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Mon. Not. R. Astron. Soc. 000, 1–35 (2002) Printed 2 February 2008 (MN LATEX style file v2.2)
Stellar population synthesis at the resolution of 2003
G. Bruzual1⋆ and S. Charlot2,3⋆
1Centro de Investigaciones de Astronomı´a, AP 264, Me´rida 5101-A, Venezuela
2Max-Planck Institut fu¨r Astrophysik, Karl-Schwarzschild-Strasse 1, 85748 Garching, Germany
3Institut d’Astrophysique de Paris, CNRS, 98 bis Boulevard Arago, 75014 Paris, France
MNRAS, in press
ABSTRACT
We present a new model for computing the spectral evolution of stellar populations
at ages between 1 × 105 yr and 2 × 1010 yr at a resolution of 3 A˚ across the whole
wavelength range from 3200 A˚ to 9500 A˚ for a wide range of metallicities. These
predictions are based on a newly available library of observed stellar spectra. We
also compute the spectral evolution across a larger wavelength range, from 91 A˚ to
160 µm, at lower resolution. The model incorporates recent progress in stellar evolution
theory and an observationally motivated prescription for thermally-pulsing stars on the
asymptotic giant branch. The latter is supported by observations of surface brightness
fluctuations in nearby stellar populations. We show that this model reproduces well the
observed optical and near-infrared colour-magnitude diagrams of Galactic star clusters
of various ages and metallicities. Stochastic fluctuations in the numbers of stars in
different evolutionary phases can account for the full range of observed integrated
colours of star clusters in the Magellanic Clouds. The model reproduces in detail
typical galaxy spectra from the Early Data Release (EDR) of the Sloan Digital Sky
Survey (SDSS). We exemplify how this type of spectral fit can constrain physical
parameters such as the star formation history, metallicity and dust content of galaxies.
Our model is the first to enable accurate studies of absorption-line strengths in galaxies
containing stars over the full range of ages. Using the highest-quality spectra of the
SDSS EDR, we show that this model can reproduce simultaneously the observed
strengths of those Lick indices that do not depend strongly on element abundance
ratios. The interpretation of such indices with our model should be particularly useful
for constraining the star formation histories and metallicities of galaxies.
Key words: galaxies: formation – galaxies: evolution – galaxies: stellar content –
stars: evolution.
1 INTRODUCTION
The star formation history of galaxies is imprinted
in their integrated light. The first attempts to inter-
pret the light emitted from galaxies in terms of their
stellar content relied on trial and error analyses (e.g.,
Spinrad & Taylor 1971; Faber 1972; O’Connell 1976;
Turnrose 1976; Pritchet 1977; Pickles 1985). In this
technique, one reproduces the integrated spectrum of a
galaxy with a linear combination of individual stellar
spectra of various types taken from a comprehensive
library. The technique was abandoned in the early 1980’s
because the number of free parameters was too large to
be constrained by typical galaxy spectra. More recent
models are based on the evolutionary population synthesis
technique (Tinsley 1978; Bruzual 1983; Arimoto & Yoshii
⋆ E-mail: bruzual@cida.ve (GBA); charlot@iap.fr (SC)
1987; Guiderdoni & Rocca-Volmerange 1987; Buzzoni 1989;
Bruzual & Charlot 1993; Bressan, Chiosi & Fagotto 1994;
Fritze-v. Alvensleben & Gerhard 1994; Worthey 1994;
Leitherer & Heckman 1995; Fioc & Rocca-Volmerange
1997; Maraston 1998; Vazdekis 1999; Schulz et al. 2002).
In this approach, the main adjustable parameters are the
stellar initial mass function (IMF), the star formation rate
(SFR) and, in some cases, the rate of chemical enrichment.
Assumptions about the time evolution of these parameters
allow one to compute the age-dependent distribution of
stars in the Hertzsprung-Russell (HR) diagram, from which
the integrated spectral evolution of the stellar population
can be obtained. These models have become standard tools
in the interpretation of galaxy colours and spectra.
Despite important progress over the last decade, mod-
ern population synthesis models still suffer from serious
limitations. The largest intrinsic uncertainties of the mod-
els arise from the poor understanding of some advanced

2 G. Bruzual and S. Charlot
phases of stellar evolution, such as the supergiant phase
and the asymptotic-giant-branch (AGB) phase (see Charlot
1996; Charlot, Worthey & Bressan 1996; Yi 2003). Stars in
these phases are very bright and have a strong influence
on integrated-light properties. The limitations arising from
these uncertainties in the interpretation of galaxy spectra
are further amplified by the fact that age, metallicity and
dust all tend to affect spectra in similar ways. This is es-
pecially true at the low resolving power of most current
population synthesis models, i.e., typically ∼ 250 at opti-
cal wavelengths (see however Vazdekis 1999; Schiavon et al.
2002). As a result, light-weighted ages and metallicities de-
rived from integrated galaxy spectra tend to be strongly de-
generate (e.g., Worthey 1994). For old stellar populations,
this degeneracy may be broken by studying surface bright-
ness fluctuations, that are more sensitive to the details of
the stellar luminosity function than ordinary integrated light
(Liu et al. 2000; Blakeslee et al. 2001). This method, how-
ever, is mostly applicable to studies of nearby ellipticals and
spiral bulges.
The general contention is that the age-metallicity de-
generacy can be broken by appealing to refined spec-
tral diagnostics involving individual stellar absorption-
line features (e.g., Rose 1985; Jones & Worthey 1995;
Vazdekis & Arimoto 1999). Several spectral indices of
this kind have been defined at optical and near-
infrared wavelengths (e.g., Faber 1973; Rose 1984;
Dı´az, Terlevich & Terlevich 1989; Worthey et al. 1994). In
the widely used ‘Lick system’, the strengths of 25 spec-
tral indices were parametrized as functions of stellar ef-
fective temperature, gravity and metallicity using a sam-
ple of 460 Galactic stars (Burstein et al. 1984; Gorgas et al.
1993; Worthey et al. 1994; Worthey & Ottaviani 1997;
Trager et al. 1998). This convenient parametrization allows
one to compute integrated index strengths of model galax-
ies with any stellar population synthesis code. In practice,
however, the applications are limited to studies of old stel-
lar populations because of the lack of hot stars in the Lick
stellar library. Also, the Lick indices were defined in spectra
which were not flux-calibrated and whose resolution (∼ 9 A˚
FWHM) is three times lower than achieved in modern spec-
troscopic galaxy surveys, such as the Sloan Digital Sky Sur-
vey (SDSS; York et al. 2000). Thus high-quality galaxy spec-
tra must first be degraded to the specific calibration and
wavelength-dependent resolution of the Lick system for Lick
index-strength analyses to be performed (Section 4.4). Ide-
ally, one requires a population synthesis model that can pre-
dict actual spectra of galaxies at the resolution of modern
surveys. The model of Vazdekis (1999) fulfills this require-
ment. However, it is limited to two narrow wavelength re-
gions, 3820–4500 A˚ and 4780–5460 A˚.
In this paper, we present a new model for computing the
spectral evolution of stellar populations of different metal-
licities at ages between 1 × 105 yr and 2 × 1010 yr at a res-
olution of 3 A˚ FWHM across the whole wavelength range
from 3200 A˚ to 9500 A˚ (corresponding to a median resolv-
ing power λ/∆λ ≈ 2000). These predictions are based on
a new library of observed stellar spectra recently assembled
by Le Borgne et al. (2003). We also compute the spectral
evolution across a larger wavelength range, from 91 A˚ to
160 µm, at lower spectral resolution. This model should be
particularly useful for interpreting the spectra gathered by
modern spectroscopic surveys in terms of constraints on the
star formation histories and metallicities of galaxies.
The paper is organized as follows. In Section 2 be-
low, we present the stellar evolution prescription and the
stellar spectral library on which our model relies. We con-
sider several alternatives for these ingredients. We adopt
an observationally motivated prescription for thermally-
pulsing AGB stars, which is supported by observations of
surface brightness fluctuations in nearby stellar popula-
tions (Liu et al. 2000; Liu, Graham & Charlot 2002). We
also briefly recall the principle of the isochrone synthesis
technique for computing the spectral evolution of stellar
populations (Charlot & Bruzual 1991). In Section 3, we in-
vestigate the influence of the main adjustable parameters of
the model on photometric predictions and compare our re-
sults with previous work. Comparisons with observed colour-
magnitude diagrams and integrated colours of star clusters
of various ages and metallicities are also presented in this
section. In Section 4, we compute the spectral evolution of
stellar populations and compare our model with observed
galaxy spectra from the SDSS EDR (Stoughton et al. 2002).
We compare in detail the predicted and observed strengths
of several absorption-line indices and identify those indices
that appear to be most promising for constraining the stellar
content of galaxies. We summarize our conclusions in Sec-
tion 5, where we also suggest ways of including the effects of
gas and dust in the interstellar medium on the stellar radia-
tion computed with our model. Readers interested mainly in
the photometric predictions of the model may skip directly
to Section 3, while those interested mainly in applications
of the model to interpret galaxy spectra may skip directly
to Section 4.
2 THE MODEL
In this section, we present the main two ingredients of our
population synthesis model: the stellar evolution prescrip-
tion and the stellar spectral library. We consider several al-
ternatives for each of these. We also briefly review the prin-
ciple of the isochrone synthesis technique for computing the
spectral evolution of stellar populations.
2.1 Stellar evolution prescription
To account for current uncertainties in the stellar evolution
theory, we consider three possible stellar evolution prescrip-
tions in our model (Table 1). We first consider the library of
stellar evolutionary tracks computed by Alongi et al. (1993),
Bressan et al. (1993), Fagotto et al. (1994a), Fagotto et al.
(1994b), and Girardi et al. (1996). This library encompasses
a wide range of initial chemical compositions, Z = 0.0001,
0.0004, 0.004, 0.008, 0.02, 0.05, and 0.1 with Y = 2.5Z+0.23
(Z⊙ = 0.02 and Y⊙ = 0.28) assumed. The range of ini-
tial masses is 0.6 6 m 6 120M⊙ for all metallicities, ex-
cept for Z = 0.0001 (0.6 6 m 6 100M⊙) and Z = 0.1
(0.6 6 m 6 9M⊙). The tracks were computed using
the radiative opacities of Iglesias, Rogers & Wilson (1992)1
1 The stellar evolutionary tracks for Z = 0.0001, which were
computed last, include slightly updated opacities and equation

Stellar population synthesis at the resolution of 2003 3
Table 1. Different stellar evolution prescriptions.
Name Metallicity range Source
Padova 1994 0.0001–0.10 Alongi et al. (1993)
Bressan et al. (1993)
Fagotto et al. (1994a)
Fagotto et al. (1994b)
Girardi et al. (1996)
Padova 2000 0.0004–0.03 Girardi et al. (2000)a
Geneva 0.02 Schaller et al. (1992)
Charbonnel et al. (1996)
Charbonnel et al. (1999)
a Girardi et al. (2000) computed tracks only for low- and
intermediate-mass stars. In the Padova 2000 library, these calcu-
lations are supplemented with high-mass tracks from the Padova
1994 library, as suggested by Girardi et al. (2002).
and include all phases of stellar evolution from the zero-
age main sequence to the beginning of the thermally puls-
ing regime of the asymptotic giant branch (TP-AGB; for
low- and intermediate-mass stars) and core-carbon ignition
(for massive stars). For solar composition, the models are
normalized to the temperature, luminosity, and radius of
the Sun at an age of 4.6 Gyr. The tracks include mild
overshooting in the convective cores of stars more massive
than 1.5M⊙, as suggested by observations of Galactic star
clusters (Bressan et al. 1993; Meynet, Mermilliod & Maeder
1993; Demarque, Sarajedini & Guo 1994). For stars with
masses between 1.0 and 1.5M⊙, core overshooting is in-
cluded with a reduced efficiency. Overshooting is also in-
cluded in the convective envelopes of low- and intermediate-
mass stars, as suggested by observations of the red giant
branch and horizontal branch of star clusters in the Galac-
tic halo and the Large Magellanic Cloud (hereafter LMC;
Alongi et al. 1991). We refer to this set of tracks as the
‘Padova 1994 library’.
Recently, Girardi et al. (2000) produced a new version
of this library, in which the main novelties are a revised equa-
tion of state (Mihalas et al. 1990) and new low-temperature
opacities (Alexander & Ferguson 1994). The revised library
includes stars with masses down tom = 0.15M⊙, but it does
not contain stars more massive than 7M⊙ (the new equa-
tion of state affects mainly the evolution of stars less massive
than 0.6M⊙). The chemical abundances also differ slightly
from those adopted in the 1994 release, Z = 0.0004, 0.004,
0.008, 0.019, and 0.03, with Y = 2.25Z + 0.23 (Z⊙ = 0.019
and Y⊙ = 0.273) assumed. Following the arguments of
Girardi et al. (2002), we combine the new library of low-
and intermediate-mass tracks with high-mass tracks from
the older Padova 1994 library to build an updated library
encompassing a complete range of initial stellar masses. This
can be achieved at all but the highest metallicity (Z = 0.03),
for which there is no counterpart in the Padova 1994 library
(Z = 0.02 and 0.05 available only). We refer to this set of
tracks as the ‘Padova 2000 library’.
of state. According to Girardi et al. (1996), these updates do not
compromise the consistency with the predictions at higher metal-
licities.
The third stellar evolution prescription we consider,
for the case of solar metallicity only, is the comprehen-
sive library of tracks computed by Schaller et al. (1992, for
m > 2M⊙), Charbonnel et al. (1996, for 0.8 6 m < 2M⊙)
and Charbonnel et al. (1999, for 0.6 6 m < 0.8M⊙). The
abundances are X = 0.68, Y = 0.30, and Z = 0.02, and the
opacities are from Rogers & Iglesias (1992, for m > 2M⊙)
and Iglesias & Rogers (1993, for 0.8 6 m/M⊙ < 2). The
tracks include all phases of stellar evolution from the zero-
age main sequence to the beginning of the TP-AGB or core-
carbon ignition, depending on the initial mass. The models
are normalized to the luminosity, temperature, and radius
of the Sun at an age of 4.6 Gyr. Mild overshooting is in-
cluded in the convective cores of stars more massive than
1.5M⊙. Differences with the solar-metallicity calculations
of Bressan et al. (1993) in the Padova 1994 library include:
the absence of overshooting in the convective cores of stars
with masses between 1.0 and 1.5M⊙ and in the convective
envelopes of low- and intermediate-mass stars; the higher
helium fraction; the inclusion of mass loss along the red gi-
ant branch; the treatment of convection during core-helium
burning; and the internal mixing and mass loss of massive
stars. The signatures of these differences in the stellar evo-
lutionary tracks have been investigated by Charlot et al.
(1996). We refer to this alternative set of tracks for solar
metallicity as the ‘Geneva library’.
We supplement the Padova and Geneva tracks of low-
and intermediate-mass stars beyond the early-AGB with
TP-AGB and post-AGB evolutionary tracks.2 The TP-AGB
phase is one of the most difficult evolutionary phases to
model because of the combined effects of thermal pulses
(i.e., helium shell flashes), changes in surface abundance
caused by heavy element dredge-up (e.g., carbon) and im-
portant mass loss terminated by a superwind and the ejec-
tion of the stellar envelope (see the reviews by Habing 1995
and Habing 1996). This phase must be included in popula-
tion synthesis models because the stochastic presence of a
few TP-AGB stars has a strong influence on the integrated
colours of star clusters (e.g., Frogel, Mould & Blanco 1990;
Santos & Frogel 1997; see also Section 3.3.2 below). We ap-
peal to recent models of TP-AGB stars which have been
calibrated using observations of stars in the Galaxy, the
LMC and the Small Magellanic Cloud (SMC). In particular,
we adopt the effective temperatures, bolometric luminosities
and lifetimes of TP-AGB stars from the multi-metallicity
models of Vassiliadis & Wood (1993).3 These models, which
2 The different stellar evolution prescriptions in the Padova and
Geneva models lead to different upper mass limits for degenerate
carbon ignition and hence AGB evolution. The limit is Mup ≈
5M⊙ at all metallicities in the Padova tracks and Mup ≈ 7M⊙
in the Geneva tracks.
3 Vassiliadis & Wood (1993) adopt slightly different stellar evo-
lution parameters (e.g., helium fraction, opacities, treatment of
convection) from those used in the Padova models. In the end,
however, the duration of early-AGB evolution is similar to that
in the Padova tracks. It is 10–25 per cent shorter for stars with
initial mass m . 1M⊙ to 10–25 per cent longer for stars with
m = 5M⊙ in the Vassiliadis & Wood (1993) models for all the
metallicities in common with the Padova tracks (Z = 0.004, 0.008,
and 0.02). This similarity justifies the combination of the two sets
of calculations.

