Photometric Evolution of Galaxies in Cosmological Scenarios

13 Pages·0.79 MB·English

by  Gertrud Contardo

February 1, 2008
Photometric Evolution of Galaxies in Cosmological Scenarios
Gertrud Contardo1,2, Matthias Steinmetz1,3, and Uta Fritze–von Alvensleben4
[email protected],[email protected],[email protected]
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ABSTRACT
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The photometric evolution of galaxies in a hierarchically clustering universe is inves-
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tigated. The study is based on high resolution numerical simulations which include the

1 effects of gas dynamics, shock heating, radiative cooling and a heuristic star formation
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scheme. The outcome of the simulations is convolved with photometric models which
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7 enables us to predict the appearance of galaxies in the broad band colors U, B, V, R,
2 I and K. We demonstrate the effect of the mutual interplay of the hierarchical build-
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up of galaxies, photometric evolution, k-correction, and intervening absorption on the
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8 appearance of forming disk galaxies at redshift one to three. We also discuss to what
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extend the numerical resolution of current computer simulations is sufficient to make
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quantitative predictions on surface density profiles and color gradients.
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Subject headings: cosmology: theory – galaxies: formation, evolution – methods: nu-
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1Max-Planck-Institut fu¨r Astrophysik,Postfach 1523, 85740 Garching, Germany
2Present address: European Southern Observatory,Karl-Schwarzschild-Str. 2, 85748 Garching, Germany
3Steward Observatory,Universityof Arizona, Tucson, AZ 85721, USA
4Universit¨atssternwarte G¨ottingen, Geismarlandstraße 11, 37083 G¨ottingen, Germany
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1. Introduction heating and cooling, hydrodynamic shocks, ra-
diative cooling and star formation (Katz 1992;
Over the past few years, the advent of a new
Navarro&White1993; Steinmetz&Mu¨ller1994,
generation of large telescopes and the superb
1995; Evrard, Summers & Davis 1994, Tissera,
imagingquality oftherefurbishedHubble-Space-
Lambas & Abadi, 1997). However, the required
Telescope have changed the way we can look at
numerical resolution (≈ 1kpc) together with the
the formation and evolution of galaxies. Galax-
demandingnumerical algorithms and the limited
ies are routinely identified at redshift z ≈ 1 and
computationalpowerofthepresentgeneration of
alsoobjectsatredshiftsz ≈ 3havebeenoptically
supercomputers constrain current simulations to
resolved (Steidel et al. 1996). Theoretical work
small box sizes, i.e., each simulation only creates
hasbeenguidedbythehierarchicalclusteringhy-
very few galaxies. Thus hydrodynamical simula-
pothesis. In this scenario, the Cold Dark Matter
tions can deal with the details of the galaxy for-
(CDM) model is probably the best known ex-
mation process, but can make only limited pre-
ample, structures form as halos of progressively
dictions on statistical properties.
larger mass merge, virialize and form new higher
Numerical simulations have also helped iden-
mass objects. Thus, the galaxy formation pro-
tifying some of the major problems of the hi-
cess can be modeled from ab-initio conditions
erarchical clustering hypothesis: Since cooling
and model predictions can be rigorously com-
times scale inversely with density, the dissipa-
pared to observational data. Two complemen-
tive collapse of gas should have been more ef-
tary techniques have been shown to beespecially
ficient at high redshift because the dark matter
powerful.
