Recovering Stellar Population Properties and Redshifts from Broad-Band Photometry of Simulated Galaxies: Lessons for SED Modeling

2.2 MB·English

by  Stijn Wuyts

Draftversion January27,2009
PreprinttypesetusingLATEXstyleemulateapjv.11/26/03
RECOVERING STELLAR POPULATION PROPERTIESAND REDSHIFTS FROM BROAD-BAND
PHOTOMETRY OF SIMULATED GALAXIES: LESSONS FOR SED MODELING
Stijn Wuyts1,2,3, Marijn Franx2, Thomas J. Cox1,3, Lars Hernquist1, Philip F. Hopkins4, Brant E.
Robertson5,6,7, Pieter G. van Dokkum8
Draft version January 27, 2009
ABSTRACT
9
Wepresentadetailedanalysisofourabilitytodeterminestellarmasses,ages,reddeningandextinction
0
values, and star formation rates of high-redshift galaxies by modeling broad-band SEDs with stellar
0
populationsynthesis. Inordertodoso,wecomputedsyntheticoptical-to-NIRSEDsformodelgalaxies
2
taken from hydrodynamical merger simulations placed at redshifts 1.5 ≤ z ≤ 2.9. Viewed under

n different angles and during different evolutionary phases, the simulations represent a wide variety of
a galaxytypes(disks,mergers,spheroids). We showthatsimulatedgalaxiesspanawide rangeinSEDs
J
and color, comparable to these of observed galaxies. In all star-forming phases, dust attenuation has

7 a large effect on colors, SEDs, and fluxes. The broad-band SEDs were then fed to a standard SED
2 modeling procedure and resulting stellar population parameters were compared to their true values.

Disk galaxies generally show a decent median correspondence between the true and estimated mass
O] andage,butsufferfromlargeuncertainties(∆logM =−0.06+−00..0163,∆logagew =+0.03+−00..1492). During
themergeritself,wefindlargeroffsets: ∆logM =−0.13+0.10and∆logage =−0.12+0.40. E(B−V)
C −0.14 w −0.26
values are generally recovered well, but the estimated total visual absorption A is consistently too
h. low, increasingly so for larger optical depths (∆AV = −0.54+−00..4406 in the mergerVregime). Since the
p largest optical depths occur during the phases of most intense star formation, it is for the highest
- SFRs that we find the largest underestimates (∆logSFR = −0.44+0.32 in the merger regime). The
o −0.31
masses, ages, E(B−V), A , and SFR of merger remnants (spheroids) are very well reproduced.
r V
t WediscusspossiblebiasesinSEDmodelingresultscausedbymismatchbetweenthetrueandtemplate
s
a star formation history, dust distribution, metallicity variations and AGN contribution. Mismatch
[ between the real and template star formation history, as is the case during the merging event, drives

the age, and consequently mass estimate, down with respect to the true age and mass. However, the
1
largeroptical depth towardyoung stars during this phase reduces the effect considerably. Finally, we
v
testedthephotometricredshiftcodeEAZYonthesimulatedgalaxiesplacedathighredshift. Wefind
7
a small scatter in ∆z/(1+z) of 0.031.
3
3 Subject headings: galaxies: distances and redshifts - galaxies: high redshift - galaxies: ISM - galaxies:
4 stellar content
.
1
0 1. INTRODUCTION biased samples missing quiescent galaxies lacking emis-
9 sion lines in their spectra (Kriek et al. 2006). For these
Understanding the growth and aging of galaxies over
0 reasons,most studies of high-redshift galaxieshave used
cosmictimerequiresreliableestimatesoftheirmass,for-
:
v mation epoch and star formation history. With the cur- stellarmassestimates derivedby modeling ofthe broad-
i rent generation of telescopes, stellar velocity dispersion band stellar energy distribution (SED) to characterize
X
the mass.
measurements can probe the gravitational potential in
r Since age estimates from Hα equivalent widths (van
a whichthe baryonicgalaxycontentresides out to z ∼1.3
(vanDokkum& Stanford2003;Holdenetal. 2005). Be- Dokkumetal. 2004;Erbet al. 2006c)orBalmer/4000˚A
yond this redshift, gas velocity dispersions can be mea- break strengths (Kriek et al. 2006) are very demand-
sured from emission lines, but do not always trace the ing in terms of telescope time and only attainable for
potential due to outflows (Franx et al. 1997; Pettini et the brightest galaxies, stellar ages as well are commonly
al. 1998, 2001; Shapley et al. 2003), and would lead to derived from broad-band photometry.
Over the past few years, SED modeling has been
Electronicaddress: [email protected] proven extremely valuable in characterizing the galaxy
1 Harvard-Smithsonian Center for Astrophysics, 60 Garden population in the early universe (e.g., Papovich et al.
Street,Cambridge,MA02138
2001; Shapley et al. 2001, 2005; F¨orster Schreiber et
2 Leiden University, Leiden Observatory, P.O. Box 9513, NL-
2300RA,Leiden,TheNetherlands. al. 2004). Nevertheless, a number of assumptions are
3 W.M.KeckPostdoctoral Fellow required for the limited number of data points (11 pass-
4 Department of Astronomy, University of California Berkeley, bandsinourcase,butoftenless)toleadtoasinglesolu-
Berkeley,CA94720
5 Kavli Institute for Cosmological Physics, and Department of tion in terms of physical properties such as stellar mass,
Astronomy and Astrophysics, University of Chicago, Chicago, IL stellar age, dust extinction, star formation rate (SFR),
60637 and often redshift.
