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Mon. Not. R. Astron. Soc. 000, 000–000 (2005) Printed 4 February 2008 (MN LATEX style file v2.2)
Modelling galaxy spectra in presence of interstellar dust.
II. From the UV to the far infrared
Lorenzo Piovan1,2, Rosaria Tantalo1 & Cesare Chiosi1
1Department of Astronomy, University of Padova, Vicolo dell’Osservatorio 2, 35122 Padova, Italy
2Max-Planck-Institut fu¨r Astrophysik, Karl-Schwarzschild-Str. 1, Garching bei Mu¨nchen, Germany
E-mail: piovan@pd.astro.it; tantalo@pd.astro.it; chiosi@pd.astro.it
Submitted to MNRAS: September 2005; Revised: March 2006
ABSTRACT
In this paper, we present spectrophotometric models for galaxies of different mor-
phological type whose spectral energy distributions (SEDs) take into account the
effect of dust in absorbing UV-optical light and re-emitting it in the infrared (IR).
The models contain three main components: (i) the diffuse interstellar medium
(ISM) composed of gas and dust whose emission and extinction properties have
already been studied in detail by Piovan et al. (2006), (ii) the large complexes
of molecular clouds (MCs) in which new stars are formed and (iii) the stars of
any age and chemical composition.
The galaxy models stand on a robust model of chemical evolution that as-
suming a suitable prescription for gas infall, initial mass function, star formation
rate and stellar ejecta provides the total amounts of gas and stars present at any
age together with their chemical history. The chemical models are taylored in
such a way to match the gross properties of galaxies of different morphological
type. In order to describe the interaction between stars and ISM in building up
the total SED of a galaxy, one has to know the spatial distribution of gas and
stars. This is made adopting a simple geometrical model for each type of galaxy.
The total gas and star mass provided by the chemical model are distributed over
the whole volume by means of suitable density profiles, one for each component
and depending on the galaxy type (spheroidal, disk and disk plus bulge). The
galaxy is then split in suitable volume elements to each of which the appropriate
amounts of stars, MCs and ISM are assigned. Each elemental volume bin is at
the same time source of radiation from the stars inside and absorber and emitter
of radiation from and to all other volume bins and the ISM in between. They
are the elemental seeds to calculate the total SED.
Using the results for the properties of the ISM and the Single Stellar Popu-
lations (SSPs) presented by Piovan et al. (2006) we derive the SEDs of galaxies
of different morphological type. First the technical details of the method are
described and the basic relations driving the interaction between the physical
components of the galaxy are presented. Second, the main parameters are exam-
ined and their effects on the SED of three prototype galaxies (a disk, an elliptical
and a starburster) are highlighted. The final part of the paper is devoted to assess
the ability of our galaxy models in reproducing the SEDs of a few real galaxies
of the Local Universe.
Key words: Galaxies – dust, extinction, emission; ISM – radiative transfer;
Galaxies – formation, evolution, population synthesis; Galaxies – ellipticals, spi-
rals, starbursters
1 INTRODUCTION
In the early thirties of the past century, nearly at the
same time of the Hubble discoveries (external galaxies
and expansion of the Universe), another important dis-
covery albeit less spectacular was made by Trumpler, i.e.
the existence of the interstellar dust, whose implications
could not be even imagined seventy years ago. He sug-
gested the existence of a solid component, made by par-
c© 2005 RAS

2 L. Piovan, R.Tantalo & C. Chiosi
ticles of many irregular shapes and dimensions, mixed
and associated to the ISM and absorbing the stellar ra-
diation: the interstellar dust. It was soon clear that the
dust grains diffusing and absorbing the light emitted by
the stars, in particular in the UV-optical region, cannot
be neglected when measuring the light emitted by distant
stars and galaxies.
In the local universe a turning point was the IRAS
survey that discovered ten of thousands of galaxies, the
major part of them too weak to be included in the optical
catalogs, emitting more energy in the infrared than in all
the other spectral regions. Galaxies with IR luminosity
as high as LIR > 1011L⊙, are the main population of
extragalactic objects in the Local Universe.
Which is the reason of this huge IR luminosity?
What powers the IR emission? Observations show that a
great deal of the IR luminosity is emitted by dust, which
absorbs the UV-optical light emitted by stars formed in-
side the MCs in huge bursts of activity and re-emits it in
the IR. About the 30% or more of the stellar light in the
Local Universe is reprocessed by dust in the IR-submm
range (Soifer et al. 1987).
An important new element in the study of high-
redshift universe has been the detection by the COBE
satellite of a FIR and sub-mm background radia-
tion of extragalactic origin, the so-called Cosmic In-
fraRed Background (CIRB). This radiation implies
that galaxies in the past should have been much
more active in the far-IR than in the optical, and
very luminous. It is likely that dust plays a fun-
damental role in shaping the SED of these galaxies
(Puget et al. 1996; Guiderdoni et al. 1997; Fixsen et al.
1998; Hauser 1998; Pozzetti et al. 1998). Observations
with SCUBA (Barger et al. 1999; Hughes et al. 1998),
ISOPHOT (Puget et al. 1999; Dole et al. 1999) and ISO-
CAM (Elbaz et al. 1998, 1999) have measured the CIRB
at selected wavelengths trying to detect and identify the
sources of this radiation. Even if it is not easy to identify
these objects and to measure their redshift (Lilly et al.
1999; Barger et al. 1999), from the observations it turns
out that the IR luminosity seems to be emitted be the
counterparts at high redshift of the local LIRGs and
ULIRGs, (ongoing high star formation, obscuration and
reprocessing of the stellar radiation by a dusty environ-
ment).
Observations of high-z galaxies at z = 3 − 4
(Steidel et al. 1996; Madau et al. 1996) confirm that
these objects are characterized by strong obscuration and
emission by dust in the IR, in such a way that only taking
into account their emission all over the spectral range it
is possible to study their properties. Going to even higher
redshifts, dust still plays a fundamental role even in ob-
jects at redshift z & 4, as indicated by the observations of
QSOs and galaxies (McMahon et al. 1994; Omont et al.
1996; Soifer et al. 1998).
It clearly appears how it is no longer possible to leave
dust aside in studies of the Milky Way, the Local and the
High Redshift Universe.
Stars and dust are therefore tightly interwoven, even
if the presence of dust is more spectacular in galaxies
with strong star formation. In disk galaxies, with active,
mild star formation, dust is partly associated to the dif-
fuse ISM, partly to the molecular regions with star for-
mation, and, finally, partly to the circumstellar envelopes
of AGB stars. The contribution from all the three kinds
of source is evenly balanced. In starburst galaxies, the
situation is the same as above but now the key role is
played by the regions of intense star formation. In el-
liptical galaxies, which show weak emission in the FIR
(IRAS), dust is essentially associated to AGB stars of
small mass that continuously loose matter refueling the
ISM of gas and dust. The great importance of dust in
relation to the formation and evolution of galaxies is evi-
dent. Dust strongly affects the observed SED of a galaxy,
hampering its interpretation in term of the fundamental
physical parameters, such as age, metallicity, initial mass
function (IMF), mix of stellar populations, star formation
history (SFH). Determinations of luminosity functions,
number counts and many large-scale relations, such as
the Tully-Fisher just to mention one, are also affected by
the dust content of galaxies (Calzetti 2001). The strong
effect of dust, both for local (Bell & Kennicutt 2001) and
high redshift galaxies (Madau et al. 1996; Steidel et al.
1999), is the reason why the evolution with the redshift
of the galaxy star formation rate (SFR) is still a matter
of vivid debate (Madau et al. 1996; Steidel et al. 1999;
Barger et al. 2000).
To get precious informations on the process of galax-
ies formation and evolution, we need to measure the SFR
in galaxies at different redshifts, to understand when and
how galaxies form their stars. To this purpose, many
wide-field and all-sky surveys are currently running or
have been just completed, e.g. the Galaxy Evolution Ex-
plorer [GALEX] (Martin et al. 1997) and the Sloan Dig-
ital Sky Survey [SDSS] (York et al. 2000) in the UV-
optical range; the Two Micron All-Sky Survey [2MASS]
(Skrutskie et al. 1997) and the Deep Near-Infrared Sur-
vey of the Southern Sky [DENIS] (Epchtein et al. 1997)
in the near infrared. Recently, the Spitzer Space Tele-
scope has open the gate to dedicated studies aimed at im-
proving our knowledge of the Universe in the middle and
far infrared (MIR and FIR), e.g. the SIRTF Wide-Area
Infrared Extragalactic Survey (SWIRE - Lonsdale et al.
2003) and the SIRTF Nearby Galaxies Survey (SINGS
- Kennicutt et al. 2003). The IR data will increase even
more with the coming ASTRO-F mission (Pearson et al.
2004) and the advent of the James Webb Space Telescope
(JWST). Combined with other astronomical databases,
they provide a huge amount of UV-optical and IR data for
millions of galaxies. Both spectral intervals are strongly
affected by dust.
To fully exploit the information on the physical prop-
erties of the observed objects, this wealth of data must be
accompanied by the continuous upgrade of the theoreti-
cal models of galaxy formation and evolution. This means
that the effects of dust must be included in the SEDs
of single stellar populations (SSP), assemblies of coeval
stars with the same initial chemical composition, and in
the SEDs of galaxies, composite systems made of stars of
any age and chemical composition, gas and dust. Current
theoretical models for both SSPs and galaxies in presence
of dust and still unsatisfactory for many different reasons:
the lack of theoretical spectra for very cool likely dust-
rich stars, the poor knowledge of the dust properties in
c© 2005 RAS, MNRAS 000, 000–000

Galaxies spectra with interstellar dust 3
high metallicity environments and of the production of
dust itself, the relation between gas and dust content.
With a few exceptions (e.g Bressan et al. 1998;
Mouhcine & Lanc¸on 2002; Piovan et al. 2003, 2006),
the light emitted by SSPs is modelled neglecting the
presence of dust around their stars, both for AGB and
young stars (e.g. Bertelli et al. 1994; Tantalo et al. 1998;
Girardi et al. 2002; Bruzual & Charlot 2003). When we
fold many SSPs using the classical evolutionary popula-
tion synthesis technique (EPS) we simply convolve their
fluxes with the SFH of the galaxy. Many spectropho-
tometric models of galaxies are built in this way: there
is no dust at the level of SSPs and again no dust at
the level of the galaxy model (see e.g. Arimoto & Yoshii
1987; Arimoto & Tarrab 1990; Bruzual & Charlot
1993; Leitherer & Heckman 1995; Leitherer et al.
1999; Tantalo et al. 1996; Kodama & Arimoto 1997;
Kodama et al. 1998; Tantalo et al. 1998; Buzzoni 2002,
2005). There are many reasons for this lack of realistic
dusty models. First, before IRAS (1983) and COBE
(1989), the important role played by dust in the galaxy
SEDs was not fully appreciated and consequently only
the stellar component was taken into consideration
(Tinsley 1972; Searle et al. 1973; Huchra 1977). Sec-
ond, the inclusion of the dusty component and the
IR emission, in particular, require a higher level of
sophistication of the models. Indeed one has to develop
a 3D-model in which the sources of radiation and the
emitting/absorbing medium are distributed; one has to
face and solve the problem of the radiative transfer;
one has to know optical properties of the dust; one has
to simulate in a realistic way the interactions among
the various physical components of a galaxy and the
computational cost is often very high.
Despite the above difficulties, many efforts have
been made to develop more and more complex and
refined models, trying to take into account both the
effects of attenuation and emission by dust. Considering
the complexity of the problem, many even sophisticated
studies are limited to the UV-optical region of the
spectrum and consider or suggest and discuss only the
attenuation of the stellar radiation by dust at various
levels of detail (Guiderdoni & Rocca-Volmerange
1987; Bressan et al. 1994; Tantalo et al. 1996;
Fioc & Rocca-Volmerange 1997; Tantalo et al. 1998;
Buzzoni 2002; Bruzual & Charlot 2003; Buzzoni 2005) .
In some cases, the emission of dust in the IR/sub-mm
range is considered (Rowan-Robinson & Crawford 1989;
Guiderdoni et al. 1998, e.g.), but no detailed model
of the stellar sources whose radiation is reprocessed
by dust is developed. In this case there is not a clear
relationship between the sources of UV flux and the
reprocessed IR flux. There are also models that include
at different level of sophistication the effects of obscura-
tion and emission by dust, but many of them have been
developed to study particular objects or aspects of the
radiative transfer, or the effects of the space distribu-
tion of the dust (Efstathiou & Rowan-Robinson 1995;
Bianchi et al. 1996; Wise & Silva 1996; Cimatti et al.
1997; Gordon et al. 1997; Ferrara et al. 1999;
Gordon et al. 2001; Misselt et al. 2001; Dopita et al.
2005; Dopita 2005). They cannot be applied to a gen-
eral spectrophotometric study of galaxies of different
morphological type. The most recent models are those
by Devriendt et al. (1999), Devriendt & Guiderdoni
(2000), Silva et al. (1998), Silva (1999), Takagi et al.
(2003, 2004, 2003). The model of Silva et al. (1998) has
been later updated and improved by including the ra-
dio emission (Bressan et al. 2002), the nebular emission
(Panuzzo et al. 2003) and the X-ray emission (Silva et al.
2003). They present some important differences in the
way they approach the problem. For instance, the
models of Silva et al. (1998) and Takagi et al. (2003)
are merely theoretical and all properties are derived
from a few important assumptions and/or ingredients,
whereas those of Devriendt & Guiderdoni (2000) rescale
the SEDs to match the average IRAS colors.
As in the meantime, much progress has been made
in many aspects of this complex problem, for instance
better understanding of the dust properties (Li & Draine
2001; Draine & Li 2001), more complete grids of stel-
lar evolutionary models and isochrones (Salasnich et al.
2000; Girardi et al. 2000), new libraries of stellar spec-
tra at high resolution (Zwitter et al. 2004), better chemi-
cal models (Portinari et al. 1998), new SSPs with dust
(Piovan et al. 2003, 2006), and finally more detailed,
multi-phase chemical models (Dwek 1998), we intend
to present here a new model of population synthesis in
dusty conditions trying to take advantage of some of
these advancements. It follows the theoretical approach
of Silva et al. (1998), but yet improves upon important
aspects. Major changes are related to the chemistry and
optical properties of the dust (going from using updated
cross sections for absorption and emission processes, to
including new grain size distribution laws, to more accu-
rate description of the radiative transfer for star forming
regions), to better models of star formation and chemical
enrichment histories in galaxies including the most recent
chemical yields and the effect of galactic winds (whenever
required), and finally to more recent libraries of SSPs to
calculate the photometric properties of the galaxies. The
resulting galaxy SEDs go from the far UV to the far IR.
2 STRATEGY OF THE STUDY
The model we have adopted is shortly summarized in
Sect. 3 where first we define the galaxy components we
are dealing with, i.e. bare stars, stars embedded in MC
complexes, and diffuse ISM (Sect. 3.1); second we out-
line the recipes and basic equations for the gas infall,
chemical evolution, initial mass function and SFR (Sect.
3.2); third we describe how the total amounts of stars,
MCs and ISM present in the galaxy at a certain age
are distributed over the galaxy volume by means of suit-
able density profiles, one for each component (Sect. 3.3)
that depend on the galaxy type: disk galaxies (Sect.
3.3.1), spheroidal galaxies (Sect. 3.3.2), and compos-
ite galaxies with both disk and bulge (Sect. 3.3.3). In
Sect. 4 we briefly summarize some useful basic relation-
ships/equations by Piovan et al. (2006) on modelling the
dusty ISM. In Sect. 5 we explain how the SEDs of galax-
ies of different morphological type are calculated. First
the technical details of the method are described and
c© 2005 RAS, MNRAS 000, 000–000