4 G. Bruzual and S. Charlot
include predictions for both the optically-visible and the su-
perwind phases, predict maximum TP-AGB luminosities in
good agreement with those observed in Magellanic Cloud
clusters. The models are for the metallicities Z = 0.001,
0.004, 0.008, and 0.016, which do not encompass all the
metallicities in the Padova track library. For simplicity, we
adopt the Z = 0.001 prescription of Vassiliadis & Wood
(1993) at all metallicities Z 6 0.0004 and their Z = 0.016
prescription at all metallicities Z > 0.02.
Carbon dredge-up during TP-AGB evolution can lead
to the transition from an oxygen-rich (M-type) to a carbon-
rich (C-type) star (e.g., Iben & Renzini 1983). Since C-type
stars are much redder than M-type stars and can dominate
the integrated light of some star clusters, it is important to
include them in the models. The minimum initial mass limit
for a carbon star to form increases with metallicity. This is
supported observationally by the decrease in the ratio of C
to M stars from the SMC, to the LMC, to the Galactic bulge
(Blanco, Blanco & McCarthy 1978). While the formation of
carbon stars is relatively well understood, no simple pre-
scription is available to date that would allow us to describe
accurately the transition from M to C stars over a wide range
of initial masses and metallicities. Groenewegen & de Jong
(1993) and Groenewegen, van den Hoek & de Jong (1995)
have computed models of TP-AGB stars, which reproduce
the ratios of C to M stars observed in the LMC and the
Galaxy. We use these models to define the transition from
an M-type star to a C-type star in the TP-AGB evolution-
ary tracks of Vassiliadis & Wood (1993). We require that,
for a given initial main-sequence mass, the relative dura-
tions of the two phases be the same as those in the models
of Groenewegen & de Jong (1993) and Groenewegen et al.
(1995). Since these models do not extend to sub-Magellanic
(Z . 0.004) nor super-solar (Z > 0.02) metallicities, we
apply fixed relative durations of the M-type and C-type
phases in the Padova tracks for more extreme metallicities.
As shown by Liu et al. (2000), this simple but observation-
ally motivated prescription for TP-AGB stars provides good
agreement with the observed optical and near-infrared sur-
face brightness fluctuations of (metal-poor) Galactic globu-
lar clusters and (more metal-rich) nearby elliptical galaxies.
For the post-AGB evolution, we adopt the evolution-
ary tracks of Vassiliadis & Wood (1994), whose calculations
cover the range of metallicities 0.001 6 Z 6 0.016. We
use the Weidemann (1987) relationship to compute the core
mass of a star after ejection of the planetary nebula (PN) at
the tip of the AGB from its initial mass on the main sequence
(see Weidemann 1990 for a review; and Magris & Bruzual
1993). To each low- and intermediate-mass star in the
Padova and Geneva libraries, we then assign the post-AGB
evolution computed by Vassiliadis & Wood (1994) corre-
sponding to the closest core mass and metallicity. These au-
thors did not consider the evolution of stars with core masses
less than 0.569M⊙, corresponding to a main sequence pro-
genitor mass less than about 1.1M⊙. For lower-mass stars,
we adopt the 0.546M⊙ post-AGB evolutionary track com-
puted for the metallicity Z = 0.021 by Scho¨nberner (1983),
with an extension by Ko¨ster & Scho¨nberner (1986). Since
we will consider stellar population ages of up to 20 Gyr,
and the post-AGB calculations do not generally extend to
this limit, we further supplement the tracks using white
dwarf cooling models by Winget et al. (1987) at luminosi-
ties L . 0.1L⊙. Following the suggestion by Winget et al.,
we adopt their ‘pure carbon’ models for masses in the range
0.4 6 m 6 1.0M⊙, in which the cooling times differ by
only 15 per cent from those in models including lighter ele-
ments. The prescription is thus naturally independent of the
metallicity of the progenitor star. Specifically, we interpolate
cooling ages for white dwarfs as a function of luminosity at
the masses corresponding to the Vassiliadis & Wood (1994)
and Scho¨nberner (1983) tracks. Since Winget et al. (1987)
do not tabulate the temperatures nor the radii of their model
white dwarfs, we assign effective temperatures as a function
of luminosity using the slope of the white dwarf cooling se-
quence defined by the calculations of Scho¨nberner (1983),
i.e., ∆ log Teff ≈ 0.23∆ logL.
The resulting tracks in the Padova and Geneva li-
braries cover all phases of evolution from zero-age main se-
quence to remnant stage for all stars more massive than
0.6M⊙ (0.15M⊙ for the Padova 2000 library). Since the
main-sequence lifetime of a 0.6M⊙ star is nearly 80 Gyr,
we supplement these libraries with multi-metallicity mod-
els of unevolving main-sequence stars in the mass range
0.09 6 m < 0.6M⊙ (Baraffe et al. 1998). These models
provide smooth extensions of the Padova and Geneva cal-
culations into the lower main sequence. For the purpose
of isochrone synthesis, all tracks must be resampled to a
system of evolutionary phases of equivalent physical signifi-
cance (Charlot & Bruzual 1991). We define 311 such phases
for low- and intermediate-mass stars and 260 for massive
stars.
2.2 Stellar spectral library and spectral
calibration
The second main ingredient of population synthesis models
is the library of individual stellar spectra used to describe
the properties of stars at any position in the Hertzsprung-
Russell diagram. We consider different alternative stellar
spectral libraries and different ways to calibrate them (see
Tables 2 and 3). We also refer the reader to Table A1 of
Appendix A for a qualitative assessment of the spectral pre-
dictions of our model for simple stellar populations of vari-
ous ages and metallicities computed using different spectral
libraries.
2.2.1 Multi-metallicity theoretical and semi-empirical
libraries at low spectral resolution
Theoretical model atmospheres computed for wide ranges of
stellar effective temperatures, surface gravities and metallic-
ities allow one to describe the spectral energy distribution
of any star in the HR diagram. Lejeune, Cuisinier & Buser
(1997) and Lejeune, Cuisinier & Buser (1998) have com-
piled a comprehensive library of model atmospheres for stars
in the metallicity range 10−5Z⊙ . Z . 10Z⊙, encom-
passing all metallicities in the Padova track libraries (Sec-
tion 2.1). The spectra cover the wavelength range from 91 A˚
to 160 µm at resolving power λ/∆λ ≈ 200 − 500. The li-
brary consists of Kurucz (1995, private communication to
R. Buser) spectra for the hotter stars (O–K), Bessell et al.
(1989), Bessell et al. (1991) and Fluks et al. (1994) spectra
for M giants, and Allard & Hauschildt (1995) spectra for M
dwarfs.

Stellar population synthesis at the resolution of 2003 5
Table 2. Different libraries of stellar spectra.
Name Type Wavelength Median Metallicity Source
rangea resolving power range
BaSeL theoretical 91 A˚ to 160 µm 300 10−5Z⊙ to 10Z⊙ Kurucz (1995, priv. comm.)
Bessell et al. (1989)
Bessell et al. (1991)
Fluks et al. (1994)
Allard & Hauschildt (1995)
Rauch (2002)
STELIB observational 3200 A˚ to 9500 A˚ 2000 −2.0 < [Fe/H] < +0.50 Le Borgne et al. (2003)
Pickles observational 1205 A˚ to 2.5 µm 500 Z⊙ Pickles (1998)
Fanelli et al. (1992)
a The STELIB and Pickles libraries can be extended at shorter and longer wavelengths using the BaSeL
library, as described in the text.
There are three versions of this library. The first ver-
sion contains the model spectra as originally published
by their builders, only rebinned on to homogeneous scales
of fundamental parameters (effective temperature, grav-
ity, metallicity) and wavelength. We refer to this library
as the ‘BaSeL 1.0 library’. In a second version of the li-
brary, Lejeune et al. (1997) corrected the original model
spectra for systematic deviations that become apparent
when UBV RIJHKL colour-temperature relations com-
puted from the models are compared to empirical calibra-
tions. These semi-empirical blanketing corrections are es-
pecially important for M-star models, for which molecu-
lar opacity data are missing. The correction functions are
expected to depend on the fundamental model parame-
ters: temperature, gravity and metallicity. However, because
of the lack of calibration standards at non-solar metallic-
ities, Lejeune et al. (1997) applied the blanketing correc-
tions derived at solar metallicity to models of all metal-
licities. While uncertain, this procedure ensures that the
differentiation of spectral properties with respect to metal-
licity is at least the same as in the original library (and
hence not worsened; see Lejeune et al. 1997 for details).
This constitutes the ‘BaSeL 2.2 library’. Finally, Westera
(2001) and Westera et al. (2002) recently produced a new
version of the library, in which they derived semi-empirical
corrections for model atmospheres at non-solar metallicities
using metallicity-dependent UBV RIJHKL colour calibra-
tions. This new version is also free of some discontinuities
affecting the colour-temperature relations of cool stars in
the BaSeL 1.0 and BaSeL 2.2 libraries, which were linked to
the assembly of model atmospheres from different sources.
We refer to this as the ‘BaSeL 3.1’ (WLBC99) library.
The BaSeL libraries encompass the range of stellar ef-
fective temperatures 2000 6 Teff 6 50, 000 K. Some stars
can reach temperatures outside this range during their evo-
lution. In particular, in the stellar evolutionary tracks of
Section 2.1, Wolf-Rayet stars and central stars of planetary
nebulae can occasionally be hotter than 50,000 K. To de-
scribe the hot radiation from these stars, we adopt the non-
LTE model atmospheres of Rauch (2002) for Z = Z⊙ and
Z = 0.10Z⊙ that include metal-line blanketing from all ele-
Table 3. Different spectral calibrations.
Option Calibration Source
BaSeL 1.0 theoreticala Lejeune et al. (1997)
Lejeune et al. (1998)
BaSeL 2.2 semi-empiricalb Lejeune et al. (1997)
Lejeune et al. (1998)
BaSeL 3.1 semi-empiricalc Westera (2000)
Westera et al. (2002)
a Original calibration of model atmospheres included in the
BaSeL library (see Table 2).
b Empirical blanketing corrections derived at solar metallicity
and applied to models of all metallicities in the BaSeL library.
c Metallicity-dependent blanketing corrections.
ments from H to the Fe group (we thank T. Rauch for kindly
providing us with these spectra). The models cover the tem-
perature range 50, 000 6 Teff 6 1, 000, 000 K at wavelengths
between 5 and 2000 A˚ at a resolution of 0.1 A˚. We degrade
these models to the BaSeL wavelength scale and extrapolate
blackbody tails at wavelengths λ > 2000 A˚. We use the re-
sulting spectra to describe all the stars with Teff > 50, 000 K
and Z > 0.10Z⊙ in the stellar evolutionary tracks. For com-
pleteness, we approximate the spectra of stars hotter than
50,000 K at Z = 0.0004 and Z = 0.0001 by pure blackbody
spectra. Cool white dwarfs, when they reach temperatures
cooler than 2000 K, are also represented by pure blackbody
spectra, irrespective of metallicity.
The BaSeL libraries do not include spectra for carbon
stars nor for stars in the superwind phase at the tip of the
TP-AGB. Our prescription for these stars is common to all
spectral libraries in Table 2 and is described in Section 2.2.4
below.

6 G. Bruzual and S. Charlot
2.2.2 Multi-metallicity observational library at higher
spectral resolution
To build models with higher spectral resolution than offered
by the BaSeL libraries, one must appeal to observations of
nearby stars. The difficulty in this case is to sample the
HR diagram in a uniform way. Recently, Le Borgne et al.
(2003) have assembled a library of observed spectra of stars
in a wide range of metallicities, which they called ‘STELIB’.
When building this library, Le Borgne et al. took special care
in optimizing the sampling of the fundamental stellar param-
eters across the HR diagram for the purpose of population
synthesis modelling. The library contains 249 stellar spectra
covering the wavelength range from 3200 A˚ to 9500 A˚ at a
resolution of 3 A˚ FWHM (corresponding to a median resolv-
ing power λ/∆λ ≈ 2000), with a sampling interval of 1 A˚
and a signal-to-noise ratio of typically 50 per pixel.4 After
correction for stellar radial velocities (Le Borgne 2003, pri-
vate communication), two narrow wavelength regions (6850–
6950 A˚ and 7550–7725 A˚) had to be removed from the
spectra because of contamination by telluric features. For
stars cooler than 7000 K, we replaced these segments in
the spectra with metallicity-dependent model atmospheres
computed at 3 A˚ resolution using the SPECTRUM code
(Gray & Corbally 1994, we thank C. Tremonti for kindly
providing us with these computations based on the most
recent Kurucz model atmospheres). For hotter stars, we re-
placed the segments with spectra from the lower-resolution
library of Pickles (see below), resampled to 1 A˚/pixel. These
fixes are purely of cosmetic nature, and we do not use the
predictions of the population synthesis models in these two
narrow wavelength regions (we do not correct the STELIB
spectra for the telluric feature around 8950–9075 A˚ that it
is weaker than the other two features and falls in a noisier
region of the spectra).
Most stars in the STELIB library were selected from
the catalog of Cayrel de Strobel et al. (1992), which includes
[Fe/H] determinations from high-resolution spectroscopic
observations of stars in open and globular clusters in the
Galaxy and of supergiant stars in the Magellanic Clouds.
The STELIB library contains stars with metallicities in the
range −2.0 < [Fe/H] < +0.50, spectral types from O5 to M9
and luminosity classes from I to V. The coverage in spectral
type is not uniform at all metallicities (see Appendix A): hot
(Teff & 10, 000K) stars are under-represented at non-solar
metallicities, and the library lacks very cool (Teff < 3200K)
stars at all metallicities. These limitations are not critical.
The spectra of hot stars are not expected to depend strongly
on metallicity because the opacities in these stars are domi-
nated by electron scattering. Thus, the spectra of hot stars
with solar metallicity should be representative of hot stars
4 The STELIB spectra were gathered from two different tele-
scopes. At the 1 m Jacobus Kaptein Telescope (La Palma), the
instrumental setup gave a dispersion of 1.7 A˚/pixel and a resolu-
tion of about 3 A˚ FWHM. At the Siding Spring Observatory 2.3 m
telescope, the instrumental setup gave a dispersion of 1.1 A˚/pixel
and the same resolution of 3 A˚ FWHM. The two sets of spectra
had to be resampled onto a homogeneous wavelength scale for
the purpose of population synthesis modelling. Le Borgne et al.
(2003) adopted a uniform sampling interval of 1 A˚, a ‘round’
number close to the smallest of the two observational dispersions.
at all but the most extreme metallicities. Also, the lack of
cool M-dwarf stars has a negligible influence on model pre-
dictions, because these stars do not contribute significantly
to the integrated light of stellar populations (as found when
adopting representative spectra for these stars; see Appendix
A). For the coolest giant stars, we adopt in any case the pre-
scription outlined in Section 2.2.4 below.
The main interest of the STELIB library is that it en-
ables the interpretation of integrated spectra of star clus-
ters and galaxies taken at relatively high resolution in
the wavelength range 3200–9500 A˚. To allow for a consis-
tent modelling of spectral properties outside this range, we
must extend the STELIB spectra at ultraviolet and infrared
wavelengths using one of the spectral libraries described
above. We consider three different types of extensions, cor-
responding to the three colour-temperature calibrations of
the BaSeL 1.0, 2.2 and 3.1 libraries (Section 2.2.1). To as-
sign STELIB spectra to stars on the evolutionary tracks,
we therefore proceed as follows (the reader is referred to
Appendix A for more detail). We first distribute the stars
in several metallicity bins centered on the metallicities for
which tracks are available (Section 2.1). Some stars with
intermediate metallicities may be included into two consec-
utive bins, while hot solar-metallicity stars are included in
all bins. We then select one of the three BaSeL libraries
to set the colour-temperature scale.5 For each metallicity,
we assign to each log g–log Teff position in the HR diagram
the STELIB spectrum of the associated luminosity class
that best matches the BaSeL spectrum corresponding to
these values of log g and log Teff (here log g is the gravity).
We then extend the selected STELIB spectrum blueward
of 3200 A˚ and redward of 9500 A˚ with the ultraviolet and
infrared ends of the BaSeL spectrum. There are, therefore,
three possible implementations of the STELIB library in
our model, which we refer to as the ‘STELIB/BaSeL 1.0’,
the ‘STELIB/BaSeL 2.2’ and the ‘STELIB/BaSeL 3.1’ li-
braries. For solar metallicity, we can also use the Pickles
library described below to extend the STELIB/BaSeL 3.1
models blueward of 3200 A˚ and redward of 9500 A˚ (Sec-
tion 4.1 and Fig. 9).
2.2.3 Solar-metallicity observational library with wider
spectral coverage
Pickles (1998) has assembled a library of 131 Galactic stars
in wide ranges of spectral types (O5–M10) and luminosity
classes (I–V) in three metallicity groups (11 metal-weak, 12
metal-rich, and 108 solar-metallicity stars). The metal-weak
and metal-rich stars sample very sparsely the HR diagram
and do not allow us to build accurate population synthe-
sis models. We therefore focus on solar-metallicity stars, for
which the sampling is adequate. The interest of the Pickles
(1998) library is that it has a wider spectral coverage than
the STELIB library at solar metallicity, despite the coarser
resolution. The spectra extend over the wavelength range
from 1150 A˚ to 2.5 µm with a sampling interval of 5 A˚/pixel
5 The effective temperatures published by Le Borgne et al.
(2003) for the STELIB stars are incomplete and were not derived
in a homogeneous way. We prefer to rely on the homogeneous
colour-temperature scales of the BaSeL libraries.

Stellar population synthesis at the resolution of 2003 7
and a median resolving power λ/∆λ ≈ 500 (corresponding
to the highest resolution at which spectra are available for
all stars in the Pickles library). The library does not include
main-sequence and subgiant stars hotter than 40,000 K, gi-
ant stars hotter than 32,000 K and supergiant stars hot-
ter than 26,000 K and cooler than 4000 K. When needed,
we select spectra for these stars from the solar-metallicity
BaSeL 3.1 library described above.
The quality of the spectra in the ultraviolet is of partic-
ular importance for application to studies of distant galax-
ies. In the Pickles library, the spectra at ultraviolet wave-
lengths are based on a limited number of International Ul-
traviolet Explorer (IUE) observations for each stellar type.
Fanelli et al. (1992) have compiled more refined average IUE
spectra as a function of spectral type and luminosity class
from a sample of 218 stars. The sampling interval of these
spectra is 1–1.2 A˚ from 1205 to 1935 A˚ and 2 A˚ from 1935
to 3150 A˚. We replace the spectra of the Pickles library at
wavelengths from 1205 to 3185 A˚ by the type-averaged spec-
tra compiled by Fanelli et al. (1992). For completeness, we
extend the spectra further into the extreme ultraviolet using
spectra from the BaSeL 3.1 library at wavelengths from 91
to 1195 A˚.
We also use BaSeL 3.1 spectra to extend the Pickles
spectra into the infrared at wavelengths from 2.5 µm to
160 µm. For cool M-giant stars, we adopt a more refined pre-
scription. The spectra of M0–M10 giant stars are the only
non-observed ones in the Pickles library, as they are based
on the synthetic M-giant spectra computed by Fluks et al.
(1994). To extend these spectra into the infrared, we ap-
peal to model atmospheres by Schultheis et al. (1999). These
have a more refined definition of the strong infrared absorp-
tion features in cool stars than the BaSeL spectra (we thank
M. Schultheis for kindly providing us with these spectra).
The Schultheis et al. spectra cover the wavelength range
from 5000 A˚ to 10 µm and are available for 10 equally spaced
stellar temperatures in the range 2600 6 Teff 6 4400 K
(the emission of these stars is negligible at wavelengths less
than 5000 A˚). The sampling interval increases from 2.5 A˚
at the short wavelength end (λ/∆λ ≈ 2000) to 400 A˚ at
the long wavelength end (λ/∆λ ≈ 250). At wavelengths be-
tween 5000 A˚ and 2.5 µm, the colours computed from these
spectra agree well with those computed from the Fluks et al.
models in the Pickles library. We therefore extend the spec-
tra of M-giant stars at wavelengths from 2.5 µm to 10 µm
in the Pickles library using the Schultheis et al. spectra. For
completeness, we extend the resulting M-star spectra further
into the infrared using spectra from the BaSeL 3.1 library
at wavelengths from 10 µm to 160 µm. In what follows, we
refer to this modified version of the Pickles (1998) library
simply as the ‘Pickles library’.
2.2.4 Carbon stars and stars in the superwind phase
None of the libraries described above includes spectra for
C-type stars nor for stars in the superwind phase at the tip
of the TP-AGB (Section 2.1). We construct period-averaged
spectra for these stars, based on models and observations of
Galactic stars. We adopt these spectra to represent upper
TP-AGB stars of all metallicities in our model.
We construct period-averaged spectra for C-type TP-
AGB stars as follows. We use solar-metallicity model at-
mospheres for carbon stars with temperatures in the range
2600 . Teff . 3400 K from Ho¨fner et al. (2000, we thank
R. Loidl for kindly providing us with these spectra). The
spectra cover the wavelength range from 2500 A˚ to 12.5 µm.
The sampling interval increases from 2.5 A˚ at the short-
wavelength end (λ/∆λ ≈ 1000) to 800 A˚ at the long-
wavelength end (λ/∆λ ≈ 200). The spectral features in
the model spectra are in reasonable agreement with obser-
vations of carbon stars (Loidl, Lanc¸on & Jørgensen 2001).
However, we find that the model UBV RIJHK broadband
colours do not reproduce well the observations of 39 car-
bon stars by Mendoza & Johnson (1965). We therefore ap-
ply an empirical correction to the model spectra as follows.
We first derive mean colour-colour relations for C stars from
the sample of Mendoza & Johnson (1965) by fitting 2nd or-
der polynomials to the relations defined by the data. We de-
rive in the same way a mean relation between K-band bolo-
metric correction BCK and J−K colour. These mean rela-
tions are taken to represent period-averaged observations.
The temperature scale proposed by Mendoza & Johnson
(1965) for carbon stars does not appear to be robust (e.g.,
Dyck, van Belle & Benson 1996). Thus, we prefer to adjust
the calibration of Teff as a function of J−K colour in such a
way that the reddest stars observed by Mendoza & Johnson
(1965) have roughly the temperature of the coolest C-type
stars in our model (Teff ≈ 2600K). Based on these re-
lations, we apply a smooth continuum correction to each
Ho¨fner et al. (2000) spectrum in order to reproduce the
mean observed UBV RIJHK colours at the corresponding
Teff . The absolute scale of the corrected spectrum is then
set by the relation between BCK and J−K colour.
We also construct spectra for stars in the superwind
phase at the end of the TP-AGB evolution. These stars may
be of either M or C type, depending on initial mass, metal-
licity and age. Their spectra are difficult to model because
of the influence of expanding circumstellar shells of gas and
dust. To describe stars in the superwind phase, we there-
fore rely primarily on observations. Le Sidaner & Le Bertre
(1996) and Le Bertre (1997) have assembled broadband
spectral energy distributions of 27 oxygen-rich and 23
carbon-rich stars with circumstellar dust shells. They also
derived bolometric luminosities from the known pulsation
periods of all stars. For only some objects, however, is a
complete set of optical-infrared observations available (we
thank T. Le Bertre for kindly providing us with some un-
published JHKL data). We extract a sample of 16 TP-
AGB stars with complete V RIJHKL information and par-
tial UB information (this includes 4 M-type and 12 C-type
stars). The colours of M-type and C-type stars follow sim-
ilar relations to within the observed scatter for this small
sample. We thus do not distinguish between M-type and C-
type stars and use the sample as a whole to build spectra
for TP-AGB stars in the superwind phase in our model. As
before, we fit mean colour-colour relations to the data and
take these to represent period-averaged observations. Most
optical/infrared colours correlate well with bolometric lumi-
nosity logL. In addition, there is a tight correlation between
K-band bolometric correction BCK and logL. These rela-
tions are useful because the effective temperatures of the
stars are not known. In the evolutionary tracks, the bolo-
metric luminosity of stars in the superwind phase increases
with initial mass at roughly constant Teff ≈ 2800K. By anal-