halospresentatthattimeweredenser,aswasthe
Inso-calledsemi-analyticalstudies(Kauffmann,
universe as a whole. Thus gas cools and settles
White&Guiderdoni1993; Coleetal.1994), phe-
into rotationally supported disks already when
nomenological recipes are used to model the ac-
the first level of the hierarchy collapses. Conse-
cumulation of gas at the center of dark matter
quently, models predict an overabundance of low
halos and its transformation into stars. The in-
mass galaxies as well as disk galaxies which for
volved free parameters are calibrated by match-
a given circular velocity are too massive (White
ing present day properties of galaxies, e.g., the
& Rees 1978). A related problem is the size
properties of the Milky Way or the Tully-Fisher
of present day disk galaxies: Due to the fre-
relation. Thesetechniques arecomparablycheap
quent merging angular momentum is efficiently
as far as computation is concerned and thus al-
transported from thebaryons to thedark-matter
low alarge coverage of theparameter space. The
halo resulting in disk galaxies which are too con-
major strength of the semi-analytical approach
centrated compared to present day disk galax-
liesinmodelingstatisticalpropertiesofthewhole
ies (Navarro, Frenk & White 1995; Navarro &
galaxy population as, e.g., the luminosity func-
Steinmetz 1997). Feedback processes due to star
tion of galaxies. Its disadvantage is that little
formation, like stellar winds or supernovae, have
can be said on details of the galaxy formation
repeatedly been envisioned to solve this over-
process or the exact structure and kinematics of
cooling problem (e.g., Dekel & Silk 1986). How-
galaxies.
ever, a simulation which includes the effect of
Numerical hydrodynamical simulations which star formation and which is consistent with ob-
follow the formation of individual galaxies in de- servations has not been performed yet.
tail fill in that gap. Indeed, advanced numeri-
Inthispaperwemergetheapproachofnumer-
cal simulations include all the relevant physical
icalsimulationswithtraditionalmethodsofspec-
processes: gravitation, gas dynamics, adiabatic
trophotometric synthesis. This hybrid scheme
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enablesustoperformanevenmorerealisticcom- massinputbysupernovaeandevolving starsinto
parison between model predictions and actual the ISM. The supernova energy is added to the
observations. The structure of the paper is the thermal energy of the surrounding gas. Input
following: In section 2 details of the numerical in kinetic energy (Navarro & White 1993) is not
simulations and the star formation scheme are directly implemented but is described by an effi-
providedandthespectrophotometricmodelingis ciency parameter which is of the order of a few
presented. In section 3 we apply these methods per cent, an assumption that is justified since we
tomodeltheappearanceof highredshiftgalaxies preferably concentrate on the formation of lumi-
as they form in CDM like universes. In section 4 nous galaxies like the Milky Way.
we describe to what extend current simulations
may even allow us to analyze the detailed struc- 2.2. Initial conditions
ture of galaxies at high and low redshift. Section
We use idealized initial conditions as pro-
5 summarizes the results and draws our conclu-
posed by Katz (1991) and discussed in more
sions.
detail in SM2: We consider an isolated sphere
on which small scale fluctuations according to a
2. Methods
CDM power spectrum are superimposed. To in-
corporate the effects of fluctuations with longer
2.1. Numerical simulations
wavelengths, the density of the sphere has been
The simulations were performed using Grape- enhanced and rigid rotation corresponding to a
SPH (Steinmetz 1996), a hybrid scheme of a spin parameter of λ = 0.08 has been added.
smoothedparticlehydrodynamics(SPH)approach The simulation is identical to that presented in
with a direct summation N-body routine which SM1 and SM2 where a disk galaxy similar to the
uses the hardware N-body integrator GRAPE. Milky Way forms. These idealized initial condi-
The code is specially designed to follow a three tions are fairly realistic for the early formation
component system of gas, stars, and dark matter epochs (z > 2) when the sphereitself has not yet
and has high resolution in space and time due to collapsed. The late formation epoch, however,
the useof individualsmoothinglengths and time is dominated by the collapse of the sphere and
steps. It includes the effects of pressure gradi- hence proceeds more smoothly than under more
ents, adiabatic heating and cooling, shocks and realistic conditions. Due to the smooth infall at
radiative cooling. low redshifts the simulation does not suffer from
In the simulations presented here, a star for- the angular momentum problem. Furthermore,
mation scheme similar to the one in Steinmetz this model allows for very high numerical reso-
& Mu¨ller (1994, 1995, henceforth SM1 and SM2; lution (spatial resolution 1kpc, mass resolution
see also Katz 1992) is used: Star formation is 107M⊙) at comparably low computational cost.
modeledbycreatingnewcollisionless “star parti-
cles” in regions wherethegas is locally Jeans un- 2.3. Simulation outcome
stable and where the cooling timescale is shorter
At any redshift, the simulations provide the
than the local dynamical time scale. The orbits
spatial distribution of star particles. Each star
of these newly formed star particles are subse-
particlecorrespondstoapopulationofaboutone
quently followed in a self-consistent fashion, as-
million stars which have formed in a burst, i.e.,
suming that they are only affected by gravita-
the wholegalaxy is asuperpositionof several ten
tional forces. Young star particles devolve en-
thousands of mini starbursts. Each of the star
ergy and metal enriched mass to their surround-
particlesisdescribedbyitsage(timepassedsince
ing gas, an effect that mimics the energy and
creation) and its metallicity.