6 EnricoFermiInstitute, Chicago,IL60637 First, the star formation history (SFH) is generally
7 SpitzerFellow
8 Department of Astronomy, Yale University, New Haven, CT modelled by a simple functional form: a single burst,
06520-8101 constant star formation, or an exponentially declining
2
model. Inreality,high-redshiftgalaxiesshowevidenceof limited samples of observed and simulated galaxies.
more complex SFHs, often with brief recurrent episodes We start with a description of the simulations in §2.
of star formation (e.g. Papovich et al. 2001; Fergu- Next, we explain the methodology of our SED modeling
son et al. 2002; Papovich et al. 2005). Second, we in §3. §4 discusses how well we can measure stellar pop-
use the approximation of a single foreground screen of ulation properties when a spectroscopic redshift is avail-
dust in accounting for the attenuation, even though in able. §5 repeats the analysis,nowleavingthe redshift as
reality the dust will be distributed in between the stars. an extra free parameter (i.e., fitting for the photometric
Third, we fit solar metallicity models. This is a com- redshift). Finally, we summarize the results in §6.
mon approachin modeling of high-redshift galaxy SEDs
2. THESIMULATIONS
in order to reduce the number of degrees of freedom in
the fitting procedure by one (e.g., F¨orster Schreiber et 2.1. Main characteristics
al. 2004; Shapley et al. 2005; Rigopoulou et al. 2006). The simulations on which we test our SED modeling
In addition, the tracks and spectral libraries on which were performed by Robertson et al. (2006). We refer
the stellar population synthesis models are based, have the reader to that paper for a detailed description of
the best empirical calibration for solar metallicity. Al- the simulations. Briefly, the simulations were performed
though consistent with the current metallicity estimates with the parallel TreeSPH code GADGET-2 (Springel
from near-infrared (NIR) spectroscopy of high-redshift
2005). The code uses an entropy-conservingformulation
galaxies (van Dokkum et al. 2004; Erb et al. 2006a; of smoothed particle hydrodynamics (Springel & Hern-
Maiolinoetal. 2008),itmustbe keptinmindthatthese quist2002),andincludesgascooling,amultiphasemodel
measurements are currently limited to the bright end of for the interstellar medium (ISM) to describe star for-
the galaxy population. Fourth, SED modeling generally mation and supernova feedback (Springel & Hernquist
assumes a purely stellar origin of the light, while obser- 2003), and a prescription for supermassive black hole
vational evidence for a substantial fraction of low lumi- growth and feedback (Springel et al. 2005b).
nosityAGNathighredshifthasbeenaccumulating(van At the start, each simulation consists of 120000 dark
Dokkum et al. 2004; Reddy et al. 2005; Papovich et al. matter particles, 80000 gas particles, and 80000 stellar
2006; Kriek et al. 2007; Daddi et al. 2007b). They may particles. Theyrepresenttwostable,coplanardiskgalax-
contribute to the optical SEDs. ies,eachembeddedinanextendeddarkmatterhalowith
Finally, one adopts a certain attenuation law, initial Hernquist(1990)profile. We haverealisationswhere the
mass function (IMF), and stellar population synthesis
disks start with a gas fraction of 40% and 80%. Stel-
code. Their appropriateness at low and high redshifts is lar masses at the start of the simulation varied from
much debated. 7.0×109 M⊙ to 2.3×1011 M⊙ per disk galaxy. Intotal,
In this paper, we address the impact of the first four we study 6 simulations (2 different gas fractions, and 3
assumptions (related to SFH, dust attenuation, metal- different masses) for which at 30 timesteps all informa-
licity, and AGN) using hydrodynamical simulations of tion was stored in a snapshot. Each snapshot was ana-
merging galaxies (see Robertson et al. 2006; Cox et al. lyzedasseenfrom30differentviewinganglesandplaced
2006). TheSPHsimulationsfollowthestarformationon at8redshiftsbetweenz =1.5and3(§2.2). Werepeated
a physical basis, resulting in more complex SFHs than ouranalysison a limited number of snapshotsandview-
areallowedintypicalSEDmodeling. Theykeeptrackof ing angles of merger simulations of non-coplanar disks
the distribution and metallicity of gas and stellar parti- andconcludethatthe resultspresentedinthis paperare
cles, allowing a determination of the line-of-sight depen- robust against such variations.
dent extinction toward each stellar particle separately Foragivenvirialvelocity,thehaloconcentration,virial
and a knowledge of the stellar metallicity as a function massandvirialradiuswerescaledfollowingRobertsonet
oftime. Here,weapply the sameSEDmodeling thatwe
al. (2006) to approximate the structure of disk galaxies
use for observed galaxies to broad-band photometry ex- at redshift z =3. In practice, this means that the mass-
tractedfromthe simulationoutputs, andstudy howwell and redshift-dependent halo concentration measured by
the mass, age, dust content, and SFR of the simulated Bullock et al. (2001) was adopted:
galaxies can be recovered.