8 G. Bruzual and S. Charlot
ogy with our approach above, we apply smooth continuum
corrections to the 2800 K carbon-star model of Ho¨fner et al.
(2000) to generate 12 new spectra reproducing the observed
colours of TP-AGB stars in the superwind phase for different
luminosities in the range 3.55 6 logL/L⊙ 6 4.65.
2.3 Isochrone synthesis
In this paper, we use the isochrone synthesis technique
to compute the spectral evolution of stellar populations
(Charlot & Bruzual 1991; Bruzual & Charlot 1993). This
technique is based on the property that stellar populations
with any star formation history can be expanded in series of
instantaneous starbursts, conventionally named ‘simple stel-
lar populations’ (SSPs). The spectral energy distribution at
time t of a stellar population characterized by a star for-
mation rate ψ(t) and a metal-enrichment law ζ(t) can be
written (e.g., Tinsley 1980)
Fλ(t) =
∫ t
0
ψ(t− t′)Sλ
[
t′, ζ(t− t′)
]
dt′ , (1)
where Sλ [t′, ζ(t− t′)] is the power radiated per unit wave-
length per unit initial mass by an SSP of age t′ and metal-
licity ζ(t−t′). The above expression assumes that the initial
mass function (IMF) is independent of time.
The function Sλ [t′, ζ(t− t′)] is the sum of the spectra of
stars defining the isochrone of an SSP of metallicity ζ(t− t′)
at age t′. To compute Sλ(t′, Zi) at a given metallicity Zi
of the stellar evolutionary tracks (Table 1), we interpolate
the isochrone at age t′ from the tracks in the HR diagram.
In practice, each evolutionary stage defined in the tracks is
interpolated separately (Section 2.1). The different evolu-
tionary stages along the isochrone are populated by stars
of different initial masses in proportions given by the IMF
weight φ(m) [defined such that φ(m)dm is the number of
stars born with masses between m and m + dm]. We then
use one of the spectral libraries described in Section 2.2 to
assign spectra to stars in the various evolutionary stages.
The spectral energy distribution of the SSP is obtained by
summing the spectra of individual stars along the isochrone.
The IMF is an adjustable parameter of the model. Ex-
cept when otherwise indicated, we adopt in this paper the
parametrization by Chabrier (2003b, his table 1) of the
single-star IMF in the Galactic disc. This is
φ(logm) ∝
{
exp
[
− (logm−logmc)
2
2σ2
]
, for m 6 1M⊙ ,
m−1.3 , for m > 1M⊙ ,
(2)
with mc = 0.08M⊙ and σ = 0.69 (the two expressions in
equation 2 are forced to coincide at 1M⊙). The spectral
properties obtained using the above IMF are very similar
to those obtained using the Kroupa (2001) universal IMF
(see Fig. 4 below). We adopt here the Chabrier (2003b)
IMF because it is physically motivated and provides a bet-
ter fit to counts of low-mass stars and brown dwarfs in
the Galactic disc (Chabrier 2001; Chabrier 2002; Chabrier
2003a). For reference, the Salpeter (1955) IMF corresponds
to φ(logm) ∝ m−1.35, or equivalently φ(m) ∝ m−2.35. Un-
less otherwise specified, we adopt lower and upper IMF
mass cutoffs mL = 0.1 M⊙ and mU = 100 M⊙. As in
Bruzual & Charlot (1993), the spectral energy distribution
of a model SSP is normalized to a total mass of 1 M⊙ in
Figure 1. Evolution of the B−V and V −K colours and stellar
mass-to-light ratio M/LV of simple stellar populations for differ-
ent metallicities, Z = 0.004 (dotted line), Z = Z⊙ = 0.02 (solid
line) and Z = 0.05 (dashed line), for the standard model of Sec-
tion 3. All models have the Chabrier (2003b) IMF truncated at
0.1M⊙ and 100M⊙ (see equation 2).
stars at age t′ = 0, and the spectra are computed at 221 un-
equally spaced time steps from 0 to 20 Gyr. Each spectrum
covers the wavelength range from 91 A˚ to 160 µm, with a
resolution that depends on the spectral library employed.
3 PHOTOMETRIC EVOLUTION
In the isochrone synthesis framework, the spectral evolution
of simple stellar populations (SSPs) is the most fundamental
prediction of population synthesis models. It determines the
spectral evolution of stellar populations with any history
of star formation (Section 2.3). In this section, we examine
the predictions of our model for the photometric evolution
of SSPs. This allows us to illustrate the basic influence of
the various adjustable parameters on model properties. We
compare our results with previous work. We also compare
the photometric properties of the model with observations
of nearby star clusters.
In all applications in the remainder of this paper, we
adopt a ‘standard’ reference model computed using the
Padova 1994 evolutionary tracks, the STELIB/BaSeL 3.1
spectral library and the IMF of equation (2) truncated
at 0.1M⊙ and 100M⊙. We mention in Section 3.1 below
the reason for preferring the Padova 1994 tracks over the
Padova 2000 tracks for the standard model.
3.1 Influence of the adjustable parameters
The spectral evolution of an SSP depends primarily on
the assumed metallicity, stellar evolution prescription, stel-

Stellar population synthesis at the resolution of 2003 9
lar spectral library and IMF. Here, we illustrate the influ-
ence of these adjustable parameters on the evolution of the
B−V and V −K colours and stellar mass-to-visual light ra-
tio M/LV of an SSP. Optical and near-infrared colours re-
flect the relative contributions of hot and cool stars to the
integrated light, while the stellar mass-to-light ratio reflects
the absolute magnitude scale of the model. When comput-
ing M/LV , we account for the mass lost by evolved stars
to the interstellar medium in the form of winds, planetary
nebulae and supernova ejecta.
Fig. 1 shows the evolution of the B−V and V −K
colours and M/LV for three different metallicities, Z =
0.004, Z = Z⊙ = 0.02 and Z = 0.05, for our standard SSP
model. The irregularities in the photometric evolution arise
both from the discrete sampling of initial stellar masses in
the track library and from ‘phase’ transitions in stellar evo-
lution. For example, the evolution of low-mass stars through
the helium flash causes a characteristic feature in all proper-
ties in Fig. 1 at ages near 109 yr. At fixed age, the main effect
of increasing metallicity is to redden the colours and increase
M/LV . The reason for this is that, at fixed initial stellar
mass, lowering metallicity causes stars to evolve at higher ef-
fective temperatures and higher luminosities (Schaller et al.
1992; Fagotto et al. 1994a, Girardi et al. 2000). Another no-
ticeable effect of varying Z is to change the relative num-
bers of red and blue supergiants. The evolution of the B−V
colour at early ages in Fig. 1 shows that the signature of red
supergiants in the colour evolution of an SSP depends cru-
cially on metallicity (see also Cervin˜o & Mas-Hesse 1994).
We note that increasing metallicity at fixed age has a simi-
lar effect as increasing age at fixed metallicity, which leads
to the well-known age-metallicity degeneracy.
In Fig. 2, we illustrate the influence of the stellar
evolution prescription on the predicted photometric evo-
lution of an SSP for fixed (solar) metallicity and fixed
(STELIB/BaSeL 3.1) spectral calibration. We show mod-
els computed using the Padova 1994, the Geneva and the
Padova 2000 track libraries (Section 2.1). The largest dif-
ference between the Padova 1994 and Geneva prescriptions
arises at early ages and results from the larger number of
evolved, blue massive (Wolf-Rayet) stars in the Padova mod-
els than in the Geneva models (see fig. 2b of Charlot 1996).
Also, since the minimum mass for quiet helium ignition is
lower in the Geneva model than in the Padova 1994 model
(1.9M⊙ versus 2.2M⊙), the photometric signature of the he-
lium flash occurs at slightly later ages in the Geneva model
in Fig. 2. Differences between the Padova 1994 and Padova
2000 track libraries pertain only to stars less massive than
7M⊙, with turnoff ages greater than about 5× 107 yr (Sec-
tion 2.1). In the Padova 2000 model, the finer resolution
in initial stellar mass around 2.0M⊙ makes the evolution
through the helium flash much smoother than in the Padova
1994 model. At late ages, the V −K colour is significantly
bluer in the Padova 2000 model than in the Padova 1994
model. The reason for this is that the red giant branch is
50 to 200 K warmer (from bottom to tip) in the Padova
2000 tracks than in the Padova 1994 tracks. As a result,
the integrated V −K colour of a solar-metallicity SSP in the
Padova 2000 model reaches values typical of old elliptical
galaxies (V −K ∼ 3.0–3.3 along the colour-magnitude re-
lation; Bower, Lucey & Ellis 1992) only at ages 15–20 Gyr.
Since this is older than currently favored estimates of the age
Figure 2. Evolution of the B−V and V −K colours and stellar
mass-to-light ratio M/LV of simple stellar populations of solar
metallicity computed using the Geneva (dotted line), Padova 1994
(standard model; solid line) and Padova 2000 (dashed line) stel-
lar evolution prescriptions and the STELIB/BaSeL 3.1 spectral
calibration. All models have the Chabrier (2003b) IMF truncated
at 0.1M⊙ and 100M⊙ (see equation 2).
of the Universe, and since the giant-branch temperature in
the Padova 2000 tracks has not been tested against observa-
tional calibrations (e.g. Frogel, Persson & Cohen 1981), we
have adopted here the Padova 1994 library rather than the
Padova 2000 library in our standard model (see above).6
We now consider the influence of the spectral calibra-
tion on the photometric evolution of an SSP for fixed (so-
lar) metallicity and fixed (Padova 1994) stellar evolution
prescription. In Fig. 3, we compare the results obtained
with four different spectral libraries: the STELIB/BaSeL 3.1
library (standard model); the BaSeL 3.1 library; the
STELIB/BaSeL 1.0 library; and the Pickles library (re-
call that, at solar metallicity, the BaSeL 3.1 library is
6 It is intriguing that the Padova 2000 models, which include
more recent input physics than the Padova 1994 models, tend to
produce worse agreement with observed galaxy colours. The rela-
tively high giant branch temperatures in the Padova 2000 models,
though attributable to the adoption of new opacities, could be
subject to significant coding uncertainties (L. Girardi 2002, pri-
vate communication). This is supported by the fact that the im-
plementation of the same input physics as used in the Padova 2000
models into a different code produces giant branch temperatures
in much better agreement with those of the Padova 1994 models
(A. Weiss 2002, private communication). We regard the agree-
ment between the Girardi et al. (2002) model and our standard
model at late ages in Fig. 5 as fortuitous, as the spectral cali-
bration adopted by Girardi et al. (2002) relies on purely theoret-
ical model atmospheres, which do not reproduce well the colour-
temperature relations of cool stars (e.g., Lejeune et al. 1997).

10 G. Bruzual and S. Charlot
Figure 3. Evolution of the B−V and V −K colours and stel-
lar mass-to-light ratio M/LV of simple stellar populations of so-
lar metallicity computed using the Padova 1994 stellar evolution
prescription and the BaSeL 3.1 (dotted line), STELIB/BaSeL 1.0
(short-dashed line), STELIB/BaSeL 3.1 (standard model; solid
line) and Pickles (long-dashed line) spectral calibrations. All mod-
els have the Chabrier (2003b) IMF truncated at 0.1M⊙ and
100M⊙ (see equation 2).
identical to the BaSeL 2.2 library; Section 2.2.1). Fig. 3
shows that the differences between these spectral calibra-
tions have only a weak influence on the predicted photo-
metric evolution of an SSP. The good agreement between the
STELIB/BaSeL 3.1, the BaSeL 3.1 and the Pickles calibra-
tions follows in part from the consistent colour-temperature
scale of the three libraries. Also the empirical corrections
applied by Lejeune et al. (1997) and Westera et al. (2002)
to the BaSeL 1.0 spectra, illustrated by the differences be-
tween the STELIB/BaSeL 3.1 and STELIB/BaSeL 1.0 mod-
els in Fig. 3, imply changes of at most a few hundredths of a
magnitude in the evolution of the B−V and V −K colours.
It is important to note that the spectral calibration has a
stronger influence on observable quantities which are more
sensitive than integrated colours to the details of the stel-
lar luminosity function, such as colour-magnitude diagrams
(Section 3.3) and surface brightness fluctuations (Liu et al.
2000). Fig. 8 of Liu et al. (2000) shows that, for example,
the observed near-infrared surface brightness fluctuations of
nearby galaxies clearly favor the BaSeL 2.2/3.1 spectral cal-
ibration over the BaSeL 1.0 one.
It is also of interest to examine the influence of the IMF
on the photometric evolution of an SSP for fixed (solar)
metallicity, fixed (Padova 1994) stellar evolution prescrip-
tion and fixed (STELIB/BaSeL 3.1) spectral calibration.
Fig. 4 shows the evolution of the B−V and V −K colours
and M/LV for four different IMFs: Chabrier (2003b, see
equation 2 above), Kroupa (2001, universal IMF), Salpeter
(1955) and Scalo (1998). In all cases, the IMF is truncated
Figure 4. Evolution of the B−V and V −K colours and stel-
lar mass-to-light ratio M/LV of simple stellar populations of so-
lar metallicity computed using the Padova 1994 stellar evolution
prescription and the STELIB/BaSeL 3.1 spectral calibration, for
different IMFs: Chabrier (2003b, standard model; solid line; see
equation 2), Kroupa (2001, dotted line), Salpeter (1955, short-
dashed line) and Scalo (1998, long-dashed line). All IMFs are
truncated at 0.1M⊙ and 100M⊙.
at 0.1M⊙ and 100M⊙. The evolution of the B−V colour
does not depend sensitively on the IMF, because the opti-
cal light is dominated at any age by stars near the turnoff.
The V −K colour is slightly more sensitive to the relative
weights of stars of different masses along the isochrone, es-
pecially at ages less than about 109 yr, when the mass of
the most evolved stars differs significantly from the turnoff
mass. The M/LV ratio is far more sensitive to the shape of
the IMF, especially near the low-mass end that determines
the fraction of the total mass of the stellar population locked
into faint, slowly evolving stars. For reference, the fraction
of mass returned to the ISM by evolved stars at the age of
10Gyr is 31, 44, 46, and 48 per cent for the Salpeter, the
Scalo, the Kroupa and the Chabrier IMFs, respectively.
3.2 Comparison with previous work
Most current population synthesis models rely on readily
available computations of stellar evolutionary tracks and
stellar atmospheres, such as those mentioned in Section 2.1
and Section 2.2.1 above. In general, however, publically
available stellar evolutionary tracks do not include the un-
certain evolution of stars beyond the early-AGB phase. Also,
the widely used model atmospheres of Kurucz (1992, and
other releases) do not include spectra of stars outside the
temperature range 3500K 6 Teff 6 50, 000K. We there-
fore expect differences between our model and previous work
to originate mainly from our observationally motivated pre-
scription for TP-AGB stars, the spectral calibration of very