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an age between 3 and 4Gyr. The majority of
these star particles has a metallicity of above so-
lar (SM1). There is little offset between the age
of the oldest stars (3.9Gyr) and the age of the
universe at that redshift (4.6Gyr). This feature
is common to any hierarchically clustering uni-
verseinwhichthefirststarsforminsmallclumps
whichcollapseathighredshifts. Theactualvalue
here is only an upper limit since (i) the limited
numerical resolution cannot follow star forma-
tion in clumps with less then ≈ 106M⊙and (ii)
the amount of substructure is underrepresented
due to the idealized initial conditions. At larger
radii (r > 2kpc), younger stars with an age of
about 1Gyr and below are dominating which re-
flects ongoing star formation in the gaseous disk.
Duetothevacuumboundaryconditions,theevo-
lution of the galaxy is fairly quiescent at red-
Fig. 1.—Upperleft: distributionofstarparticles shifts below one. Gas in the disk is successively
at redshift z = 3.5. The sidelength of the plots transformed into stars. Due to the still insuffi-
corresponds to 100 pixels of the HST/WFPC2. cient numerical resolution, however, encounters
Upper right: face-on view of the galaxy at red- between disk stars and dark matter particles act
shift z = 1. Lower left: edge-on view of the as a kinematic heating term. While at z = 1
galaxy at redshiftz = 1. Lower right: age of star the velocity dispersion of disk stars is still small
particles at z = 1 as a function of their distance (≈ 10km/sec), the stellar disk is successively
to the galaxy center. heated up between z = 1 and z = 0 up to ve-
locity dispersions near 100km/sec at z = 0. We
therefore focus our analysis mainly on redshift
The actual distribution of star particles is
one, when the amount of artificial heating is still
shown in figure 1. Details on the formation his-
negligible.
tory of themodelgalaxy, of its kinematical prop-
erties as well as of its chemical evolution can be
2.4. Spectral synthesis
found in SM1 and SM2. Here we concentrate on
some features important for the discussion later As mentioned above, each star particle, which
in this paper. At redshift 3.5, two protogalac- has a typical mass of a few million solar masses,
tic clumps can be seen which are going to merge corresponds to a population of several million
within the following ≈ 108 years. At lower red- stars which have been formed at the same time
shifts, the stars originating in these two clumps t from a gas cloud with a metallicity of Z. A
f
canbefoundinthebulgeofthegalaxy. Atz = 1, star particle can thus be considered as a pop-
themodelgalaxy already resembles aMilky Way ulation of stars which have formed in a burst-
type galaxy with a bulge-to-disk ratio of 1:3 in like manner. The luminosity evolution of such a
mass (SM2). In the lower right panel of figure burst is then followed by an evolutionary spec-
1, we plot the age of the star particles as a func- tral synthesis model (Fritze-von Alvensleben &
tion of the distance to the galaxy center. The Gerhard 1995; Fritze-von Alvensleben & Burk-
central 1-2kpc are dominated by old stars with ert 1995; Einsel et al. 1995): The evolution of
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this instantaneously formed population of stars
is followed in the Hertzsprung–Russell diagram
(HRD) using results of stellar evolution theory.
Setsofstellartracks(Maeder1990)forfivediffer-
entmetallicities (Z = 10−4,10−3,4×10−4, 10−2,
4×10−2)andfor27stellar massesintherangeof
0.15M⊙ to 60M⊙ have been compiled by Einsel
et al. (1995). A Miller-Scalo (1979) initial mass
function (IMF) is assumed with upper and lower
mass limits of 60M⊙ and 0.15M⊙, respectively.