−0.13
The reason we use merger simulations for this exer- C (M ,z)≈9 Mvir (1+z)−1, (1)
cise is threefold. First, galaxy mergers are believed to vir vir M
play an important role in galaxy evolution (see, e.g., (cid:18) coll,0(cid:19)
Holmberg 1941; Zwicky 1956; Toomre & Toomre 1972; where Mcoll,0 ∼ 8×1012 h−1 M⊙ is the linear collapse
massatz=0,andthatthefollowingscalingrelationswere
Toomre 1977), increasingly so at high redshift (see, e.g.,
used for the virial mass and virial radius of the progeni-
Glazebrook et al. 1995; Driver, Windhorst,& Griffiths
tors:
1995; Abraham et al. 1996). Moreover, along their evo-
lutionary path they are visible as vastly different galaxy V3
M = vir (2)
types, allowing to test the recovery of stellar population vir 10GH(z)
parameters under a wide range of conditions: gas-rich
V
star-formingdisks,dust-obscuredmergers,andquiescent R = vir , (3)
vir
10H(z)
spheroids. Finally, in a separate paper we will compare
predictions of the color distribution and mass density where V is the virial velocity and H(z) is the Hubble
vir
of high-redshift galaxies derived from these simulations parameter. Disk sizes were initialized according to the
with the observed galaxy population in deep fields. A Mo et al. (1998) formalism for dissipational disk galaxy
good understanding of what it is we measure with SED formationassumingthefractionofthetotalangularmo-
modeling is crucial in order to compare identical mass- mentum contained in the disk equals the fraction of the
3
totalmasscontainedinthedisk(Mdisk =0.041tomatch
Mvir
theMilkyWay-likemodelbySpringeletal. 2005a). The
disk scale length is then derived from the halo concen-
trationC (Eq.1)andthe galaxyspinλ. The adopted
vir
value of λ=0.033 is motivated by cosmological N-body
simulations (Vitvitska et al. 2002).
We set the ages of the stars existing at the start of
the simulation such as to represent a constant star for-
mation history prior to the start of the simulation at
a star formation rate (SFR) equal to that calculated in
the first phases of the simulation. The corresponding
metallicities of stars present at the start of the simula-
tion were then set according to the closed box model:
Z(t) = −yln[f (t)], where Z(t) is the metallicity of a
gas
stellar particle formed at time t, the yield y=0.02 and
f (t)isthegasfractionofthesystemattheconsidered
gas
time. Similarly,thegasatthestartofthesimulationwas
assignedauniformmetallicityZ (t )=−yln[f (t )]
gas S gas S
where t represents the start of the simulation, and
S
f (t ) = 0.4 or 0.8 respectively for our 2 gas fraction
gas S
runs. The closed box model represents an upper limit
on the allowed enrichment by heavy elements, which in
reality may be reduced by outflows or infall of metal-
poor gas (Edmunds 1990). The fact that we consider
2 gas fractions guarantees a wide range of progenitor
types, with ages of a few 100 Myr and Z = 0.004
gas
at the start of the simulation for f = 0.8 to typical
gas
stellar ages of a Gyr and nearly solar gas metallicity for
f =0.4. Startingfromtheinitialconditionsdescribed
gas
above, the GADGET-2 code computed the subsequent
evolution of the stellar populations using the star for-
mation and metal enrichment prescriptions outlined by
Springel & Hernquist (2003). The mass-weighted mean
stellar metallicity for the f = 0.4 runs increases in
gas
∼ 700 Myr from 0.4 Z⊙ to 0.9 Z⊙, after which it re-
mains constant. The metal enrichment of stars in the
f =0.8 runs proceeds rapidly, increasing in a few 100
gas
Myr from 0.1 Z⊙ to 0.5 Z⊙ and leveling off after ∼ 0.5
Gyr at values between 0.8 Z⊙ and Z⊙.
The overall timespan covered by each simulation was
2 Gyr. Fig. 1(a) illustrates the star formation history
of one of the merger simulations. Specifically, we show
a simulation starting with 40% gas fraction and ending
witha stellarmass of1.5×1011 M⊙, butthe SFHofthe
other simulations looks qualitatively similar. Fig. 1(b) Fig. 1.— Evolution of a typical merger simulation. (a) The
illustrates the build-up of stellar mass. In orderto allow star formationhistory, (b) the mass build-up, (c) the gas exhaus-
a fair test of the SED modeling with Bruzual & Char- tion, (d) the accretion rate history onto the black hole(s), (e) the
evolution of the intrinsic (i.e., unattenuated) and attenuated V-
lot (2003) templates (that include mass loss), we take
bandluminosity,(f)thedistributionofeffectivevisualextinctions
into account mass loss of each of the stellar particles for (attenuated minus intrinsic V-band magnitude) corresponding to
which the time of formation and gas mass from which it differentviewingangles,and(g)theintrinsicandattenuatedU−V
color. Crosssymbols inpanel (e) and(g) presentthe evolution of
was formed are storedin the simulation snapshots. This
theintrinsicphotometry. Fortheattenuatedphotometryinpanels
explains the slow decrease in total stellar mass at late (e) to (g), a binned representation is used where a darker inten-
times in Fig. 1(b). Fig. 1(c) shows the exhaustionof gas sityindicatesalargernumberofviewingangles. Thedashedcurve
from which the stars are formed, and Fig. 1(d) presents representsthemedianevolution. Thedottedlinesindicate thein-
tervalcontainingthecentral68%oftheviewingangles. Thecross
theaccretionhistoryontotheblackhole(s). Wedrawthe
symbols mark the sampling of snapshots when the full physical
time axis relative to the actual moment of merging, de- information of all SPH particles was stored to disk. After a first
fined as the timestep when the two black hole particles bump in the star formation rate during the first passage of the
become one, coinciding with the peak in the accretion progenitors, a peak instar formationisreached for abrief period
duringwhichseveralhundredsofsolarmassesofgasareconverted
history. Crosssymbolsindicatethe snapshots,separated
into stars. The typical extinction for a random line of sight is
by 70 Myr, when all physical information was stored to peaking around the same time. Shortly after, the accretion onto
disk. thesupermassiveblackholeismaximal,coincidingwiththemerger
As time progresses, the orderly rotation and star for- between the two progenitor black holes. The reddest U-V colors
arereachedduringthemergerremnantphase.