Stellar population synthesis at the resolution of 2003 11
Figure 5. Evolution of the B−V and V −K colours and stel-
lar mass-to-light ratio M/LV of simple stellar populations of so-
lar metallicity computed using our model (with the Padova 1994
stellar evolution prescription and the STELIB/BaSeL 2.2 spec-
tral calibration; solid line), the Fioc & Rocca-Volmerange (1997)
PE´GASE version 2.0 model (dotted line) and the Girardi et al.
(2002) model (dashed line). All models have the Kroupa (2001)
present-day IMF truncated at 0.01M⊙ and 100M⊙.
hot and very cool (giant) stars and the adoption of a new
library of observed stellar spectra at various metallicities.
In Fig. 5, we compare the evolution of the B−V and
V −K colours and the mass-to-visual light ratio M/LV of
a solar-metallicity SSP predicted by our model with those
predicted by two publically available population synthe-
sis codes: the PE´GASE model (Fioc & Rocca-Volmerange
1997; version 2.0) and the Girardi et al. (2002) model. For
practical reasons, we adopt in all models the same IMF
as in Girardi et al. (2002), i.e., the Kroupa (2001) present-
day IMF truncated at 0.01M⊙ and 100M⊙.7 Also, for the
purpose of this comparison, we compute our model us-
ing the Padova 1994 stellar evolution prescription and the
STELIB/BaSeL 2.2 spectral calibration (which is identi-
cal to the BaSeL 3.1 calibration for solar metallicity; Sec-
tion 2.2.1).
The PE´GASE model shows good general agreement
with our model in Fig. 5. There are marked discrepancies
at ages around 107 yr, where the PE´GASE model is red-
der in B−V but bluer in V −K than our model, and at
ages around 108 yr, where it is nearly a magnitude red-
der in V −K. General agreement is expected because the
PE´GASE model relies on the same Padova 1994 tracks as
7 The present-day IMF in equation (6) of Kroupa (2001) is much
steeper at masses between 0.08M⊙ and 1.0M⊙ than the universal
Galactic-disc IMF proposed in his equation (2). The universal
IMF should be better suited to studies of the past history of star
formation in galaxies.
used in our model to describe the evolution of stars up to
the end of the early-AGB and on the same BaSeL 2.2 spec-
tral calibration. The discrepancy at early ages arises from
a difference in the spectral calibration of stars hotter than
50,000 K. In the PE´GASE model, the spectra of these stars
are taken from Clegg & Middlemass (1987), while in our
model, they are taken from the more recent computations
of Rauch (2002). The discrepancy in the V −K colour at
ages around 108 yr arises from a different prescription for
TP-AGB evolution. Fioc & Rocca-Volmerange (1997) use
‘typical’ TP-AGB luminosities and evolutionary time-scales
from Groenewegen & de Jong (1993), while in our model,
the evolution through this phase and its spectral calibration
are more refined (Section 2.1 and Section 2.2).
The Girardi et al. (2002) model in Fig. 5 relies on
the Padova 2000 stellar evolutionary tracks and on model
atmospheres by Castelli, Gratton & Kurucz (1997) and
Fluks et al. (1994). These model atmospheres do not include
any empirical colour-temperature correction and are akin to
the Kurucz (1995, private communication to R. Buser) and
Fluks et al. (1994) spectra included in the BaSeL 1.0 library.
It is interesting to note that, when combined with these
purely theoretical model atmospheres, the Padova 2000 evo-
lutionary tracks, in which the giant branch is relatively
warm (Section 3.1), produce B−V and V −K colours in
good agreement with those predicted both by the PE´GASE
model and by our model at late ages. At ages less than
107 yr and around 108 yr, the Girardi et al. (2002) model
deviates from our model in a similar way as the PE´GASE
model. The discrepancy at early ages is caused again by
a different treatment of stars hotter than 50,000 K, which
Girardi et al. (2002) describe as simple blackbody spectra.
The discrepancy at ages 108–109 yr follows primarily from
the treatment of TP-AGB evolution, which is based on a
semi-analytic prescription by Girardi & Bertelli (1998) in
the Girardi et al. (2002) model. It is worth recalling that
our prescription for TP-AGB evolution has been tested suc-
cessfully against observed optical and near-infrared surface
brightness fluctuations of nearby star clusters and galaxies
(Section 2).
3.3 Comparison with observations of star clusters
3.3.1 Colour-magnitude diagrams
To establish the reliability of our model, it is important to
examine the accuracy to which it can reproduce observed
colour-(absolute) magnitude diagrams (CMDs) of star clus-
ters of different ages and metallicities. Table 4 contains a list
of star clusters for which extensive data are available from
the literature. The clusters are listed in order of increas-
ing [Fe/H]. For each cluster, we list the distance modulus
(m − M)0 and the colour excess E(B−V ) from the same
references as for the stellar photometry. The reddening-
corrected CMDs of these clusters are presented in Figs 6 and
7, where we show the absolute V magnitude as a function
of various available optical and infrared colours. Superim-
posed on the data in each frame are four isochrones. The
red isochrones are computed using the Padova 1994 tracks,
while the black isochrones are computed using the Padova
2000 tracks. In each case, the dashed and solid isochrones
are computed using the BaSeL 1.0 and BaSeL 3.1 spectral

12 G. Bruzual and S. Charlot
Table 4. Star cluster data.
Cluster Alias (m −M)0 E(B−V ) [Fe/H]obs Zmod [Fe/H]mod tmod/Gyr References
NGC6397 12.31 0.18 −1.94 0.0004 −1.65 14 1, 2, 3
NGC6809 M55 13.82 0.07 −1.80 0.0004 −1.65 13 4, 5
NGC5139 ωCen 13.92 0.12 −1.62 0.0004 −1.65 13 4, 5
NGC104 47Tuc 13.32 0.05 −0.71 0.004 −0.64 13 4, 6
NGC6528 14.45 0.52 −0.35 0.008 −0.33 13 7, 8
NGC6553 13.60 0.70 −0.35 0.008 −0.33 13 7, 8, 9
NGC2682 M67 9.50 0.06 +0.01 0.02 +0.09 4 10, 11, 12, 13, 14
Hyades 3.40 0.00 +0.15 0.02 +0.09 0.7 15, 16, 17, 18
(1) King et al. (1998); (2) D’Antona (1999); (3) Kaluzny (1997); (4) Rosenberg et al. (2000a); (5)
Rosenberg et al. (2000b); (6) Kaluzny et al. (1998); (7) Bruzual et al. (1997); (8) Ortolani et al. (1995);
(9) Guarnieri et al. (1998); (10) Eggen & Sandage (1964); (11) Gilliland et al. (1991); (12) Janes & Smith
(1984); (13) Montgomery, Marschall & Janes (1993); (14) Racine (1971); (15) Micela et al. (1988); (16)
Upgren (1974); (17) Upgren & Weis (1977); (18) Mermilliod (2000).
calibrations, respectively. The isochrones were selected by
adopting the available model metallicity closest to the clus-
ter [Fe/H] value and then choosing the age that provided
the best agreement with the data. Age and metallicity are
the same for all the isochrones for each cluster. Columns 6, 7
and 8 of Table 4 list the metallicity Zmod, the corresponding
[Fe/H]mod and the age tmod adopted for each cluster. The
listed ages are in good agreement with previous determina-
tions.
Fig. 6 shows the CMDs of two Galactic open clus-
ters of near-solar metallicity in various photometric bands:
the young Hyades cluster and the intermediate-age M67
cluster. For clarity, stars near and past the turnoff are
plotted as large symbols. In the case of the Hyades, the
700 Myr Padova 1994/BaSeL 3.1 isochrone reproduces well
the upper main sequence, the turnoff and the core-He
burning phase in all UBV IR bands. For M67, the 4 Gyr
Padova 1994/BaSeL 3.1 isochrone fits remarkably well the
upper main sequence, the subgiant branch, the red giant
branch, the core-He burning clump and the AGB in all
bands. For both clusters, the models predict slightly bluer
UBV colours than observed on the lower main sequence.
The offset is smaller in R − I for the Hyades and in V − R
for M67, but the data are sparse in both cases. It is worth
noting that, forMV > 10, the BaSeL 3.1 spectral calibration
provides better agreement with the data than the BaSeL 1.0
calibration. Lower-main sequence stars, in any case, con-
tribute negligibly to the integrated light of a star cluster or
a galaxy. At the age of the Hyades, the Padova 1994 and
2000 isochrones differ very little, as they rely on the same
stellar evolution prescription for massive stars (Section 2.1).
At the age of M67, the Padova 2000 isochrone tends to pre-
dict stars bluer and brighter than the Padova 1994 isochrone
near the tip of the red giant branch. As seen in Section 3.1
above, this small but significant difference has a noticeable
influence on integrated-light properties (see also below).
Fig. 7 shows the optical-infrared CMDs of six old Galac-
tic globular clusters of different metallicities. NGC 6397 is
the most metal-poor cluster in our sample, with [Fe/H] =
−1.94 (Table 4). Fig. 7(a) shows that models with Z =
0.0004 ([Fe/H]mod ≈ −1.65) at an age of 14 Gyr provide
excellent fits to the Hubble Space Telescope (HST) data for
this cluster, all the way from the main sequence, to the red
giant branch, to the AGB and to the white-dwarf cooling se-
quence. The models, however, do not fully reproduce the ob-
served extension of the blue horizontal branch (see also be-
low). This problem persists even if the age of the isochrones
is increased. For this cluster, the Padova 2000/BaSeL 3.1
isochrone appears to fit the shape of the horizontal branch
and the main sequence near MV = 8 marginally bet-
ter than the Padova 1994/BaSeL 3.1 isochrone. Ground-
based data for the other two low-metallicity clusters in
our sample, NGC 6809 ([Fe/H] = −1.80) and NGC 5139
([Fe/H] = −1.62), are also reproduced reasonably well by
the [Fe/H]mod = −1.65 isochrones at an age of 13 Gyr
(Figs 7b and 7c). As in the case of NGC 6397, the mod-
els do not reproduce the full extension of the blue horizon-
tal branch. This suggests that this mismatch is not purely
a metallicity effect and that the evolution of these stars, or
their spectral calibration, or both, may have to be revised in
the models. It is worth pointing out that the BaSeL 3.1 spec-
tral calibration provides a better fit of the upper red-giant
stars than the BaSeL 1.0 calibrations at these low metallic-
ities.
The CMD of the intermediate-metallicity cluster
NGC 104 ([Fe/H] = −0.71) is well reproduced by the
Padova 1994/BaSeL 3.1 model with [Fe/H]mod = −0.64 at
the age of 13 Gyr (Fig. 7d). This age should be regarded
only as indicative, as the stars in NGC 104 are known to
be overabundant in α elements relative to the solar com-
position, whereas the model has scaled-solar abundances
(see Vazdekis et al. 2001 for a more detailed analysis). The
NGC 6528 and NGC 6553 clusters of the Galactic bulge in
Figs. 7e–7g are more metal-rich, with [Fe/H] = −0.35. The
Padova 1994/BaSeL 3.1 model with [Fe/H]mod = −0.41 pro-
vides good fits to the CMDs of these clusters at the age
of 13 Gyr. For both clusters, the position of the core-He
burning clump and the extension of the red giant branch
toward red V − I and V −K colours are especially well ac-
counted for. As in the case of M67 (Fig. 6), the Padova 2000
isochrones tend to predict stars bluer and brighter than the
Padova 1994 isochrones on the upper red giant branch, pro-
viding a slightly worse fit to the observations. Also, as is the
case at other metallicities, the BaSeL 3.1 spectral calibra-
tion provides a better fit of the upper red-giant stars than
the BaSeL 1.0 calibration.
Overall, Figs 6 and 7 show that our model provides
excellent fits to observed CMDs of star clusters of different

Stellar population synthesis at the resolution of 2003 13
Figure 6. Comparison of model isochrones with observed colour-magnitude diagrams of the Hyades and M67
Galactic open clusters in various photometric bands. For clarity, stars near and past the turnoff are plotted
as large symbols. For each cluster, the adopted distance modulus and colour excess are listed in Table 4
along with the sources of the stellar photometry. Each panel contains four isochrones: the red isochrones are
computed using the Padova 1994 tracks, while the black isochrones are computed using the Padova 2000
tracks. In each case, the dashed and solid isochrones are computed using the BaSeL 1.0 and BaSeL 3.1
spectral calibrations, respectively. All isochrones pertaining to a given cluster have fixed age and metallicity
(see Table 4).
ages and metallicities in a wide range of photometric bands.
The data tend to favor the combination of the Padova 1994
stellar evolution prescription with the BaSeL 3.1 spectral
calibration. This justifies our adoption of this combination
in our standard model.
3.3.2 Integrated colours
We must also check that our model can reproduce the inte-
grated colours of star clusters of various ages and metal-
licities, which are sensitive to the numbers of stars pop-
ulating different phases along the isochrones. Figs 8(a)
and 8(b) show the integrated, reddening-corrected U−B,
B−V and V −K colours of LMC clusters in various
age ranges, according to the classification scheme of
Searle, Wilkinson & Bagnuolo (1980, hereafter SWB). Also
shown as error bars are the colours of young star clusters
in the merger remnant galaxy NGC 7252 from Miller et al.
(1997) and Maraston et al. (2001). The solid line shows the
evolution of our standard SSP model for Z = 0.4Z⊙, at
ages ranging from a few Myr at the blue end of the line
to 13 Gyr at the red end of the line. The scatter in cluster
colours in Figs 8(a) and 8(b) is intrinsic (typical observa-
tional errors are indicated in each panel). It is largest in
V −K colour (Fig. 8b) but is also present, to a lesser extent,
in U−B and B−V colours (Fig. 8a). This scatter cannot be
accounted for by metallicity variations. The age-metallicity
degeneracy implies that the evolution of SSPs with various
metallicities are similar to that of the Z = 0.4Z⊙ model
in these colour-colour diagrams. For reference, the heavy
dashed line in Figs 8(a) and 8(b) shows the colours of the
standard SSP model of Section 3 for the metallicity Z = Z⊙
at ages from 100 Myr to 1 Gyr. The scatter in the observed
integrated colours of star clusters is most likely caused by
stochastic fluctuations in the numbers of stars populating
different evolutionary stages.
We illustrate this by generating random realiza-
tions of integrated cluster colours using a Monte Carlo
technique pioneered by Barbaro & Bertelli (1977) (see
also Chiosi, Bertelli & Bressan 1988; Girardi et al. 1995;
Santos & Frogel 1997; Bruzual 2002; Cervin˜o et al. 2001;
Cervin˜o et al. 2002). For a given cluster age, we draw stars
randomly from the IMF of equation (2) and place them in
their evolutionary phase along the isochrone at that age,
until a given cluster mass is reached. The small dots in
Figs 8(a) and 8(b) show the results of 22,000 such real-
izations for clusters of mass 2 × 104M⊙ and metallicity
Z = 0.4Z⊙, at ages between 105 and 13 Gyr (see Bruzual
2002 for more detail). It is clear from these figures that
the models can account for the full observed ranges of inte-

14 G. Bruzual and S. Charlot
Figure 7. Comparison of model isochrones with observed colour-magnitude diagrams of six old Galactic
globular clusters. For each cluster, the adopted distance modulus and colour excess are listed in Table 4
along with the sources of the stellar photometry. Each panel contains four isochrones: the red isochrones are
computed using the Padova 1994 tracks, while the black isochrones are computed using the Padova 2000
tracks. In each case, the dashed and solid isochrones are computed using the BaSeL 1.0 and BaSeL 3.1
spectral calibrations, respectively. All isochrones pertaining to a given cluster have fixed age and metallicity
(see Table 4).
grated cluster colours, including the scatter of nearly 2 mag
in V −K colour. The reason for this is that the V −K colour
is highly sensitive to the small number of bright stars pop-
ulating the upper giant branch. Fluctuations are smaller in
the U−B and B−V colours, which are dominated by the
more numerous main-sequence stars. The predicted scatter
would be smaller in all colours for clusters more massive
than 2 × 104M⊙, as the number of stars in any evolution-
ary stage would then be larger (Bruzual 2002; Cervin˜o et al.
2002).
To further illustrate the relation between cluster mass
and scatter in integrated colours, we plot in Fig. 8(c) the
absolute V magnitude as a function of V −K colour for the
same clusters as in Figs 8(a) and 8(b). The three models
shown correspond to the evolution of, from bottom to top,
a 2×104M⊙ SSP with metallicity Z = 0.4Z⊙, a 3×106M⊙
SSP with metallicity Z = Z⊙ and a 6 × 106M⊙ SSP with
metallicity Z = Z⊙. We show stochastic realizations of in-
tegrated colours only for the two least massive models, as
the predicted scatter is small for the most massive one. As
in Figs 8(a) and 8(b), random realizations at various ages
of 2 × 104M⊙ clusters with metallicity Z = 0.4Z⊙ can ac-
count for the full observed range of LMC cluster proper-
ties in this diagram. The NGC 7252 clusters are consis-
tent with being very young (100–800 Myr) and massive
(106 − 107M⊙) at solar metallicity, in agreement with the
results of Schweizer & Seitzer (1998).
Our models, therefore, reproduce remarkably well the
full observed ranges of integrated colours and absolute mag-
nitudes of star clusters or various ages and metallicities. It
is worth pointing out that, because of the stochastic nature
of the integrated-light properties of star clusters, single clus-
ters may not be taken as reference standards of simple stellar
populations of specific age and metallicity.
4 SPECTRAL EVOLUTION
We now turn to the predictions of our models for the spectral
evolution of stellar populations. In Section 4.1 below, we
begin by describing the canonical evolution of the spectral
energy distribution of a simple stellar population. We also
illustrate the influence of metallicity on the spectra. Then,
in Section 4.2, we compare our model with observed galaxy
spectra extracted from the SDSS EDR. Section 4.3 presents
a more detailed comparison of the predicted and observed
strengths of several absorption-line indices.