4 L. Piovan, R.Tantalo & C. Chiosi
basic relationships/equations describing the interaction
between the physical components of the galaxy are pre-
sented. Second, we shortly described the SSPs library in
use (Piovan et al. 2003, 2006) and the space of the pa-
rameters. Third, three prototype galaxies (a disk galaxy,
an elliptical galaxy and a starburst galaxy) are used to
show the effects on the galaxy SED of varying the pa-
rameters. This is presented in Sect. 5.2.1 for an elliptical
galaxy, in Sect. 5.2.2 for a disk galaxy, and finally 5.2.3
for a starburst galaxy. The final part of the paper is de-
voted to assess the ability of our model in reproducing the
SED of a few galaxies of different morphological type be-
longing to the Local Universe. In Sect. 6, we present two
late-type spiral galaxies, in Sect. 7, we show two early-
type galaxies and finally in Sect. 8 we examine two well
studied starburst galaxies. Some concluding remarks are
drawn in Sect. 9. Finally, the mathematical derivation
of some expressions presented in this paper are given in
Appendices A, B, and C.
3 GALAXY MODELS
3.1 The main components and outline of the
model
First, the galaxy models we are dealing with contain at
least three components:
1) The diffuse ISM, made of gas and dust. The physical
properties of the ISM with dust have been thoroughly
discussed by Piovan et al. (2006). In Sect. 4, we briefly
summarize the main properties and useful equations of
the model we eventually choose for the ISM of galaxies.
2) The large complexes of MCs in which active star
formation occurs. In our model we do not take HII regions
and nebular emission into account. Very young stars are
totally or partially embedded in these parental MCs and
the SEDs emitted by these stars are severely affected by
the dusty MCs environment around them and skewed
toward the IR. (see Piovan et al. 2006, for more details)
3) The populations of stars that are no longer embed-
ded in their parental MCs. These stars can be subdivided
in the intermediate age AGB stars (from about 0.1 Gyr
to a few Gyr) that are intrinsically obscured by their own
dust shells as described in Piovan et al. (2003), and the
old stars which shine as bare objects.
Second, the amount of stars and gas (and its compo-
nents) present in a galaxy at any age must be the result of
the star formation activity framed in a suitable scenario.
Third, we have to adopt a suitable scheme for the
3D distribution of the three components in the galaxy
volume, in order to describe their interaction, and to cal-
culate the transfer of the radiation across the ISM of the
galaxy.
3.2 Gross history of star formation and
chemical enrichment
The star formation and chemical enrichment histories of
the model galaxies are described by the so-called infall-
model developed by Chiosi (1980), and ever since used
by many authors among whom we recall Bressan et al.
(1994), Tantalo et al. (1996), Tantalo et al. (1998), and
Portinari et al. (1998). In brief, within a halo of Dark
Matter of mass MD, radius RD, and hence known gravi-
tational potential, the mass of the luminous matter, ML,
is supposed to grow with time by infall of primordial gas
according to the law
dML (t)
dt
= M0 exp
(
− t
τ
)
(1)
where τ is the infall time scale. The constant M0 is fixed
by assuming that at the present age tG the mass ML (t)
is equal to ML (tG), the luminous asymptotic mass of
the galaxy (see also for more details Tantalo et al. (1996,
1998)):
M0 =
ML (tG)
τ [1− e(−tG/τ)] (2)
Therefore, the time variation of the baryonic mass is
ML (t) =
ML (tG)
τ [1− e(−tG/τ)]
[
1− e(−t/τ)
]
(3)
Indicating with Mg (t) the mass of gas at the time t,
the corresponding gas fraction is G (t) = Mg(t)ML(tG) . Denot-
ing with Xi (t) the mass abundance of the i-th chemical
species, we may write Gi (t) = Xi (t)G (t) where by defi-
nition
∑
i Xi = 1. The general set of equations governing
the time variation of the generic elemental species i in
presence of gas infall, star formation, and gas restitu-
tion by dying stars has been introduced and numerically
solved by Talbot & Arnett (1971) for closed models and
modified by Chiosi (1980) to include the infall term for
open models:
dGi (t)
dt
= −Xi (t)Ψ (t) + (4)
+
∫ Mu
Ml
Ψ(t′M )Ri(t
′
M )Φ (M) dM +
[
d
dt
Gi (t)
]
inf
where Ψ (t) is the SFR, Φ (M) is the IMF (by mass), Ml
and Mu are respectively the lower and upper bounds of
the IMF, τM and t′M = t − τM are the lifetime and the
birth time of a star of mass M . Ri(t′M ) is the fraction of
a star of initial mass M that is ejected back in form of
the species i. The first term on right-end side represents
the depletion of the species i from the ISM due to the
start formation; the second term represents the growth
of the species i ejected back to the ISM by stars. The last
term
[
d
dtGi (t)
]
inf
is the gas accretion rate by infall. In
the above formulation only the ejecta of single stars are
included.
It has been modified to include the contribution
of Type Ia supernovae assuming that the originate
in close binary systems (Matteucci & Greggio 1986;
Portinari et al. 1998) which are supposed to obey the
same IMF of single stars:
c© 2005 RAS, MNRAS 000, 000–000

Galaxies spectra with interstellar dust 5
dGi (t)
dt
= −Xi (t) Ψ (t) + (5)
+
∫ MBl
Ml
Ψ(t′M )Ri(t
′
M )Φ (M) dM +
+ (1− A)
∫ MBu
MBl
Ψ(t′M )Ri(t
′
M )Φ (M) dM +
+
∫ Mu
MBu
Ψ(t′)Ri(t′M )Φ (M) dM +
+ A
∫ MBu
MBl
Φ (MB)
MB
∫ 0.5
0
F (µ)Ψ(t′M1 )Ri(t
′
M1 )dµdMB +
+ ESNIi ·A
∫ MBu
MBl
Φ (MB)
MB
∫ 0.5
µl
F (µ) Ψ(t′M2 )dµdMB +
+
[
d
dt
Gi (t)
]
inf
MBl and MBu are the lower and upper limit for the mass
of the binary system (MB is the total mass of the bi-
nary system, M1 and M2 represents the mass of the pri-
mary and secondary star), F (µ) is the distribution of
the fractionary mass of the secondary µ = M2/MB , µl
is the minimum value of this mass ratio and ESNIi are
the ejecta of SNæ Ia, assumed to be independent of MB
or µ (Portinari et al. 1998). In the range between MBl
and MBu of binary systems suitable to become a SN Ia,
the contribution of single stars (the fraction 1−A of the
total) is separated from that of binaries producing SNæ
Ia (the fraction A of the total).
The first three integrals on the right-end side rep-
resent the contribution of the ejecta of single stars. The
fourth integral represents the contribution of the primary
star in a binary system, assumed to be unaffected by its
companion, as far as the released chemical ejecta are con-
cerned. The fifth term is the contribution of SNæ Ia ex-
ploding when the secondary star pours all its ejecta on the
primary star. The factor multiplying ESNIi is RSNI (t),
the rate of SNæ Ia as described in Greggio & Renzini
(1983). Following Portinari et al. (1998) we have adopted
MBl = 3M⊙, MBu = 12M⊙ and A = 0.2. The distribu-
tion function of the fractionary mass of the secondary is
F (µ) = 24µ2 (Greggio & Renzini 1983).
The SFR, i.e. the number of stars of mass M born
in the time interval dt and mass interval dM , is given
by dN/dt = Ψ(t) Φ (M) dM . The rate of star formation
Ψ (t) is the Schmidt (1959) law adapted to our model
Ψ (t) = νMg (t)
k which, normalized to ML (tG), becomes
Ψ (t) = νML (tG)
k−1 G (t)k (6)
The parameters ν and k are extremely important: k yields
the dependence of the star formation rate on the gas con-
tent. Current values are k = 1 or k = 2. The factor ν
measures the efficiency of the star formation process.
In this type of model, because of the competition between
gas infall, gas consumption by star formation, and gas
ejection by dying stars, the SFR starts very low, grows
to a maximum and then declines. The time scale τ (eqn.
1) roughly corresponds to the age at which the star for-
mation activity reaches the peak value.
The chemical models are meant to provide the mass
of stars, M∗ (t), the mass of gas Mg (t) and the metallicity
Z (t) to be used as entries for the population synthesis
code.
We also introduce in the model composite galaxies
made of a disk and a bulge. In this case the mass of the
galaxy is the sum of the two components. The disk and
the bulge are assumed to evolve independently and for
each component the evolution of its M∗ (t), Mg (t) and
Z (t) will be followed.
3.3 The spatial distribution of stars and ISM
In the classical EPS, the structure of a galaxy has no
effect on the total SED which is simply obtained by con-
volving the SSP spectra with the SFH. The galaxy struc-
ture is mimicked by considering different SFHs for the
various morphological types and/or componenents of a
galaxy, e.g. bulge and disk (Buzzoni 2002). This simple
convolution is no longer suitable to be used when the ISM
and the absorption and IR/sub-mm emission by dust are
taken into account. In this case the spatial distribution of
the ISM, dust and stars in the galaxy should be specified.
To this aim we start from the observational evidence that
the spatial distribution of stars and ISM depends on the
galaxy type. In our models we consider three prototype
distributions, i.e. a pure disk, a spheroid and combination
of the two to simulate late-type (with no bulge), early-
type (classical ellipticals), and intermediate-type (with a
prominent bulge) galaxies, respectively.
3.3.1 Disk galaxies
The mass density distribution of stars, ρ∗, diffuse ISM,
ρM , and MCs, ρMC , inside a disk galaxy can be repre-
sented by double decreasing exponential laws so that the
mass density decreases moving away from the equatorial
plane and the galactic center or both.
Taking a system of polar coordinates with origin at
the galactic center [r, θ, φ], the height above the equato-
rial plane is z = r cos θ and the distance from the galactic
center along the equatorial plane is R = r sin θ, where θ
is the angle between the polar vector r and the z-axis
perpendicular to the galactic plane passing through the
center. The azimuthal symmetry rules out the angle φ
and therefore the density laws for the three components
are:
ρi = ρ0i exp
(
−r sin θ
Rid
)
exp
(
−r |cos θ|
zid
)
(7)
where “i” can be “ ∗ ”, “M” or “MC” that is stars, dif-
fuse ISM and star forming MCs. R∗d, R
MC
d , and R
M
d are
the radial scale lengths of stars, MCs and ISM, respec-
tively, whereas z∗d , z
MC
d , z
M
d are the corresponding scale
heights above the equatorial plane. To a first approxi-
mation, we assume the same distributions for stars and
MCs so that R∗d = R
MC
d and z
∗
d = z
MC
d thus reducing the
number of scale parameters. Distributions with different
scale parameters for the three components are, however,
possible.
The constants ρ0i vary with the time step. Let us
c© 2005 RAS, MNRAS 000, 000–000

6 L. Piovan, R.Tantalo & C. Chiosi
indicate now with tG the age of the galaxy to be mod-
elled. For the gaseous components only the normalization
constants ρ0MC (tG) and ρ0M (tG) are required as both
loose memory of their past history and what we need is
only the amount and chemical composition of gas at the
present time. This is not the case for the stellar compo-
nent for which ρ0∗ (t) is needed at each time 0 < t < tG.
In other words to calculate the stellar emission we need
to properly build the mix of stellar populations of any
age τ ′ = tG − t as result of the history of star formation.
The normalization constants are derived by integrat-
ing the density laws over the volume and by imposing the
integrals to equal the mass obtained from the chemical
model. In general, the mass of each component Mi is
given by
Mi =
∫
V
ρ0i exp
(
−r sin θ
Rid
)
exp
(
−r |cos θ|
zid
)
dV (8)
The mass of stars born at the time t is given by Ψ(t), and
therefore ρ0∗ (t) will be obtained by using M∗ (t) = Ψ(t).
MM (tG) is the result of gas accretion, star formation and
gas restitution by dying stars. The current total mass
MMC (tG) is a fraction of MM (tG). The double integral
(in r and θ) is numerically solved for ρ0i to be used in
eqn. 7.
The galaxy radius Rgal is left as a free parameter of
the model, thus allowing for systems of different sizes and
distributions of the components.
There is a final technical point to examine, i.e. how
to subdivide the whole volume of a disk galaxy into a
number of sub-volumes so that the energy source inside
each of these can be approximated to a point source lo-
cated in their centers. This requires that the coordinates
[r, θ, φ] are divided in suitable intervals. As far as the
radial coordinate is concerned, test experiments carried
out in advance have indicated that subdividing the galaxy
radius in a number of intervals nr going from 40 to 60
would meet the condition, secure the overall energy bal-
ance among the sub-volumes, speed up the computational
time and yield numerically accurate results.
The number of radial intervals is derived by imposing
that the mass density among two adjacent sub-volumes
scales by a fixed ratio ρj/ρj+1 = ζ, where ζ is a constant.
Upon simple manipulations the above relation becomes
rj+1 = rj+ζ. Therefore, the radial grid is equally spaced
in constant steps given by Rgal/nr (Silva 1999).
The grid for the angular coordinate θ is chosen in
such a way that spacing gets thinner approaching the
equatorial plane, thus allowing for more sub-volumes in
regions of higher mass density. We split the angle θ going
from 0 to pi in nθ sub-values. We need an odd value for
nθ so that we have (nθ − 1) /2 sub-angles per quadrant.
Following Silva (1999), the angular distance α1 between
the two adjacent values of the angular grid is chosen in
such a way that Rgal subtends a fraction f . 1 of the disk
scale height (zd); in other words α1 = arcsin (fzd/Rgal).
Logarithmic angular steps are then imposed ∆ log θ =
(2/ (nθ − 3)) log (pi/2α1) where nθ is determined by the
condition that the second angular bin near the equatorial
plan is gα1, with g . 3. This implies nθ = 2 log(pi/2α1)log g +3.
The grid for the angular coordinate φ is chosen to be suit-
ably finely spaced near φ = 0 and to get progressively
broader and broader moving away clockwise and coun-
terclockwise from φ = 0. The angular steps are spaced
on the logarithm scale. As a matter of fact, thanks to the
azimuthal symmetry it is sufficient to calculate the radia-
tion field impinging on the volume V (ri, θi, φi = 0) from
all other volumes V (rk, θk, φk). A grid thinner at φ ≃ 0
than elsewhere guarantees the approximation of point-
like energy sources at the center of the volume elements
and the conservation of the total energy in turn.
3.3.2 Early-type galaxies
The luminosity distribution of early-type galaxies can
be described by the density profiles of Hubble, de Vau-
couleurs and King (Kormendy 1977), the most popu-
lar of which is the King law that yields a finite cen-
tral density of mass (Froehlich 1982). However, following
Fioc & Rocca-Volmerange (1997), we use a density pro-
file slightly different from the King law in order to secure
a smooth behavior at the galaxy radius Rgal. We suppose
that the mass density profiles for stars, MCs, and diffuse
ISM are represented by the laws
ρi = ρ0i
[
1 +
(
r
ric
)2
]−γi
(9)
where again “i” can be “∗”, “M” or “MC” (stars, diffuse
ISM and MCs) and r∗c , r
MC
c , r
M
c are the core radii of the
distributions of stars, MCs, and diffuse ISM, respectively.
The density profile has to be truncated at the galactic
radius Rgal, which is a free parameter of the model. This
would prevent the mass M (r) →∞ for r →∞. In anal-
ogy to what already made for disk galaxies, the constants
ρ0∗ (t), ρ0MC (tG) and ρ0M (tG) can be found by integrat-
ing the density law over the volume and by equating this
value of the mass to the correspondent one derived from
the global chemical model
ρ0i =
Mi
4pi
(
ric
)3
∫ Rgal/r
i
c
0
x2
(1 + x2)γ
dx
(10)
where x = r/ric while ρ0i and Mi have the same meaning
as in Sect. (3.3.1). The integral is numerically evaluated
and solved for ρ0i.
Like in the case of disk galaxies, the last step is to fix
the spacing of the coordinate grid [r, θ, φ]. The problem
will be simpler and the calculations will be faster than in
the previous case because of the spherical symmetry. The
spacing of the radial grid is made keeping in mind the en-
ergy conservation constrain. Also in this case we take a
sufficiently large number of grid points (nr ≃ 40 − 60).
The condition on the density ratio between adjacent vol-
umes, ρj/ρj+1 = ξ with ξ constant (Silva 1999), implies
ri = rc
√
√
√
√
[
1 +
(
Rgal
rc
)2
]i/nr
− 1 (11)
where usually rc = r∗c . The coordinate θ is subdivided
c© 2005 RAS, MNRAS 000, 000–000

Galaxies spectra with interstellar dust 7
into an equally spaced grid, with nθ elements in total,
and θ1 = 0, θnθ = pi. Since the distribution is spheri-
cally symmetric, i.e. independent from θ, we do not need
a thinner grid toward the equatorial plane. For the az-
imuthal coordinate Φ we adopt the same grid we have
presented for disk galaxies.
3.3.3 Intermediate-type galaxies
Intermediate-type galaxies are characterized by the rela-
tive proportions of their bulge and disk: they go from the
early S0 and Sa where the bulge is big, to the late Sc and
Sd where the bulge is small or negligible. In our models,
we take all this into account by means of different SFHs
for the disk and the bulge. Furthermore, both in the bulge
and disk we consider the three components (ISM, MCs
and stars) in a realistic way. In analogy to what already
made for purely disk galaxies we adopt a system of po-
lar coordinates with origin at the galactic center [r, θ, φ].
Azimuthal symmetry rules out the coordinate φ.
In the disk, the density profiles for the three compo-
nents are the double decreasing exponential laws of eqn.
(7). Accordingly, we introduce the scale lengths R∗d,B ,
RMd,B , R
MC
d,B , z
∗
d,B, z
M
d,B and z
MC
d,B , where the suffix B indi-
cates that now the scale lengths are referred to the disk-
bulge composite model. In the bulge the three compo-
nents are distributed according to the King-like profiles
defined in eqn. (9), where now the core radii r∗c,B, r
M
c,B
and rMCc,B are referred to the bulge. The constants of nor-
malization are derived in the same way described in Sects.
3.3.1 and 3.3.2 The two SFHs of disk and bulge are as-
sumed to be independent and are simply obtained from
the chemical models where the mass of disk and bulge are
specified. The content in stars, MCs and ISM in a given
point of the galaxy will be simply given by the sum of
the contributions for the disk and bulge.
Owing to the composite shape of the galaxy (a sphere
plus a disk), we have to define a new mixed grid sharing
the properties of both components, i.e. those described in
Sect. 3.3.1 and Sect. 3.3.2. Let us indicate with RB the
bulge radius and with Rgal the galaxy radius. The radial
grid is defined in the following way. We build two grids
of radial coordinates, rB,i and rD,i, one for the disk and
one for the bulge, in analogy to what we did in Sects.
3.3.1 and 3.3.2. As the grid of the bulge is not equally
spaced, but thicker toward the center of the galaxy, we
take the coordinates ri,B of the bulge grid if ri < RB ,
while if ri > RB , we take the coordinates of the disk rD,i
until Rgal. For the angular coordinate θ we proceed in
the same way. We build θB,i and θD,i as in Sects. 3.3.1
and 3.3.2. In this case the disk grid is thinner toward the
equatorial plane of the galaxy whereas the bulge grid is
equally spaced, so we take the coordinates θD,i of the
disk as long as θD,i+1 − θD,i < θB,i+1 − θB,i and θB,i
elsewhere. For the azimuthal grid there is no problem as
it is chosen in the same way both for the disk and the
bulge.
3.4 The elemental volume grid
Assigned the geometrical shape of the galaxies, the den-
sity distributions of the three main components, and
the coordinate grid (r, θ, φ) (The number of grid points
for the three coordinates is nr + 1, nθ + 1, nφ), the
galaxy is subdivided into (nr, nθ , nΦ) small volumes V ,
each one identified by the coordinates of the center
(riV , θjV , φkV ) given by the mid-point of the coordi-
nate grid riV = (ri + ri+1) /2, θjV = (θj + θj+1) /2
and φkV = (φk + φk+1) /2. Thereinafter the volume
V (riV , θjV ,ΦkV ) will be simply indicated as V (i, j, k).
The mass of stars, MCs, and diffuse ISM, in each vol-
ume are easily derived from the corresponding density
laws ρi (i, j, k)V (i, j, k) where i stands for stars, MCs,
and ISM. By doing this, we neglect all local gradients in
ISM and MCs (gradients inside each elemental volume).
Since the elemental volumes have been chosen sufficiently
small, the approximation is fairly reasonable.
4 EXTINCTION AND EMISSION OF THE
DIFFUSE ISM
Piovan et al. (2006) presented a detailed study of the ex-
tinction and emission properties of dusty ISMs. They take
into account three dust components, i.e. graphite, sili-
cates and PAHs and the final global agreement reached
between theory and the ISM extinction and emission data
of MW, LMC and SMC has been very good. As we are
now going to include this dusty ISM model in our galax-
ies, it is wise to briefly summarize here the basic quanti-
ties and relationships in usage.
First of all, the total cross section of scattering, ab-
sorption and extinction is given by
σp (λ) =
∫ amax,i
amin,i
pia2Qp (a, λ)
1
nH
dni(a)
da
da (12)
where the index p stands for absorption (abs), scatter-
ing (sca), total extinction (ext), the index i identifies
the type of grains, amin,i and amax,i are the lower and
upper limits of the size distribution for the i-type of
grain, nH is the number density of H atoms, Qp (a, λ) are
the dimension-less absorption and scattering coefficients
(Draine & Lee 1984; Laor & Draine 1993; Li & Draine
2001) and, finally dni(a)/da is the distribution law of
the grains (Weingartner & Draine 2001a). With the aid
of the above cross sections it is possible to calculate the
optical depth τp(λ) along a given path
τp (λ) = σp (λ)
∫
L
nHdl = σp (λ)×NH (13)
where L is the optical path and all other symbols have
their usual meaning. In this expression for τp(λ) we have
implicitly assumed that the cross sections remain con-
stant along the optical path.
Let us name jsmallλ , j
big
λ and j
PAH
λ the contributions
to the emission by small grains, big grains and PAHs, re-
spectively. How these quantities are calculated is widely
described in Piovan et al. (2006) to whom the reader
c© 2005 RAS, MNRAS 000, 000–000