mation in the disks is disturbed by each others gravi-
4
tational pull. The star formation history shows a first, its contribution to the total light is significant.
but rather shallow, bump during the first passage of the Galaxies, certainly in their actively star-forming
disks. Next,gravitationaltorquesenablethegastoloose phases, are not devoid of gas and dust. It is therefore
angularmomentumandflowtothecenterswhereittrig- crucial to account for the obscuring and reddening ef-
gers a starburst (Larson & Tinsley 1978; Noguchi 1988; fect dust has on the stellar and AGN emission. We
Hernquist 1989; Barnes & Hernquist 1991, 1996; Mi- compute the optical depth along the line of sight to-
hos & Hernquist 1994, 1996). Meanwhile, part of the ward each stellar particle. To do so, we compute the
inflowing gas is fed to the central supermassive black local gas density on a fine grid derived from the SPH
holes(SMBHs). Once the SMBHsgrowmassiveenough, formalism and the particle distribution (Hopkins et al.
they producea luminousquasar(Sanders etal. 1988a,b; 2005a) and integrate out from each particle along the
Hernquist 1989; Sanders & Mirabel 1996; Genzel et lineofsighttolargedistance. Thesimulationsarebased
al. 1998) whose feedback contributes to halting subse- on the GADGET multi-phase ISM model developed by
quent star formation (Di Matteo et al. 2005; Springel Springel & Hernquist (2003). This model calculates the
et al 2005a), leaving a red spheroid galaxy as remnant local mass fraction in the warm/hot (T = 105−107 K,
(Robertson et al. 2006; Cox et al. 2006). diffuse, partially ionized) and cold (T = 103 K, in the
simulations both associated with molecular clouds and
2.2. Extracting photometry from the simulation output HI cloud cores) phases of dense gas, assuming pressure
Theevolutionarypathasoutlinedin§2.1isfollowedby equilibrium between the two phases. Following Hopkins
theGADGET-2codeatafine timeresolution(∆t∼104 et al. (2005b), the attenuation along the line of sight
yr). At sparser timesteps (70 Myr apart), the positions, is then derived from the density of the warm/hot-phase
masses,ages,andmetallicitiesofallparticleswerestored. component only. Hopkins et al. (2005b) found typi-
It is from these simulation snapshots that we derive the cally small volume filling factors (< 0.01) and cross sec-
observed SEDs of the merger as a function of time. The tions of the cold-phase “clumps”, motivating their ap-
appliedtechniqueissimilartothatusedbyRobertsonet proach. The assumption that most of the lines of sight
al. (2007) to translate simulations of the most massive only pass through the warm/hot-phase component pro-
z ∼4−14 galaxies into observables. vides effectively a lower limit on the optical depths. We
Thelightavirtualobserverwouldreceivefromthesim- use a gas-to-dust ratio equal to that of the Milky Way,
ulatedmerger,iscomposedofstellarandAGNemission, (AB/NHI)MW = 8.47×10−22 cm2, with a linear scaling
the latter only contributing significantly during a brief factor accounting for gas metallicities deviating from so-
period of time. We ignore any contribution from emis- lar: AB/NHI = (Z/0.02)(AB/NHI)MW. As default, we
sion lines produced by the gas content of the galaxies, adopt the Calzetti et al. (2000) attenuation law for the
possibly contributing on the order of 0.1 mag in the op- wavelength dependence of the optical depth. Changes
tical broad-band photometry. Furthermore, we account in the synthetic photometry when adopting a SMC-like
forattenuationbyinterstellardustandLymanforestat- or Milky Way-like attenuation law from Pei (1992) will
tenuation by the intervening medium between the red- be discussed. The computationof opticaldepths was re-
shifted galaxyand the observerfollowingMadau(1995). peated for 30 viewing angles, with directions uniformly
Thecombinationofthesesteps,describedinthissection, spacedinsolidangledcosθdφ. Fig.1(f)presentsthedis-
leads to observables that are similar to the real obser- tribution of effective visual extinction values (observed
vations that we model with stellar population synthesis minus intrinsicV-bandmagnitude) asa functionoftime
codes. since the merger. The extinction varies in the follow-
First, we focus on the computation of intrinsic (i.e., ing way. In the early stages typical extinction values
unattenuated) magnitudes from the stellar component. are modest, with the exception for a few lines-of-sights
Each of the stellar particles is treated as a single stellar were the disks are seen edge-on. The overall extinction
population characterized by its mass, age, and metal- alongalllines-of-sightreachesapeakduringthe merger-
licity. We choose to use the Salpeter (1955) IMF, as triggered starburst and drops to very low values after
was done in previous observational work (e.g. F¨orster star formation has ceased.