Stellar population synthesis at the resolution of 2003 15
Figure 8. (a) U−B versus B−V and (b) V −K versus B−V integrated colours of star clusters. The different
symbols represent LMC globular clusters in various age ranges according to the SWB classification scheme
(classes I–III: filled circles; class IV: squares; class V: triangles; classes VI–VII: open circles). The U−B
and B−V colours are from van den Bergh (1981) and the V −K colours from Persson et al. (1983). The
points with error bars are young star clusters in the merger remnant galaxy NGC 7252 (Miller et al. 1997;
Maraston et al. 2001). The solid line shows the evolution of the standard SSP model of Section 3 for the
metallicity Z = 0.4Z⊙ at ages from a few Myr to 13 Gyr. The small dots show the results of 22,000 stochastic
realizations of the integrated colours of clusters of mass 2× 104M⊙ at ages between 105 and 13 Gyr, for the
same metallicity and IMF as for this SSP model. The heavy dashed line shows the colours of the standard
SSP model of Section 3 for the metallicity Z = Z⊙ at ages from 100 Myr to 1 Gyr. (c) Absolute magnitude
MV versus V −K colour. The data are the same as in (a) and (b). Three models show the evolution of, from
bottom to top, a 2× 104M⊙ SSP with metallicity Z = 0.4Z⊙, a 3× 106M⊙ SSP with metallicity Z = Z⊙
and a 6 × 106M⊙ SSP with metallicity Z = Z⊙. Small circles indicate the positions of the models at the
ages 6, 7, 10, 100, 400 and 500 Myr and 1, 1.4, 2 and 10 Gyr (these marks can be used to roughly date the
clusters). Stochastic realizations of integrated colours are shown only for the two least massive models, as
the predicted scatter is small for the most massive one. Typical observational error bars are indicated at the
bottom of each panel.
4.1 Simple stellar population
Fig. 9 shows the spectral energy distribution of the standard
SSP model of Section 3 at various ages and for solar metal-
licity. As is possible for this metallicity (Section 2.2.2), we
have extended the STELIB/BaSeL 3.1 library blueward of
3200 A˚ and redward of 9500 A˚ using the Pickles medium-
resolution library (Section 2.2.3). In Fig. 9, therefore, the
model includes libraries of observed stellar spectra across
the whole wavelength range from 1205 A˚ to 2.5 µm.
The spectral evolution of an SSP may be understood
in terms of the evolution of its stellar content. At 106 yr,
the spectrum in Fig. 9 is entirely dominated by short-lived,
young massive stars with strong ultraviolet emission on the
upper main sequence. Around 107 yr, the most massive stars

16 G. Bruzual and S. Charlot
Figure 9. Spectral evolution of the standard SSP model of Sec-
tion 3 for the solar metallicity. The STELIB/BaSeL 3.1 spectra
have been extended blueward of 3200 A˚ and redward of 9500 A˚
using the Pickles medium-resolution library. Ages are indicated
next to the spectra (in Gyr).
leave the main sequence and evolve into red supergiants,
causing the ultraviolet light to decline and the near-infrared
light to rise. From a few times 108 yr to over 109 yr, AGB
stars maintain a high near-infrared luminosity. The ultravi-
olet light continues to drop as the turnoff mass decreases on
the main sequence. After a few gigayears, red giant stars ac-
count for most of the near-infrared light. Then, the accumu-
lation of low-mass, post-AGB stars causes the far-ultraviolet
emission to rise until 13 Gyr. The most remarkable feature
in Fig. 9 is the nearly unevolving shape of the optical to
near-infrared spectrum at ages from 4 to 13 Gyr. The rea-
son for this is that low-mass stars evolve within a narrow
temperature range all the way from the main sequence to
the end of the AGB.
The scale of Fig. 9 is not optimal to fully appreciate
the spectral resolution of the model. However, some varia-
tions can be noticed in the strengths of prominent absorp-
tion lines. At ages between 0.1 and 1 Gyr, for example,
there is a marked strengthening of all Balmer lines from Hα
at 6563 A˚ to the Balmer continuum limit at 3646 A˚. This
characteristic signature of a prominent population of late-B
to early-F stars is, in fact, a standard diagnostic of recent
bursts of star formation in galaxies (e.g., Couch & Sharples
1987; Poggianti et al. 1999; Kauffmann et al. 2003). It is
interesting to note how, over the same age interval, the
‘Balmer break’ (corresponding to the Balmer continuum
limit) evolves into the ‘4000 A˚ break’ (arising from the
prominence in cool stars of a large number of metallic lines
blueward of 4000 A˚). Other prominent absorption features
in Fig. 9 include the Mg II resonance doublet near 2798 A˚,
the Ca II H and K lines at 3933 A˚ and 3968 A˚, and the Ca II
Figure 10. Spectra of the standard SSP model of Section 3 at
different ages for different metallicities, as indicated. The promi-
nent metallic features show a clear strengthening from the most
metal-poor to the most metal-rich models, even though the shape
of the spectral continuum is roughly similar in all models.
triplet at 8498, 8542, and 8662 A˚. These features tend to
strengthen with age as they are stronger in late-type stars
than in early-type stars, whose opacities are dominated by
electron scattering. However, the strengths of these features
also depend on the abundances of the heavy elements that
produce them.
Fig. 9 also shows that the strengths of many absorption
lines, in contrast to the spectral continuum shape, continue
to evolve significantly at ages between 4 and 13 Gyr. Since
the strengths of such features are expected to react differ-
ently to age and metallicity, they can potentially help us
resolve the age-metallicity degeneracy that hampers the in-
terpretation of galaxy spectra (see Section 3.1; Rose 1985;
Worthey 1994; Vazdekis 1999). This is illustrated by Fig. 10,
in which we show the spectra of SSPs of different ages and
metallicities, whose spectral continua have roughly similar
shapes. The prominent metallic features in these spectra,
such as the Ca II H and K lines, the many Fe and Mg lines
between 4500 and 5700 A˚, and several TiO, H2O and O2
molecular absorption features redward of 6000 A˚, show a
clear strengthening from the most metal-poor to the most
metal-rich stellar populations. As we shall see in Sections 4.2
and 4.3 below, the analysis of these features in observed
galaxy spectra provide useful constraints on the metallici-
ties, and in turn on the ages, of the stellar populations that
dominate the emission.
4.2 Interpretation of galaxy spectra
We now exemplify how our model can be used to interpret
observed galaxy spectra. The observational sample we con-

Stellar population synthesis at the resolution of 2003 17
Figure 11. Model fits (red spectra) of two galaxies extracted from the SDSS Early Data Release (black
spectra). The fits were derived using the optimized data compression algorithm of Heavens, Jimenez & Lahav
(2000), as described in the text. The emission lines of SDSS 385–118 were removed to perform the fit.
sider is the Early Data Release of the Sloan Digital Sky
Survey (Stoughton et al. 2002; see Section 1). This sur-
vey will obtain u, g, r, i, and z photometry of almost a
quarter of the sky and spectra of at least 700,000 objects.
The ‘main galaxy sample’ of the EDR includes the spec-
tra of 32,949 galaxies with r-band Petrosian magnitudes
brighter than 17.77 after correction for foreground Galac-
tic extinction (Strauss et al. 2002). The spectra are flux-
and wavelength-calibrated, with 4096 pixels from 3800 A˚
to 9200 A˚ at resolving power λ/∆λ ≈ 1800. This is simi-
lar to the resolution of our model in the wavelength range
from 3200 A˚ to 9500 A˚. The SDSS spectra are acquired us-
ing 3-arcsecond diameter fibres that are positioned as close
as possible to the centres of the target galaxies. For the
purpose of first illustration, we select SDSS spectra of two
representative galaxies of different types according to their
4000 A˚ discontinuities. We adopt here the 4000 A˚ discontinu-
ity index defined by Balogh et al. (1999) as the ratio of the
average flux density Fν in the narrow bands 3850–3950 A˚
and 4000–4100 A˚. The original definition of this index by
Bruzual (1983) uses wider bands (3750–3950 A˚ and 4050–
4250 A˚), and hence, it is more sensitive to reddening effects.
We select two spectra with median signal-to-noise ratios per
pixel larger than 30 and with discontinuity indices near op-
posite ends of the sample distribution, Dn(4000) = 1.26
(SDSS 385–118) and Dn(4000) = 1.92 (SDSS 267–110).
The galaxies have measured line-of-sight velocity dispersions
σV ≈ 70 kms−1 and 130 kms−1, respectively. The spectra
are corrected for foreground Galactic extinction using the
reddening maps of Schlegel, Finkbeiner & Davis (1998) and
the extinction curve of Fitzpatrick (1999).
To interpret these spectra with our model, we use
MOPED, the optimized data compression algorithm of
Heavens, Jimenez & Lahav (2000). In this approach, galaxy
spectra are compressed into a reduced number of linear com-
binations connected to physical parameters such as age, star
formation history, metallicity and dust content. The linear
combinations contain as much information about the pa-
rameters as the original spectra. There are several advan-
tages to this method. First, it allows one to explore a wide

18 G. Bruzual and S. Charlot
range of star formation histories, chemical enrichment histo-
ries and dust contents by choosing appropriate parametriza-
tions (Reichardt, Jimenez & Heavens 2001). Second, it al-
lows one to estimate the errors on derived physical param-
eters. And third, it is extremely fast and hence efficient to
interpret large numbers of galaxy spectra. Our model has
already been combined with the MOPED algorithm to in-
terpret SDSS EDR spectra (Mathis et al., in preparation).
The results presented for the two galaxies considered here
are based on a decomposition of the star formation history
into six episodes of constant star formation in the age bins
0.0–0.01, 0.01–0.1, 0.1–1.0, 1.0–2.5, 2.5–5 and 5–13 Gyr. The
metallicity in each bin can be one of Z = 0.4Z⊙, Z⊙ or
2.5Z⊙. The attenuation by dust is parametrized using the
simple two-component model of Charlot & Fall (2000, see
Section 5 below). The effective attenuation optical depth af-
fecting stars younger than 0.01 Gyr can be τˆV = 0.0, 0.1,
0.5, 1, 1.5, 2 or 3, while that affecting older stars is µτˆV ,
with µ = 0.0, 0.1, 0.3, 0.5 or 1 (see equation 6 below; we
are grateful to H. Mathis for providing us with the results
of these fits).
Fig. 11 shows the resulting spectral fits of SDSS 385–
118 and SDSS 267–110. Figs 12 and 13 show details of the
‘high-pass’ spectra of the fitted models and observed galaxies
(note that we display the emission lines of SDSS 385–118 in
Figs 11a and 12, even though these were removed to perform
the fit). The high-pass spectra were obtained by smoothing
the original spectra using a top-hat function of width 200 A˚
and then dividing the original spectra by the smoothed spec-
tra (see Baldry et al. 2002). The model reproduces the main
stellar absorption features of both galaxies extremely well.
In particular, in the spectrum of SDSS 385–118, the ab-
sorption wings of Balmer lines are well fitted up to high
orders in the series. With such an accuracy, the model can
be used reliably to measure the contamination of Balmer
emission lines by underlying stellar absorption in galaxies
(see Tremonti 2003). This is especially important, for ex-
ample, to constrain attenuation by dust using the Hα/Hβ
ratio. The spectrum of SDSS 267–110 in Fig. 13 shows no
obvious emission lines and exhibits strong stellar absorption
features characteristic of old stellar populations. Among the
most recognizable features, the Ca II H and K lines, the G
band near 4300 A˚, the magnesium features near 5100 A˚ and
5200 A˚, the iron features between 5270 A˚ and 5800 A˚, the
NaD feature near 5900 A˚, and the TiO bands near 6000 A˚
and 6200 A˚ are all well reproduced by the model. In Sec-
tion 4.3 below, we compare in a more quantitative way the
strengths of these features in our model with those in the
SDSS EDR spectra.
It is of interest to mention the physical parameters of
the model fits in Figs 11–13. For SDSS 385–118, the al-
gorithm assigns 91 per cent of the total stellar mass of
∼ 109M⊙ to stars with metallicity Z = 0.4Z⊙ formed be-
tween 2.5 and 13 Gyr ago, and the remainder to stars of the
same metallicity formed in the last Gyr or so. The galaxy is
best fitted with µτˆV = 0.5. For SDSS 267–110, 50 per cent
of the total stellar mass of ∼ 1010M⊙ is attributed to stars
formed 5–13 Gyr ago and the remainder to stars formed
2.5–5 Gyr ago, all with solar metallicity. The dust attenu-
ation optical depth is found to be negligible, with τˆV = 0.
The total stellar masses quoted here do not include aperture
corrections for the light missed by the 3-arcsec diameter fi-
bres. The errors in the derived mass fractions in our various
bins are relatively modest, of the order of 20 per cent, for
these spectra with high signal-to-noise ratios (Mathis et al.,
in preparation).
The examples described above illustrate how our model
can be used to interpret observed high-resolution spectra
of galaxies at wavelength from 3200 A˚ to 9500 A˚ in terms
of physical parameters such as age, star formation history,
chemical enrichment history and dust content.
4.3 Spectral indices
It is important to establish in a more quantitative way
the ability of our model to reproduce the strengths of
prominent stellar absorption features in observed galaxy
spectra. The atomic and molecular features that are most
commonly measured in the visible spectra of galaxies are
those defined in the extended Lick system (Worthey et al.
1994; Worthey & Ottaviani 1997; Trager et al. 1998; see
Section 1). This system includes a total of 25 spectral in-
dices that were defined and calibrated in the spectra of 460
Galactic stars covering the wavelength range from 4000 A˚
to 6400 A˚ at a resolution of ∼ 9 A˚ FWHM. In the Lick
system, an index is defined in terms of a central ‘feature
bandpass’ bracketed by two ‘pseudo-continuum bandpasses’.
By convention, atomic indices are expressed in angstroms of
equivalent width, while molecular indices are expressed in
magnitudes.
We compare the Lick index strengths predicted by our
model with those measured in SDSS EDR spectra with high
signal-to-noise ratios. We do not use here the index strengths
included in the SDSS EDR. Instead, we re-measure index
strengths in the SDSS spectra in the same way as in the
model spectra (we are grateful to J. Brinchmann for pro-
viding us with the results of these measurements). Our ap-
proach differs in two ways from previous absorption-line
studies of galaxies. First, in previous studies, Lick indices
were generally modelled by parametrizing index strengths
as functions of stellar effective temperature, gravity and
metallicity (see Section 1). In our model, the index strengths
are measured directly from the spectra using the bandpass
definitions of Worthey & Ottaviani (1997) and Trager et al.
(1998). Second, we consider all types of galaxies in our anal-
ysis, including star-forming galaxies, while all previous anal-
yses focused on passively evolving stellar populations older
than about 1 Gyr. The inclusion of star-forming galaxies re-
quires that emission lines be removed from the SDSS spec-
tra before measuring the indices. This is achieved follow-
ing the careful procedure outlined by Tremonti (2003, see
also Kauffmann et al. 2003) that is based on accurate fits
of the emission line-free regions of the spectra with model
spectra broadened to the observed stellar velocity disper-
sion. The subtraction of emission lines is important mainly
for Balmer-line indices and a few metallic-line indices (e.g.,
G4300, Fe5015). We include the errors resulting from line
subtraction into the observational errors of these indices.
Fig. 14 shows the strengths of eight indices measured in
this way in 543 spectra with high median signal-to-noise
ratio per pixel, S/Nmed > 40, in the ‘main galaxy sam-
ple’ of the SDSS EDR. These indices, whose strengths are
plotted as a function of Dn(4000), were chosen for illustra-
tion purposes because they are produced by different ele-

Stellar population synthesis at the resolution of 2003 19
Figure 12. Detailed comparison of ‘high-pass’ spectra for the same model (in red) of SDSS galaxy 385–118
(in black) as in Fig. 11(a). The high-pass spectra were obtained by smoothing the original spectra using a
top-hat function of width 200 A˚ and then dividing the original spectra by the smoothed spectra.
ments (see below). The typical observational errors, indi-
cated in the upper left corner of each panel, are very small
for this sample of high-quality spectra. Different symbols in
Fig. 14 correspond to different velocity dispersions (crosses:
σV 6 100 kms−1; dots: 100 < σV 6 250 kms−1; open
circles: σV > 250 kms−1). As expected, early-type galaxies
characterized by large Dn(4000) strengths tend to have large
velocity dispersions (see Kauffmann et al. 2003). However,
we cannot make statistical inferences about the properties
of SDSS galaxies based on this sample alone because of the
selection by signal-to-noise ratio applied to test the model.
Superimposed on the data in Fig. 14 are three models show-
ing the evolution of the index strengths of SSPs with differ-
ent metallicities, Z = 0.4Z⊙, Z⊙ and 2.5Z⊙, at ages between
5× 107 yr and 15 Gyr. The models have 3 A˚ FWHM spec-
tral resolution, corresponding to a nominal stellar velocity
dispersion σV ≈ 70 kms−1 at 5500 A˚. As a complement to
Fig. 14, Fig. 15 shows the evolution in the same diagrams of
Z = Z⊙ models broadened to velocity dispersions σV = 70,
150 and 300 km s−1. We also show in Fig. 15 the evolu-
tion of a model with continuous star formation with a law
ψ(t) ∝ exp [−t/(4Gyr)], for Z = Z⊙ and σV = 70 kms−1.
The models in Figs 14 and 15 summarize the influence of
metallicity, velocity dispersion and star formation history on
the strengths of Lick indices. Fig. 14 shows that, as found in
many previous studies of Lick indices, ‘metallic-line indices’
such as Fe4531, C24668, Mg1, Mg2, Mgb and Fe5270 react
sensitively to changes in metallicity in old stellar popula-
tions [corresponding to the largest Dn(4000) values], while
‘Balmer-line indices’ such as HδA do not, as they are con-
trolled mainly by the temperature of the main-sequence
turnoff (see references in Section 1). We note that Dn(4000)
is also sensitive to metallicity, as it is produced by the accu-
mulation of a large number of metallic lines just blueward of
4000 A˚. Stellar velocity dispersion is another parameter af-
fecting the strengths of Lick indices (e.g., Trager et al. 1998;
Vazdekis 2001). As Fig. 15 shows, σV greatly influences the
strengths of indices whose definitions involve narrow pseudo-
continuum bandpasses, such as Fe4531 and Fe5270. Fig. 15
further shows that a model with continuous star formation

20 G. Bruzual and S. Charlot
Figure 13. Detailed comparison of ‘high-pass’ spectra for the same model (in red) of SDSS galaxy 267–110
(in black) as in Fig. 11(b). The high-pass spectra were obtained by smoothing the original spectra using a
top-hat function of width 200 A˚ and then dividing the original spectra by the smoothed spectra.
can account for the observed strengths of most indices in
galaxies with low velocity dispersions. This is remarkable, as
our model provides the first opportunity to study the index
strengths of star-forming galaxies in this way. Old SSP mod-
els do not seem to reproduce well the observed strengths of
indices such as C24668, Mg1, Mg2 and Mgb in galaxies with
high velocity dispersions. This is not surprising, as massive
galaxies show departures in the relative abundances of dif-
ferent heavy elements from the Galactic stars on which the
models are based (e.g., Worthey, Faber & Gonza´lez 1992).
We wish to investigate in more detail the ability of our
model to reproduce simultaneously the strengths of differ-
ent indices in individual galaxy spectra. To carry out such
an analysis, we need a library of models encompassing a
full range of physically plausible star formation histories.
We generate a library of Monte Carlo realizations of dif-
ferent star formation histories similar to that with which
Kauffmann et al. (2003) interpreted the Dn(4000) and HδA
index strengths of a complete sample of 120,000 SDSS galax-
ies using our model. In this library, each star formation
history consists of two parts: (1) an underlying continuous
model parametrized by a formation time tform and a star
formation time scale parameter γ > 0, such that galaxies
form stars according to the law ψ(t) ∝ exp [−γt(Gyr)] from
time tform to the present. The time tform is taken to be dis-
tributed uniformly from the Big Bang to 1.5 Gyr before
the present day and γ over the interval 0 to 1; (2) random
bursts are superimposed on these continuous models. Bursts
occur with equal probability at all times after tform. They
are parametrized in terms of the ratio between the mass of
stars formed in the burst and the total mass formed by the
continuous model from time tform to the present. This ratio
is taken to be distributed logarithmically between 0.03 and
4.0. During a burst, stars form at a constant rate for a time
distributed uniformly in the range 3 × 107–3 × 108 yr. The
burst probability is set so that 50 per cent of the galaxies
in the library have experienced a burst over the past 2 Gyr
(see Kauffmann et al. 2003 for more detail). We distribute
our models uniformly in metallicity from 0.25 to 2 times so-
lar (all stars in a given model have the same metallicity)