8 L. Piovan, R.Tantalo & C. Chiosi
should refer for more details. Let us summarize here just
the key relationships in usage.
The contribution to the emission by very small grains
of graphite and silicates is
jsmallλ = pi
∫ aflu
amin
∫ Tmax
Tmin
a2Qabs (a, λ)Bλ (T (a))×
×dP (a)
dT
dT
1
nH
dn (a)
da
da (14)
where dP (a) /dT is the distribution temperature from
Tmin to Tmax attained by grains with generic dimen-
sion a under an incident radiation field and Bλ (T (a))
is the Planck function. Qabs (a, λ) are the absorption co-
efficients, dn (a) /da is the Weingartner & Draine (2001a)
distribution law for the dimensions, aflu is the upper
limit for thermally fluctuating grains, amin is the lower
limit of the distribution.
The emission by big grains of graphite and silicates
is evaluated assuming that they behave like black bodies
in equilibrium with the radiation field. Therefore we have
jbigλ = pi
∫ amax
aflu
a2Qabs (a, λ)Bλ (T (a))
1
nH
dn (a)
da
da
(15)
where amax is the upper limit of the distribution and the
meaning of the other symbols is the same as in eqn. 14.
The emission by PAHs is given by
jPAHλ =
pi
nHhc
∫ λmax
λmin
I
(
λ
′
)
λ
′
∫ ahighPAH
alowPAH
dn (a)
da
×
× a2
[
QIPAHabs
(
a, λ
′
)
SION
(
λ
′
, λ, a
)
χi+ (16)
+ QNPAHabs
(
a, λ
′
)
SNEU
(
λ
′
, λ, a
)
(1− χi)
]
dadλ
′
where the ionization of PAHs is taken into ac-
count (Weingartner & Draine 2001b) and χi = χi (a)
is the fraction of ionized PAHs with dimension a.
SION
(
λ
′
, λ, a
)
and SNEU
(
λ
′
, λ, a
)
give the energy
emitted at wavelength λ by a molecule of dimension a, as
a consequence of absorbing a single photon with energy
hc/λ
′
. alowPAH and a
high
PAH are the limits of the distribution
and I
(
λ
′
)
is the incident radiation field.
5 THE GALAXY SED
Given the main components of a galaxy, their spatial dis-
tribution, the coordinate system, and the grid of elemen-
tal volumes, to proceed further one has to model the in-
teraction among stars, dusty ISM and MCs to simulate
the total SED emerging from the galaxy.
Let us consider a generic volume V ′ = V (i′, j′, k′)
of the galaxy: it will receive the radiation coming from
all other elemental volumes V = V (i, j, k). The radiation
travelling from one volume to another interacts with the
ISM comprised between any two generic volumes. There-
fore one has to take into account the energy that is both
absorbed and emitted by the ISM under the interaction
with the radiation field. Two simplifying hypotheses are
worth being made here:
(i) The dust contained in a generic volume V does
not contribute to the radiation field impinging on the vol-
ume V ′. This approximation stands on the notion that,
in first approximation, owing to the low optical depths of
the diffuse ISM in the MIR/FIR, dust cannot effectively
absorb the radiation it emits, except for high density re-
gions such as MCs, for which dust self-absorption has al-
ready been taken into account. In other words, the dust
contained in V ′ will be transparent to the IR radiation
emitted by the dust contained in the volume V . There-
fore, only stars and MCs will contribute to the incoming
radiation.
(ii) Following Rybicki & Lightman (1979), the radia-
tive transfer from a generic volume V to V ′ is simply cal-
culated by means of the so-called effective optical depth
defined by
τeff =
√
τabs (τabs + τsca) (17)
The above relation stands on the following considera-
tions: scattering increases the absorption, however as
photons are not destroyed, the effective optical depth
must be lower than the sum of the optical depths by scat-
tering and absorption but higher than the one by sole ab-
sorption (Rybicki & Lightman 1979). Although this ex-
pression for τeff has been derived for photons randomly
travelling across an absorbing diffusive medium, so that
it would strictly apply only to an infinite, homogeneous,
isotropically scattering medium, we make use of it here.
The results from the above approximation have been
compared by Silva et al. (1998) with those by Witt et al.
(1992) and Ferrara et al. (1999) using Monte-Carlo meth-
ods to solve radiative transfer problems. The results fully
agree with those by Witt et al. (1992) and Ferrara et al.
(1999) in the case of spherical symmetry and partially
disagree in the case of disk galaxies. For these latter the
quality of agreement depends on view angle between the
galaxy and the observer (Silva et al. 1998).
The total radiation field incident on V ′ is
J
(
λ,V ′
)
=
nr
∑
i=1
nθ
∑
j=1
nΦ
∑
k=1
V ·
[
jMC (λ, V ) + j∗ (λ, V )
]
r2 (V, V ′)
(18)
× e[−τeff (λ,V,V
′)]
where the summations are carried over the whole ranges
of i, j, k with i 6= i′, j 6= j′ and k 6= k′; r2(V, V ′) is the
value averaged over the volume of the square of the dis-
tance between the volumes V and V ′; τeff (λ, V, V ′) is
the effective optical depth from V to V ′ defined by eqn.
(17), which by means of eqn. (13) becomes
τeff
(
λ, V, V ′
)
=
√
σabs(λ)× (σabs (λ) + σsca (λ))×
×
∫ V (i′,j′,k′)
V (i,j,k)
nH(l)dl (19)
This integral represents the number of H atoms contained
in the cylinder between V and V ′. All details on the
c© 2005 RAS, MNRAS 000, 000–000

Galaxies spectra with interstellar dust 9
derivation of this quantity and r2(V, V ′) are given in Ap-
pendix A and B.
The two terms jMC (λ,V ) and j∗ (λ, V ) are the emis-
sion by MCs and stars per unit volume of V (i, j, k). They
are evaluated at the center of the volume element.
Let us now define two kinds of SSPs: those that are
already free of the parental cloud and are indicated as
sspf (classical free SSPs), and those that are still em-
bedded in their parental dusty molecular clouds and are
indicated as sspd (dusty SSPs).
Let us denote with fd the fraction of the SSP lumi-
nosity that is reprocessed by dust and with t0 the time
scale for this to occur, in such a way that
fd =



1 t 6 t0
2− t/t0 t0 < t 6 2t0
0 t > t0
(20)
where t0 is a suitable parameter determining the evapora-
tion time of the parental MCs. Accordingly, the fraction
of SSP luminosity that escapes without interacting with
dust is ff = 1− fd.
The parameter t0 will likely depend on the properties of
the ISM and type of galaxy in turn. Plausibly, t0 will be
of the order of the lifetime of massive stars. It will be
discussed in more detail in Sect. 5.1.
The monochromatic luminosity of a free SSP of given
age τ ′ = tG − t, born at t, and metallicity Z for unit of
SSP mass is therefore
Lfλ
(
τ ′, Z
)
=
∫ MU
ML
Φ(M) fλ
(
M, τ ′, Z
)
dM
∫ MU
ML
Φ(M) dM
(21)
Knowing the the monochromatic luminosity of the
naked SSPs Lfλ (τ
′, Z), the monochromatic luminosity of
the dust enshrouded SSPs Ldλ (τ
′, Z) has been derived as
described in Piovan et al. (2006). The emission of stars
and MCs per unit volume, jMC (λ, V ) and j∗ (λ, V ) re-
spectively, are given by
j∗ (λ, V ) =
∫ tG
2t0
ρ∗ (t)L
f
λ
(
τ ′, Z
)
dt+
+
∫ 2t0
t0
(
t
t0
− 1
)
ρ∗ (t)L
f
λ
(
τ ′, Z
)
dt (22)
and
jMC (λ, V ) =
∫ t0
0
ρ∗ (t)L
d
λ
(
τ ′, Z
)
dt+
+
∫ 2t0
t0
(
2− t
t0
)
ρ∗ (t)Ldλ
(
τ ′, Z
)
dt (23)
It is worth noticing that luminosity of the MCs de-
pends only on the luminosity of the young embedded
stars and not on the mass of molecular gas enclosed in
the MCs. The factors (2− t/t0) and (1− (2− t/t0)) =
(t/t0 − 1) follows from relations (20) and the definition
of ff .
Once calculated the incident radiation field J (λ, V ′)
we can obtain the emission per unit volume from the
dusty ISM. At this point the azimuthal and spherical
symmetries of the galaxy models become very important.
The emission per unit volume from the dusty ISM cal-
culated at the center of the volume elements is the same
everywhere, independently of the coordinate Φ. Therefore
it is sufficient to calculate the dust emission at Φ = 0 for
all possible values of r and θ on this ”galaxy slice”. It is
obvious that the symmetry will be lost when considering
the total emission from a certain volume element because
owing to the adopted spacing of the galaxy the elemental
volumes are not equal. However, as long as we refer to the
emission per unit volume, the symmetry properties above
allows us to avoid tedious and lengthy numerical calcu-
lations. The total radiation field for unit volume emitted
by a single element is
jTOT (λ, V ) = jMC (λ, V )+j∗ (λ, V )+jISM (λ, V ) (24)
where jISM (λ, V ) is the radiation outgoing from a unit
volume of the dusty diffuse ISM and is given by the sum
of the contributions from silicates, graphite and PAHs
described by eqns. (14), (15), and (16). The total out-
going emission from the volume V is therefore given by
jTOT (λ, V ) × V obviously different from volume to vol-
ume.
The radiation emitted by each elemental volume
(nr, nθ , nΦ) has to travel across a certain volume of the
galaxy itself before reaching the edge, escaping from the
galaxy, and being detected by an external observer. While
finding its way out, the radiation is absorbed and diffused
by the ISM. The external observer will see the galaxy
along a direction fixed by the angle Θ, where Θ = 0
means that the galaxy is seen face-on, whereas Θ = pi/2
means that the galaxy is seen edge-on. To this aim, we
need to determine the properties of the cylinder of mat-
ter from the center of each element V to the edge of
the galaxy, along the direction Θ in order to calculate
the amount of radiation emitted by the galaxy along this
direction. Therefore, the monochromatic luminosity mea-
sured by an external observer is
L (λ,Θ) = 4pi
nrr
∑
i=1
nθ
∑
j=1
nΦ
∑
k=1
V × jTOT (λ, V )
×e[−τeff (λ,V,Θ)] (25)
where τeff (λ,V,Θ) is the effective optical depth between
V (i, j, k) and the galactic edge along the direction Θ. The
details on the derivation of the effective optical depth
τeff (λ, V,Θ) are described in Appendix C.
5.1 SSPs in usage and parameters of the galaxy
model
In this section first we shortly present the libraries of stel-
lar models, isochrones, and stellar spectra that are used
to calculate the SEDs of SSPs and galaxies. Second we
summarize the results for SSP intrinsically affected by
dust calculated by Piovan et al. (2003, 2006) and in the
case of young SSPs we describe the effect of the parame-
c© 2005 RAS, MNRAS 000, 000–000

10 L. Piovan, R.Tantalo & C. Chiosi
ters of the model. Finally, we present the other parame-
ters governing the the ISM and chemical model and the
galaxy geometry.
(1) Libraries of stellar models and stel-
lar spectra: We adopt the set of isochrones
by Tantalo et al. (1998) (anticipated in the
data base for galaxy evolution models by
Leitherer, Alloin, von Alvensleben, Gallager, Huchra & et al.
(1996)). The underlying stellar models are those of the
Padova Library calculated with convective overshooting
and are amply described by Fagotto et al. (1994a,b,c),
so that no detail is given here.
The library of stellar spectra is from Lejeune et al.
(1998), which stands on the Kurucz (1995) release of the-
oretical spectra, however with several important imple-
mentations (see Piovan et al. 2003, 2006, for more de-
tails).
(2) Dust enshrouded SSPs As already men-
tioned, young stars and AGB stars are both surrounded
by their own dust. The young stars because they are im-
mersed in MCs, the AGB stars because they eject dust
on their own. In both cases the UV-optical light emit-
ted by the stars is absorbed and re-emitted in the FIR.
But for old ellipticals, in which star formation stopped
at early epochs because of the galactic wind so that no
young stellar populations embedded into parental MCs
are present, for all the other morphological types the im-
pact of young dusty populations on the galaxy SED has
to be considered. This indeed is stronger than the one
caused by dusty AGB stars (see below). The reason of it
can be reduced to the fact that while for young SSPs all
the emitted energy interacts with the dusty environment,
in the case of old SSPs only AGB stars interact with the
dust. However, as the ranges of wavelength interested in
the case of young SSPs and dusty AGBs are different,
the accurate description of the region around 1 − 2µm
requires that the dusty shells around AGB stars are fully
taken into account. SSPs for AGB stars and young stars
with this effect built in are by Piovan et al. (2003) and
Piovan et al. (2006).
Intermediate age and old SSPs: In this paper we de-
cided not to use the SSPs of Piovan et al. (2003) where
the effects of circumstellar dusty shells around the AGB
stars (of intermediate/old ages) are included. The main
reason is that dust enshrouded AGB stars are available
only for three metallicities. Work is in progress to build
a more complete set of SEDs in which the effects of the
dusty shells around AGB stars are included.
Young SSPs: In general dust around young stars
shifts the UV/optical radiation into the MIR/NIR. How-
ever, the SED of young SSPs (Piovan et al. 2006) is gov-
erned by a number of parameters describing the MC it-
self, chief among which are the optical depth τV in the
V band, the scale radius of the cloud R, the C abun-
dance bC in the two log-normal populations of very small
carbonaceous grains according to the distribution law of
Weingartner & Draine (2001a), and finally the ionization
state of PAHs. In addition to these, there is another pa-
rameter related to young MCs, namely the evaporation
time t0. Let us examine their effect in some detail.
(i) The MC optical depth τV in the V band. Up to now
in our library of SSPs only two values are considered, i.e.
τV = 5 and 35, corresponding to intermediate and high
optical depths. The effect of changing the optical depth
is simple: the higher the optical depth, the higher is the
amount of energy shifted toward longer wavelengths. A
remark is worth here. Using a certain set of SSPs (i.e.
a set with given parameters) we implicitly fix the op-
tical depth. Clearly, the optical depth of MCs not only
increases with the cloud mass, decreases with the cloud
size, and in general increases with the cloud density, but
also increases with the metallicity. Therefore the ideal
situation would be the one in which MCs in galaxy mod-
els cover the whole range of masses, radii, densities and
metallicities.
(ii) The scale radius of the MC. Two values are al-
lowed, R = 1 and 5. They correspond to MCs of different
compactness. Keeping constant all other parameters, the
peak of emission shifts to longer wavelengths at increas-
ing scale radius (see also Takagi et al. 2003).
(iii) The carbon abundance bC per H nucleus fixes the
abundance of this element in the two log-normal popu-
lations of very small grains in the Weingartner & Draine
(2001a) law. As shown byWeingartner & Draine (2001a),
the sole extinction curve is unable to constrain bC . It
provides only an upper limit for bC , which at given ra-
tio RV = A (V ) /E (B − V ) is reached when the very
small carbonaceous grains and PAHs are able to account
for the ultraviolet bump of the extinction curve. Values
lower than the upper limit are possible. Without other
constraints, for instance the IR emission of the region of
interest, it is not possible to determine bC , which plays
an important role in the IR emission of galaxies. Specif-
ically, it drives the emission of PAHs in the MIR gener-
ated by young MCs. The effect of varying bC is simple: for
higher values of bC, the PAH emission in the MIR reaches
higher flux levels. In contrast, the UV-optical flux and the
shape of the absorbed stellar emission do not depend on
bC , because the extinction curve remains the same for
different values of bC . As the global abundance of C is
fixed, the distribution of the grains has to compensate for
the small number of small grains with an higher number
of big grains. Therefore, for low values of bC we expect
that the emission in the FIR slightly increases (the total
energy budget has clearly to be conserved).
(iv) The ionization state of PAHs. The optical proper-
ties we have adopted are different for ionized and neutral
PAHs (see Li & Draine 2001, for more details). The ion-
ization state of PAHs affects the PAH emission profile in
the MIR. We considered three ionization models. The first
is the one by Weingartner & Draine (2001b). The second
model adopts for the MCs the same ionization profile
calculated by Li & Draine (2001) for the diffuse ISM of
the MW. The third model simply takes into account only
neutral PAHs (very low ionization). In other words, we
have a sequence of models going from ionized to neutral
PAHs (see Piovan et al. 2006, for more details).
(v) t0: Following the simple recipe by Silva et al. (1998),
this is the scale time required by a new generation of
stars to get rid of the parental MCs (see also Piovan et al.
2006). In Silva et al. (1998) model, star formation is re-
duced to a point source scheme, in which stars born at
the center of dusty MCs slowly evaporate them to even-
tually shine free. As pointed from Takagi et al. (2003), if
c© 2005 RAS, MNRAS 000, 000–000