Schreiber et al. 2004; Wuyts et al. 2007). We then in- Finally, in computing the observer-frame apparent
terpolate the corresponding luminosity for each stellar magnitudes, we redshift the attenuated SED and con-
particle froma gridofSSP templates with differentages volve it with the same set of filtercurves that we have
and metallicities from the stellar population synthesis deep observations for in the Chandra Deep Field South
code by Bruzual& Charlot(2003,hereafter BC03). Fig. (CDFS; Wuyts et al. 2008): B435, V606, i775, z850, J,
1(e) illustrates the evolution of the intrinsic rest-frame H,Ks, [3.6µm],[4.5µm], [5.8µm],and[8.0µm]. Here,we
V-band luminosity for one of the simulations. apply the depression factors DA(z) and DB(z) given by
For the AGN emission, we scale a luminosity- Madau (1995) for the Lyman forest attenuation of the
dependent template SED by the bolometric black hole continuum between Lyα and Lyβ and between Lyβ and
luminosity given by the simulation. The template SED the Lyman limit respectively. The flux blueward of the
was derived from the optically blue (i.e., unreddened) Lymanlimit (λL =912˚A)wassetto 0, asis done by the
quasar sample by Richards et al. (2006) with locally at- HYPERZcode(v1.1,Bolzonellaetal. 2000)thatweuse
tenuatedlightbeingreprocessedasanIRbumplongward for SED modeling.
of λ > 1 µm. A full discussion of the AGN template is In practice, it is computationally more convenient to
presented by Hopkins, Richards,& Hernquist (2007). In interpolatetheapparentmagnitudesinagivenpassband
most of our analysis, we will consider the stellar light for each of the stellar particles on a precompiled grid of
only. §4.5 addresses the impact AGN can have on the BC03 apparent magnitudes at the redshift of interest.
outcome of SED modeling during the brief period when The internal dust attenuation is then applied using the
5
value ofthe Calzetti etal. (2000)attenuationlaw atthe weightedage(anddependstoalesserdegreeonthegrad-
effective wavelength for that passband. We tested that ual increase in stellar metallicities). It bends down to
thismethod,asopposedtoattenuatingthefullresolution bluerU−V asnewstarformationistriggeredduringfirst
BC03spectrumandthenconvolvingwiththefiltercurve, passageoftheprogenitors,andagainduringtheshorter-
leadstophotometricdifferencesofatmostafewpercent. livednuclearstarburstphase. Eventually,thecolortrack
We note that we never attempt to separate the light leads to the regionin color-colorspace where also quies-
into the contribution from the two progenitors. Instead, cent observed galaxies reside. In reality, the path taken
we always study the total photometry, as if the merging in color-color space will not merely depend on the star
system were unresolved. formation history. Taking into account attenuation by
In future studies, we will employ full-fledged radiative dust, the integrated colors get redder. This is particu-
transfercodessuchasSUNRISE(Jonsson2006)totrans- larlytrueduringthephasesofactivestarformation. We
late the simulation snapshot information to observables. note that the precise shape of the color track depends
SUNRISE calculates scattering, absorption, and reemis- not only on initial conditions (gas fraction, mass, disk
sionoflightpassingthroughthecoldand/orhotphaseof orientations, ...) but also on viewing angle. In fact, as
the ISM, with the optional inclusion of a subgrid model illustrated in Fig. 3, color differences between different
that accounts for the obscuring effects of birth clouds in viewing angles at a given time can be of similar size as
whichyoung star-formingregionsare embedded (Groves colorchangesbetweendifferenttimesforagivenviewing
etal. 2008). Reemissionbydustonlyinfluencesthespec- angle. Atlatertimes,the roleofdustisminimalandthe
tralshape longwardofthe wavelengthbandsusedinour remnantconvergestocolorstypicalforquiescentgalaxies
SED modeling. Preliminary analysis of SUNRISE SEDs (i.e., within the red wedge).
indicates that the other effects might lead to a stronger
extinction during the star-forming phases, while leaving 2.4. The colors and SEDs of simulated and observed
galaxies
the spheroid photometry unchanged with respect to the
photometry computed in this paper. It will be interest- Prior to analyzing the performance of our SED mod-
ing,inthelightofthefindingspresentedhere,toinvesti- eling procedure, it is important to confirm that the sim-
gate the shape of the effective attenuation law obtained ulated galaxies have spectral shapes resembling those of
withsuchamoresophisticatedcode,andits dependence real high-redshift galaxies in observed deep fields, thus
onthe parametersofthe radiativetransfer. For the sake validatingtheirroleastestobjects. Tothisend,weindi-
of this paper, our line-of-sight photometry has the ad- cate the binned color distribution of simulated galaxies,
vantage of being transparent and simple. viewed from different angles and during different phases
of their evolution, in a rest-frame U −V versus V −J
2.3. The color evolution of merging galaxies
color-color diagram (Fig. 4). Plus symbols show the lo-
With the synthetic photometry at hand, we are now cation of observed galaxies in the HDFS (Labb´e et al.
