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Astron. Astrophys. 364, 517-531 (2000)

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3. Modelling galaxy SEDs in the presence of a dusty ISM

The optical-NIR SEDs of our sample objects have been modelled using the population synthesis code GRASIL (Silva et al. 1998), taking into full account the effects (optical extinction and thermal reprocessing) of a dusty interstellar medium in galaxy spectra. We defer the reader to that paper for a through description of this model and for precise definitions of the parameter, while for convenience we summarize the main features below.

3.1. The GRASIL code

The code provides a self-consistent description of the formation and evolution of a galactic system in its various stellar and ISM components, including its secular evolution during the Hubble time and episodes of enhanced star-formation possibly following interactions and mergers.

As a preliminary step the code allows to solve the equations ruling the chemical evolution, providing the star formation and metallicity histories SFR(t) and Z(t) as a function of time. The computations presented here were performed adopting one-zone (no spatial dependence) open models including the infall of primordial gas, according to the standard equations of galactic chemical evolution. As usual, the star formation rate is determined by the amount of gas in the system according to a Schmidt-type law  1


We have generated 3 different [FORMULA], in order to provide a wide range of spectral evolution patterns. The peak occurs at about 1, 2 and 3 Gyr (hereafter model (a), (b) and (c) respectively), getting broader from (a) to (c). As a result, half of the final stellar mass M (i.e. at 13 Gyr) has been assembled at galactic times of 2, 3.7 and 4.7 Gyr in the three cases respectively. A standard Salpeter IMF between 0.1 and 100 [FORMULA] is assumed.

As described by Silva et al. (1998), GRASIL calculates self-consistently the absorption of starlight by dust, the heating and thermal emission of dust grains, for an assumed geometrical distribution of the stars and dust, and a specific grain model.

In the GRASIL model several parameters affect the overall modifications imprinted by dust on the SED. However, if we confine ourselves to the attenuation of stellar radiation in the optical/UV/NIR bands, we can obtain most of the possible spectral behaviours by adjusting only two quantities: the [FORMULA] (see Eq. (8) in Silva et al. 1998 for a precise definition) of newly formed stars from parent molecular clouds (MCs) and the total mass of dust. Indeed [FORMULA] controls the fraction of light from very young stellar generations hidden inside MCs and converted to IR photons, since the MCs optical thickness is very high below [FORMULA]m (cf. Silva et al. 1998). On the other hand, the effects of the diffuse (cirrus) dust depend on several quantities: the radial and vertical scale lengths for stars and dust distributions [FORMULA] and [FORMULA], the residual gas in the galaxy [FORMULA], the dust to gas ratio [FORMULA] and the fraction of gas which is in the MCs component [FORMULA]. However we found that most, if not all, the possible attenuation laws of the diffuse dust, arising from different choices of these quantities, can be closely mimicked by simply adjusting the amount of gas, while fixing the other quantities to the `typical' values: [FORMULA] Kpc, [FORMULA], [FORMULA] and [FORMULA]. Obviously, while different choices of [FORMULA], [FORMULA], [FORMULA], [FORMULA] and [FORMULA] can yield similar attenuation laws on the optical spectrum, the spectral shapes of the corresponding IR continuum re-radiation can be rather different.

Strictly speaking the residual gas [FORMULA] is not a parameter, being instead the outcome of the chemical evolution code, through the Schmidt law. However we use the trick of forcing [FORMULA] to different values, in order to describe with a monoparametric sequence the effects of a global attenuation on the SED. Besides this, a larger `freedom' on [FORMULA] takes into account that the Schmidt law should not be taken too literally, as a strict relationship between the total gas content and the SFR in the system. The law may only provide an order of magnitude description, in particular for the secular evolution of the SFR, the so-called "inactive phase" of galaxy evolution bringing essentially to the formation of spiral disks. Several other physical parameters influence the rate of star-formation with respect to the simple available amount of residual gas, in particular the gas pressure and temperature, which may drastically change as a consequence of a violent dynamical event, like an interaction or a merger, followed by gas compression and efficient cooling. Overall, we use the criterion of considering acceptable values from 0.2 to 5 times the `true' [FORMULA] given by the chemical evolution code.

3.2. An extensive grid of model template spectra

The code allowed us to build a very large set of model spectra describing all possible age and mass distributions for the stellar populations, for the dusty ISM, and relative assemblies.

For each of the 3 histories SFR(t) we have generated two grids of models: one with [FORMULA] Myr and another with [FORMULA] Myr. Silva et al. (1998) found that the former value is typical for normal spirals while the latter is more suited for starbursting systems. Each of these grids consists of 1400 models computed with ages [FORMULA] ranging from 0.2 to 10 Gyr in steps of 0.2 Gyr and [FORMULA] from 0 to 1 (in units of the final mass of stars) in 28 logarithmic steps.

In total we have therefore [FORMULA] model spectra with different age, gas content, MCs escape timescale, and [FORMULA] which we compared with the observed sample SED, allowing for the obvious scaling in luminosity.

In addition we considered one further grid of spectra to see how our observed SEDs compare with those expected for spheroidal systems: for these we used the [FORMULA] (c) model, but truncated at 3 Gyr to simulate the onset of a galactic wind. The adopted geometry in this case was a modified King profile (Eq. (3) in Silva et al. 1998) with [FORMULA] Kpc.

An example of the resulting fits to the observed broadband spectra of sixteen galaxies in our sample is reported in Fig. 2. The analysis of the 52 fitted SEDs reveals the presence of two dominant different kinds of spectral behaviours: (a) objects which are red and show a strong convergence in the UV region, and (b) blue spectra that are flatter at all wavelengths, dominated by young stellar populations.

[FIGURE] Fig. 2. Observed broadband spectra for sixteen galaxies in our sample, fitted with the synthetic models described in Sect. 3.

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© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001