Galaxies spectra with interstellar dust 11
the time of the star forming activity is shorter than the
escaping time scale t0, the light coming from young stars
is completely hidden at the UV-optical wavelenghts. In
general, in Silva et al. (1998) model, for times shorter
than t0, no light escapes from dusty star forming re-
gions and therefore the light observed in the UV-NIR
should be negligible for any aperture size of the galax-
ies. This is not what we observe in real galaxies espe-
cially in their central regions. The discrepancy is cured
by adopting the more realistic descriptions in which stars
are randomly distributed inside the MC, and solving the
radiation transfer problem with the ray tracing method
(see Piovan et al. 2006). We can reproduce in detail in
this way the inner regions of starbursters like Arp220
and M82. Even with the new scheme, the parameter t0
drives the amount of energy emitted by the young stars
that is absorbed and reprocessed by the local dust (i.e.
in the region immediately around the stars themselves).
The evaporation is simulated by letting more and more
energy to escape without being reprocessed by dust. The
time scale t0 likely goes from 3 to 100 Myr, i.e. the evo-
lutionary lifetime of a 100 and 5 M⊙ respectively. High
values of t0 mean that young stars are longer hidden by
the parental clouds and accordingly much of the light
they emit in the UV-visible range is shifted to the FIR
for a long period of time. In such a case a large fraction
of the IR light emitted by a galaxy could be due to young
stars still embedded in MCs. The opposite for low values
of t0.
(3) Parameters of the ISM model are the frac-
tionary mass of gas in the ISM fM and the metallicity
Z.
(a) fM: The fraction of diffuse gas present in a galaxy
with respect to the total amount of gas can be inferred
from observational data on the ratio between the molec-
ular and atomic gas. In disk galaxies for instance most of
hydrogen in MCs is in form of H2, whereas the inter-cloud
medium is mainly made of atomic HI . This parameter
bears very much on emission and extinction by the dif-
fuse ISM. The larger fM , the bigger is the amount of
gas present in the diffuse ISM. Therefore, the emission
(proportional to the number density of H atoms) will be
higher. Furthermore, extinction of the diffuse ISM as well
will increase because of the bigger absorption by dust,
which is also proportional to the number density of H
atoms in the diffuse ISM.
(b) Metallicity Z: The metallicity reached by the ISM
of the galaxy fixes the properties of the dust, drives the
intensity of the ISM emission and its ability in extinguish-
ing the radiation field. We adopted as standard models
for Z . Z⊙ the three compositions of MW, LMC and
SMC, that allow us to cover well this range of metallici-
ties. The dust to gas ratio scales with the metallicity: the
higher the metal content of a galaxy, the higher is the
abundance of grains per H atom. This simply implies
that the ISMs of high metallicity galaxies will both ab-
sorb and emit more energy. For metallicities higher than
the solar one (Z & Z⊙), we keep the relative proportions
of silicates, graphite and PAHs of the diffuse ISM of the
MW, scaled to the higher dust to gas ratio.
(4) Parameters of the chemical models: Chief
among others are the exponent k and the efficiency ν of
the star formation law, the infall time scale τ , and lim-
ited to the case of elliptical galaxies the parameters fixing
the gravitational and thermal energy of the gas and driv-
ing the onset of galactic winds. In the case of galaxies
composed by disk and bulge, the number of parameters
increases. There are kB , νB and τB together with kD,
νD and τD, and the bulge to disk mass ratio MB/MD.
Finally, we will also consider the case in which galaxies
may undergo a burst of star formation. The burst is in-
troduced superimposing it to the star formation history
law described by eqn. (6). The burst is described by the
following parameters: the age tBUR at which the burst
occurs, the enhancement factor νBUR amplifying the cur-
rent efficiency ν, and, finally, the duration ∆tBUR.
(5) Parameters of the geometrical models: In
the case of early type galaxies (our spherical case) the pa-
rameters are r∗c , r
MC
c , r
M
c , i.e. the core radii for the distri-
bution of stars, MCs and ISM, respectively. In the case of
disk galaxies the spatial distributions of the three compo-
nents are fixed by the radial scale lengths R∗d, R
MC
d , and
RMd , and the scale heights z
∗
d , z
MC
d , and z
M
d , with obvious
meaning of the various symbols. For composite galaxies
with disk and bulge the number of parameters increases
dramatically as we are dealing with two distributions:
the King law (as for early-type galaxies) for the bulge,
described with the parameters r∗c,B, r
MC
c,B , r
M
c,B and a dou-
ble decreasing exponential law for the disk, described by
the parameters R∗d,B, R
MC
d,B , R
M
d,B and z
∗
d,B, z
MC
d,B , z
M
d,B. In
all types of model, the scale length of the young and old
stellar populations is the same. Even if this reduces the
number of parameters, in reality it would be interesting,
for starburst galaxies in particular, to consider different
spatial distributions for old and young stars (see Calzetti
2001). Work is in progress to improve upon this type of
model. The remaining geometrical parameters are: the
radius of the galaxy Rgal and, if a bulge is present, the
radius RB of this, and finally the angle of inclination go-
ing from edge-on to face-on galaxies, i.e. from Θ = 0◦ to
Θ = 90◦ with respect to the z-axis perpendicular to the
equatorial plane of the galaxy.
5.2 Role of the parameters in template model
galaxies
In this section we analyze in detail the effect of the various
parameters on galaxy SEDs. To this aim we calculate
three template galaxies, i.e. an old early-type galaxy, a
late-type spiral galaxy, and finally a starburst galaxy.
5.2.1 Early-type galaxies
Early-type galaxies are simulated by means of spherical
models whose total baryonic mass is 1011M⊙ and total
dark matter mass is 5 times higher (see Tantalo et al.
1996, for details). For the purposes of this section we
limit ourselves to consider the typical SFH of an elliptical,
characterized by a strong initial burst of stellar activity,
early onset of galactic wind, and quiescence ever since.
As the model stands on the infall scheme, the SFR starts
small, increases to a peak value and then declines ever
since. The time scale at which the peak occurs is of the
c© 2005 RAS, MNRAS 000, 000–000

12 L. Piovan, R.Tantalo & C. Chiosi
10
100
300
SF
R
[M
s
u
n
/y
r]
SFR
1 5 10 13
0
0.2
0.4
0.6
0.8
1
Age (Gyr)
M
s
ta
r,

M
ga
s
&
M
L
(in
10
11

M
s
u
n
)
Mgas
M
star
ML
1 5 10 13
0
0.2
0.4
0.6
0.8
1
Age (Gyr)
M
s
ta
r/M
L
&
M
ga
s/M
L
Mgas/ML
M
star/ML
0
0.02
0.04
0.06
0.08
Z
&
<
Z>
<Z>
Z
Figure 1. Basic quantities of the chemical model for a pro-
totype early-type galaxy as function of the age: the top-left
panel shows the star formation rate in M⊙/yr; the top-right
panel displays the maximum (Z, solid line) and mean metal-
licity (〈Z〉, dotted line); the bottom-left panel shows the mass
of living stars Mstar(solid line), the gas mass Mgas (dotted
line), and the total mass of baryons ML (dashed line); finally
the bottom-right panel displays the ratios Mstar/ML (solid
line) and Mgas/ML (dotted line). All masses are in units of
1011 M⊙. Ages are in Gyr.
order of the infall time scale that is fixed at τ=0.1 Gyr
(Tantalo et al. 1996) which means that the model tends
to the closed-box approximation but for the occurrence
of galactic winds. The exponent for the star formation
law is k=1. The efficiency of star formation is ν = 6. The
reason for the above choice and more details can be found
in Tantalo et al. (1996, 1998). The four panels of Fig. 1
show a few relevant quantities characterizing the galaxy.
To study the effect of the parameters we consider two
stages of the history of an early-type galaxy: the age of
0.15 Gyr, when the SFR reaches the peak and the present
age of 13 Gyr after billion years of passive evolution.
In the very early stages of high star formation we
can assume that dust is mostly concentrated in the dense
regions of star formation. Following this idea we assign
a low gas content to the diffuse ISM (fM = 0.3, which
implies that the mass in dusty MCs is about twice mass
of the diffuse ISM). We adopt t0 ∼ 40 Myr, a long evap-
oration time, which sounds reasonable for a high density
star forming environment. Once the galactic wind has
taken place and star formation has ceased, we can adopt
fM = 1 and t0 = 0.
In the 13 Gyr model there is no longer star forma-
tion and the evolution is merely passive. If the galaxy is
free of gas and only stars are present, the SED is ex-
pected to drop off long-ward of about 2µm. However
elliptical galaxies of the local universe emit in the IR
(Guhathakurta et al. 1986). The origin of this flux in the
MIR/FIR may be due to diffuse dust which emits at those
wavelengths. Therefore to match this part of the spec-
trum one has to allow for a small amount of diffuse ISM
which is likely to exist. By imposing fM = 1 for our model
of age 13 Gyr, we assume that all the gas is in form of
diffuse ISM. Interesting questions to rise are: how much
gas can be present today in an elliptical galaxy? What is
the source of this gas?
To answer the above questions let us examine how
the gas content of an elliptical galaxy is expected
to evolve with time (Gibson & Matteucci 1997; Chiosi
2000). According to the classical scenario (Larson 1974),
all the gas present in elliptical galaxies at the onset of the
galactic wind is supposed to be expelled from the gravi-
tational potential well of the galaxy into the intracluster
medium. Despite the radiative losses, the energy input
from supernova explosions, stellar winds and dynamical
interactions overwhelms the gravitational potential and
makes galactic wind to occur in such a way to happen
later and later at increasing galaxy mass. Star formation
suddenly ceases and consequently the energy input by
Type II (early on) and Type I (afterwards) either stops
(Type II) or get very small (Type I). All this requires
about 0.5 Gyr. Subsequently low mass stars (. 2M⊙)
loose mass by stellar wind (during the red giant and the
asymptotic giant branch phases) thus refueling the galaxy
of gas in amounts that are comparable to those before the
galactic wind (Chiosi 2000). What is the fate of this gas?
In the most plausible scenario (Gibson & Matteucci
1997) the phase of galactic wind should last for about
0.5-1 Gyr thanks to the energy input by Type Ia su-
pernovae and then stop. The amount of gas lost by low
mass stars during this time interval turns out to be very
large (Chiosi 2000) and it is not entirely clear how it
can exceed the gravitational energy. Nevertheless, there
is general consensus that on a rather short time scale the
gas may escape the galaxy. Most likely a sort of dynam-
ical equilibrium is reached in which gas is continuously
ejected by stars and lost by the galaxy. It may happen
that a tiny amount of gas is always present in the galaxy,
thus accounting for the IR emission.
After the onset of the galactic wind, our chemical
model is not able to describe this complex situation. Dy-
ing stars emit lots of gas whose fate is uncertain. Basing
on the flux level observed in real galaxies, the gas content
of the galaxy is reduced by a factor of the order of 1000.
Finally, we are left with the geometrical param-
eters to fix. For the exponents γ∗ and γMC a value
around 1.5 could be taken for ellipticals. The value for
the ISM is more uncertain. Following Froehlich (1982),
Witt et al. (1992), and Wise & Silva (1996) we choose
γM ≃ 0.5 − 0.75, that is the ISM is less concentrated
toward the center than the stars.
Before galactic wind, at the ages of 0.15, the gas is
made of molecular clouds and diffuse ISM. Therefore, we
need the scale lengths of MCs, dusty ISM and stars for
which we assume rMCc = r
∗
c = r
M
c = 0.5 kpc. Afterwards,
we need only the scale lengths for ISM and stars. Both are
kept unchanged (0.5 kpc). In general we will assume r∗c =
rMCc in spheroidals to reduce the number of parameters.
In Table 1, columns (2) and (3), we summarize the
set of parameters we have used to model our test ellipti-
cals.
At the age of 13 Gyr only the geometrical parameters
need to be discussed. First we consider the galaxy radius
Rgal, which is let vary from 20 to 0.5 kpc, i.e. from very
c© 2005 RAS, MNRAS 000, 000–000

Galaxies spectra with interstellar dust 13
0.5 1 2 4
2
10
50
200
Time [Gyr]
M
s
u
n
/y
r
0.2 0.5 1
7
8
9
10
λ [µ m]
lo
g(
λ
⋅

L λ

/ L
s
u
n
)
20 Kpc
0.5 Kpc
0.5 1 10 100 300
5
6
7
8
9
λ [µ m]
20 Kpc
0.5 Kpc
7
8
9
10
lo
g(
λ
⋅

L λ

/ L
s
u
n
)
0.5 Kpc 20 Kpc
20 Kpc
0.5 Kpc
Figure 2. Top-left panel: star formation history of the pro-
totype elliptical galaxy with ML = 1011M⊙ at the age of 13
Gyr. Top-right panel: SEDs of elliptical galaxies with radii
of 20, 10, 5, 3, 1 and 0.5 kpc. The full range of wavelengths is
represented, from 0.1 to 500µm. Bottom-left panel: details
on the UV-optical/NIR region of the SEDs. Bottom-right
panel: contribution to the total emission of the diffuse ISM
for the different radii.
expanded to very compact systems. In Fig. 2, we show
the resulting SEDs together with the emission in the UV-
optical region (bottom-left panel) and the contribution to
the total flux by the diffuse ISM (bottom-right panel). At
decreasing size of the galaxy, the optical depth increases:
the dimension of the galaxy scales linearly, the density of
matter and the numerical density of H atoms nH increase
as ∝ r−3 and, therefore, the optical depth τ increases as
∝ r−2. From the top-right and bottom-left panels of Fig.
2 we can see the effect of it on the UV-optical/NIR part
of the spectrum: the smaller the dimension, the stronger
is the extinction of the UV-optical light. For the same
reason the emission of dust in the FIR becomes stronger
at decreasing dimensions because of the higher density
(bottom-right panel of Fig. 2). The emission, in fact, lin-
early depends on the numerical density of H atoms.
As the mass of the physical components of the galaxy
and all their scale lengths are fixed (in our example all
equal to 0.5 Kpc), in models of smaller size more gas,
stars and dust are stored in the outer regions with re-
spect to the larger size models. In such a case the mat-
ter distribution tends to become uniform, a limit situa-
tion reached when rc ≫ Rgal. For compact objects, the
peak of emission in the FIR also shifts toward shorter
wavelengths. This is due to the higher temperature of
the grains, thanks to the combined effect of the higher
local emission and the presence of more sources in the
outer regions (bottom-right panel of Fig. 2).
Other geometrical parameters are the scale length
r∗c and the ratio r
∗
c/r
M
c that at fixed r
∗
c gives r
M
c . We
calculate a grid of models characterized by seven values
of r∗c , i.e. 0.1, 0.5, 1, 3, 5, 7 and 9 kpc (Rgal is fixed at
10 kpc), and ten values of the ratio r∗c/r
M
c , i.e. 0.005,
0.05, 0.1, 0.2, 0.4, 1, 3, 10, 50 and 100, for a total of 170
0.5 1 2
7
8
9
10
lo
g(
λ
⋅

L λ

/ L
su
n
)
r
c
M
= 90 Kpc
r
c
M
= 1 Kpc
r
c
* /r
c
M
= 0.1 5
6
7
8
r
c
M
= 90 Kpc
r
c
M
= 1 Kpc
0.1 1 3 10 100
7
8
9
10
λ [µ m]
lo
g(
λ
⋅

L λ

/ L
su
n
)
r
c
M
=0.03 Kpc
r
c
M
=3 Kpc
r
c
* /r
c
M
= 3
3 10 100 300
5
6
7
8
9
λ [µ m]
r
c
M
=0.03 Kpc
r
c
M
=3 Kpc
Figure 4. In the top-left and bottom-left panels we show
the total emission of the prototype elliptical galaxy at the
age of 13 Gyr. The ratio r∗c/r
M
c between the scale lengths is
kept fixed and two values are considered: r∗c/r
M
c = 0.1 and
r∗c/r
M
c = 3. In both cases r
∗
c is then varied from 0.1 to 9 kpc.
The corresponding value of rMc is shown. In the right panels
(top and bottom), the contribution to the total emission of
the diffuse ISM is shown in detail.
models covering large intervals of r∗c and r
M
c . The results
obtained for various combinations of these parameters
are presented in figs. 3 and 4. In Fig. 3, we show the re-
sults obtained keeping fixed r∗c and leaving free the ratio
r∗c/r
M
c , or equivalently r
M
c . Four values of r
∗
c are consid-
ered. For each of these on the left panel we show the total
galaxy flux at varying rMc , whereas on the right panel we
display the corresponding contribution of the diffuse ISM
to the total flux. For the two smallest values of r∗c , 0.5
and 1 kpc, at varying rMc the emission in the FIR grows,
reaches a peak value, and then declines. This can be ex-
plained in the following way. For rMc ≪ r∗c and rMc ≫ r∗c ,
the diffuse ISM is concentrated either in the inner or in
the outer regions of the galaxy. In both cases the spatial
distributions of the ISM does not favors the interaction
with the stellar radiation: the FIR flux increases as rMc
grows from very small values to rMc ≈ r
∗
c , which repre-
sents the best condition in which the intensity of the local
radiation field is strong in high density regions. Moving to
rMc ≫ r∗c the flux decreases, because the dust is concen-
trated in regions of weaker radiation field. The emission
peak shifts to longer wavelenghts because for small r∗c ,
as rMc increases, the dust is confined in regions of lower
radiation field intensity. For the two highest values of r∗c ,
5 and 7 kpc, the flux simply increases as dust goes from
being concentrated in the inner regions of the galaxy, to
being shifted toward the outer regions with higher den-
sity of stars.
In Fig. 4 we keep fixed the ratio r∗c/r
M
c and let r
∗
c
vary from 0.1 to 9 kpc. The result is the same for both
cases no matter whether r∗c/r
M
c < 1 or > 1. The FIR
emission is stronger when both r∗c and r
M
c are small,
i.e. when stars and dust occupy the same inner region
of the galaxy. With high values of the two radial scale
c© 2005 RAS, MNRAS 000, 000–000

