This work makes use of an evolutionary synthesis model that reproduces the integrated spectrum of a galaxy. A description of this model is also given in Poggianti & Barbaro (1996); here the essential informations are presented.
The emission of the stellar component is computed with a modified version
of the model by Barbaro & Olivi (1986, 1989 (BGOF)), that synthesizes
the SED of a galaxy in the spectral range 
Å.
The BGOF model includes, besides the main sequence and the central helium
burning phase, also the advanced stellar evolutionary phases such as
AGB and Post-AGB. It takes into account the chemical evolution of the galaxy,
therefore the contribution to the integrated spectrum of stellar
populations of different metallicities.
This model has been successfully employed in the studies of star clusters
in the Magellanic Clouds and of elliptical galaxies (Barbaro & Olivi 1986,
1989, 1991; Barbaro 1992; Barbaro et al. 1992).
The stellar evolutionary background has not been changed, while
updates have been made to the library of stellar
spectra: the new Kurucz stellar atmosphere models (version 1993) have replaced
the previous ones (Kurucz 1979) and
the computation of the spectrum has been extended up to
25000 Å. In the infrared region, for stars with
K Kurucz's models (1992)
have been used. For stars with lower effective temperatures
the library of observed stellar spectra by
Lançon-Rocca Volmerange
(1992, LRV) has been employed: such spectra cover the spectral range
Å, with a resolution between 25 and 70 Å.
The connection between the optical spectra (
Å) and the LRV
spectra has been made by means of black body curves.
For each star the black body temperature has been determined by
imposing that
the resulting colours reproduce the observed ones
(Koornneef 1983 (V-K, J-K, H-K); Bessell & Brett 1988
(V-I, V-K,
J-H, H-K, J-K)).
A set of models of the different types has been computed for an age 15 Gyr and for all the evolutionary times corresponding to various redshifts according to Eq. (4). The SFR of an elliptical is approximated with an exponentially decreasing function and the average metallicity is assumed solar. Two time scales have been explored as e-folding times of the SFR: 1 Gyr (E) and 1.4 (E2). For the spirals, Auddino (1992) galaxy model have been employed: this is a chemical evolutionary model that includes an inflow and assumes the SFR to be proportional to the gas fraction. This model provides the SFR and the metallicity as a function of time for galaxies in the type range Sa-Sd. The model parameters for each Hubble type are determined requiring the model SED to reproduce the observed colours of local galaxies. The SEDs obtained from this model reproduce the spectral emission and absorption characteristics of local galaxies (Barbaro & Poggianti 1996), as well as their observed average gas fractions.
The inclusion of very advanced stellar phases of extremely metal rich stars
(Greggio & Renzini 1990) could modify the evolutionary corrections of
ellipticals for the bluest bands at redshifts 
,
because the evolution of the ultraviolet spectral region would be influenced
by this kind of stellar objects. The K corrections would not be affected,
being the SED of local ellipticals well reproduced by the models also
in the UV range.
Anyway the metallicity of stars in ellipticals is still uncertain: the 
index, commonly used to estimate the global metallic content, is difficult
to interpret, due to the excess in early-type galaxies of the ratio
between the 
elements (among which oxygen and magnesium)
and the iron with respect to the solar value.
Concerning the spirals, the models do not take into account the intrinsic extinction due to the presence of dust, that is expected to be progressively more significant at increasing redshifts and at decreasing effective wavelength. In some cases it will be necessary to consider a further correction for intrinsic extinction (Di Bartolomeo et al. 1995).
In principle a first test of the model could be done by comparing the results with the observations of integrated SEDs of star clusters; good candidates are the young star clusters in the Magellanic Clouds (Barbaro & Olivi 1991). However a great dispersion in the infrared colours of these objects has been observed; such a dispersion is explained considering the stochastic fluctuactions in the mass distribution of the evolved stars (Barbaro 1992). For this reason and for the uncertainty in the determination of the age and the metallicity of each cluster, the comparison has been made with galaxies, for which the stochastic effects are expected negligible.
Table 1: Colours of the models of age 15 Gyr
Table 1 (click here) presents the colours of models of age 15 Gyr of different morphological types; in the case of the elliptical, the dependence of colours from the average metallicity is shown: solar (El1, correspondent to the E model), Z=0.01 (El2) and Z=0.005 (El3). Notice that the optical-IR colours ((V-J), (V-H), (V-K)) change drastically with the Hubble type, while the IR-IR colours ((J-H), (J-K), (H-K)) change slightly along the type sequence, with differences comparable to the observative uncertainty.
Table 2: Comparison models-observations for early-type galaxies;
*= ellipticals only, without S0
Observations in the near-IR have been obtained from Persson et al. (1979)
for early-type galaxies in Virgo, in Coma and in the field and from
Bower et al. (1992a,b) for a sample of early-type objects in Virgo and in
Coma.
The average galaxy colours observed by the different authors, corrected for
redshift, reddening and aperture effects, are compared in Table 2 (click here) with
the model results for ellipticals of various metallicities.
The agreement is satisfactory.
Persson et al. corrected the colours by using Schild & Oke (1971) and
Whitford (1971) V-band K-corrections; for the infrared bands, they computed
the corrections using several late-type stars from Woolf et al. (1964).
Bower et al. defined the U and V band K corrections from a series of
template early-type galaxy SEDs, among which those of Coleman et al.,
and the infrared K-corrections from the SED of the K3 giant star 
Tau
(Woolf et al. 1964).
For spirals, a great dispersion in the infrared colours
within the same morphological type is observed
(Gavazzi & Trinchieri 1989), therefore spirals are not included in
Table 2 (click here);
the colours of the models for the spirals are inside the range of observed
values.
Moreover the updated evolutionary synthesis model has been used successfully in the studies of galaxies at intermediate redshifts (Poggianti & Barbaro 1995, 1996).
Figure 1: SEDs of 15 Gyr old models normalized at 5500 Å.
From top to bottom (at 1000 Å):
Sc (dotted line); Sa (short dashed line); E2 (long dashed line); E (solid line)
Figure 2: SEDs of the elliptical model for 9 redshifts: 0, 0.1, 0.3,
0.5, 0.7, 1.0, 1.5, 2.0, 2.5, 3.0