able to follow the color evolution of simulated galaxies 2003), MS1054–03 (Fo¨rster Schreiber et al. 2006), and
throughout the merger event. We illustrate the spa- the CDFS (Wuyts et al. 2008) selected by their photo-
tially resolved color evolution for a face-on view of a metricredshift(orspectroscopicwhenavailable)toliein
typical simulation in Fig. 2. This particular simulation the sameredshift range(1.5<z <3.0). We alsoapplied
has an initial gas fraction of 80% and final stellar mass astellarmasscutatM∗ >1.4×1010M⊙fortheobserved
of 1.2×1011 M⊙. The 3-color images are composed of sample; the lowest initial stellar mass for the considered
rest-frame U (blue), V (green), and J (red). On each set of simulations. Here, we do not attempt to statisti-
postage stamp, we indicate the snapshot number, time cally compare the two samples. The abundances of dif-
since the merger, and whether the intrinsic (Int) or at- ferenttypesofgalaxiesaspredictedfromthesimulations
tenuated (Att) colors are plotted. The interval between will be addressed by Wuyts et al. (2009b). For our cur-
consecutive snapshots is 70 Myr. The color distribution rentpurposeofanalyzingtheeffectsofstarformationhis-
is clearly not homogeneous throughout the merger evo- tory, dust, metallicity and AGN on SED modeling, it is
lution. Instead, color gradients are present, with the sufficienttonotethatthereisalargeoverlapbetweenthe
nuclear regions being intrinsically bluer due to new star color-colorspacespannedbythesimulatedandobserved
formation, but effectively redder than the surrounding galaxies. Every simulated galaxy considered in this pa-
material due to the presence of dust. We return to this per has counterparts in the real universe with similar
point in an analysis of observedversus simulated galaxy rest-frame optical and optical-to-NIR colors. However,
colorsbyWuytsetal. (2009b). Inthispaper,werestrict the observed distribution extends to colors that are red-
ourselves to the study of integrated colors. derbyafew0.1mag,bothinU−V andinV−J,thanthe
The corresponding evolutionary tracks in integrated simulations considered here. Given the one-sided nature
rest-frameU−V versus V −J color-colorspaceare pre- of the different color spread, it is unlikely that this can
sentedin Fig.3. Labb´eet al. (2005)firstintroducedthe beattributedtophotometricuncertaintiesalone. There-
observed-frame equivalent of this diagram to illustrate fore, we caution that our results may not necessarily be
the wide range of galaxy types at high redshift ranging extrapolated to the reddest galaxies present in observed
fromblue,relativelyunobscuredstar-formingsystemsto samples. Wuyts et al. (2009b) discuss several possible
dustystarburststo quiescentredgalaxies. The colorcri- origins of the color discrepancy, particularly in V −J,
terionproposedbyLabb´eetal. (inpreparation)toselect rangingfromthe method to compute model photometry
galaxies of quiescent nature is plotted as the red wedge to differences between the evolutionary history of high-
in Fig. 3. redshift galaxies in the real universe and in our merger
Considering the intrinsic (unattenuated) colors, the simulations. There we analyze, for example, the pres-
evolutionarytrackhasadirectrelationtothemeanlight- ence of color gradients, and the dependence of the color
6
Fig. 2.— Three-color postage stamps (rest-frame U (blue), V (green), J (red)) of a typical merger simulation. The top three rows
illustratetheintrinsicevolution, ignoringextinction. Thebottom threerowsshowtheevolutionwhentakingintoaccount attenuation by
dust. Significantchanges incolorareobservedovertime,andbetween intrinsicandattenuated images.
distribution on the adopted attenuation law and stel- et al. 2006).
lar population synthesis code. Other models than BC03 Toascertainthatobservedandsimulatedgalaxieswith
that include a more significant contribution of the ther- similarU−V andV−J colorshavesimilarSEDsoverthe
mally pulsing asymptotic giant branch (particularly in wholespectralrange,Fig.5presentstherest-frameSEDs
the near-IR) result in a color distribution that is shifted ofobjectsinregion1-6ofFig.4. Again,thebinneddistri-
towards redder V −J colors (Maraston 2005; Maraston butionrepresentsthesimulations,withdarkergrayscales
7
Fig. 3.— Evolutionary tracks ina rest-frameU−V versus V −J color-color diagram for the typical merger simulation shown in Fig.
2. Weillustratetheintrinsiccolorevolutionaswellasthe evolutionofattenuated colorswithtimeasweviewthemergingpairface-and
edge-on. Snapshots 70 Myrapart aremarked with smalldots. Key phases corresponding to the numbers indicated inFig. 2 and Fig. 14
areindicatedwithlargesymbols. Timesince(orbefore)thenactualmomentofmergingisindicatedinthetoprightcornerofeachpanel.
Colors can vary significantly at a given time (by ∼ 0.5 mag) as we view the merging system from different lines of sight. The starburst
occuringduringthemergerisverydusty, leadingtoreddercolorsatthatstage.
indicating a larger number of objects. Overplotted with
black dots is the broad-band photometry of our ob-
servedsamplewithinthesameregionofcolor-colorspace,
placed at the respective rest-frame wavelength. The
SEDs are normalized to the rest-frame V-band. By se-
lection,the observedandsimulatedphotometrymatches
well at rest-frame U and J. In between the UVJ filters,
andoutsidetheU-to-Jrange,nocorrespondencewasim-
posed. ThefactthattheUVspectralshapeandtheNIR
tail of the observed and simulated SEDs show a general
agreement, is encouraging. We conclude that the simu-
lated photometry can be adopted as a realistic input to
our SED modeling procedure. The results of our anal-
ysis will be applicable to observed galaxies with similar
colors.
3. SEDMODELING:METHODOLOGY
We characterize physical parameters such as stellar
Fig. 4.— Rest-frame U −V versus V −J color-color diagram
mass,stellarage,dustattenuation,andSFRbymatching
showingthebinnedcolordistributionofthesimulationsseenunder
differentviewinganglesandatdifferentepochs. Overplotted(plus the observed-framebroad-bandphotometry to synthetic
symbols)aretherest-framecolorsofobservedgalaxieswithM∗> templates from the stellar population synthesis code by
1.4×1010 M⊙ at 1.5<z<3intheHDFS, MS1054–03, andthe BC03. We use the HYPERZ stellar population fitting
CDFS. Observed galaxies with matching colors are found for all
code,version1.1(Bolzonellaetal. 2000)andfittheSED
simulated galaxies. The reddest observed sources in U −V and
V −J are not reproduced by the considered set of simulations. twice: firstfixingtheredshifttothetruevalue(forwhich
Rest-frameSEDsforsourcesinregions1-6aredisplayedinFig.5. we computed the simulated photometry), next adopt-
ing a photometric redshift estimate obtained from the
EAZY version 1.0 photometric redshift code (Brammer
8
Fig. 5.—Rest-frameSEDsofsimulatedgalaxiesinregions1-6ofFig.4. Adarkerintensityofthebinnedrepresentationindicatesalarger
densityofsimulatedgalaxieswiththatfluxlevel. Ineachpanel,wegivethecentral68%intervalofthedistributionoftimesbeforeorsince
themergerforthesimulationsnapshotswithphotometryintherespectiveregion. Overplotted(black dots)aretherest-framebroad-band
SEDsofobserved1.5<z<3galaxieswithM∗>1.4×1010 M⊙ intheHDFS,MS1054–03,andtheCDFS.Ageneralagreementbetween
observedandsimulatedspectralshapesisobserved,alsooutsidetheU-to-J rangewherethecorrespondencewasnotimposedbyselection.