14 L. Piovan, R.Tantalo & C. Chiosi
Table 1. Columns (2) through (5): parameters for a sample of model galaxies, namely two ellipticals (E) at the ages of 13 and
0.15 Gyr, a disk (D) at the age of 13 Gyr and a starburst (SB) at the age of 13 Gyr. Columns (6) through (11) best-fit parameters
of the models we have adopted to match the SEDs of the spiral galaxies M100 and NGC 6946, the elliptical galaxies NGC2768
and NGC4494, and finally the local starburst galaxies Arp220 and M82.
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
Model – Galaxy E E D SB M100 NGC6946 NGC2768 NGC4494 Arp220 M82
Age1 13 0.15 13 13 13 13 13 13 13 13
D2 – – – – 19 5.5 21.5 20 76 3.25
ML3 1 1 1 1 2 1.2 2.2 2 1.35 0.18
t04 0 40 5 15 or 30 5 3 0 0 80 100
fM5 1 0.3 0.5 0.5 0.35 0.55 1 1 0.5 0.9
r∗c/r
M
c
6 0.5 0.5 – 0.5 – – 0.5 0.5 1.0 0.2
r∗c = r
MC
c
7 0.5 0.5 – 0.5 – – 0.5 0.5 0.5 0.35
RMd
8, – – 5 – 5 5 – – – –
R∗d = R
MC
d
9 – – 5 – 5 5 – – – –
zMd
10 – – 0.4 – 0.5 1 – – – –
z∗d = z
MC
d
11 – – 0.4 – 0.5 1 – – – –
Rgal 12 10 10 10 10 19 13 20 12 17 10
τ13 0.1 0.1 4 9 4 5 0.1 0.1 9 9
ν14 6 6 0.7 1 0.7 0.7 2 2 0.4 1.2
tBUR15 – – – 12.95 – – – – 12.95 12.95
∆tBUR16 – – – 0.05 – – – – 0.05 0.05
νBUR17 – – – 30 – – – – 60 5
Θ18 – – 60◦ – 27◦ 35◦ – – – –
1Age in Gyr. 2Distance of the galaxy in Mpc. 3Baryonic mass of the galaxy in units of 1011M⊙. 4Evaporation time in Myr of
young SSPs from dusty parental regions. In the 13 Gyr models and the galaxies NGC2768 and NGC4494 with no ongoing star
formation, the parameter is set equal to 0. 5Fractionary gas content in the diffuse ISM. 6Ratio between the core radii of stars
and ISM in the spherical models. 7Scale radii in kpc of stars and MCs in the spherical models. 8Radial scale in kpc of the diffuse
ISM in the disk models. 8Radial scales in kpc of stars and MCs in the disk models. 9Vertical scale in kpc of the diffuse ISM in
the disk models. 10Vertical scales in kpc of stars and MCs. 11Radius of the galaxy in kpc. 12Infall time scale in Gyr. 13Efficiency
of star formation. 14Age of the beginning of the burst for starburst models in Gyr. 15Length of the burst for starburst models.
16Multiplying factor for the star formation for starburst models. 17Inclination angle.
0.5 1 2
7
8
9
10
lo
g(λ

⋅

L λ

/ L
su
n)
0.01 Kpc
100 Kpcrc
*
= 0.5 Kpc
6
7
8
r
c
M
= 100 Kpc
r
c
M
= 0.01 Kpc
0.1 1 3 10 100
7
8
9
10
λ [µ m]
lo
g(λ

⋅

L λ

/ L
su
n)
r
c
*
= 5 Kpc
0.1 Kpc
1000 Kpc
3 10 100 300
5
6
7
λ [µ m]
r
c
M
= 0.1 Kpc
r
c
M
= 1000 Kpc 0.5 1 2
7
8
9
10
lo
g(λ

⋅

L λ

/ L
su
n)
0.02 Kpc
200 Kpcrc
*
= 1 Kpc 6
7
8
r
c
M
= 200 Kpc
r
c
M
= 0.02 Kpc
0.1 1 5 10 100
7
8
9
10
λ [µ m]
lo
g(λ

⋅

L λ

/ L
su
n)
r
c
*
= 7 Kpc
0.14 Kpc
1400 Kpc
10 100 300
5
6
7
λ [µ m]
r
c
M
= 0.14 Kpc
r
c
M
= 1400 Kpc
Figure 3. Left Panels: the SEDs of the test elliptical galaxy at the age of 13 Gyr for r∗c = 0.5, 1, 5 and 7 kpc. For each of these
the ratio r∗c/r
M
c is varied from 0.005 to 50. The corresponding values of r
M
c are also shown. Right Panels: the contribution to
the total emission by the diffuse ISM. The arrows show the evolution of the cirrus emission going from the smaller to the higher
values of rMc . All the other parameters are kept fixed.
lengths, stars and dust are more dispersed across the
galaxy, therefore the FIR emission is weaker and the peak
shifts toward longer wavelengths.
To show the effects of t0, the time scale for a young
SSP to evaporate the MC in which it is embedded, and
fM , the fractionary gas mass in the diffuse ISM, we take
the 0.15 Gyr old model galaxy, at the peak of star for-
mation. In Fig. 5, we show the SEDs for several values
of t0. The effect of this parameter is strong and straight-
forward: the longer this time scale, the higher is the ob-
scuration of the UV-optical light because the energy of
newly born young and luminous objects is long trapped
by the dusty environment (top-right panel). Simultane-
ously, more energy is emitted in the FIR by the dusty
c© 2005 RAS, MNRAS 000, 000–000

Galaxies spectra with interstellar dust 15
0.01 1 2
0.1
10
50
200
Time [Gyr]
M
s
u
n
/y
r
0.1 1 10 100 500
8
9
10
11
12
λ [µ m]
lo
g(
λ
⋅

L λ

/ L
s
u
n
)
100 Myr
1.5 Myr
0.5 1 10 100 300
λ [µ m]
100 Myr
1.5 Myr
9.5
10
11
12
lo
g(
λ
⋅

L λ

/ L
s
u
n
)
100 Myr
1.5 Myr
1.5 Myr 100 Myr
Figure 5. Top-left panel: star formation history of the pro-
totype elliptical galaxy of ML = 1011M⊙ with a mark on the
modelled age at 0.15 Gyr. Top-right panel: SEDs of ellip-
ticals at varying the time scale t0 from 1.5 Myr to 100 Myr.
The considered values are 1.5, 4.5, 15, 30, 60 and 100 Myr. All
the other parameters are kept fixed. We also show the SED of
the same galaxy calculated with the classical EPS technique.
Bottom-left panel: contribution to the total emission by
dusty MCs at varying t0. Bottom-right panel: contribution
to the total emission of the diffuse ISM for the same set of
time scales t0.
MCs regions (bottom-left panel). In any case it is clear
from the top-right and the bottom-right panel that an
increase of t0, corresponds to a decrease of the emission
by the diffuse ISM, whose peak also shifts toward longer
wavelengths. The explanation is that increasing t0 the
UV-optical intensity of the local radiation field dramati-
cally drops, leaving a cooler and weaker mean radiation
field to heat the dust.
Finally, we compare in Fig. 6 the SEDs of our test
galaxy at varying the amount of gas in the diffuse ISM,
i.e. fM . The remaining gas is stored in MCs. As shown by
the top panels, increasing the amount of gas in the diffuse
ISM has little influence on the global SED. The reason is
that the galaxy is at the peak of star formation, where the
attenuation and IR emission are clearly dominated by the
star forming MCs. Similar albeit smaller effects of fM are
expected in starburst galaxies with high star formation
rate. In any case, as expected, increasing the amount of
gas in the diffuse ISM yields stronger attenuation of the
light emitted by old and young stars (top and bottom left
panels). The emission by the diffuse ISM (which anyhow
scarcely contributes to the total flux) increases with the
amount of gas and also becomes cooler because of the
weaker local radiation field heating the grains (bottom
right panel).
5.2.2 Late-type galaxies
We consider a disk galaxy of 1011 M⊙ at the age of 13
Gyr. In our model disk galaxy (i.e. with infall scheme and
the Schmidt law of star formation) and likely in real disk
0.1 1 2
10
11
12
13
lo
g(
λ
⋅

L λ

/ L
su
n
)
fM=0.9
fM=0.1
classical EPS
0.1 1 3
8
9
10
λ [µ m]
lo
g(
λ
⋅

L λ

/ L
su
n
)
fM=0.9
fM=0.1
10 100 300
9
10
λ [µ m]
fM=0.1
fM=0.9
fM=0.1
fM=0.9
MCs flux
Figure 6. Top panels: SEDs of test ellipticals at varying the
fraction of gas in the diffuse ISM fM with respect to the total
amount of gas. The range of values goes from 0.1 to 0.9. All
the other parameters are kept fixed. The considered values are
0.1, 0.3, 0.5, 0.7 and 0.9. We also show the SED of the same
galaxy calculated with the classical EPS technique. Bottom-
left panel: contribution to the total emission by dusty MCs at
varying fM . Bottom-right panel: contribution to the total
emission of the diffuse ISM for the same set of time scales fM .
galaxies as well, the star forming activity never ceases.
Due to the lack of significant galactic winds in disk galax-
ies, the gas remain for ever in the disk and continuously
refuels star formation. This means that our model has to
take all possible components into account even at the age
of 13 Gyr: young stars just formed and still embedded in
their parental molecular cloud, bare stars of any age and
diffuse ISM. The task is more complicate than with the
spheroidal models due to the lower degree of symmetry
(only the azimuthal one).
The choice of the three main parameters driving the
star formation and chemical enrichment of a disk galaxy,
i.e. the infall time scale τ , the exponent k, and the ef-
ficiency ν of the star formation rate, rests on the fol-
lowing considerations. In the star formation rate, k typ-
ically varies from 1 (Schmidt 1963)to 2 (Larson 1991).
In our model for a late-type galaxy the choice is guided
by the Portinari et al. (1998) results for the Solar Vicin-
ity. Therefore we adopt k = 1, and ν = 0.7, whereas
for the infall time scale we assume τ = 4. The resulting
star formation rate starts small, grows to a maximum at
about 3.5 Gyr, and then gently declines to the present
day value.
The temporal evolution of a few physical quantities
characterizing the model galaxy is shown in Fig. 7.
To proceed further other parameters must be spec-
ified. First, we fix the geometrical parameters, i.e. the
radial and vertical scale heights, for which we make the
most simple choice, i.e. R∗d = R
MC
d = R
M
d = 5 kpc and
z∗d = z
MC
d = z
M
d = 0.4 kpc (the spatial scales for the
three components are the same) in agreement with typ-
ical values found for local spiral galaxies such as M100
and M51 (Beckman et al. 1996). Second, we need to spec-
c© 2005 RAS, MNRAS 000, 000–000

16 L. Piovan, R.Tantalo & C. Chiosi
1
10
90
SF
R
[M
su
n
/y
r] SFR
1 5 10 13
0
0.2
0.4
0.6
0.8
1
Age (Gyr)
M
st
ar
,

M
ga
s
&
M
L
(in
10
11

M
su
n
)
Mgas
M
star
ML
1 5 10 13
0
0.2
0.4
0.6
0.8
1
Age (Gyr)
M
st
ar
/M
L
&
M
ga
s/M
L
Mgas/ML
M
star/ML
0
0.02
0.04
0.06
0.08
Z
&
<
Z>
<Z>
Z
Figure 7. Basic quantities of the chemical model for the test
late-type galaxy as function of the age: the top left panel shows
the star formation rate in M⊙/yr; the top right panel displays
the maximum (Z, solid line) and mean metallicity (〈Z〉, dot-
ted line); the bottom left panel shows the mass of living stars
Mstar (solid line), the gas mass Mgas (dotted line), and the to-
tal mass of baryons ML (dashed line); finally the bottom right
panel displays the ratios Mstar/ML (solid line) and Mgas/ML
(dotted line). All masses are in units of 1011 M⊙. Ages are in
Gyr.
0.5 1 2
7
8
9
10
lo
g(
λ
⋅

L λ

/ L
su
n
)
0.5 Kpc
20 Kpc
classical EPS
α
0.1 1 3 10 100
4
6
7
8
9
λ [µ m]
lo
g(
λ
⋅

L λ

/ L
su
n
)
0.5 Kpc
20 Kpc
γ
3 10 100 300
7
8
10
λ [µ m]
0.5 Kpc
20 Kpc
0.5 Kpc
20 Kpc
δ
0.5 Kpc
0.5 Kpc
20 Kpc
β
Figure 8. Top panels: SEDs of prototype disk galaxies at
varying the radius of the galaxy Rgal, going from 0.5 to 20 Gyr.
All the other parameters are kept fixed. We also show the SED
of the test galaxy calculated with the classical EPS technique.
Bottom-left panel: contribution to the total emission com-
ing from dusty MCs at varying Rgal. Bottom-right panel:
contribution to the total emission of the diffuse ISM for the
same set of radii Rgal.
ify the fraction fM of the gas present in form of diffuse
ISM. The task is not easy and to a certain extent be-
yond the aims of this study because it would require a
multi-component description taking into account all heat-
ing and cooling processes that transform atomic likely hot
gas into cool molecular gas. So, as already presented in
Sect. 5.1, we consider fM as a parameter, and, for the sake
of illustration, we adopt fM = 0.5. This means that half
of the gas is in the diffuse medium and half in the MCs.
Third, for the timescale t0 we assume ≃ 5 Myr which
roughly corresponds to the lifetime of the most massive
stars. This means that the heavily obscured part of young
stars lifetime is rather short. For the sake of illustration
we consider the case with inclination angle Θ = 60◦.
In Table 1, column (4), we summarize the set of pa-
rameters we have used to model our test disk galaxy.
In the same way we did for the ellipticals we calcu-
lated a sequence of models with Rgal going from 20 to
0.5 kpc, from very expanded to very compact systems.
In Fig. 8 we show the resulting SEDs (top panels α and
β) also with the spectrum calculated with the classical
EPS. In the bottom panels we show the emission in the
UV-optical region (bottom-left panel) coming from MCs
and the contribution to the total flux coming from the
diffuse ISM (bottom-right panel). The effect of the ra-
dius is the same as for ellipticals: for smaller galaxies,
higher optical depths, the stronger will be the extinction
of the UV-optical light. For the same reason the emission
of dust in the FIR will be stronger for the smaller dimen-
sions because of the higher density (bottom-right panel
of Fig. 8).
In the case of disk galaxies the degree of symmetry is
lower than for spheroidal systems as only azimuthal sym-
metry is conserved. In Fig. 9, we show the SED at varying
the radial scale lengths RMd and R
∗
d. In the four left pan-
els we keep fixed RMd and vary R
∗
d, the opposite in the
four right panels. Examining the four panels on the left,
we notice that once fixed RMd , the attenuation becomes
weaker going from low to high values of R∗d (panels α and
β). This is simply due to the fact that growing the value
of R∗d, more stars are distributed in the outer regions of
the galaxy and thus they are less obscured. It is worth
noticing how in our model disk galaxy the attenuation is
partially due to young MCs and partially to the diffuse
ISM. The ultimate reason of this is the low evaporation
time for dusty regions we have chosen for the model. In
panel γ we see the effect of attenuation on the emission
of MCs: again it is stronger for R∗d < R
M
d , because for
these values young dusty SSPs are confined in the inner
region
(
RMCd = R
∗
d
)
. The effect of varying the star scale
on the diffuse ISM emission (panel δ) is that this emis-
sion becomes weaker and cooler at the increasing of R∗d,
because more stars are distributed in the outer regions
of the galaxy weakly heating the ISM. Passing now to
the four right panels the above effects are reversed. R∗d is
fixed and the obscuration of the stellar light by the dif-
fuse ISM (panels α and γ) grows at the increasing of RMd ,
because the ISM shifts toward the outer regions more and
more wrapping the stellar component. In the same way
the emission of the ISM becomes stronger at the increas-
ing of RMd , because dust is more evenly distributed in the
regions occupied by stars.
c© 2005 RAS, MNRAS 000, 000–000

Galaxies spectra with interstellar dust 17
0.5 1 2
8
9
10
lo
g(
λ
⋅

L λ

/ L
su
n
)
Rd
*
= 9 Kpc
Rd
*
= 1 Kpc
classical EPS
αRd
M
= 5 Kpc
0.1 1 3
7
λ [µ m]
lo
g(
λ
⋅

L λ

/ L
su
n
) Rd
*
= 9 Kpc
Rd
*
= 1 Kpc γ
10 100 300
8
9
10
λ [µ m]
Rd
*
= 9 Kpc
Rd
*
= 1 Kpc
δ
Rd
*
= 1 Kpc
Rd
*
= 9 Kpc
MCs β
0.5 1 2
8
9
10
lo
g(
λ
⋅

L λ

/ L
su
n
)
Rd
M
= 9 Kpc
Rd
M
= 1 Kpc
classical EPS
αRd
*
= 5 Kpc
0.1 1 3
6.5
7
λ [µ m]
lo
g(
λ
⋅

L λ

/ L
su
n
) Rd
M
= 1 Kpc
Rd
M
= 9 Kpc γ
10 100 300
8
9
10
λ [µ m]
Rd
M
= 1 Kpc
Rd
M
= 9 Kpc
δ
Rd
M
= 9 Kpc
Rd
M
= 1 Kpc
MCs β
Figure 9. Four Left Panels: in panels α and β we show the SEDs of the 13 Gyr test disk galaxy with fixed RMd = 5 kpc. The
radial scale length R∗d is varied from 1 to to 9 kpc. The following values are considered, 1, 2, 3, 4, 5, 7 and 9 kpc. The SED obtained
with the classical EPS technique is also shown in panel α for the sake of comparison. The dashed line in panel β represents the
contribution of MCs to the total flux in the FIR. In panel γ we show the effect of varying R∗d on the MCs flux. In particular the
uv-optical/NIR spectral region is shown. Finally, in panel δ we plot the contribution of the diffuse ISM to the total emission. Four
Right Panels: the same as above but for fixed R∗d and varying R
M
d . R
M
d goes from 1 to 9 kpc.
0.5 1 2
9
10
lo
g(
λ
⋅