The spectrum of an individual star burst is syn-
thesized from Kurucz’s (1992) library of stellar
spectra, luminosities in various filter bands are
obtainedbyconvolutionwithfilterresponsefunc-
Fig. 2.— Luminosityevolution ofastellarpopu-
tions (see also Leitherer et al. 1996, Fritze-von
lationformedwithin2.5×107 yearswithmetallic-
Alvensleben & Kurth 1996).
ity Z = 1×10−4. The dotted line shows the evo-
The discrete set of stellar masses for which
lution as computed with the original code. The
stellar evolution tracks are available together
luminosity indicated by the dashed line is calcu-
with the burst-like star formation history can
lated with the averaged stellar evolution tracks
cause some problems for the late time evolution
and smoothed subsequently (solid line). The
of the population. In the original implementa-
numbersright of the peaks assign the mass m in
i
tion,allstarswithinamassinterval m ;m
i−1/2 i+1/2 M⊙of the star that reaches the red giant branch
have been assigned to the temperahture and lu- i at that time.
minosity of the stellar track of a star of mass
mi. For masses below 2M⊙, the lifetime on the
red giant branch (a few 108yr) is, however, short the construction of isochrones. The luminosity
evolution of an individual star is split into two
comparedtothedifferenceinthelifetimeof stars
onneighboringevolutionarytracks(109yr). This parts, main sequence and post main sequence.
Ascanbeseeninfigure3,thepostmainsequence
causes all stars within a given mass interval to
evolution between neighboring masses is almost
synchronously enter the red giant branch. Since
identical, concerningthetimedependenceaswell
the luminosity increases hundredfold, and since
as the luminosity evolution. The main sequence
every mass interval contains a substantial frac-
evolution lMS(t,m)hasalsoaverysimilarshape,
tionofthetotalmassofthepopulation(afewper
but the evolution is faster for the higher masses
cent),pronouncedspikesintheluminositycanbe
and the star is also brighter. These two effects
seen (figure 2, dotted line). Such a discreteness
can, however, be compensated by the following
dominatedbehaviorisunknownforextendedstar
ansatz for the luminosity evolution of a star with
formation histories (as e.g. in models of spiral
mass m+∆m:
galaxies), since these spikes are convolved (and
thus smoothed) with the star formation history. m+∆m α
′
lMS(t,m+∆m) = lMS t,m .
These discreteness effects in the luminosity m
(cid:18) (cid:19)
evolution of burst-like formed populations are (cid:0) (cid:1) (1)
circumvented by methods which are based on In this ansatz, α is the exponent of the mass-
isochrones (see, e.g., Bruzual & Charlot 1993). luminosity relation, typical values being α ≈ 3
We propose an alternative method that avoids formasseslessthanafewM⊙. Therescaledtime
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t′ can be inferred by rescaling t with the ratio of up the luminosities according to the initial mass
the life times on the main sequence τMS, i.e., function (IMF) the total luminosity of the stel-
lar population is obtained as a function of time.
t′ = tτMS(m+∆m) = t m+∆m β (2) The luminosity of populations which formed in a
τMS(m) (cid:18) m (cid:19) singlestarburstnowevolves muchsmoother(see
figure 2, dashed line). The remaining small wig-
with β ≈ −2; stars with a higher mass reach a
gles result from discontinuities in the evolution
given evolutionary stage faster. For each mass m
near the interface of two adjacent mass intervals.
within the mass interval m ;m the lu-
i−1/2 i+1/2
We remove these wiggles by averaging over time
minosity evolution can thhus be calculateid. The intervals of 1.5×108 years, as indicated by the
local value of the slope of the mass-luminosity
solid line in figure 2.
and mass-lifetime relation, α and β, can be
TheluminosityevolutionintheU andK band
drawn from neighboring masses m . In figure 3
i
of a single star burst is shown for 5 different
we demonstrate the success of our interpolation
metallicitiesinfigure4. Dataforarbitrarymetal-
scheme by comparing the evolution of a star of
licities Z can then be obtained by interpolation
mass M = 1.6M⊙ with the evolution as inferred
in logZ.
from a star with M = 1.4M⊙ and M = 1.8M⊙
using the interpolation scheme above. Differ-
2.5. k correction
ences in the main sequence evolution are almost
undetectable and also the post main sequence For apparent magnitudes and colors of galax-
evolution differs only by a very small time shift ies at high redshifts the modifications due to the
(less than 10 per cent of the lifetime on the post- redshift of the spectrum have to be taken into
main-sequence). account.