et al. in preparation). In each case, the full B -to-8 several authors have used an IMF with fewer low mass
435
µm SED, sampled with identical passbands as available stars,suchaspresentedbyKroupa(2001). Wenotethat
for the GOODS-CDFS (B , V , i , z , J, H, K , the choice of IMF is not the focus of this study, and our
435 606 775 850 s
[3.6 µm], [4.5 µm], [5.8 µm], [8.0 µm]), was fed to HY- results remain valid as long as we use the same IMF to
PERZ.Randomphotometricuncertaintieswereassigned compute the synthetic photometry as to model the re-
as to mimic real observations in the CDFS, and fluxes sulting SEDs. Likewise, we use for consistency the same
in each band were perturbed accordingly. Precisely, for stellarpopulationsynthesiscode(BC03)tocomputeand
each of the 43200 SEDs corresponding to a simulated to fit the synthetic SEDs.
galaxy observed during a certain phase of its evolution, When refering to the age derivedfrom SED modeling,
placed at a certain redshift, and observed along a cer- we mean the mass-weighted age obtained by integrating
tain line-of-sight, we compute 5 realizations of the SED over the different ages of SSPs that build up the best-fit
byintroducingagaussianperturbationinallbandswith SFH, weighted with their mass fraction taking into ac-
the amplitude derivedfromthe depth of GOODS-CDFS countmasslossovertime. Thismeasureaimstoquantify
observations in the respective bands. A minimum error theageofthebulkofthestars. ForanSSP,itequalsthe
of 0.08 mag was adopted for all bands, preventing small time passed since the single burst. For a CSF history,
errors from dominating the fit. it is essentially half the time passed since the onset of
As in Wuyts et al. (2007), we selected the least χ2 star formation. The τ SFH represents an intermedi-
300
solution out of three possible star formation histories: a ate case.
single stellar population (SSP) without dust, a constant
4. RESULTSFROMSEDMODELINGATFIXEDREDSHIFT
starformation(CSF)historywithdust(A varyingfrom
V
0 to 4 in steps of 0.2), and an exponentially declining First, in §4.1, we present the overall performance of
starformationhistory with a fixede-folding timescale of thestandardSEDmodelingappliedtothe’full’photom-
300 Myr (τ ) and identical range of A values. Ages etry, taking into accountthe effects of both attenuation,
300 V
were constrained to be larger than 50 Myr, to prevent metallicity,andAGNcontributionasrealisticallyaspos-
improbably young ages, and smaller than the age of the sible. Second, we discuss the impact from different as-
universe at the observed redshift. We used a Calzetti pects influencing the colors and luminosities of galaxies
et al. (2000) attenuation law, and assumed solar metal- separately. Inordertoisolateeffectsfromstarformation
licity and a Salpeter (1955) IMF with lower and upper history (§4.2), dust attenuation (§4.3), metallicity varia-
mass cut-offs 0.1M⊙ and 100M⊙. In recent literature, tions (§4.4), and AGN contribution(§4.5), we computed
the photometry for each snapshot with and without at-
9
tenuation, with and without AGN contribution, and us- the extinction (see §4.3). Briefly, such a SFH mismatch
ing solar metallicity, or the metallicity as computed by leads to age underestimates, hence M underestimates,
the simulation for each stellar particle. To each of these LInt
and, added to an insufficient dust correction, to mass
sets of SEDs, we applied the modeling described in §3.
underestimates. Finally, the correspondence is best at
Thisapproachenablesustoreconstructtheanalysisstep log(M/M )∼0, where the merger remnants reside.
final
by step, addingone aspectata time. Finally, we discuss
The reddening (Fig. 6(c)) is overall well reproduced.
what our analysis means for galaxies with different rest-
Only at the highest reddening levels, the agreement de-
frame colors (§4.6).
teriorates. The latter correspondto the times when and
4.1. Overall performance viewing angles under which the effect of increased ex-
tinction toward young stars is maximal, as will be ex-
The combined effects of mismatch between true and
plained in §4.3. As opposed to the reddening, however,
template SFH, attenuation by dust, metallicity varia-
the extinction (Fig. 6(d)) shows large systematic under-
tionsandAGNactivityonourabilitytocharacterizethe
estimates. Using
stellar population of a galaxy are summarized in Fig. 6.
