be-
from both SED fitting and/or a combination of UV light tween models and observations, since all SAMs we consider
with 24µm observations. We compare the resulting SFRF predict a smooth, featureless, single slope power-law shape
with the predictions of 3 independent semi-analytical mod- for the SFRF. Modifications in the assumed star formation
els of galaxy formation and evolution (Wanget al. 2008; law,takingintoaccounttherelationbetweenstarformation
Somerville et al.2008andmorgana)andweobtainthefol- and the atomic and molecular gas content of galaxies may
lowing results: alleviate thistension,since thepropertiesofmodelgalaxies
withlowSFRlevelsareverysensitivetothismodelinglayer
• The agreement between the observed and predicted
(Lagos et al. 2011,see e.g.).
high-SFR end (SFR>10M /yr) of the SFRF is good over
⊙ On the other hand, thanks to the new facilities (e.g.
the whole redshift range (once the observational errors are
Herschel),futureobservationsintheIRregion,abletochar-
taken into account). This result implies that theoretical
acterisethepropertiesoftheIRpeak,willfinallydetermine
models are able to reproduce the space density evolution
theSFRlevelsoftheseobjectsandtherelevanceofthisfea-
of the strongest starbursts. It is worth noting that the pre-
ture. This is a fundamental task, since the low-SFR end of
dictions of the three models are remarkably similar in this
the SFRF is the region where SAM predictions differ most
SFR range.
and therefore provides potentially strong constraints to the
• TheSFRFofmassivegalaxies,asseenbytheGOODS-
different approaches to star formation and stellar feedback.
MUSICischaracterised byacomplexevolution bothin the
typical SFR and in the normalisation. Theoretical models
are able to cope with the SFR⋆ evolution, but they predict
anegligibledensityevolution.Inparticular,allmodelsover- ACKNOWLEDGEMENTS
predictthespacedensityofSFR∼1M /yrgalaxies.Wein-
⊙ WethankGabriellaDeLuciaandPierluigiMonacoforstim-
terpretthisbehaviourasduetothewelldocumentedexcess
ulating discussions. We are grateful to Jie Wang for letting
ofintermediatemassgalaxies(1010M⊙ <M⋆ <1011M⊙)in us use the outputs of his simulations. FF acknowledges the
SAMs(Fontanot et al. 2009b).
supportof anINAF-OATsfellowship granted on’Basic Re-
• Theobservedlow-SFRendofSFRFischaracterisedby
search’fundsandfinancialcontributionfromtheASIproject
a doublepeaked shape. Despitetheuncertainties in thede-
“IR spectroscopy of the Highest Redshift BH candidates”
termination of such low SFRs from SED fitting methods,
(agreement ASI-INAF1/009/10/00).
it is worth noting that none of the theoretical model we
consider is able to reproduce this feature, and all of them
predict a smooth decrease of the space density of low-SFR
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