The cosmological redshift causes the spectral
energy distribution F0(λ) of a galaxy in its rest-
frame at redshift z to be detected in the ob-
r
servers restframe as F (λ) with:
F0(λ/(1+zr))
F (λ,z ) = . (3)
r
(1+z )
r
The apparent magnitude in some “X” filter
band is thus
LX0
mX = BDM(zr)−2.5log +MX⊙+k(zr).
LX⊙!
(4)
with the luminosity LX0 in the galaxy’s rest
frame, the bolometric distance modulus
Fig. 3.— Comparison of the luminosity evolu-
tion of three stars of mass M = 1.4M⊙, 1.6M⊙ BDM(zr) = 5log(DL(zr)/Mpc)+25,
and 1.8M⊙, respectively. The dashed line has
and the luminosity distance (Mattig 1958)
beenobtained byinterpolating between theM =
c
1.4M⊙ and1.8M⊙ trackasdescribedinthetext. DL(zr) = H0q02 {zrq0+(q0−1)
By averaging these approximated stellar evo-
lution tracks in each massinterval and byadding × −1+ (2q0zr +1) . (5)
(cid:20) q (cid:21)(cid:27)
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minosity in a given pass band filter can be con-
verted into number of photons emitted per unit
timepersolidangle. Thisnumberiscorrectedby
intervening absorption due to neutral hydrogen
using the models of Madau (1995). By specify-
ing exposure time and pixel size, the number of
photonsreceived by each pixelis calculated. The
pixel map then is convolved with the numerical
resolution of the simulation and the sky back-
ground is added. Finally it is convolved with the
point-spread function of the instrument. The re-
sulting array contains the expectation value for
each pixel to receive a photon. This number is
then random-sampled. Together with the detec-
tor characteristics (quantum efficiency, readout
noise, dark current, gain) an artificial image can
be created which subsequently can be analyzed
in the same way as raw observational data.
Fig. 4.— Luminosity evolution in the U and K
band of a single age stellar population for the
metallicities Z = 1×10−4,1×10−3,4×10−3,1×
10−2, and 4×10−2. The total mass of the pop-
ulation is 1×107M⊙. Fig. 5.— Artificial HST images of a forming
galaxy at z = 3.5. Images are 50 pixels across,
The k correction is calculated from the spectral “exposure time” is 30000 sec. Top row: U-band;
energy distribution F (λ) and the filter response bottom row: I-band. Left column: rest frame;
function S (λ) (Lamla 1982) according to the middle column: including k-correction; right col-
X
following equation (Oke & Sandage 1968) umn: including k-correction and absorption due
to intervening hydrogen.
k = −2.5log(LXObs./LX0) (6)
∞
= 2.5log (1+zr) 0 F0(λ)SX(λ) dλ (.7) 3. Applications
∞
0 F0(λR/(1+zr))SX(λ) dλ
3.1. Appearance of high redshift galaxies
R
2.6. Creating artificial images
In this paragraph we discuss the appearance
Fromtheluminosityofthesetofstarparticles,
of the simulated galaxies in an exposure as it
artificial images can be easily generated. The lu-
is typical for HST/WFPC2 observations. De-
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Fig. 6.— Artificial HST images of a forming
galaxy at z = 1. Images are 50 pixels across,
“exposure time” is 30000 sec. Top row: U-band;
bottom row: I-band. Left column: face on,
rest frame; middle column: face on, including
Fig. 7.— Evolution of the model galaxy in the
k-correction; right column: edge-on, including k-
U−B vs. V −R plane. Solid line: model galaxy,
correction
including k-correction and intervening absorp-
tion; dashed line: model galaxy, k-corrected,
tector characteristics and sky background have no absorption; dotted line: E galaxy; dashed-
been taken from the WFPC2 handbook and a dotted: Sd galaxy (from M¨oller et al. 1997).
generousexposuretimeof30000shasbeenspeci-
fied. Fortheadoptedcosmologicalmodel(Ω = 1,
vening neutral hydrogen suppresses the U-band
H0 = 50kms−1Mpc−1) and redshift range (z =
emission of the proto galaxy by further 3.5 mag
1 − 4), the formal numerical resolution of the
(m = 29.2) and makes it invisible even in long
U
simulation surpasses the pixel resolution of the
exposures.