Stellar population synthesis at the resolution of 2003 21
Figure 14. Strengths of G4300, Fe4531, C24668, Mg1, Mg2, Mgb, Fe5270 and HδA as a function of Dn(4000)
for 543 galaxies with S/Nmed > 40 in the ‘main galaxy sample’ of the SDSS EDR (the median observational
error bars are indicated in the upper left corner of each panel). Different symbols correspond to different ve-
locity dispersions (crosses: σV 6 100 km s−1; dots: 100 < σV 6 250 kms−1; open circles: σV > 250 km s−1).
The lines show the evolution of the standard SSP model of Section 3 for the metallicities Z = 0.008 (dot-and-
dashed line), Z = 0.02 (solid line) and Z = 0.05 (dashed line) at ages from 5× 107 yr to 15 Gyr. The models
have 3 A˚ FWHM spectral resolution, corresponding to a nominal stellar velocity dispersion σV ≈ 70 km s−1
at 5500 A˚.
and uniformly in velocity dispersion from 70 kms−1 (the
nominal resolution of the models at 5500 A˚) to 350 kms−1.
Our final library consists of 150,000 different star formation
histories.
We use this library to evaluate the ability of our model
to reproduce the strengths of various indices in observed
galaxy spectra. To start with, we examine the accuracy to
which the model can reproduce the strength of any indi-
vidual index at the same time as the 4000 A˚ discontinuity
in SDSS spectra. We also require consistency with the ob-
served stellar velocity dispersion. We enlarge here our ob-
servational sample to 2010 spectra with S/Nmed > 30 in the
‘main galaxy sample’ of the SDSS EDR. For each individ-
ual Lick index, we first select for each SDSS spectrum the
models in the library whose stellar velocity dispersions are
within 15 kms−1 of the observed one. We then select among
these models the one that reproduces the observedDn(4000)
and selected index strength with the lowest χ2. We report in
Fig. 16, for 24 indices, the distribution of the index strength
Ifit in the best-fitting model minus that Iobs in the observed
spectrum, divided by the associated error σI (equation 3
below), for the 2010 galaxies in our sample. For reference,
a dotted line in each panel indicates a Gaussian distribu-
tion with unit standard deviation. The shaded histograms
in Fig. 16 show the contributions to the total distributions
by galaxies with σV > 180 km s−1, corresponding roughly to
the median stellar velocity dispersion of our SDSS sample.
The error σI associated to each index fit in this analysis
includes both the observational error σIobs and a theoretical
error σImod reflecting the uncertainties in the model spectral
calibration. We therefore write

22 G. Bruzual and S. Charlot
Figure 15. Strengths of G4300, Fe4531, C24668, Mg1, Mg2, Mgb, Fe5270 and HδA as a function of Dn(4000)
for the same SDSS galaxies as in Fig. 14. The lines show the evolution of the standard SSP model of Section 3
for solar metallicity and for stellar velocity dispersions σV = 70 km s−1 (nominal model velocity dispersion,
solid line), 150 km s−1 (dot-and-dashed line) and 300 km s−1 (dashed line) at ages from 5 × 107 yr to
15 Gyr. The long-dashed line shows the evolution of a model with continuous star formation with a law
ψ(t) ∝ exp [−t/(4Gyr)], for Z = Z⊙ and σV = 70 km s−1.
σI =
[
(σI
obs)2 + (σI
mod)2
]1/2
. (3)
Table 5 lists, for each index, the median observational error
σIobs for the galaxies in our sample. For many indices, this
is much smaller than the observed 1%–99% percentile range
∆I of index strengths in the sample (also listed), indicating
that variations in index strength are highly significant. We
adopt a representative, fixed theoretical error σImod for each
index. This is taken to be half the maximum difference in the
strength of the index between SSP models calibrated using
the STELIB/BaSeL 1.0 and STELIB/BaSeL 3.1 spectral li-
braries over wide ranges of ages (1–13 Gyr) and metallicities
(0.004–0.05). Table 5 shows that the theoretical error σImod
obtained in this way is comparable to the median observa-
tional error σIobs for most indices. Also listed in Table 5 is
the quantity ∆I/σI indicating the ‘resolving power’ of each
index. Here σI is the median error from equation (3) for the
galaxies in our sample.
We can identify in Fig. 16 those Lick indices that
our model fails to reproduce well when compared to
high-quality galaxy spectra: CN1, CN2, C24668, Mg1 and
NaD. The distributions of
(
Ifit − Iobs
)
/σI for these in-
dices all show significant tails relative to a Gaussian dis-
tribution. These departures are most likely caused by
differences in element abundance ratios between SDSS
galaxies and the Galactic stars used to build our model.
Several recent studies have addressed the influence of
changes in element abundance ratios on the strengths
of Lick indices (Tripicco & Bell 1995; Tantalo et al. 1998;
Trager et al. 2000; Vazdekis et al. 2001; Proctor & Sansom
2002; Thomas, Maraston & Bender 2003). These studies
were motivated by the observational evidence that the abun-
dance ratios of α-elements to iron are enhanced in massive
early-type galaxies relative to the solar composition. The
discrepancies found in these studies between models with

Stellar population synthesis at the resolution of 2003 23
Figure 16. Fits of the strengths of individual indices in combination with Dn(4000) in the spectra of 2010
galaxies with S/Nmed > 30 in the ‘main galaxy sample’ of the SDSS EDR. The stellar velocity dispersion of
the models are required to be within 15 kms−1 of the observed ones. Each panel shows the distribution of
the fitted index strength Ifit minus the observed one Iobs, divided by the associated error σI (equation 3).
For reference, a dotted line in each panel indicates a Gaussian distribution with unit standard deviation.
The shaded histograms show the contributions to the total distributions by galaxies with σV > 180 km s−1,
corresponding roughly to the median stellar velocity dispersion of the sample.
scaled-solar abundances and observations of Lick indices in
nearby star clusters and galaxies are similar to those iden-
tified above in Fig. 16. Enhanced abundances of Mg, C and
N have been invoked to account for the departures of mod-
els from observations of CN1, CN2, C24668 and Mg1. Some
indices like NaD could also be contaminated by interstellar
absorption. As Fig. 16 shows, the discrepancies pertaining
to these indices tend to arise in galaxies with large velocity
dispersions.
Our main goal here is to identify those indices that can
be fitted by our model in observed galaxy spectra. Among
the indices the model can recover within the errors at the
same time as Dn(4000) in Fig. 16, we expect a subset to
also be reproducible simultaneously. In particular, since the
Balmer-line indices Hβ, HγA and HδA are not expected to
depend sensitively on metallicity, they should also be repro-
ducible in combination with metallic-line indices. We fur-
ther expect our model to be able to reproduce metallic-
line indices that do not depend sensitively on changes in
α-element to iron abundance ratios. The model with vari-
able element abundance ratios of Thomas et al. (2003) is
useful for identifying ‘composite’ indices that are sensitive
to metallicity but not to α/Fe. The original [MgFe] index
of Gonza´lez (1993) and the new [MgFe]′ index proposed by
Thomas et al. (2003), which is even less sensitive to α/Fe,
are both well calibrated in our model (see Fig. 18 below).
After some experimentation, we identified two other indices
with similarly weak dependence on α/Fe,
[Mg1Fe] = 0.6Mg1 + 0.4 log(Fe4531 + Fe5015) , (4)
[Mg2Fe] = 0.6Mg2 + 0.4 log(Fe4531 + Fe5015) . (5)
Fig. 17 illustrates the evolution of [MgFe]′, [Mg1Fe] and
[Mg2Fe] for SSPs with different metallicities, α/Fe abun-

24 G. Bruzual and S. Charlot
Table 5. Observed 1%–99% percentile range ∆I and median ob-
servational error σIobs for 28 spectral features in 2010 spectra
with S/Nmed > 30 in the ‘main galaxy sample’ of the SDSS EDR.
Also listed for each index is the theoretical error σImod reflecting
the uncertainties in the model spectral calibration. The quantity
∆I/σI , where σI is the median of σI = [(σIobs)2 + (σImod)2]1/2
for the sample, indicates the ‘resolving power’ of each index. The
values for atomic indices are expressed in angstroms of equivalent
width, while those for molecular indices (indicated by a star) are
expressed in magnitudes. An exception is Dn(4000), whose value
is the ratio of the average flux densities in two narrow bands
(Section 4.2).
Feature 1%–99% σIobs σImod ∆I/σI
range ∆I
⋆CN1 −0.137. . . 0.126 0.013 0.023 10
⋆CN2 −0.089. . . 0.174 0.013 0.022 10
Ca4227 0.15. . . 1.87 0.22 0.22 6
G4300 0.06. . . 6.36 0.34 0.52 10
Fe4383 0.97. . . 6.27 0.36 0.40 10
Ca4455 0.05. . . 1.99 0.24 0.11 7
Fe4531 1.13. . . 4.18 0.32 0.25 8
C24668 −0.01. . . 8.62 0.41 0.39 15
Hβ 1.28. . . 4.73 0.24 0.39 7
Fe5015 1.40. . . 6.55 0.39 0.47 8
⋆Mg1 −0.004. . . 0.164 0.006 0.010 14
⋆Mg2 0.050. . . 0.322 0.008 0.019 13
Mgb 1.32. . . 5.13 0.24 0.59 6
Fe5270 0.81. . . 3.65 0.25 0.15 10
Fe5335 0.93. . . 3.48 0.26 0.15 9
Fe5046 0.50. . . 2.40 0.22 0.10 8
Fe5709 0.11. . . 1.40 0.18 0.10 6
Fe5782 0.17. . . 1.28 0.15 0.08 7
NaD 0.77. . . 5.45 0.17 0.33 12
⋆TiO1 −0.014. . . 0.072 0.005 0.006 11
⋆TiO2 0.025. . . 0.105 0.004 0.015 5
HδA −3.20. . . 6.09 0.49 0.93 9
HγA −6.90. . . 4.69 0.45 1.01 11
Dn(4000) 1.12. . . 2.23 0.02 0.08 13
[MgFe] 1.13. . . 3.91 0.15 0.18 12
[MgFe]′ 1.12. . . 3.95 0.16 0.18 12
⋆[Mg1Fe] 0.197. . . 0.483 0.011 0.014 16
⋆[Mg2Fe] 0.226. . . 0.576 0.011 0.014 19
dance ratios and stellar velocity dispersions. The left-hand
panels show the predictions of the Thomas et al. (2003)
model for the metallicities Z = 0.5Z⊙, Z⊙ and 2.2Z⊙ and
for [α/Fe]= 0.0, 0.3 and 0.5, for a Salpeter (1955) IMF trun-
cated at 0.1 and 100 M⊙. The right-hand panels show the
predictions of our model for the same IMF for the metal-
licities Z = 0.4Z⊙, Z⊙ and 2.5Z⊙ and for stellar velocity
dispersions 70 6 σV 6 300 kms−1. It is clear from this fig-
ure that [MgFe]′, [Mg1Fe] and [Mg2Fe] are affected sensi-
tively by changes in Z and σV but not by changes in α/Fe.
We note that, since Mg1 and Mg2 are defined over broader
bandpasses than the Mgb index involved in the definition of
[MgFe]′ (471 A˚ versus 64 A˚), [Mg1Fe] and [Mg2Fe] may be
slightly more sensitive to flux-calibration uncertainties and
attenuation by dust in observed galaxy spectra.
Based on these arguments, we use our library of models
with different star formation histories to fit simultaneously
the observed strengths of Hβ, HγA, HδA, [MgFe]′, [Mg1Fe],
[Mg2Fe] and Dn(4000) in the 2010 SDSS spectra with
S/Nmed > 30 in our sample. As before, for each SDSS spec-
trum, we select the best-fitting model in the library among
those with stellar velocity dispersions within 15 km s−1 of
the observed one. Fig. 18 shows the resulting distributions of
(
Ifit − Iobs
)
/σI for all galaxies in the sample, for the same
24 indices as in Fig. 16 and for [MgFe], [MgFe]′, [Mg1Fe] and
[Mg2Fe]. The highlighted frames indicate the seven indices
used to constrain the fits. Fig. 18 demonstrates that our
model can account simultaneously for the observed strengths
of Hβ, HγA, HδA, [MgFe]′, [Mg1Fe], [Mg2Fe] and Dn(4000)
in high-quality galaxy spectra. The strengths of these in-
dices are always recovered within the errors. In addition,
the model recovers reasonably well the strengths of several
other indices which were not used to constrain the fits, such
as G4300, Ca4455, Fe4531, Fe5015, Fe5270, Fe5335, Fe5709
and Fe5782. As expected from Fig. 16, indices like CN1,
CN2, C24668, Mg1 and NaD cannot be fitted accurately be-
cause of their strong dependence on element abundance ra-
tios. The fact that Mgb appears to be better reproduced
than Mg1 and Mg2 in Fig. 18 is a consequence of the larger
relative error on this index (see Table 5). Interestingly, TiO1
and TiO2 that could be fitted individually in Fig. 16 do not
appear to be well reproducible in combination with the other
indices in Fig. 18.
The agreement between model and observations for
many indices in Fig. 18 is all the more remarkable in that
the measurement errors for this sample of high-quality SDSS
spectra are very small. As Table 5 shows, for indices such
as HγA, HδA, Dn(4000), [MgFe]′, [Mg1Fe] and [Mg2Fe], the
typical error σI amounts to only about 5–10 per cent of the
total range spanned by the index over the full sample. Our
model, therefore, represents an ideal tool for interpreting the
distribution of these indices in complete samples of galaxies
in terms of the parameters describing the stellar populations.
Such analyses may include all types of galaxies, from star-
forming galaxies to passively evolving, early-type galaxies,
for which stellar velocity dispersions should first be deter-
mined.
4.4 Comparison with previous work
In most previous studies of absorption-line features in
galaxy spectra, index strengths were computed in the
Lick/image dissector scanner (IDS) system (see for exam-
ple Worthey et al. 1994). To compare our results with these
previous studies, we must therefore transform our predic-
tions to the Lick/IDS system. This amounts to computing
index strengths as if they were measured in spectra which
are not flux-calibrated and whose resolution ranges from 8 A˚
to 10 A˚ FWHM, depending on wavelength. We follow the
procedure outlined in the appendix of Worthey & Ottaviani
(1997) and calibrate the transformation from STELIB to
Lick/IDS spectra using 31 stars in common between the two
libraries. We first broaden the STELIB spectra of these stars
to the wavelength-dependent Lick/IDS resolution. Then, we
identify the median offsets between the index strengths mea-
sured in the broadened STELIB spectra and those measured
from the non-fluxed Lick/IDS spectra for the 31 stars. The
resulting median offsets are listed in Table 6 for 25 spectral
features. To compute predictions in the Lick/IDS system,
therefore, we first broaden our model galaxy spectra to the
Lick/IDS resolution and then subtract the median offsets of

Stellar population synthesis at the resolution of 2003 25
Figure 17. Left: Evolution of the strengths of [MgFe]′, [Mg1Fe] and [Mg2Fe] according to the model
with variable element abundance ratios of Thomas et al. (2003) for the metallicities Z = 0.5Z⊙ (short-
dashed lines), Z⊙ (solid lines) and 2.2Z⊙ (long-dashed lines). For each metallicity, three lines corre-
sponding to [α/Fe]=0.0, 0.3 and 0.5 are shown (hardly distinguishable). The dotted line shows the evo-
lution of an SSP with solar metallicity computed using the Padova 1994 stellar evolution prescription, the
STELIB/BaSeL 3.1 spectral calibration and a Salpeter (1955) IMF (0.1–100 M⊙), for a stellar velocity
dispersion σV = 200 km s−1. Right: Evolution of the strengths of [MgFe]
′, [Mg1Fe] and [Mg2Fe] in SSPs
computed using the Padova 1994 stellar evolution prescription, the STELIB/BaSeL 3.1 spectral calibration
and a Salpeter (1955) IMF (0.1–100 M⊙), for the metallicities Z = 0.4Z⊙ (short-dashed line), Z⊙ (dotted
line) and 2.5Z⊙ (long-dashed line) and for σV = 200 km s
−1. The shaded area around the solar-metallicity
model indicates the range spanned by models with stellar velocity dispersions 70 6 σV 6 300 km s−1.
Table 6 from the index strengths measured in the broadened
spectra.
In Fig. 19, we compare different models for the evolution
of the HδA, Fe5270 and Mg2 index strengths of a simple stel-
lar population with solar composition (Z = Z⊙, [α/Fe] =0)
and a Salpeter (1955) IMF. The left-hand panels show model
predictions computed in the Lick/IDS system. The solid line
shows our standard model transformed to the Lick/IDS sys-
tem, as described above. Also shown, where available, are
the models of Worthey (1994, dotted line), Vazdekis et al.
(1996, long-dashed line), Worthey & Ottaviani (1997, dot-
and-dashed line) and Thomas et al. (2003, short-dashed
line). These models differ from ours in that they rely on the
implementation of the ‘fitting formulae’ of Worthey et al.
(1994) and Worthey & Ottaviani (1997) – who parametrized
index strengths as functions of stellar effective temperature,
gravity and metallicity (see Section 1 above) – into different
population synthesis codes. The predictions are restricted to
stellar populations older than 1 Gyr. As Fig. 19 shows, the
strengths of HδA, Fe5270 and Mg2 predicted by our model
when transformed to the Lick/IDS system are consistent
with the predictions from these previous models to within
the typical theoretical errors listed in Table 5.
The recent model of Vazdekis (1999) offers another el-
ement of comparison, as it predicts the spectra of simple
stellar populations of various ages and metallicities at a res-

26 G. Bruzual and S. Charlot
Figure 18. Simultaneous fit of the strengths of several indices in the spectra of 2010 galaxies with S/Nmed >
30 in the ‘main galaxy sample’ of the SDSS EDR. The highlighted frames indicate the seven indices used to
constrain the fits. The stellar velocity dispersion of the models are required to be within 15 km s−1 of the
observed ones. Each panel shows the distribution of the fitted index strength Ifit minus the observed one
Iobs, divided by the associated error σI (equation 3). For reference, a dotted line in each panel indicates a
Gaussian distribution with unit standard deviation. The shaded histograms show the contributions to the
total distributions by galaxies with σV > 180 km s−1, corresponding roughly to the median stellar velocity
dispersion of the sample.
olution of ∼ 1.8 A˚. Thus, the strengths of HδA, Fe5270 and
Mg2 can be measured in these spectra in the same way as
in our model, without having to transform predictions to
the Lick/IDS system. In the right-hand panels of Fig. 19,
we compare the strengths of HδA, Fe5270 and Mg2 in our
model with those measured in the Vazdekis (1999) spectra
broadened to a resolution of 3 A˚ FWHM, for an SSP with
solar composition and a Salpeter (1955) IMF. The predic-
tions of both models agree to within the typical theoretical
errors listed in Table 5. As a further check, we compare in
Fig. 20 the spectra predicted by both models for 10 Gyr-
old SSPs with scaled-solar abundances, for the metallicities
0.4Z⊙ and Z⊙. The spectra are shown in the two narrow
wavelength regions covered by the Vazdekis (1999) model,
3820–4500 A˚ and 4780–5460 A˚. The overall agreement be-
tween the two models is excellent at both metallicities. We
conclude that our model agrees reasonably well with previ-
ous models of spectral indices of galaxies.
5 SUMMARY AND CONCLUSIONS
We have presented a new model for computing the spec-
tral evolution of stellar populations of different metallici-
ties at ages between 1 × 105 yr and 2 × 1010 yr at a reso-
lution of 3 A˚ FWHM across the whole wavelength range
from 3200 A˚ to 9500 A˚ (corresponding to a median resolv-
ing power λ/∆λ ≈ 2000). These predictions are based on
a new library of observed stellar spectra recently assembled
by Le Borgne et al. (2003). The spectral evolution can also
be computed across a larger wavelength range, from 91 A˚
to 160 µm, at lower resolution. The model incorporates re-