Here, we plot the best estimate from SED modeling ver- AV
R = =4.05 (7)
sus the true1 value of the considered stellar population V E(B−V)
property. We bin the distribution of points for different
to translate the selective absorption E(B − V) into a
initial conditions, timesteps and lines-of-sight. Darker
total visual absorption A results in an underestimate
intensities represent a higher density in the bin. The V
over the whole range of A values, particularly during
solidcurverepresentsthe medianofthedistributionand V
thehighlyobscuredphases. Anobserverislimitedbythe
the dotted curves mark the central 68% interval.
light that he/she receives. In §4.3, we discuss in depth
The youngestagesinFig.6(a)correspondto the early
howthesumofemittingsourcesthatareeachattenuated
stages of simulations with an initial gas fraction of 80%.
according to Calzetti et al. (2000) does not follow that
The stars present at the start of these simulations were
same reddening law.
assigned young ages and low metallicities (see §2.1). In
Finally, since the reliability of SFR indicators from X-
§4.4,wedescribehowmodelingsub-solarmetallicitypop-
rays over optical and IR to radio wavelengths has been
ulations with solar metallicity templates can lead to age
topic of much recent debate (e.g., Reddy et al. 2006;
overestimates. Since the lower gas fraction runs start
Papovich et al. 2006; 2007; Daddi et al. 2007a), it is
with higher stellar ages and metallicities, they do not
interesting to investigate its recovery by modeling the
show this trend. Fig. 6(b) compares the recovered and
optical-to-8µmSEDs. This is presentedinFig.6(e). At
true stellar mass, normalized to the final stellar mass
of the simulation. At low M/M ratios, i.e., at the lowand intermediate SFRs (SFRtrue <100 M⊙/yr), we
final findasatisfyingagreement,withamedianoffsetthatin-
start of the high gas fraction simulations, the mass esti-
creasesslightlytowardshigherSFRs. Formorethan84%
mates agree well with the true values. Here, the reason
is that biases in age and extinction average out. On the of the galaxies with SFRtrue >100 M⊙/yr, we underes-
timate the SFR, typically by factor of 3. These systems
one hand, the overestimated age leads to an overesti-
often suffer strong dust obscuration, and therefore this
mate ofthe intrinsic mass-to-lightratio ( M > bias in SFR directly relates to the large underestimates
LInt estimate
M ). Ontheotherhand,theamouhntofiextinction of extinction at the high AV end in Fig. 6(d).
LInt true Inorderto quantifythe performanceofthe SEDmod-
thendsitobeunderestimated( LInt < LInt ). eling in estimating stellar mass-weighted ages, we define
LAtt estimate LAtt true ∆log(agew) as log(agew,recovered)−log(agew,true). Sim-
As aresult,the massestimathe forithis phaseihsrelaitively ilar definitions are used to quantify the offset in mass,
robust: reddening and extinction, always indicating an underes-
M =L LInt M (4) timatewithanegativevalueof∆=parameterrecovered−
estimate Att L L parameter . Fig. 7 presents the performance of the
(cid:20) Att(cid:21)estimate(cid:20) Int(cid:21)estimate true
SED modeling on the full photometry (including dust,
L M
≈L Int (5) metallicity variations, and AGN), expressed by the ∆
Att
L L
(cid:20) Att(cid:21)true(cid:20) Int(cid:21)true values,as a function oftime since the merger. We adopt
=M (6) thesamebinnedplotstyleasinFig.6,withdarkerinten-
true
where L is the intrinsic and L is the attenuated sities meaning a higher density in the bin. Open boxes
Int Att
(i.e., observed) luminosity. The largest systematic mass containlessthan1%ofthetotalnumberofSEDsatthat
underestimates occur at intermediate M/M , during timestep.
final
the merger-triggered star-forming phases of the simula- WequantifytheperformanceoftheSEDmodelingsep-
tion. This can be explained in terms of a mismatch be- aratelyforgalaxiesinthe ’disk’,’merger’,and’spheroid’
tweenthetrue SFHandtheSFHofthebest-fitting tem- regime by computing the median and the central 68%
plate(see§4.2),incombinationwithanunderestimateof interval of the distribution of ∆ values for all sim-
ulation snapshots (under a range of viewing angles)
1 Hereafter,weuse’true’whenreferringtothevalueofastellar in that phase. We find ∆logage = +0.03+0.19,
w,disk −0.42
population property as computed using information on all SPH ∆logage =−0.12+0.40,and∆logage =
particlesinthesimulation. Quantitiesderivedbyfittingtemplates w,merger −0.26 w,spheroid
tointegratedSEDsarereferredtoas’estimates’. While’true’mass −0.03+0.12. The underestimate and scatter is largestfor
−0.14
and mass-weighted age can be read directly from the simulation, thephasesofmerger-triggeredstarformation. Theseare
wenote that parameters as ’true’reddening andvisualextinction
the statistics for low and high gas fraction runs com-
dependontheadoptedstellarpopulationsynthesiscodeanddetails
oftheradiativetransfer,whichthemselvesmayhavebiases. bined. Considering simulations with an initial gas frac-
10
Fig. 6.— Overall performance of the SED modeling. Recovered versus true (a) mass-weighted stellar age, (b) ratio of current to final
stellar mass, (c) effective reddening (i.e., attenuated minus intrinsic B−V color), (d) effective visual extinction (i.e., attenuated minus
intrinsic V-band magnitude), and (e) star formation rate. The SED modeling was performed on the total (stellar+AGN) attenuated
photometrycorrespondingtosimulationswitharangeofmasses,startingwith40%and80%gasfractions,andseenatdifferenttimesteps
andunder different viewingangles. Thesolidcurves indicate the mediananddotted curves comprisethe central 68% of the distribution.
The total visual extinction AV is the least constrained of the studied parameters. In particular for heavily extincted galaxies the AV is
greatlyunderestimated.