WFPC2 camera by about 50%.
In the I-band, the k-correction has the oppo-
In figure 5 and 6 we show a U and I-band
site effect: in its restframe, the apparent magni-
image of the simulated galaxy at redshifts z =
tudeis m = 24.6 andalso thelessluminouspro-
I
1 and z = 3.5. Each image has a side length
genitor is barely visible. The luminosity of the
of 100 pixels, corresponding to 70kpc (z = 3.5)
galaxy is dominated by stars which have formed
and82kpc(z = 1), respectively. Grayscales have
within the last few 108yr and also massive stars
been chosen logarithmically to cover the interval
M > 8M⊙ are abundant. Thus, these lumps
betweenasignal-to-noise of1to30(U band)and
strongly emit in the near UV (≈ 4000˚A). The
100 (I band).
cosmicredshifttranslatesthesefrequenciestothe
In the restframe U-band image of the z=3.5
I-band resulting in a negative k-correction of 1.7
galaxy, only the most massive clump is visible.
magnitudes (m = 22.9). The galaxy thus has
I
Ithasanapparentmagnitudeofm = 24.8. Ap-
U a brightness compatible to the brightest galax-
plying the k-correction makes the clump barely
ies in the Steidel et al. (1996) sample. Since at
visible (m = 25.7). At these redshifts, the
U z = 3.5 the I-band corresponds to wavelengths
U-band is centered at wavelengths shortward longwardof1217˚A,theluminosityisnotaffected
of 912˚A in the galaxy’s restframe where stel-
by intervening absorption.
lar emission is depleted due to absorption in
The restframe U-band image of the z = 1
the stellar atmosphere. Absorption due to inter-
8
galaxy consists of a luminous bulge of stars with
a typical age of 3 − 4Gyrs (see figure 1, lower
right panel) and some light from star forming re-
gions in the disk. At redshift 1, however, the
U-band corresponds to restframe wavelengths
near 1800˚A where the emission of old stars is
small. Thus the bulge component virtually dis-
appears after applying the k-correction. Simi-
lar to the z = 3.5 I-band, k-correction enhances
the star forming regions in the disk. Young
massive stars emit strongly at restframe wave-
lengths near 2000˚Awhich areredshifted into the
U-band. Similar effects can be seen in the I-
band image: Since the I-band corresponds to a
restframe wavelength of 4000˚A, also the light of
the old bulge component is clearly visible, al-
though slightly dimmed. For the disk popula-
tion the k-correction favors shorter wavelengths
at which the contribution of newly formed stars
is larger. Consequently, the k-corrected I-band
image looks more structured and the regions of
active star formation are more pronounced.
Fig. 8.— Left column: Surface density versus
Infigure7theevolutionofthemodelgalaxyin radius. The solid line corresponds to the bolo-
the U−B vs. B−R plane is shown and, for com- metric luminosity, the dashed, dotted, dashed-
parison, the evolution of a Sa and Sd galaxy us- dotted and dashed-triple-dotted line correspond
ing traditional spectrophotometric models (see, to the broadband colors U, V, I and K, respec-
e.g., Bruzual & Charlot, 1993, Fritze-von Al- tively. Right column: color indices U−V(solid),
vensleben, 1993) is plotted. B−V(dotted), V −I(dashed)andV −K(dashed-
dotted) versus radius. From top to bottom:
3.2. Surface brightness, color gradients
z = 1 including k-correction, z = 1 restframe
and z = 0.