Stellar population synthesis at the resolution of 2003 27
Figure 19. Evolution of the strengths of HδA, Fe5270 and Mg2 of an SSP with solar composition (Z = Z⊙,
[α/Fe]=0) and a Salpeter (1955) IMF according to different models. Left: Predictions computed in the
Lick/IDS system. In each panel, the solid line shows the standard model of Section 3 transformed to the
Lick/IDS system, as described in the text. Also shown, where available, are the models of Worthey (1994,
dotted line), Vazdekis et al. (1996, long-dashed line), Worthey & Ottaviani (1997, dot-and-dashed line) and
Thomas et al. (2003, short-dashed line). Right: Index strengths measured in the same way in the spectra of
the standard model of Section 3 (solid line) and in the spectra of the Vazdekis (1999) model broadened to
a resolution of 3 A˚ FWHM (long-dashed line).
cent progress in stellar evolution theory and an observa-
tionally motivated prescription for thermally-pulsing AGB
stars, which is supported by observations of surface bright-
ness fluctuations in nearby stellar populations (Liu et al.
2000; Liu et al. 2002). We have shown that this model re-
produces well the observed optical and near-infrared colour-
magnitude diagrams of Galactic star clusters of various ages
and metallicities, and that stochastic fluctuations in the
numbers of stars in different evolutionary phases can ac-
count for the full range of observed integrated colours of
star clusters in the Magellanic Clouds and in the merger
remnant galaxy NGC 7252.
Our model reproduces in detail typical galaxy
spectra extracted from the SDSS Early Data Release
(Stoughton et al. 2002). We have shown how this type of
spectral fit can constrain physical parameters such as the
star formation history, metallicity and dust content of galax-
ies. Our model is also the first to enable accurate studies of
absorption-line strengths in galaxies containing stars over
the full range of ages. We have shown that it can reproduce
simultaneously the observed strengths of those Lick indices
that do not depend strongly on element abundance ratios
in 2010 spectra with S/Nmed > 30, taken from the ‘main
galaxy sample’ of the SDSS EDR. This comparison requires
proper accounting for the observed velocity dispersions of
the galaxies. Indices whose strengths depend strongly on el-
ement abundance ratios cannot always be fitted accurately,
because the stars in the model spectral library have fixed
composition at fixed metallicity. Based on the model with
variable element abundance ratios of Thomas et al. (2003),
we have identified a few spectral features which depend neg-
ligibly on element abundance ratios and are well reproduced

28 G. Bruzual and S. Charlot
Figure 20. Comparison of the standard model of Section 3 (solid line) with the Vazdekis (1999) model
broadened to a resolution of 3 A˚ FWHM (dotted line), for 10 Gyr-old SSPs with scaled-solar abundances
and a Salpeter (1955) IMF, for the metallicities 0.4Z⊙ and Z⊙. The spectra are shown in the two narrow
wavelength regions covered by the Vazdekis (1999) model.
by our model: [MgFe]′, [Mg1Fe] and [Mg2Fe] (equations 4–
5). These features, when combined with a Balmer-line index
such as Hβ, HγA or HδA, should be particularly useful for
constraining the star formation histories and metallicities
of galaxies. Several other popular indices, such as the Ca II
triplet index near 8500 A˚ (Dı´az et al. 1989), can also be
measured directly from the model spectra. Most interest-
ingly, our model offers the possibility to explore new indices
over the full wavelength range from 3200 A˚ to 9500 A˚.
It is worth mentioning that, for applications to stud-
ies of star-forming galaxies, the influence of the interstellar
medium on the stellar radiation predicted by our model must
be accounted for. The emission-line spectrum of the H ii re-
gions and the diffuse gas ionized by young stars can be com-
puted by combining our model with a standard photoioniza-
tion code (see for example Charlot & Longhetti 2001). To
account for the attenuation of starlight by dust, the simple
but realistic prescription of Charlot & Fall (2000) is partic-
ularly well suited to population synthesis studies. In this
prescription, the attenuation of starlight by dust may be
accounted for by inserting a factor exp[−τˆλ(t′)] in the inte-
grand on the right-hand side of equation (1), where τˆλ(t′)
is the ‘effective absorption’ curve describing the attenuation
of photons emitted in all directions by stars of age t′ in a
galaxy. This is given by the simple formula
τˆλ(t
′) =
{
τˆV
(
λ/5500 A˚
)−0.7
, for t′ 6 107 yr,
µτˆV
(
λ/5500 A˚
)−0.7
, for t′ > 107 yr,
(6)
where τˆV is the total effective V -band optical depth seen by
young stars. The characteristic age 107 yr corresponds to the
typical lifetime of a giant molecular cloud. The adjustable
parameter µ defines the fraction of the total dust absorp-
tion optical depth of the galaxy contributed by the diffuse
interstellar medium (µ ≈ 1/3 on average, with substantial
scatter). Note that equation (6) neglects the absorption of
ionizing photons by dust in the H ii regions, that should be
accounted for to study line luminosities (see Charlot et al.
2002).

Stellar population synthesis at the resolution of 2003 29
Table 6. Median offsets in the strengths of 25 spectral fea-
tures between the STELIB spectra broadened to the wavelength-
dependent Lick/IDS resolution and the non-fluxed Lick/IDS spec-
tra for the 31 stars in common between the two libraries. A posi-
tive offset denotes that the index measured from STELIB spectra
is larger than that measured from Lick/IDS spectra. The val-
ues for atomic indices are expressed in angstroms of equivalent
width, while those for molecular indices (indicated by a star) are
expressed in magnitudes.
Feature Median Offset
(STELIB minus Lick/IDS)
⋆CN1 −0.011
⋆CN2 −0.001
Ca4227 −0.02
G4300 0.05
Fe4383 0.52
Ca4455 −0.13
Fe4531 −0.12
C24668 0.43
Hβ 0.13
Fe5015 0.47
⋆Mg1 −0.020
⋆Mg2 −0.018
Mgb 0.03
Fe5270 0.17
Fe5335 0.07
Fe5046 0.20
Fe5709 0.03
Fe5782 0.04
NaD 0.01
⋆TiO1 0.003
⋆TiO2 0.004
HδA 0.83
HγA −0.89
HδF 0.20
HγF −0.29
The high-resolution population synthesis model pre-
sented in this paper enables more refined spectral analy-
ses of galaxies than could be achieved using previous low-
resolution models. In particular, in recent studies of our own,
it has become clear that the ability to resolve stellar ab-
sorption features in galaxy spectra demonstrates a need in
many galaxies to account for the stochastic nature of star
formation (e.g., Kauffmann et al. 2003; see also Section 4.3
above). Traditional models with continuous star formation
histories tend to smooth away valuable spectral signatures
of stochastic starbursts. Our preliminary results also sug-
gest that the new high-resolution model makes it possi-
ble to break, in many cases, the age-metallicity degener-
acy which has impaired most previous population synthe-
sis studies of the star formation and enrichment histories
of galaxies. We hope that this model will contribute to the
refinement of such studies in the future. Our model is in-
tended for use by the general astronomical community and
is available from http://www.cida.ve/∼bruzual/bc2003 and
http://www.iap.fr/∼charlot/bc2003.
ACKNOWLEDGMENTS
We are grateful to J. Brinchmann and H. Mathis for their
help in producing the results presented in Sections 4.2 and
4.3 of this paper and to T. Le Bertre, R. Loidl, T. Rauch
and M. Schultheis for providing data in advance of pub-
lication. Special thanks to C. Tremonti for her help re-
garding the implementation of the STELIB library into our
model. G. Kauffmann and S. White provided useful advice
on the analysis of SDSS galaxy spectra. We thank the ref-
eree, A. Vazdekis, and F. Schweizer for helpful comments
on the original manuscript. We also thank the many col-
leagues who, over the last decade, have helped us improve
our population synthesis model through the feedback they
provided.
G.B.A. acknowledges generous financial support from
the European Commission (under ALAMED contract
No. CIL-CT93-0328VE), the Landessternwarte Heidelberg-
Ko¨nigstuhl (under grant No. SFB-328) and the Max-
Planck Institut fu¨r Astrophysik, Germany, the Universitat
de Barcelona, Spain, the Swiss National Science Foundation
(under grant No. 20-40654.94), FAPESP, Brazil, the Obser-
vatoire Midi-Pyre´ne´es and the Institut d’Astrophysique de
Paris, CNRS, France and the Consejo Nacional de Investiga-
ciones Cient´ıficas y Tecnolo´gicas of Venezuela (under grant
No. F-155). S.C. thanks the Alexander von Humboldt Foun-
dation, the Federal Ministry of Education and Research, and
the Programme for Investment in the Future (ZIP) of the
German Government for their support through a Sofja Ko-
valevskaja award. This research was supported in part by the
National Science Foundation under Grant No. PHY94-07194
to the Institute for Theoretical Physics, Santa Barbara.
Funding for the creation and distribution of the SDSS
Archive has been provided by the Alfred P. Sloan Founda-
tion, the Participating Institutions, the National Aeronau-
tics and Space Administration, the National Science Foun-
dation, the US Department of Energy, the Japanese Mon-
bukagakusho, and the Max Planck Society. The SDSS Web
site is http://www.sdss.org/. The Participating Institutions
are the University of Chicago, Fermilab, the Institute for
Advanced Study, the Japan Participation Group, the Johns
Hopkins University, the Max Planck Institute for Astron-
omy (MPIA), the Max Planck Institute for Astrophysics
(MPA), New Mexico State University, Princeton University,
the United States Naval Observatory, and the University of
Washington.
REFERENCES
Alexander, D. R., Ferguson, J. W. 1994, ApJ, 437, 879
Allard, F., Hauschildt, P. H., 1995, ApJ, 445, 433
Alongi, M., Bertelli, G., Bressan, A., Chiosi, C., 1991,
A&A, 244, 95
Alongi, M., Bertelli, G., Bressan, A., Chiosi, C., Fagotto,
F., Greggio, L., Nasi, E., 1993, A&AS, 97, 851
Arimoto, N., Yoshii, Y., 1987, A&A, 173, 23
Baldry, I. K., Glazebrook, K., Baugh, C. M., Bland-
Hawthorn, J., Bridges, T., Cannon, R., Cole, S., Colless,
M., Collins, C., Couch, W., et al., 2002, ApJ, 569, 582
Balogh, M. L., Morris, S. L., Yee, H. K. C., Carlberg, R.
G., Ellingson, E., 1999, ApJ, 527, 54
Baraffe, I., Chabrier, G., Allard, F., Hauschildt, P. H., 1998,
A&A, 337, 403
Barbaro, G., Bertelli, G., 1977, A&A, 54,243

30 G. Bruzual and S. Charlot
Bessell, M. S., Brett, J. M., Wood, P. R., Scholz, M., 1989,
A&AS, 77, 1
Bessell, M. S., Brett, J. M., Scholz, M., Wood, P. R., 1991,
A&AS, 89, 335
Blakeslee, J. P., Vazdekis, A., Ajhar, E. A., 2001, MNRAS,
320, 193
Blanco, B. M., Blanco, V. M., McCarthy, M. F., 1978, Nat,
271, 638
Bower, R. G., Lucey, J. R., Ellis, R. S., 1992, MNRAS, 254,
601
Bressan, A., Fagotto, F., Bertelli, G., Chiosi, C., 1993,
A&AS, 100, 647
Bressan, A., Chiosi, C., Fagotto, F. 1994, ApJS, 94, 63
Bruzual A., G., 1983, ApJ, 273, 105
Bruzual A., G., 2002, IAU Symp. 207, Extragalactic Star
Clusters, ed. D. Geisler, E. Grebel, D. Miniti (San Fran-
cisco: ASP), 616
Bruzual A., G., Charlot, S., 1993, ApJ, 405, 538
Bruzual A., G., Barbuy, B., Ortolani, S., Bica, E.,
Cuisinier, F., Lejeune, T., Schiavon, R., 1997, AJ, 114,
1531
Burstein, D., Faber, S. M., Gaskell, C. M., Krumm, N.,
1984, ApJ, 287, 586
Buzzoni, A., 1989, ApJS, 71, 817
Castelli, F., Gratton, R. G., Kurucz, R. L., 1997, A&A,
318, 841
Cayrel de Strobel, G., Hauck, B., Franc¸ois, P., The´venin,
F., Friel, E., Mermilliod, M., Borde, S. 1992, A&AS, 95,
273
Cervin˜o, M., Mas-Hesse, J. M. 1994, A&A, 284, 749
Cervin˜o, M., Go´mez-Flechoso, M. A., Castander, F. J.,
Schaerer, D., Molla´, M., Kno¨dlseder, J., Luridiana, V.,
2001, A&A, 376, 422
Cervin˜o, M., Valls-Gabaud, D., Luridiana, V., Mas-Hesse,
J. M., 2002, A&A, 381, 51
Chabrier, G., 2001, ApJ, 554, 1274
Chabrier, G., 2002, ApJ, 567, 304
Chabrier, G., 2003a, ApJ, 586, L133
Chabrier, G., 2003b, PASP, 115, 763
Charbonnel, C., Da¨ppen, W., Schaerer, D., Bernasconi, P.
A., Maeder, A., Meynet, G., Mowlavi, N. 1999, A&AS,
135, 405
Charbonnel C., Meynet G., Maeder A., Schaerer D., 1996,
A&AS, 115, 339
Charlot, S., 1996, ASP Conf. Ser. 98, From Stars to Galax-
ies: the Impact of Stellar Physics on Galaxy Evolution,
ed. C. Leitherer, E. Fritze-Von Avendsleben, J. Huchra
(San Francisco: ASP), 275
Charlot, S., Bruzual A., G., 1991, ApJ, 367, 126
Charlot, S., Fall, S. M., 2000, ApJ, 539, 718
Charlot, S., Longhetti, M., 2001, MNRAS, 323, 887
Charlot, S., Kauffmann, G., Longhetti, M., Tresse, L.,
White, S. D. M., Maddox, S. J., Fall, S. M., 2002, MN-
RAS, 330, 876
Charlot, S., Worthey, G., Bressan, A., 1996, ApJ, 457, 625
Chiosi, C., Bertelli, G., Bressan, A., 1988, A&A, 196, 84
Clegg, R. E. S., Middlemass, D., 1987, MNRAS, 228, 759
Couch, W. J., Sharples, R. M., 1987, MNRAS, 229, 423
D’Antona, F., 1999, 35th Liege Int. Astroph. Colloquium,
The Galactic Halo: from Globular Clusters to Field Stars
(astro-ph/9910312)
Demarque, P., Sarajedini, A., Guo, X.-J. 1994, ApJ, 426,
165
Dı´az, A. I., Terlevich, E., Terlevich, R., 1989, MNRAS, 239,
325
Dyck, H. M., van Belle, G. T., Benson, J. A., 1996, AJ,
112, 294
Eggen, O. J., Sandage, A. R., 1964, ApJ, 140, 130
Faber, S. M., 1972, A&A, 20, 361
Faber, S. M., 1973, ApJ, 179, 731
Fagotto, F., Bressan, A., Bertelli, G., Chiosi, C., 1994a,
A&AS, 104, 365
Fagotto, F., Bressan, A., Bertelli, G., Chiosi, C., 1994b,
A&AS, 105, 29
Fanelli, M. N., O’Connell, R. W., Burstein, D., Wu, C.-C.,
1992, ApJS, 82, 197
Fioc, M., Rocca-Volmerange, B., 1997, A&A, 326, 950
Fitzpatrick, E. L., 1999, PASP, 111, 63
Fluks, M. A., Plez, B., The, P. S., de Winter, D., Wester-
lund, B. E., Steenman, H. C., 1994, A&AS, 105, 311
Fritze-v. Alvensleben, U. A., Gerhard, O. E., 1994, A&A,
285, 751
Frogel, J. A., Persson, S. E., Cohen, J. G., 1981, ApJ, 246,
842
Frogel, J. A., Mould, J., Blanco, V. M., 1990, ApJ, 352, 96
Gilliland, R. L., Brown, T. M., Duncan, D. K., Suntzeff,
N. B., Wesley Lockwood, G., Thompson, D. T., Schild,
R. E., Jeffrey, W. A., Penprase, B. E., 1991, AJ, 101, 541
Girardi, L., Chiosi, C., Bertelli, G., & Bressan, A., 1995,
A&A, 298, 87
Girardi, L., Bressan, A., Chiosi, C., Bertelli, G., Nasi, E.
1996, A&AS, 117, 113
Girardi, L., Bertelli, G., 1998, MNRAS, 300, 533
Girardi, L., Bressan, A., Bertelli, G., Chiosi, C. 2000,
A&AS, 141, 371
Girardi, L., Bertelli, G., Bressan, A., Chiosi, C., Groenewe-
gen, M. A. T., Marigo, P., Salasnich, B., Weiss, A., 2002
A&A, 391, 195
Gonza´lez, J. J., 1993, Ph.D. thesis, Univ. California, Santa
Cruz
Gorgas, J., Faber, S. M., Burstein, D., Gonza´lez, J. J.,
Courteau, S., Prosser, C., 1993, ApJS, 86, 153
Gray, R. O., Corbally, C. J., 1994, AJ, 107, 742
Groenewegen, M. A. T., de Jong, T., 1993, A&A, 267, 410
Groenewegen, M. A. T., van den Hoek, L. B., de Jong, T.,
1995, A&A, 293, 381
Guarnieri, M. D., Ortolani, S., Montegriffo, P., Renzini, A.,
Barbuy, B., Bica, E., Moneti, A., 1998, A&A, 331, 70
Guiderdoni, B., Rocca-Volmerange, B., 1987, A&A, 186, 1
Habing, H.J., 1995, MSAI, 66, 627
Habing, H.J., 1996, A&ARv, 7, 97
Heavens, A. F., Jimenez, R., Lahav, O., 2000, MNRAS,
317, 965
Ho¨fner, S., Loidl, R., Aringer, B., Jørgensen, U. G., Hron,
J., 2000, ISO beyond the peaks: The 2nd ISO workshop
on analytical spectroscopy, ed. A. Salama, M. F. Kessler,
K. Leech, B. Schulz (ESA-SP 456), 299
Iben, I., Renzini, A., 1983, ARA&A, 21, 271
Iglesias, C. A., Rogers, F. J., 1993, ApJ, 412, 752
Iglesias, C. A., Rogers, F. J., Wilson, B. G., 1992, ApJ,
397, 717
Janes, K. A., Smith, G. H., 1984, AJ, 89, 487
Jones, L. A., Worthey, G., 1995, ApJ, 446, L31
Kaluzny, J., 1997, A&AS, 121, 455