L λ

/ L
su
n
)
zd
*
= 1.5 Kpc
zd
*
= 0.1 Kpc
classical EPS
αzd
M
= 0.4 Kpc
0.1 1 3
7
λ [µ m]
lo
g(
λ
⋅

L λ

/ L
su
n
) zd
*
= 1.5 Kpc
zd
*
= 0.1 Kpc
γ
10 100 300
8
9
λ [µ m]
zd
*
= 1.5 Kpc
zd
*
= 0.1 Kpc
δ
zd
*
= 0.1 Kpc
zd
*
= 1.5 Kpc
MCs β
0.5 1 2
8
9
10
lo
g(
λ
⋅

L λ

/ L
su
n
)
zd
M
= 0.1 Kpc
zd
M
= 1.5 Kpc
classical EPS
αzd
*
= 0.4 Kpc
0.1 1 3
7
λ [µ m]
lo
g(
λ
⋅

L λ

/ L
su
n
) zd
M
= 0.1 Kpc
zd
M
= 1.5 Kpc γ
100 200
10
λ [µ m]
zd
M
= 0.1 Kpc zd
M
= 1.5 Kpc
δ
zd
M
= 1.5 Kpc
zd
M
= 0.1 Kpc
MCs β
Figure 10. Four Left Panel: in panels α and β we show the SEDs of the test disk galaxy of 13 Gyr for the fixed value of the
vertical scale length zMd = 0.4 kpc. The scale length z
∗
d is varied from 0.1 to to 1.5 kpc. The considered values for z
∗
d are 0.1,
0.25, 0.4, 0.55, 0.7, 1 and 1.5 kpc. The SED obtained with the classical EPS technique is also shown in panel α for the sake of
comparison. The dashed line in panel β represents the emission of the MCs in the FIR. In panel γ we show the effect of varying
z∗d on the MCs flux. In particular the uv-optical/NIR spectral region is shown. Finally, in panel δ we plot the contribution of the
ISM to the total emission. Four Right Panels: the same as above but for z∗d fixed and z
M
d varying from 0.1 to 1.5 kpc.
In Fig. 10 we show the effect of the vertical scale
lengths. As we did for the radial scales, we consider two
cases: first we fix zMd and let z
∗
d vary, second we fix z
∗
d
and let zMd change. In the four left panels z
M
d is fixed. At
increasing z∗d the extinction becomes lower, because more
stars are distributed in the outer regions of the galaxy (α
panel). This effect of growing attenuation is the same
on young dusty SED (panel γ) that in this model are
distributed with the same vertical scale of bare stars. The
ISM emission tends to be stronger for lower values of z∗d
(panel δ). In the four right panels of Fig. 10 the vertical
scale of stars z∗d is kept fixed. In this case the effect of
varying the other parameter is smaller: in particular in
panel δ we can see as the emission of the diffuse ISM
grows to a maximum and then decreases. The maximum
is reached when the scale lengths of stars and dust are
similar. If zMd ≪ z∗d , or zMd ≫ z∗d the emission tends to
be lower.
c© 2005 RAS, MNRAS 000, 000–000

18 L. Piovan, R.Tantalo & C. Chiosi
2 5 10 13 15
2
10
50
Time [Gyr]
M
su
n/y
r
0.1 1 10 100 500
6
8
9
10
λ [µ m]
lo
g(λ

⋅

L λ

/ L
su
n) 100 Myr
1.5 Myr
0.5 1 10 100 300
λ [µ m]
1.5 Myr
100 Myr
lo
g(λ

⋅

L λ

/ L
su
n)
100 Myr
1.5 Myr
1.5 Myr 100 Myr
Figure 11. Top-left Panel: star formation history of the
prototype disk galaxy with ML = 1011M⊙. The age of the 13
Gyr model whose SEDs are examined in detail is marked. Top-
right Panel: SEDs of the galaxy at varying the evaporation
time scale t0 from 1.5 Myr to 100 Myr. The considered values
are 1.5, 4.5, 15, 30, 60 and 100 Myr. All the other parameters
are kept fixed. We also show the SED calculated with the
classical EPS technique. It steeply declines for wavelengths
longer than 2µm. Bottom-left Panel: contribution to the
total emission from dusty MCs at varying t0. Bottom-right
panel: contribution to the total emission of the diffuse ISM
at varying t0.
In Fig. 11, we show the effect of varying the evap-
oration time t0 of young dusty SSPs. The longer the
time scale, the higher is the effective extinction of the
UV-optical light because the energy of newly stars is ob-
scured for a longer time (top-left panel), and the higher
is the amount of energy shifted toward the FIR by MCs
(bottom-left panel). As for the elliptical galaxy of 0.15
Gyr, at increasing t0 the emission of the diffuse ISM de-
creases and becomes cooler, because the intensity of the
local radiation field is weaker.
Finally, we compare the SEDs of our disk galaxy at
varying the amount of gas in the diffuse ISM with respect
to that in dusty MCs, using the parameter fM . This is
shown in Fig. 12. The effect of fM can be easily seen in
the top panels (α and β). Increasing fM , i.e. the amount
of gas in the diffuse ISM, strongly affects the SED. The
higher the amount of gas, the stronger is the obscura-
tion, and the higher is the flux in the FIR. As expected,
increasing the amount of gas in the diffuse ISM makes
stronger also the effect of attenuation on the light from
young stars (bottom left panel). The emission of the dif-
fuse ISM becomes also cooler with more gas in the diffuse
ISM, because of the weaker radiation field heating the
grains (bottom right panel).
5.2.3 Starburst galaxies
Starburst galaxies are objects that show a recent and
transient increase in SFR by a large factor (ten at least).
The burst is often confined to a few hundred parsecs near
the nucleus, although bursts extending to wider regions
are easy to find. The high SFR of starburst galaxies is
9
10
lo
g(λ

⋅

L λ

/ L
su
n)
fM=0.9
fM=0.1
classical EPS
α
0.1 1 3
6
7
8
λ [µ m]
lo
g(λ

⋅

L λ

/ L
su
n)
fM=0.9
fM=0.1
γ
10 100 300
8
9
10
λ [µ m]
fM=0.1
fM=0.9
δ
fM=0.1
fM=0.9
β
Figure 12. Top panels: SEDs of model disk galaxies at vary-
ing the fraction of gas in the diffuse ISM fM respect to the
total amount of gas. The range of values goes from 0.1 to 0.9.
All the other parameters are kept fixed. The considered val-
ues are 0.1, 0.3, 0.5, 0.7 and 0.9. We also show the SED of the
prototype spiral calculated with the classical EPS technique.
Bottom-left panel: contribution to the total emission com-
ing from dusty MCs at varying fM . Bottom-right panel:
contribution to the total emission of the diffuse ISM for the
same set of fM .
of great interest, because it is the local analog of high
redshift galaxies during their formation, involving strong
star formation in dust rich environments.
The light emitted by newly born stars in these star
forming galaxies is absorbed by dust and re-emitted in
the FIR/MIR. One of the main problem is to disentan-
gle whether the dominant energy source heating dust is
a starburst or an AGN. In our models, AGNs as energy
source is not yet included. Future work is planned to in-
clude the AGN contribution thus providing a more real-
istic description of these systems. In Table 1, column (5),
we summarize the set of parameters we have adopted to
model our prototype starburst galaxy.
To simplify things we take a spherical model for
which we adopt a long infall time scale and relatively
low star formation efficiency, i.e. τ = 9 and ν = 1. In
this model star formation is maximum at about 3 Gyr,
slowly declines up the the present time (13 Gyr) and
never ceases. It is a sort of late type galaxy but for the
spherical symmetry. As already mentioned the specific
shape is irrelevant for the purposes of this experiment.
At the age of 12.95 Gyr (not long ago) we introduce a
short burst whose intensity is 30 times stronger than the
current SFR at the age of 12.95 Gyr.
Star formation in starbursters is tightly related to
reddening and obscuration which render the detailed in-
terpretation of their continuum and emission-lines very
complicate. Starbursters are known to possess a flat
obscuration law (with no bump) as pointed out by
Calzetti et al. (1994), who considered a mix of stars and
dust and took the effects by scattering into account. This
obscuration law is very puzzling, because starbursters are
typically objects of high metallicity and so we would ex-
pect an extinction law similar to that of the MW. It
c© 2005 RAS, MNRAS 000, 000–000

Galaxies spectra with interstellar dust 19
is worth noticing, however, that the dust obscuration
in galaxies is not strictly equivalent to dust extinction
in stars. The latter measures the optical depth of the
dust between the observer and the star, whereas the for-
mer corresponds to a more general attenuation, to which
many effects may concur such as those by extinction,
scattering, and geometrical distribution of the dust rela-
tive to the emitters (Calzetti 2001). Because of this, there
is nowadays much debate on the origin of the flat law. Is it
due to geometrical effects (Granato et al. 2000), or pecu-
liar distribution and the composition of the dust in star
forming environments? Furthermore, there is some evi-
dence that reddening by gas and stars are systematically
different (Calzetti 2001), as stars are on average less red-
dened than ionized gas. Another point is that both stars
and ionized gas are contrasted by a foreground-like dis-
tribution of dust. This could be due to dust being pref-
erentially associated to the star forming regions. In ad-
dition to this, the evidence of different amounts of gas
mass along different lines of sight, could mirror a den-
sity and reddening structure. These considerations led
Calzetti (2001) to propose a model aimed at explaining
many observational constraints: newly born stars form in
a central high density region immersed in a bath of older
stars and dust.
In our models we can easily deal with this bath of
old stars and dust: setting r∗c = r
M
c (in spherical models)
and/or R∗d = R
M
d (in disks), the region of dust coincides
with the region in which stars are present. We can also
allow for different scales between old and newly born stars
so that centrally confined burst can be superimposed to
a ”normal” galaxy, setting r∗c 6= rMCc or R∗d 6= RMCd .
However, as in all this paper, we will simply put r∗c =
rMCc or R
∗
d = R
MC
d , leaving this point aside because it
would require a deep investigation beyond the purposes
of this study.
As for our starburster galaxy we have adopted the
spherical symmetry, all scale lengths are the same as in
model for early-type galaxies. In Fig. 13 we show the ef-
fect on the total SED of varying the galaxy radius Rgal.
The effect is the same as already found for the model
elliptical and disk galaxies: the smaller the galaxy, the
higher is the optical depth and the stronger is the atten-
uation of the UV-optical light. The emission of dust in
the FIR is stronger for compact objects because of the
higher density (bottom-right panel of Fig. 13.
In Fig. 14 we show how the total SED changes at
varying the scale radii. Their effects on the emission of
diffuse ISM and young dusty MCs are also highlighted.
Two cases are considered. First, the ratio r∗c/r
M
c is fixed
and r∗c is let vary over a wide range of values (four left
panels). Second, r∗c is fixed and r
M
c is let change (four
right panels). In both groups of four, panels α and β dis-
play the total SED, the old SED without dust, the contri-
bution of MCs for the extreme values of the parameters,
whereas panels γ and δ show the contribution of MCs
and diffuse ISM to the total flux. In the four left panels
of Fig. 14 we notice that the attenuation is stronger when
r∗c and r
M
c are the lowest, both for stars (panel α) and
MCs (panel γ). The emission of diffuse ISM grows for
more compact systems, because the radiation field heat-
ing the grains is stronger in the central regions of high
0.5 1 2
8
9
10
11
lo
g(
λ
⋅

L λ

/ L
su
n
)
0.5 Kpc
20 Kpc
classical EPS
α
0.1 1 3 10 100
7
8
9
10
11
12
λ [µ m]
lo
g(
λ
⋅

L λ

/ L
su
n
)
0.5 Kpc
20 Kpc
γ
3 10 100 300
8
9
11
λ [µ m]
0.5 Kpc
20 Kpc
0.5 Kpc
20 Kpc
δ
0.5 Kpc
20 Kpc
0.5 Kpc
β
Figure 13. Top panels: SEDs of the model star-burst galaxy
at varying Rgal from 0.5 to 20 Gyr. The values are the same
as for the model elliptical and spiral. All the other parame-
ters are kept fixed. The SED derived with the classical EPS
is also shown. Bottom-left panel: contribution to the to-
tal emission by dusty MCs at varying Rgal. Bottom-right
panel: contribution to the total emission by the diffuse ISM
at varying Rgal.
10
11
lo
g(λ

⋅

L λ

/ L
su
n)
fM=0.9
fM=0.1
classical EPS
α
0.1 1 3
7.7
8
8.5
λ [µ m]
lo
g(λ

⋅

L λ

/ L
su
n)
fM=0.9
fM=0.1
γ
10 100 300
8.5
9
10
11
λ [µ m]
fM=0.1
fM=0.9
δ
fM=0.1
fM=0.9
β
Figure 15. Top panels: SEDs of the model star-burst galaxy
at varying the fraction of gas in the diffuse ISM fM with re-
spect to the total amount of gas. All the other parameters
are kept fixed. The considered values for fM are 0.1, 0.3, 0.5,
0.7 and 0.9. We also show the SED calculated with the classi-
cal EPS technique. Bottom-left panel: contribution to the
total emission by dusty MCs at varying fM . Bottom-right
panel: contribution to the total emission by the diffuse ISM
at varying fM .
density (panel δ). In the four right panels where r∗c is
fixed, there is a small effect of varying rMc , because the
emission is clearly dominated from the MCs component.
For higher values of rMc , the system is more obscured
(panel γ), because there is more dust in the outer regions
to screen the stellar light.
We compare the SEDs of our model starburster at
c© 2005 RAS, MNRAS 000, 000–000

20 L. Piovan, R.Tantalo & C. Chiosi
0.5 1 2
8
9
10
11
lo
g(
λ
⋅

L λ

/ L
su
n
) rc
M
= 45 Kpc
r
c
M
= 0.5 Kpc
r
c
M
= 45 Kpc
r
c
M
= 0.5 Kpc
classical EPS
αrc
* /r
c
M
= 0.2
0.1 1 3
8
9
λ [µ m]
lo
g(
λ
⋅

L λ

/ L
su
n
)
r
c
M
= 0.5 Kpc
r
c
M
= 45 Kpc
γ
10 100 300
8
9
10
11
λ [µ m]
r
c
M
= 45 Kpc
r
c
M
= 0.5 Kpc
δ
r
c
M
= 45 Kpc
r
c
M
= 0.5 Kpc
β
0.5 1 2
8
9
10
11
lo
g(
λ
⋅

L λ

/ L
su
n
) rc
M
= 0.1 Kpc
r
c
M
= 100 Kpc
r
c
M
= 0.1 Kpc
r
c
M
= 100 Kpc
classical EPS
αr
c
*
= 5 Kpc
0.5
8.5
λ [µ m]
lo
g(
λ
⋅

L λ

/ L
su
n
)
r
c
M
= 100 Kpc
r
c
M
= 0.1 Kpc
γ
3 10 100 300
8
10
λ [µ m]
r
c
M
= 0.1 Kpc
r
c
M
= 100 Kpc
δ
r
c
M
= 0.1 Kpc
r
c
M
= 100 Kpc
β
Figure 14. Four Left Panels: in this group panels α and β show the SEDs of the model starburst at the age of 13 Gyr for fixed
value of the ratio r∗c/r
M
c =0.2. The radial scale length r
∗
c is let varied from 0.1 to to 9 kpc. The extreme values are marked with
the corresponding rMc . The SED obtained with the classical EPS is also shown for the sake of comparison. The contribution of
MCs to the total flux is also shown for the extreme values. In panel γ we show the MC flux in the UV-optical/NIR and in panel
δ we plot the contribution of the diffuse ISM to the total emission. Four Right Panels: the same as above but for r∗c fixed and
varying rMc .
2 5 10 13 15
2
10
50
Time [Gyr]
M
su
n/y
r
0.1 1 10 100 500
7.5
8
9
10
11
λ [µ m]
lo
g(λ

⋅

L λ

/ L
su
n) 100 Myr
1.5 Myr
0.5 1 10 100 300
λ [µ m]
100 Myr
1.5 Myr
lo
g(λ

⋅

L λ

/ L
su
n)
100 Myr
1.5 Myr
1.5 Myr 100 Myr
Figure 16. Top-left panel: star formation rate of the model
star-burst galaxy of ML = 1011M⊙ on which the age of 13 Gyr
is marked. Top-right panel: SEDs at varying the evaporation
time scale t0, namely 1.5, 4.5, 15, 30, 60 and 100 Myr. All the
other parameters are kept fixed. We also show the classical
SED (dotted line). Bottom-left panel: contribution to the
total emission by dusty MCs at varying t0. Bottom-right
panel: contribution to the total emission by the diffuse ISM
at varying t0.
varying the amount of gas in the diffuse ISM. The re-
maining part of the gas is distributed among the dusty
MCs. In Fig. 15 we compare SEDs obtained with different
amounts of gas in the diffuse ISM, varying the parame-
ter fM . Increasing the amount of gas in the diffuse ISM
makes stronger the extinction of the light from old and
young stars, whereas it makes higher and cooler the FIR
flux, because of the higher density and the weaker radia-
tion field.
Finally, in Fig. 16, we show the effect of varying the
evaporation time scale of young dusty SSPs. The effect is
the same as in our model elliptical of 0.15 Gyr (see Fig. 6)
For longer time scales, the attenuation of the UV-optical
light becomes stronger (top-right panel), and the amount
of energy shifted toward the MIR/FIR by MCs becomes
higher (bottom-left panel).
6 LATE-TYPE GALAXIES OF THE LOCAL
UNIVERSE
In this section, using our models we seek to reproduce
the SEDs of two late-type galaxies of the Local Universe,
namely M100 and NGC6946.
In Table 1, columns (6) and (7), we summarize the
parameters characterizing the models that best match
the properties of the two galaxies under consideration.
Part of the parameters are based on observational hints,
the others are suitably varied to get agreement between
observational and theoretical SEDs. Specifically, the ge-
ometrical parameters and distances are from literature
and kept constant. The gas mass in the ISM and MCs
is let vary within the range indicated by current obser-
vational data. The star formation efficiency ν and infall
time scale τ are also let vary around the typical values
currently estimated for spiral galaxies. Finally the evap-
oration timescale t0 and the set of dusty SSPs in our
library are free parameters.
M100. This Sbc spiral galaxy is one of the most
important members of the Virgo Cluster, characterized
by two huge and luminous spiral arms and many other
smaller ones. The redshift of the galaxy, taken from NED1
1 http://nedwww.ipac.caltech.edu/.
c© 2005 RAS, MNRAS 000, 000–000