In figure 8 we show surface brightness profiles
and color gradients. The radial profile clearly
shows an exponential behavior for r > 5kpc and dening within the inner 5 kpc, about 2 magni-
a steepening (bulge) at smaller radii. The non- tudes in V −K and 1 magnitude in the other col-
exponential bulge component is readily visible in ors. Except U−V, the drop is much weaker in
the z = 0 plot since the surface brightness of the restframe. This reddening is consistent with
the disk has dimmed by about one magnitude. thedimmingofthebulgecomponentofthez = 1
A comparison of the k-corrected (figure 8 top) galaxy duetok-correction asdescribedinsection
galaxy at z = 1 with its restframe (figure 8 mid- 3.1. The bulge is dominated by old stars (see
dle) exhibits a substantial (slight) enhancement figure 1, lower right panel) emitting only little
of the K (I) luminosity (i.e., the k-correction near 1800˚A which corresponds to the U band at
is negative), while the V and U luminosity is z ≈ 1. The k-correction enhances the K and I
dimmed. luminosity while decreasing the U and V lumi-
At z = 1 the galaxy exhibits very strong red- nosities and thus results in the strong reddening
9
as can be seen in figure 8. Only a slight color
gradient is visible at radii r > 10kpc in the rest-
frame as well as in the k-corrected profile. Also
the effect of the k-correction is much more mod-
erate, between 0 mag in B−V, 0.6 mag in U−V
and 1.5mag in V −K. At these radii, stars are
stillbeingformedresultinginamuchflatterspec-
tral energy distribution and thus a much weaker
k-correction.
At z = 0, only very weak color gradients are
visible. The bulge differs from the disk by about
0.1 mag, only in U−V a slightly stronger color
gradient is visible. The change of color is cer-
tainly much weaker than the observed one of
about 0.2 mag in B−V and 0.5 mag in U−V
as in galaxies like, e.g., Andromeda (Segalovitz
1975,Josey&Arimoto1982). Onereasonforthis
discrepancy is the neglect of dust absorption. As Fig. 9.— k-corrected V −K (left) and U−V
we willshow in thenext paragraph, however, the (right) as a function of radius for the model
lack of significant color gradients may also be an galaxy at redshift z = 1 (top) and z = 0 (bot-
artifact of our star formation scheme and of the tom). Stars correspond to the model galaxy, er-
vacuum boundary conditions. ror bars are [10;90] percentile values based on a
bootstrap analysis (for details, see text). The
In figure 9 we investigate to what extend the
dashed lines correspond to a model with con-
color gradients at z = 1 and z = 0 reflect age
stantmetallicity whilestellaragesaretakenfrom
andmetallicity gradientsofthestellardisk. First
the simulation. The dotted lines correspond to a
we estimate the statistical error of the color in-
model with constant stellar ages while metallici-
dices. For that purpose we perform a bootstrap
tiesaretakenfromthesimulation. Acomparison
analysis, i.e., we draw 100 random samples from
of the actual values with the dashed and dotted
the distribution of stars and determine color as a
lines thus demonstrates the effect of metallicity
function of radius. We use the [10;90] percentile
and age on the color gradient.
values as the lower and upper error limits, i.e.,
only 10% of our bootstrapped samples have a
color bluer than our lower error limit and only tains very few very young stars. The color thus
10% of our bootstrapped samples have a color strongly depends on how many of these young
redwards of our upperlimit. As can beseen, col- star particles happen to be included in the boot-
ors can be measured with a statistical error of strapped sample.
about ±0.02 to 0.05 mag at z = 0. At z = 1,
We also compare the radial color profiles with
errors are at the level of about ±0.1 to ±0.2.
those obtained assuming a constant metallicity
These errors strongly depend on whether or not
for the star particles. For the z = 1 model the
stars are actively formed. While colors are fairly
colornearthecenterisconsistentwithametallic-
accurate for passively evolving populations, er-
ity of Z ≈ Z⊙, while the color at 15kpc requires
rors are much larger for regions including young
a metallicity much below 0.5Z⊙. No constant
stars. This can be easily seen in the z = 0 U−V
metallicity model fits the entire color gradient.
color at a radius of 12kpc. This radial bin con-
The metallicity gradient inferred from the color
10