Stellar population synthesis at the resolution of 2003 31
Kaluzny, J., Wysocka, A., Stanek, K. Z., Krzeminski, W.,
1998, AcA, 48, 439
Kauffmann, G., Heckman, T. M., White, S. D. M., Charlot,
S., Tremonti, C., Brinchmann, J., Bruzual, G., Peng, E.
W., et al., 2003, MNRAS, 341, 33
King, I. R., Anderson, J., Cool, A. M., Piotto, G., 1998,
ApJ, 492, L37
Ko¨ster, D., Scho¨nberner, D., 1986, A&A, 154, 125
Kroupa, P., 2001, MNRAS, 322, 231
Kurucz R. L., 1992, IAU Symp. 149, The Stellar Popula-
tions of Galaxies, ed. B. Barbuy, A. Renzini (Dordrecht:
Kluwer), 225
Le Bertre, T., 1997, A&A, 324, 1059
Le Borgne, J.-F., Bruzual, G., Pello´, R., Lanc¸on, A., Rocca-
Volmerange, B., Sanahuja, B., Schaerer, D., Soubiran, C.,
Vı´lchez-Go´mez, R., 2003, A&A, 402, 433
Leitherer, C., Heckman, T., 1995, ApJS, 96, 9
Lejeune, T., Cuisinier, F., Buser, R. 1997, A&AS, 125, 229
Lejeune, T., Cuisinier, F., Buser, R. 1998, A&AS, 130, 65
Le Sidaner, P., Le Bertre, T., 1996, A&A, 314, 896
Liu, M. C., Charlot, S., Graham, J. R. 2000, ApJ, 543, 644
Liu, M. C., Graham, J. R., Charlot, S. 2002, ApJ, 564, 216
Loidl, R., Lanc¸on, A., Jørgensen, U. G., 2001, A&A, 371,
1065
Magris, G., Bruzual A., G., 1993, 417, 102
Maraston, C., 1998, MNRAS, 300, 872
Maraston, C., Kissler-Patig, M., Brodie, J. P., Barmby, P.,
Huchra, J. P., 2001, A&A, 370, 176
Mendoza, E. E., Johnson, H. L., 1965, ApJ, 141, 161
Mermilliod, J.-C., 2000, http://obswww.unige.ch/webda/
Meynet, G., Mermilliod, J. C., Maeder, A., 1993, A&AS,
98, 477
Micela, G., Sciortino, S., Vaiana, G. S., Schmitt, J. H. M.
M., Stern, R. A., Harnden, F. R., Jr., Rosner, R., 1988,
ApJ, 325, 798
Mihalas, D., Hummer, D. G., Weibel-Mihalas, B., Da¨ppen,
W., 1990, ApJ, 350, 300
Miller, B. W., Whitmore, B. C., Schweizer, F., Fall, S. M.,
1997, AJ, 114, 2381
Montgomery, K. A., Marschall, L. A., Janes, K. A., 1993,
AJ, 106, 181
O’Connell, R. W., 1976, ApJ, 206, 370
Ortolani, S., Renzini, A., Gilmozzi, R., Marconi, G., Bar-
buy, B., Bica, E., Rich, R. M. 1995, Nat, 377, 701
Persson, S. E., Aaronson, M., Cohen, J. G., Frogel, J. A.,
Matthews, K., 1983, ApJ, 266, 105
Pickles, A. J., 1985, ApJ, 296, 340
Pickles, A. J., 1998, PASP, 110, 863
Poggianti, B. M., Smail, I., Dressler, A., Couch, W. J.,
Barger, A. J., Butcher, H., Ellis, R. S., Oemler, A., 1999,
ApJ, 518, 576
Pritchet, C., 1977, ApJS, 35, 397
Proctor, R. N., Sansom, A. E., 2002, MNRAS, 333, 517
Racine, R., 1971, ApJ, 168, 393
Rauch, T. 2002, RevMexAstronAstrofis Conf. Ser. 12, 150
Reichardt, C., Jimenez, P., Heavens, A. F., 2001, MNRAS,
327, 849
Rogers, F. J., Iglesias, C. A., 1992, ApJS, 79, 507
Rose, J. A., 1984, AJ, 89, 1238
Rose, J. A., 1985, AJ, 90, 1927
Rosenberg, A., Piotto, G., Saviane, I., Aparicio, A., 2000a,
A&AS, 144, 5
Rosenberg, A., et al. 2000b, The Largest Homoge-
neous V I Photometric Database of Galactic Glob-
ular Clusters, http://dipastro.pd.astro.it/globulars/
databases/ground/ground.html
Salpeter, E. E., 1955, ApJ, 121, 161
Santos, J. F. C., Frogel, J. A., 1997, ApJ, 479, 764
Scalo, J., 1998, ASP Conf. Ser. 142, The Stellar Initial
Mass Function (38th Herstmonceux Conference), ed. G.
Gilmore & D. Howell. (San Francisco: ASP), 201
Schaller G., Schaerer D., Meynet G., Maeder A., 1992,
A&AS 96, 269
Schiavon, R. P., Faber, S. M., Castilho, B. V., Rose, J. A.,
2002, ApJ, 580, 850
Scho¨nberner, D., 1983, ApJ, 272, 70
Schlegel, D., Finkbeiner, D., Davis, M., 1998, ApJ, 500, 525
Schultheis, M., Aringer, B., Jørgensen, U. G., Lebzelter, T.,
Plez, B., 1999, Abstract of the 2nd Austrian ISO work-
shop: Atmospheres of M, S, and C Giants, ed. J. Hron &
S. Ho¨fner, 93
Schulz, J., Fritze-v. Alvensleben, U., Mo¨ller, C. S., Fricke,
K. J., 2002, A&A, 392, 1
Schweizer, F., Seitzer, P., 1998, AJ, 116, 2206
Searle, L., Wilkinson, A., Bagnuolo, W. G., 1980, ApJ, 239,
803
Spinrad, H., Taylor, B. J., 1971, ApJS, 22, 445
Stoughton, C., Lupton, R. H., Bernardi, M., Blanton, M.
R., Burles, S., Castander, F. J., Connolly, A. J., Eisen-
stein, D. J., et al., 2002, AJ, 123, 485
Strauss, M. A., Weinberg, D. H., Lupton, R. H.,
Narayanan, V. K., Annis, J., Bernardi, M., Blanton, M.,
Burles, S., et al. 2002, AJ, 124, 1810
Tantalo, R., Chiosi, C., Bressan, R., 1998, A&A, 333, 419
Thomas, D., Maraston, C., Bender, R., 2003, MNRAS, 339,
897
Tinsley, B. M., 1978, ApJ, 222, 14
Tinsley, B. M., 1980, Fundam Cosmic Phys, 5, 287
Trager, S. C., Worthey, G. Faber, S. M., Burstein, D., Gon-
zalez, J. J., 1998, ApJS, 116, 1
Trager, S. C., Faber, S. M., Worthey, G., Gonza´lez, J. J.,
2000, AJ, 119, 1645
Tremonti, C., 2003, Ph.D. thesis, Johns Hopkins Univ.
Tripicco, M. J., Bell, R. A., 1995, AJ, 110, 3035
Turnrose, B. E., 1976, ApJ, 210, 33
Upgren, A. R., 1974, ApJ, 193, 359
Upgren, A. R., Weis, E. W., 1977, AJ, 82, 978
van den Bergh, S., 1981, A&AS, 46, 79
Vassiliadis, E., Wood, P. R., 1993, ApJ, 413, 641
Vassiliadis, E., Wood, P. R., 1994, ApJS, 92, 125
Vazdekis, A., 1999, ApJ, 513, 224
Vazdekis, A., 2001, Ap&SS, 276, 839
Vazdekis, A., Arimoto, N., 1999, ApJ, 525, 144
Vazdekis, A., Casuro, E., Peletier, R. F., Beckman, J. E.,
1996, ApJS, 106, 307
Vazdekis, A., Salaris, M., Arimoto, N., Rose, J. A., 2001,
ApJ, 549, 274
Weidemann, V., 1987, A&A, 188, 74
Weidemann, V., 1990, AR&A, 28, 103
Westera, P., 2001, Ph.D. Thesis, University of Basel
Westera, P., Lejeune, T., Buser, R., Cuisinier, F., Bruzual,
G., 2002, A&A, 381, 524
Winget, D. E., Hansen, C. J., Liebert, J., Van Horn, H. M.,

32 G. Bruzual and S. Charlot
Fontaine, H., Nather, R. E., Kepler, S. O., Lamb, D. Q.,
1987, ApJ, 315, L77
Worthey, G., 1994, ApJS, 94, 687
Worthey, G., Ottaviani, D. L., 1997, ApJS, 111, 377
Worthey, G., Faber, S. M., Gonza´lez, J. J., 1992, ApJ, 398,
69
Worthey, G., Faber, S. M., Gonza´lez, J. J., Burstein, D.,
1994, ApJ, 94, 687
Yi, S. K. 2003, ApJ, 582, 202
York, D. G., Adelman, J., Anderson, J. E., Annis, J., Bah-
call, N. A., Bakken, J. A., Barkhouser, R., et al., 2000,
AJ, 120, 1579
APPENDIX A: MAPPING OF THEORETICAL
ISOCHRONES WITH STELLAR SPECTRA
We illustrate here in a graphical way the mapping of theo-
retical isochrones with stellar spectra in our model. At fixed
metallicity Z (or [Fe/H]), an isochrone interpolated from a
set of stellar evolutionary tracks in the HR diagram is de-
fined by a sequence of evolutionary phases corresponding to
different effective temperatures log Teff and gravities log g.
To transform this theoretical isochrone into an observational
one, we must assign a stellar spectrum to each of the evo-
lutionary phases. This is straightforward in the case where
the spectra are taken from a library of theoretical model
atmospheres (i.e., BaSeL 1.0, BaSeL 2.2, BaSeL 3.1; see Ta-
bles 2 and 3), since in general such models are parametrized
in terms of Z, log Teff and log g. The only practical compli-
cation in this case is that model atmospheres are available
only for discrete values of these parameters. Thus model
spectra must be interpolated at the values of Z, log Teff and
log g corresponding to the isochrone. The relation between
colours and effective temperature for stars of fixed metallic-
ity and gravity is then tied to the adopted spectral library
(Section 2.2.1).
We now turn to the case where the STELIB library
of observed stellar spectra is used to map the theoretical
isochrones in the HR diagram. In this case, we still rely
on the colour-temperature scale of one of the BaSeL li-
braries in Table 3. The reason for this is that the effective
temperatures published by Le Borgne et al. (2003) for the
STELIB stars are incomplete and were not derived in a ho-
mogeneous way. Hence these temperatures are not suited to
model calibration. We therefore assign to each evolutionary
stage along the isochrone the STELIB spectrum of the corre-
sponding luminosity class that best matches the theoretical
BaSeL spectrum assigned to that stage. In this procedure,
the STELIB spectra are first degraded to the resolution of
the BaSeL library using a gaussian filter of 20 A˚ FWHM.
The selection is thus driven by the shape of the continuum
spectrum rather than by the strengths of absorption features
(we have checked that this approach is free of systematic bi-
ases). We refer to the three possible implementations of the
STELIB library in our model as the ‘STELIB/BaSeL 1.0’,
the ‘STELIB/BaSeL 2.2’ and the ‘STELIB/BaSeL 3.1’ li-
braries (Section 2.2.2).
Figs. A1 and A2 show the B−V and V −K colours
of those stars of the BaSeL 3.1 and STELIB/BaSeL 3.1 li-
braries that were selected as described above to map the
theoretical isochrones computed using the Padova 1994 evo-
lutionary tracks, for different metallicities. The colours are
plotted as a function of effective temperature Teff , and differ-
ent symbols represent dwarf and giant stars in each library.
In the case of the STELIB/BaSeL 3.1 library, the B−V
colours rely on the STELIB spectra alone, while the V −K
colours rely on extensions of these spectra at near-infrared
wavelengths using BaSeL 3.1 spectra (Section 2.2.2).
By construction, at fixed metallicity, the colour-
temperature scale of the STELIB/BaSeL 3.1 library is al-
ways similar to that of the BaSeL 3.1 library. The number
of STELIB stars with metallicities close to that of the evo-
lutionary tracks is indicated in parentheses at the bottom
right of each panel in Fig. A1. The inset panels in Fig. A1
show [Fe/H] as a function of log Teff for these stars. Because
of the scarcity of stars hotter than about 7000 K at non-solar
metallicities, we include hot solar-metallicity stars to sample
the colour-Teff relations at all metallicities. As mentioned in
Section 2.2.1, the spectra of these stars should be represen-
tative of hot stars at all but the most extreme metallicities.
For completeness, we also include in the STELIB library a
few SDSS-EDR spectra of cool K- and M-dwarf stars at all
metallicities (we thank C. Tremonti for kindly providing us
with these spectra). For standard IMFs, these stars never
contribute significantly to the integrated light of model stel-
lar populations. The total number of STELIB stars used to
sample the colour-temperature relation at each metallicity
(including hot solar-metallicity stars and SDSS-EDR cool
dwarf stars) is indicated at the bottom right of each panel
in Fig. A1.
Figs. A1 and A2 allow us to draw the following conclu-
sions. First, the STELIB spectra of dwarf and giant stars
used to sample the colour-Teff relation in each metallicity
bin provide reasonable coverage of the HR diagram. In prac-
tice, in regions where the sampling is scarcer (for example,
around B−V ≈ 0.1 and log Teff ≈ 3.9 at the metallicity
0.4Z⊙ in Fig. A1), we improve it by interpolating between
nearby STELIB spectra of the appropriate luminosity class.
We do not perform such interpolations in the temperature
range 3750–5000 K that is critical for bright giant stars and
is always well sampled. Second, the homogeneity in [Fe/H]
of STELIB stars included in each metallicity bin varies from
bin to bin. It is reasonable for Z > 0.4Z⊙, although we note
that for Z = 2.5Z⊙ the STELIB stars have [Fe/H] ≈ +0.25
on average, i.e., slightly lower metallicity than the tracks.
There are no stars at all hotter than 7000 K at metallicities
Z 6 0.2Z⊙. At these metallicities, the model relies heavily
on our adoption of solar-metallicity spectra at high temper-
atures. Third, both Figs. A1 and A2 show that the STELIB
library does not include giant stars as red as the reddest stars
selected from the BaSeL 3.1 library to map the theoretical
isochrones, even at solar metallicity. These stars, however,
do not contribute critically to the integrated light of model
stellar populations for standard IMFs. This is illustrated by
the close agreement between the dotted (BaSeL 3.1) and
solid (STELIB/BaSeL 3.1) lines in Fig. 3. It is worth re-
calling that, for the brightest asymptotic-giant-branch stars,
we adopt in all libraries the prescription outlined in Sec-
tion 2.2.4 (these stars have redder colours off the scales of
Figs. A1 and A2).
We have performed further extensive tests of the
UBV RIJHKL colour-temperature scales, colour-colour re-

Stellar population synthesis at the resolution of 2003 33
Figure A1. B−V colour as a function of effective temperature for those stars of the BaSeL 3.1 (grey dots:
dwarfs; grey crosses: giants) and STELIB/BaSeL 3.1 (black filled squares: dwarfs; black open squares: giants)
libraries that were selected to map the theoretical isochrones computed using the Padova 1994 evolutionary
tracks, as described in Appendix A. Each panel corresponds to a different metallicity of the evolutionary
tracks, as indicated. For each metallicity, the inset panel shows [Fe/H] as a function of log Teff for the subset
of STELIB stars included in the metallicity bin whose abundances are compatible with the [Fe/H] value of
the evolutionary tracks (indicated by a dotted line). The number of these stars is given in parentheses at the
bottom right of each panel. Also indicated is the total number N of STELIB stars included in the metallicity
bin and shown on the colour-temperature relation. This number includes, in addition to the stars shown in
the inset panel, cool K- and M-dwarf stars from the SDSS EDR (whose colours are taken to be the same at
all metallicities) and hot solar-metallicity stars (see text for detail).
lations and bolometric corrections of the different spectral
libraries used in our model (Table 2). We find that our
procedure to assign spectra from these libraries to stars in
the HR diagram does not introduce any systematic bias in
the predicted photometric evolution of stellar populations.
The libraries themselves, however, include their own un-
certainties. In particular, the ultraviolet and near-infrared
colours of the spectra, even in the most recent BaSeL 3.1
library, remain significantly more uncertain than the opti-
cal colours because in part of the lack of comparison stan-
dards at non-solar metallicities (Westera et al. 2002). The
situation should improve as more observed spectra become
available to extend the optical spectra at ultraviolet and
near-infrared wavelengths, as is the case already for solar
metallicity (Pickles library). We further conclude that, de-
spite the limitations outlined above, the STELIB library
provides reasonable coverage of the HR diagram for popu-
lation synthesis purposes, especially at metallicities greater
than 0.2Z⊙. Based on these arguments, we can assess the
expected accuracy of the spectral predictions of our model
for simple stellar populations of various ages and metallic-
ities computed using the Padova 1994 evolutionary tracks
and different spectral libraries. This qualitative assessment
is summarized in Table A1.

34 G. Bruzual and S. Charlot
Figure A2. V −K colour as a function of effective temperature for those stars of the BaSeL 3.1 (grey dots:
dwarfs; grey crosses: giants) and STELIB/BaSeL 3.1 (black filled squares: dwarfs; black open squares: giants)
libraries that were selected to map the theoretical isochrones computed using the Padova 1994 evolutionary
tracks, as described in Appendix A. Each panel corresponds to a different metallicity of the evolutionary
tracks, as indicated.
Table A1. Qualitative assessment of the spectral predictions of the model for simple stellar populations of
various ages and metallicities computed using the Padova 1994 evolutionary tracks and different spectral
libraries. For each entry, the expected reliability of the predictions is indicated separately for young (. 1Gyr)
and old (≫ 1Gyr) stellar populations (listed as young/old).
Metallicity STELIB/BaSeL 3.1 BaSeL 3.1 Pickles
(Padova 1994) optical colours line strengths UV–NIR colours UV–NIR colours
2.5Z⊙ good/good fair/faira fair/poor . . .
Z⊙ very good/very good very good/very good very good/good very good/very good
0.4Z⊙ good/good good/very good good/fair . . .
0.2Z⊙ fair/good fair/good good/fair . . .
0.02Z⊙ poor/fair poor/fair fair/poor . . .
0.005Z⊙ poor/fair poor/fair poor/poor . . .
a The STELIB spectra used to map the theoretical isochrones have [Fe/H] ≈ +0.25 on average, i.e., slightly
lower than the metallicity of the evolutionary tracks (Fig. A1). This affects line strengths but not colour
predictions, which are tied to the colour-temperature scale of the BaSeL 3.1 library for Z = 2.5Z⊙.

Stellar population synthesis at the resolution of 2003 35
This paper has been typeset from a TEX/ LATEX file prepared
by the author.