Galaxies spectra with interstellar dust 21
0.1 1 10 100 1000
6.5
7
8
9
10
11
11.5
λ [µ m]
log
(λ
⋅

L λ

/ L
su
n)
Figure 17. SED of the modelled Sbc spiral galaxy M100
at the age of 13 Gyr (continuous line). We represented
also the old SED with classical EPS (dotted line), the
emission of the diffuse ISM (dot-dashed line) and the
emission from young dusty SSPs (dashed line). Data for
M100 are taken from Buat et al. (1989, UV), Donas et al.
(1987, UV), RC3 catalogue of de Vaucouleurs et al. (1992,
UBVRI), de Jong & van der Kruit (1994, BVRIHK),
2MASS (Jarrett et al. 2003, JHK), IRAS (Soifer et al.
1989; Moshir & et al. 1990) and, finally, Stark et al. (1989,
FIR).
(Nasa/Ipac Extragalactic Database) is z = 0.00524. Us-
ing the Hubble constant H0 = 72 km/s/Mpc, it corre-
sponds to a distance of 21.8 Mpc. Shapley et al. (2001),
who performed a thorough search in literature of the
distances for the spiral galaxies of their sample, re-
port for NGC 4321 the distance of 16.1 Mpc, based on
Cepheid distance by Freedman et al. (1994) and H0 = 75
km/s/Mpc. We adopt here for the distance the average
of the two estimates, i.e. 19 Mpc. The major and minor
diameters of the galaxy in arcmin (NED) are 7.4′ × 6.3′.
Taking the average dimension of 7′, we obtain the linear
radius Rgal = 19 Kpc. Following Gnedin et al. (1995),
Knapen & Beckman (1996) and Beckman et al. (1996)
we adopt the inclination angle Θ = 27◦ and we assume
that both stars and dust have the same radial and vertical
scale lengths of 5 and 0.5 kpc, respectively.
The star formation history of M100 is derived as-
suming the total baryonic mass of 2 · 1011M⊙, ν = 0.7
and τ = 4 Gyr. With this choice, the star formation
never stops: it starts small, grows to a maximum and
then smoothly declines. We remain with the following
parameters to adjust: the gas mass in the diffuse ISM
and in MCs, the evaporation time t0 and the library of
young dusty SSPs. We may also slightly vary the radial
and vertical scale lengths with respect to current esti-
mates. For the gas masses we adopt the values given by
Young et al. (1989) based on HI and H2, According to
Young et al. (1989), MH2 = 0.77 ·Mg , where Mg is the
total gas mass. It means that this galaxy is dominated
by the molecular component. A good fit of the obser-
vational SED is obtained adopting the fractionary gas
mass in MCs fM = 0.35. For the evaporation time we
find t0 = 5Myr, consistent with a dust-poor star form-
ing medium in which the first supernovae explosions in
the newly born stellar populations evaporate the parental
gas. The library of young SSPs best suited to M100 (and
the other spiral as well) is characterized by the optical
depth τ = 35, R = 5, and high bc abundance. Nothing
can be said for the ionization state of PAHs. We adopt
the case with the complete treatment of the ionization
state. Only the detailed spectrum in the MIR region may
help clarifying the issue. It is worth noticing that for spi-
rals, more extended and cooler MCs with R = 5 fit the
FIR emission better than MCs with R = 1. In Fig. 17 we
show our best fit of the observational data. The result is
remarkably good.
NGC 6946 is a Sc/Scd nearby galaxy, highly ob-
scured by the interstellar matter of our galaxy, as it is
quite close to the Galactic plane and it is seen nearly face-
on. However, the inclination angle is uncertain due to the
global asymmetry (Blais-Ouellette et al. 2004). We adopt
Θ = 35◦ (see also Bonnarel et al. 1988; Carignan et al.
1990; Oey & Kennicutt 1990). The distance to NGC 6946
is uncertain and going from 5 (de Vaucouleurs 1979) to
10 Mpc (Rogstad et al. 1973). Our distance to this galaxy
has been taken from Shapley et al. (2001) who give 5.5
Mpc as a mean value based on previous studies. From
the NED online catalogue, the diameters of the galaxy
in arcmin are 11.5′ × 9.8′. Adopting the average dimen-
sion of 10.5′, we obtain the radius Rgal = 10 Kpc. Ac-
cording to Tacconi & Young (1986), the galaxy has some
evidence of a spiral structure extending beyond 20 kpc
with HI emission out to 30 kpc. However they adopted
the distance of 10.1 Mpc, that is two times longer than
the recent value proposed by Shapley et al. (2001) that
we have adopted here. Taking 5.5 Mpc, the radius is
Rgal = 13 Kpc consistent with the Shapley et al. (2001)
results and the NED diameters. The radial scale lengths
of stars and gas are also taken from Tacconi & Young
(1986), however rescaled to our shorter value for the dis-
tance to the galaxy. We adopt the radial scale length of
5 kpc, and for the scale height we use the same value
of 1 kpc proposed by Silva et al. (1998). As far as the
fraction of total gas embedded in young MCs is con-
cerned, the question is controversial. Young et al. (1989)
reports MHI/MH2 = 2.18: this means that only 1/3 of
the gas is in molecular form, in good agreement with
the results by Young & Knezek (1989) on the molecular
to atomic gas ratio for the morphological types Sc/Scd.
Tuffs et al. (1996) found that the bulk of the FIR lu-
minosity arises from a diffuse disk component. How-
ever, Devereux & Young (1993) reports NGC 6946 as a
galaxy where the molecular gas dominates the interstel-
lar medium and the thermal emission is explained mainly
with a warm dust component heated from young massive
stars, a result confirmed in Malhotra et al. (1996). A re-
cent work by Walsh et al. (2002) confirms the importance
of the molecular component in NGC 6946, almost as mas-
sive as the atomic one, giving the ratio MH2/MHI = 0.57,
which is high with respect to other galaxies of the same
morphological type. We find that the observational SED
is best reproduced if the molecular component is about
as massive as the atomic one. The star formation history
c© 2005 RAS, MNRAS 000, 000–000

22 L. Piovan, R.Tantalo & C. Chiosi
0.1 1 10 100 1000
6
7
8
9
10
11
11.5
λ [µ m]
log
(λ
⋅

L λ

/ L
su
n)
Figure 18. SED of the modelled Scd spiral galaxy NGC6946
at the age of 13 Gyr (continuous line). We represented also
the old SED with classical EPS (dotted line), the emission
of the diffuse ISM (dot-dashed line) and the emission from
young dusty SSPs (dashed line). Data for NGC 6946 are taken
from Rifatto et al. (1995, UV), de Vaucouleurs et al. (1992,
BV), ISO (Roussel et al. 2001, MIR), IRAS Rice et al. (1988,
MIR and FIR), Engargiola (1991, FIR), Devereux & Young
(1993, FIR), Tuffs et al. (1996); Tuffs & Gabriel (2003, FIR)
and Silva (1999).
of NGC 6946, that exhibits a moderate starburst activ-
ity, has been calculated with a baryonic mass similar to
M100 (1.2 · 1011M⊙, ν = 0.7 and τ = 5).
In Fig. 18, we show the result of our fit to the data
for NGC 6946. The evaporation time t0 is very short, 3
Myr, and the library of dusty SSPs is the same as for
M100. As compared to M100, the agreement with the
MIR is better, even if MIR spectra would allow a better
comparison between theory and observations.
7 EARLY-TYPE GALAXIES OF THE
LOCAL UNIVERSE
In this section we present two old early-type galaxies of
the Local Universe, namely NGC 2768 and NGC 4491,
and our attempts to reproduce their SEDs. In Table 1,
columns (8) and (9), we summarize the values of the pa-
rameters we have chosen. The number of parameters is
smaller than for disk galaxies. First because of the higher
degree of symmetry, and second because parameters like
t0 and fM have no role. The star formation ceased long
ago after the onset of the galactic wind, no young stars
in dusty MCs are present (t0 = 0) and all gas (if any) is
in the diffuse ISM (fM = 1). There is however, a new pa-
rameter to consider, i.e. the fraction fr of the gas contin-
uously ejected by dying and evolved stars (mostly RHB)
that is still retained in the galaxy (see Sect. 5.2.1 for de-
tails).
NGC 2768 is an elliptical galaxy of morphological
type E6 at the distance of 21.5 Mpc (Takagi et al. 2003).
As noticed by Takagi et al. (2003), this galaxy has been
detected in the sub-mm range of wavelengths thus pro-
0.1 1 10 100 1000
5
6
7
8
9
10
11.5
λ [µ m]
lo
g(λ

⋅

L λ

/ L
su
n
)
Figure 19. SED of the modelled E6 elliptical galaxy
NGC2768 at the age of 13 Gyr (continuous line). We rep-
resented also the old SED with classical EPS (dot-dashed
line) and the emission of the diffuse ISM (dashed line).
Data for NGC 2768 are taken from Longo et al. (1991,
far-UV), (de Vaucouleurs et al. 1992, UBV), NED database,
Frogel et al. (1978, JHK), IRAS Moshir & et al. (1990, MIR
and FIR) and NED database and, finally, Wiklind & Henkel
(1995, sub-mm).
viding a better constraint on the dust emission. Data for
this galaxy have been taken from the literature as listed
in Fig. 19. As in Takagi et al. (2003), all the data have
been corrected where it was necessary to be consistent
with the galaxy observed as a whole, even if there is a
certain amount of error for the IUE data of Longo et al.
(1991) that correspond to a small aperture in the cen-
ter of the galaxy. The diameters of the galaxy in arcmin
(NED) are 8.1′ × 4.3′ and using an average dimension of
6′, we obtain a radius of the galaxy of about Rgal = 20
Kpc.
The parameters chosen to model the SFH are as fol-
lows: the infall time scale is τ=0.1 Gyr, the exponent for
the star formation law is k=1 as in Tantalo et al. (1996,
1998), whereas the efficiency is ν=2. In Fig. 20 we show
the SFH with other quantities derived by the chemical
code. The onset of the galactic wind takes place at about
1.1 Gyr. The scale lengths of stars and gas have been
fixed as for the prototype elliptical of Sect. 5.2.1.
Finally, in Fig. 19, we show the theoretical SED and
its comparison with the observational data. Agreement is
excellent from the UV to FIR. Note the strong reduction
factor for the gas content.
NGC 4494 is a roughly spherical elliptical galaxy
of the morphological type E1. For this galaxy the NED
catalog reports the redshift z = 0.00451 corresponding to
a distance of about 19 kpc, using H0 = 72 km/s/Mpc.
Temi et al. (2004) report from the LEDA catalog a dis-
tance of about 21.28 Mpc. We choose the average distance
between the two determinations, i.e. 20 Mpc. The diam-
eters of the galaxy in arcmin (NED) are 4.8′ × 3.5′ and
using an average dimension of 4.2′, we obtain a dimension
of about Rgal = 12 Kpc.
c© 2005 RAS, MNRAS 000, 000–000

Galaxies spectra with interstellar dust 23
10
100
300
SF
R
[M
su
n
/y
r]
SFR
1 5 10 13
0
0.4
0.8
1.2
1.6
2
2.4
Age (Gyr)
M
st
ar
,

M
ga
s
&
M
L
(in
10
11

M
su
n
)
Mgas
M
star
ML
1 5 10 13
0
0.2
0.4
0.6
0.8
1
Age (Gyr)
M
st
ar
/M
L
&
M
ga
s/M
L
Mgas/ML
M
star/ML
0
0.02
0.04
0.06
0.08
Z
&
<Z
>
<Z>
Z
Figure 20. Basic quantities of the chemical model for the el-
liptical galaxy NGC2768 as function of the age: the top left
panel shows the star formation rate in M⊙/yr; the top right
panel displays the maximum (Z, solid line) and mean metal-
licity (〈Z〉); the bottom left panel shows the mass of living
stars Mstar (solid line), the gas mass Mgas (dotted line), and
the total mass of baryons ML (dashed line); finally the bot-
tom right panel displays the ratios Mstar/ML (solid line) and
Mgas/ML (dotted line). All masses are in units of 1011 M⊙.
Ages are in Gyr.
0.1 1 10 100 1000
5
6
7
8
9
10
11.5
λ [µ m]
log
(λ ⋅

L λ

/ L
su
n)
Figure 21. SED of the modelled E6 elliptical galaxy
NGC4494 at the age of 13 Gyr (continuous line). We rep-
resented also the old SED with classical EPS (dot-dashed
line) and the emission of the diffuse ISM (dashed line).
Data for NGC4494 have been taken from Rifatto et al. (1995,
far-UV), de Vaucouleurs et al. (1992, UBV), NED database,
Gavazzi & Boselli (1996, UBVJHK), 2MASS (Jarrett et al.
2003, JHK), IRAS (Moshir & et al. 1990, MIR and FIR) and
ISO (Temi et al. 2004).
The SFH and the evolution in metallicity of
NGC4494 are calculated in the same way as for
NGC2768, only with a slightly different value of the bary-
onic mass. The scale lengths are the same as for the other
elliptical. In Fig. 21 we show the result of our fit. The
agreement is good. The main reason of uncertainty is the
correction we made for the IUE UV-data of Rifatto et al.
(1995). As pointed in Takagi et al. (2003), only knowing
the true UV profile it is possible to properly correct these
IUE data that cover only a small region in the central re-
gion of the galaxy. Finally, the same remark on the gas
content made for the other elliptical can be made also
here.
8 STARBURST GALAXIES
Finally, we present models for two well known and thor-
oughly studied star-burst galaxies of the local universe,
namely Arp220 and M82. In Table 1, columns (10) and
(11), we summarize the values of the parameters we chose
to reproduce the SEDs of these galaxies. We adopt the
spherical geometry to describe both objects. As for ellipti-
cals, the number of parameters to deal with is much lower
than for disk galaxies. The situation, however, is different
from the case of ellipticals because now the parameters
fM and particular t0 play in the fit of the observational
data.
Arp220. Arp 220 is the brightest object in the
Local Universe. There is nowadays the general con-
sensus that Arp 220 is a starburst-dominated galaxy
and not an AGN-dominated object (Lutz et al. 1996;
Genzel et al. 1998; Lutz et al. 1999; Rigopoulou et al.
1999; Tran et al. 2001). Recently, Spoon et al. (2004) re-
analyzing the ISO MIR spectrum of Arp 220 confirm the
starburst-dominated hypothesis, suggesting that the IR
luminosity should be be probably powered by the star-
burst activity in extremely dense regions, even if the AGN
contribution cannot be definitely ruled out because of the
high extinction.
The redshift of the galaxy, taken from the NED
database is z = 0.01813. Using the Hubble constant
H0 = 72 km/s/Mpc, it corresponds to a distance of
about 76 Mpc. This value is fully consistent with the dis-
tances proposed in Soifer et al. (1987) and in Spoon et al.
(2004). The diameters of the galaxy in arcmin (NED)
are 1.5′ × 1.2′. Adopting the mean value of 1.35′, the
radius of the galaxy is of about Rgal = 16 − 17 Kpc.
Wynn-Williams & Becklin (1993) showed that almost all
the MIR flux of Arp220 comes from a small central re-
gion of about 5” aperture and this concentration of the
MIR emission has been confirmed by Soifer et al. (1999)
comparing the fluxes at a fixed MIR wavelength and vary-
ing the beam. For this reason we can quite safely use the
MIR data from small apertures even modelling the whole
galaxy.
The mass of molecular gas H2 in Arp220 according
to CO estimates is about 3·1010M⊙ (Solomon et al. 1997;
Scoville et al. 1997). Mundell et al. (2001) estimated the
nuclear column densities of H2 to be of the order of
NH2 = 2 − 4 · 1022cm−2. These values are comparable
to the mean HI column densities that are of the or-
der of NH = 1.5 · 1020Ts, with the spin temperature be-
tween 100 and 200 K. These column densities are likely
lower limits because of the uncertainty in the values of
Ts (Kulkarni & Heiles 1988), in the abundance of CO
(Frerking et al. 1982), in the excitation conditions and
optical depth, which all suggest us to adopt similar con-
c© 2005 RAS, MNRAS 000, 000–000

24 L. Piovan, R.Tantalo & C. Chiosi
0.1 1 10 100 1000
7
8
9
10
11
12
13
λ [µ m]
log
(λ ⋅

L λ

/ L
su
n)
Figure 22. SED of the model for the starburst galaxy
Arp220 at the age of 13 Gyr (continuous line). We repre-
sent also the old SED with classical EPS (dot-dashed line),
the emission of the diffuse ISM (dotted line) and, finally,
the emission of dusty MCs (dashed line). Optical and near
IR data are taken from RC3 catalog (de Vaucouleurs et al.
1992, UBV) and Jarrett et al. (2003, 2MASS - JHK).
The MIR fluxes are from Spinoglio et al. (1995, MIR),
Smith et al. (1989, MIR), Klaas et al. (1997, from MIR to
FIR), Wynn-Williams & Becklin (1993, MIR), Tran et al.
(2001, 5-16 µm ISOCAM-CVF spectrum). FIR and radio data
are from Rigopoulou et al. (1996, sub-mm), Eales et al. (1989,
UKIRT sub-mm), Dunne et al. (2000, SCUBA sub-mm),
Dunne & Eales (2001, SCUBA sub-mm). Other MIR/FIR
data are taken from Spoon et al. (2004).
tents for both atomic and molecular gas. We fix fM = 0.5.
The SFH history of Arp220 is modelled adding to the
current SFH (which peaked in past and ever since de-
creased) a very strong and short burst. The burst is ob-
tained by increasing the star formation of a factor of 60.
In Fig. 22 we show our best fit of Arp220, the agreement
is good. However, there are two points that need to be
clarified. First, we have no data of Arp220 in the near and
far UV. As outlined by Takagi et al. (2003), the data by
Goldader et al. (2002) are puzzling because, owing to the
large angular size of Arp 220 filling the field of view of the
instrument, the flux level of the sky (to be subtracted) is
highly uncertain. Second, to get satisfactory agreement
with observational data we had to extend the parame-
ter space, namely the scale radius has been lowered to
R = 0.5 and the τV = 40, this one in agreement with
Sturm et al. (1996) and Genzel et al. (1998). The ioniza-
tion of PAHs is fully considered, but it is worth noticing
that the ionization model does not bear very much on
the extinction curve we have adopted thanks to the low
carbon abundance and low contribution of PAHs.
There is another interesting point to note. Arp220 is
modelled as a 13 Gyr old galaxy with a strong burst su-
perimposed to a spiral-like SFH that reached a maximum
in the past and gently declines. This long history of star
formation slowly increases the metallicity well above the
solar value. For these high metallicities values, one should
(has to) use a MW-like extinction curve for dense regions
0.1 1 10 100 1000
6
7
8
9
10
11.5
λ [µ m]
log
(λ
⋅

L λ

/ L
su
n)
Figure 23. SED of the model for the starburst galaxy M82
at the age of 13 Gyr (continuous line). We represent also
the old SED with classical EPS (dot-dashed line), the emis-
sion of the diffuse ISM (dotted line) and the emission of the
dusty MCs (dashed line). Data are from de Vaucouleurs et al.
(1992, UBV), Johnson (1966, VRIJKL), Jarrett et al. (2003,
2MASS - JHK), Soifer et al. (1987, IRAS), Golombek et al.
(1988, IRAS), Rice et al. (1988, IRAS), Klein et al. (1988, FIR
and sub-mm), and Fo¨rster Schreiber et al. (2003).
to calculate the SED of young SSPs emerging from dusty
regions. This type of extinction curve is characterized by
a high abundance of carbon. We tried to fit the obser-
vational SED of Arp220 using the lowest available value
of bc, but the MIR emission was always too high and
the 10µm absorption features of silicates not as deep as
required. To obtain a good fit we had to use for young
dusty SSPs the extinction curve of the SMC, which is
poor of carbon. Similar result was found by Takagi et al.
(2003). There seems to be a point of contradiction, be-
cause the carbon-poor extinction curve of the SMC is
characteristic of a low metallicity environment, whereas
here we are dealing with a high metallicity one. Although
this point deserves careful future investigation, a plausi-
ble explanation could be that the high rate of type II su-
pernovae due to the strong burst alters the composition of
dust, growing the amount of silicates with respect to that
of carbonaceous grains. Another hypothesis is that this
high energy output of the star forming process destroys
molecules and small grains thus altering the distribution
of the grains. Finally the geometry of the system could
play a role.
M82. The central region of the irregular starburst
galaxy M82 seems to have suffered a strong gravitational
interaction about 108 years ago (Fo¨rster Schreiber et al.
2003) with its companion M81 and it shows a re-
markable burst of star formation activity. M82 is still
strongly interacting with M81 as proved by the com-
mon envelope of neutral hydrogen (Yun et al. 1993;
Ichikawa et al. 1995). The classical distance to M82 is
3.25±0.20 Mpc (Tammann & Sandage 1968) that makes
of M82 the nearest and most studied starburst galaxy
(see Shopbell & Bland-Hawthorn 1998, and references
c© 2005 RAS, MNRAS 000, 000–000

Galaxies spectra with interstellar dust 25
therein). For M82 data for the emission of PAHs in
the MIR region are available. The ISO-SWS data by
Sturm et al. (2000, private communication) cover a wide
region going from 2.4 to 45µm with different parts of a
SWS full grating scan that are observed with different
aperture sizes, going from 14” × 20” to 20” × 33”. The
problem is that with these small apertures it is not pos-
sible to observe the whole galaxy, but only part of it. In
our case the south-western star formation lobe. Recently,
Fo¨rster Schreiber et al. (2003, private communication)
observed M82 in the MIR range between 5.0 and 16µm
with ISOCAM on board of ISO. The total field of view
is 96” × 96”. It covers almost entirely the MIR sources
of M82 and it is more suitable to be used to model M82
as a whole. The mass of molecular gas for M82 is of the
order of 1−2·108M⊙, as derived from CO determinations
(Lo et al. 1987; Wild et al. 1992; Fo¨rster Schreiber et al.
2001). The estimates of the total mass of gas are of the
order of 109M⊙ (Solinger et al. 1977). For this reason we
use a parameter fM ∼ 0.8−0.9, with almost all the gas in
the diffuse ISM. In Fig. 23 we show the best fit obtained
for M82. The agreement with the data is good and the
main features of PAHs are well reproduced. The young
dusty SSPs used for this fit are characterized by the fol-
lowing parameters: R = 1, τV = 8, bc = 2 ·10−5 and MW
average ionization of PAHs. An interesting point is that
we found it difficult to reach the low level of flux in the
UV region. Even if data are highly uncertain, this could
be due to the model of MCs with uniform distribution of
dust, η = 1000 (see Piovan et al. 2006), we have adopted.
It might be possible that for M82, MCs with a shell-like
distribution of dust with more dust in the outer regions
and therefore with stronger attenuation of the flux from
young stars, are better suited to obtain a good fit in that
spectral region.
9 DISCUSSION AND CONCLUSIONS
In this paper, improving upon the standard EPS tech-
nique, we have developed theoretical SEDs of galaxies,
whose morphology goes from disk to spherical structures,
in presence of dust in the ISM. Properly accounting for
the effects of dust on the SED of a galaxy increases the
complexity of the problem with respect to the standard
EPS theory because it is necessary to consider the distri-
bution of the energy sources (the stars) inside the ISM
absorbing and re-emitting the stellar flux. This means
that the geometry and morphological type of the galaxy
become important and unavoidable ingredients of the
whole problem, together with the transfer of radiation
from one region to another. The emergent SEDs of our
model galaxies have been shown to reproduce very well,
even in details, the observational data for a few test galax-
ies of different morphological type. The model is versatile
and applicable to a large range of objects of astrophysical
interest at varying the star formation and chemical en-
richment histories, the geometrical shape or morphology
of the galaxies and the amounts of gas and dust contained
in their ISM.
Before concluding, it is worth mentioning a few
points of weakness that could be improved . First, the
chemical models we have adopted are from Tantalo et al.
(1996, 1998), whereas the chemical yields are from
Portinari et al. (1998). These models are state-of-the-art
in the study of the chemical evolution of galaxies. How-
ever, they do not include a proper description of the for-
mation/destruction of dust as for instance recently devel-
oped by Dwek (1998, 2005). Even if the dust content can
be related to the metallicity of the galaxy (see Sect. 5.1),
the relative proportions of the various components of the
dust would require the detailed study of the evolution of
the dusty environment and the complete information on
the dust yields (Dwek 1998, 2005; Galliano et al. 2005).
This would lead to a better and more physically sounded
correlation between the composition of dust and the star
formation and chemical enrichment history of the galaxy
itself. All this is missing in most galaxy models in which
dust is considered. The problem may be particularly se-
vere for high metallicity environments.
Second, the models for disk galaxies with central
bulge need to be tested against SEDs of local galax-
ies of intermediate type going from S0 to Sb/Sc, trying
to match some observational constraints, like the UV-
optical average colours (Buzzoni 2002, 2005).
Finally, many other physical ingredients can be im-
proved and/or considered. Just to mention a few, the
inclusion of the recent models of thermally pulsing AGB
stars with varying molecular opacities in the outer lay-
ers Marigo (2002), the extension of the SED to the radio
range, and the simulation of the nebular emission.
ACKNOWLEDGEMENTS
We would like to deeply thank A. Weiss for the many
stimulating discussions and for showing much interest in
our work. L.P. is pleased to acknowledge the hospitality
and stimulating environment provided by Max-Planck-
Institut fu¨r Astrophysik in Garching where part of the
work described in this paper has been made during his
visit as EARA fellow on leave from the Department of
Astronomy of the Padua University. This study has been
financed by the Italian Ministry of Education, University,
and Research (MIUR), and the University of Padua.
APPENDIX A: MATTER IN THE CYLINDER
BETWEEN V AND V ′
To calculate the number of H atoms contained in the
cylinder of matter between two generic volumes V =
V (i, j, k) and V ′ = V (i′, j′, k′) one has to know the total
gas mass in the cylinder
∫ V ′
V
ρM (l) dl (A1)
where ρM is the density profile of the diffuse medium,
given by the eqns. (7) or (9) or both, according to whether
we are dealing with a disk galaxy, a spherical galaxy or
a disk plus bulge one.
Normalizing the density to the central value, i.e.
ρ′ = ρM/ρ0M , and the radial distance to the radial
c© 2005 RAS, MNRAS 000, 000–000

26 L. Piovan, R.Tantalo & C. Chiosi
scale length for disks or core radius for spheroidal galax-
ies as appropriate, i.e. x = r/RMd or x = r/r
M
c ,
we may express the density profiles by means of di-
mensionless quantities. For a disk galaxy we have
ρ′(x) = exp (−x sin θ) exp
(
−x |cos θ| · RMd /zMd
)
which
depends only on the ratio RMd and z
M
d , whereas for a
spheroidal galaxy we have ρ′(x) =
[
1 + (x)2
]−γM .
In this way it is possible to calculate once for all the
mass contained in the cylinders between any two generic
volume elements of the galaxy, independently from the
mass of the galaxy, given the coordinate grid (nr, nθ, nΦ)
and ratio RMd /z
M
d (for disk galaxies only) or exponent γM
(for spheroidal galaxies). The integral of eqn. A1 is then
numerically evaluated.
APPENDIX B: THE DISTANCE R2
Following Silva (1999) the distance r2 (i, j, k, i′, j′, k′)
shortly indicated as r2 (V, V ′), which is de-
fined as volume averaged value of the square
of the distance between V (i′, j′, k′) and all the
points belonging to V (i, j, k), is r2 (V, V ′) =
∫ ∫ ∫
V
d2
(
V, V ′
)
r2 sin θdθdΦdr/V where d2 (V, V ′)
is given by d2 (V, V ′) = (ri′ sin θi′ − r sin θ cos Φ)2 +
(r sin θ sinΦ)2 + (ri′ cos θi′ − r cos θ)2 and the volume V
by V =
∫ ∫ ∫
V r
2 sin θdθdΦdr.
APPENDIX C: MATTER IN THE CYLINDER
BETWEEN V AND THE GALACTIC EDGE
The matter contained in the cylinder between a generic
element V and the edge of the galaxy extinguishes the
radiation emerging from the volume element, travel-
ling across the galaxy up to its edge, from which it
escapes toward an external observer. To determine this
mass we proceed as follows. Firstly, since the emission
jTOT (λ, V ) of eqn. (24) has been defined per unit
volume and the problem has azimuthal symmetry, we
resize the grid of azimuthal coordinates by taking many
equally spaced bins. Using this resized grid, we introduce
the Cartesian coordinates (XV , YV , ZV ) of the center
of the volume element by means of the transformations
XV = xiV sin θjV cosΦkV , YV = xiV sin θjV sinΦkV
and ZV = xiV cos θjV , where (xiV , θjV ,ΦkV ) are the
polar coordinates of centre of the volume V (i, j, k).
The starting reference system is in spherical coordinates
(O, x, θ,Φ) and corresponds to a Cartesian system
(O,X, Y, Z). Let us now consider another reference
system (O′, x′, θ′,Φ′) to which another Cartesian system
(O′,X ′, Y ′, Z′) would correspond. The transformations
from one Cartesian system to the other is given by
X = X ′ + XO′ , Y = Y
′ + YO′ and Z = Z
′ + ZO′ ,
where (XO′ , YO′ , ZO′) are the coordinates of the centre
O′ of the new system in the old one. We take the new
reference system (O′,X ′, Y ′, Z′) with the origin O′
in (XO′ , YO′ , ZO′) = (0, xiV sin θjV sinΦkV , 0), where
OO′ = xiV sin θjV sinΦkV . This represents a translation
of the origin O along the Y-axis to a new origin O′ so that
the centre of the volume lies in the plane (O′,XO′ , ZO′).
The Cartesian coordinates of the volume centre in the
new system will be X ′V = XV , Y
′
V = YV − YO′ = 0 and
Z′V = ZV . Applying the inverse relationships to pass from
Cartesian to spherical coordinates, the x′ and θ′ of the
volume centre are x′iV =
√
(X ′V )
2 + (Y ′V )
2 + (Z′V )
2 =
xiV
√
(sin θjV cosΦkV )
2 + (cos θjV )
2 and θ
′
jV =
arccos
(
Z′V /
√
(X ′V )
2 + (Y ′V )
2 + (Z′V )
2
)
=
arccos
(
cos θjV /
√
(sin θjV cosΦkV )
2 + (cos θjV )2
)
.
Obviously the new coordinate φ′k is equal to 0 or pi, be-
cause the volume belong to the plane (O′,XO′ , ZO′). For
x′i < 0 φ
′
k = pi, whereas for x
′
i > 0 φ
′
k = 0. To avoid use-
less complications, the grid of azimuthal coordinates has
been redefined in such a way that x′i is always different
from zero. We proceed now to determine the radius of the
circular section of the galaxy coincident with the plane
(O′,XO′ , ZO′). This will depend on the type of galaxy un-
der consideration. We get x′G =
√
(Rgal/RMG )
2 − Y 2O′ =
√
(Rgal/RMG )
2 − (xiV sin θjV sinΦkV )2.
where Rgal is the galactic radius and RMG is equal to R
M
d
for disks and to rMc for spherical galaxies. Let us now
consider an observer looking at the galaxy from the view
angle Θ with respect to the equatorial plane of the galaxy.
For the sake of simplicity we place the observer on the
plane (O′, XO′ , ZO′). Therefore, Θ = 0 corresponds to a
galaxy seen edge-on, whereas Θ = pi/2 to the case face-
on. Thanks to the azimuthal and equatorial symmetries
we make take Φ = 0 and Z′ 6 0.
Associated to the volume center with coordinates
(
x′i, θ
′
j ,Φ
′
k
)
there will be a point P located on the galaxy
edge with coordinates P
(
x′G, θ
′
G,Φ
′
G
)
where θ′G and Φ
′
G
are still unknown. Let us first calculate Φ′G. If Θ = 0
all the points at the galactic edge have Φ′G = 0. If
Θ = pi/2 two cases are possible: for x′i < 0 ⇒ Φ′G = pi,
whereas for x′i > 0 ⇒ Φ′G = 0. In the general case
with 0 < Θ < pi/2 we have to calculate the equation of
the straight line with angular coefficient m = tg (pi −Θ)
passing through the point Q (X ′, Z′) = Q
(
0,−R′G
)
.
We obtain Z′ = −X ′ tanΘ − x′G. We calculate now
(Z′V +X
′
V tanΘ + x
′
G) where (X
′
V , Z
′
V ) are the coordi-
nates of the volume center. If (Z′V +X
′
V tanΘ+ x
′
G) > 0
we have Φ′G = 0, whereas if (Z
′
V +X
′
V tanΘ + x
′
G) < 0
we get Φ′G = pi.
The derivation of θ′G is slightly more complicate be-
cause five cases are possible. In any case, it is a mat-
ter of lengthy trigonometrical manipulations. The line
for the center of the plane (O′X ′Z′) with inclination Θ
has equation Z′ = −X ′ tanΘ. This leads us to define the
parameter ∆ to check whether the volume V in the plane
(O′X ′Z′) falls above or below the line Z′ = −X ′ tanΘ. If
Θ = pi/2 ⇒ ∆ = 0, whereas if 0 6 Θ < pi/2 ⇒ ∆ = Z′V +
X ′V tanΘ. Finally, let us introduce the ratio χ = x
′
iV /x
′
G.
The following cases are then possible. If X ′V > 0 and ∆ >
0 ⇒ then θ′G = pi/2 + Θ − arcsin
[
χ sin
(
pi
2 −Θ+ θ
′
jV
)]
.
If X ′V > 0 and ∆ < 0 ⇒ then θ′G = pi/2 + Θ +
arcsin
[
χ sin
(
θ′jV − pi/2−Θ
)]
. If X ′V > 0 and ∆ = 0 ⇒
then θ′G = pi/2 + Θ. If X
′
V < 0 and ∆ > 0 ⇒
c© 2005 RAS, MNRAS 000, 000–000

Galaxies spectra with interstellar dust 27
then θ′G = pi/2 + Θ − arcsin
[
χ sin
(
pi/2−Θ− θ′jV
)]
.
If X ′V < 0 and ∆ < 0 we have three solutions: θ
′
G =
pi/2 + Θ + arcsin
[
χ sin
(
Θ− pi/2 + θ′jV
)]
, θ′G =
3
2pi −
Θ− arcsin
[
χ sin
(
Θ− pi/2 + θ′jV
)]
and θ′G = pi, depend-
ing on whether Z′V + X
′
V tanΘ + x
′
G is greater, smaller
or equal to 0, respectively.
Once determined the spherical coordinates of
P
(
x′G, θ
′
G,Φ
′
G
)
in the translated system, by means of
an inverse transformation of coordinates we can ob-
tain the Cartesian coordinates P (XP , YP , ZP ) in the
old system of coordinates: XP = x′G sin θ
′
G cosΦ
′
G,
YP = x′G sin θ
′
G sinΦ
′
G + xiV sin θjV cos ΦkV and ZP =
x′G cos θ
′
G. Having eventually derived the Cartesian coor-
dinates of the point P (XP , YP , ZP ) on the galactic edge
and those of volume center (XV , YV , ZV ), the calculation
of the mass in the cylinder comprised between V and
the galaxy edge is trivial and can be straightforwardly
performed as described in Appendix A.
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