6. COMPARING OBSERVATIONS AND MODELS

Template spectra can be used to test the spectrophotometric models of the galaxies. Despite their low resolution, the SNR is high enough to allow useful comparison of both the continuum shape and the spectral features. Here we show two examples of the possible use of these spectra. The first one, described in this section, is the comparison of the shape of the continuum over a large wavelength range. In the next section the absorption lines will be compared.

Two reasons suggest to start the continuum comparison from the elliptical galaxies: first, from the observational point of view this class is the most homogeneous, its average colours are better defined and the spectrum has smaller uncertainties. Second, elliptical galaxies are known to be dominated by old stellar populations and therefore the uncertainties on the star formation history (SFH) have lower consequences than in the case of the spirals: while in the latter case detailed SFH are required to fit the spectra, for the ellipticals a single parameter, the age, is usually enough to obtain a good agreement.

We used four different models: the Bruzual & Charlot model in the 1999 version (BC99), the Fioc & Rocca-Volmerange (1997) PEGASE model (FRV97) the Barbaro & Poggianti (1997) one (BP97), and the model by Worthey (1994) (W94). We have also used a previous (1996) version of the Bruzual & Charlot model (BC96) that allows for non-solar metallicities.

BC99 and BC96 use isochrones from the Padova group (Bressan et al., 1993) and two different stellar libraries, the empirical library from Pickles (1998) and the theoretical one by Lejeune et al. (1997). The latter library permits to predict the spectra of galaxies of various metallicities, from 5% to 250% solar. BC99 and BC96 give the spectra of an instantaneous burst of star formation (the so called Simple Stellar Population, SSP) that can be integrated over the time to reproduce an arbitrary SFH. We used a Salpeter Initial Mass Function (IMF) between 0.1 and 125 M. The BC96 model was used mainly because it allows to use non solar metallicities.

The FRV97 models use a different approach: starting from some hypothesis on the efficiency of the star formation processes, they model the entire life of the galaxy in order to reproduce the observed spectrum. The resulting SFH for ellipticals is a rapidly declining exponential law giving most of the star formation in the first Gyr, while for the Sc the SFH is almost constant over an Hubble time. The chemical evolution is also computed, but is not used for the final spectrum which assumes solar metallicity. The Padova isochrones are used, together with the empirical stellar library by Gunn & Stryker (1983) and Lançon & Rocca-Volmerange (1992) and the IMF by Rana & Basu (1992).

The BP97 model has the same approach of BC96, computing the galaxy integrated spectrum adding up the contribution of SSPs of (possibly) different metallicities. It uses the Padova isochrones and the Salpeter IMF between 0.1 and 100 M. The stellar spectra in the optical are either from Kurucz (1993) or from Jocoby et al. (1994), while the library by Lançon & Rocca-Volmerange (1996) are used in the near-IR. In this paper we only consider BP97 spectra up to 1.8 µm because above this limit the Kurucz sampling becomes too sparse.

The W94 model provides with single-age stellar population with metallicities between 0.01 and 3 times solar. It uses stellar evolution isochrones by VandenBerg and collaborators and by the Revised Yale Isochrones (VandenBerg & Laskarides, 1987; Green et al., 1987), Salpeter IMF and theoretical stellar spectra by Kurucz (1993) and Bessell et al. (1994). A particular emphasis was put in studying the variation with metallicity and age of several optical spectral features.

For demonstration purposes and to better study the intrinsic differences between the models, for BC99, BC96, W94 and BP97 we used SSP spectra of solar metallicity. For FRV we used both the models of elliptical galaxy they present, named E13 and E16, corresponding to two different cosmologies. In all the cases we searched for the best fitting spectrum by changing the age, the only remaining parameter, between 5 and 19 Gyr. All the spectra, both observed and modeled, were normalized to have the same total flux between 0.3 and 2.35 µm and reduced to the same resolution. The difference between comparing spectra to spectra and spectra to broad-band colours is important: both the absorption features and the continuum shape inside each band are taken into account and can dominate the results, especially when the agreement with the colours is good.

To measure the deviation it is not possible to use the standard ² because the fitting points are not totally independent of each other as the normalization of each band is given by the colour calibration (see section 3). Therefore we need a way to compare the deviations both to the spectrum noise and to the colour uncertainties. To do this we compute the square deviation ² between observed (o_i) and model (m_i) spectra in each band:

where N is the number of spectral points, and divide it for the square sum ² of the various error contributions. The final value A we use as analog to ² is the average of these ratios in the optical and in three IR bands:

which has a value of 1 if the deviations are only due to the errors in the observed spectra. The quantities ² are difficult to estimate with precision: from the RMS spread of the spectra (see section 2) and the error on the mean of the colours in table 2, we obtain = 0.03 in the optical, J and H and = 0.02 in K.

In Figure 8 we show the resulting values of A as a function of the galaxy age for the four used models and solar metallicity. Even taking into account the uncertainties on , for all the models an age exists which well reproduce the data: BC99 shows the best accord for ages between 10 and 16 Gyr, W94 select younger ages, between 8 and 9 Gyr, FRV97 reaches the best agreement for older ages, above 16 Gyr. The deviation of the BP97 model is always above 1 but steadily reduces toward older ages, reaching a value of about 2 at 16 Gyr, the maximum age available for the model. It should be noted that BC99, BP97 and W94 are single-burst models with the same IMF and metallicity, therefore the difference between them are due to something outside the user control, as isochrones or stellar spectra. FRV97 is not a single burst model, about 92% of the stars are formed in the first Gyr (about 97% in the first 4 Gyr) but the SFR never reaches a null value; this probably explains at least part of the differences with the other models and the requirement of very old ages.

Figure 8. Mean deviation of the predictions of some spectrophotometric models from the observed spectrum of the elliptical galaxies as a function of the age of the stellar population. Details about the models can be found in the text.

In Figure 9 we show the best fitting model, the BC99 spectrum for an SSP of 12 Gyr of age, solar metallicity and empirical star spectra. The overall shape of the spectrum is very well reproduced: the largest difference are in the interpolated region between 1 and 1.1µm where the model trace the position of the continuum while our interpolation an "effective" level taking into account the absorption lines. On the contrary, at a closed look it is possible to see that important discrepancies remains in the details of the absorption lines, both if theoretical and observed star spectra are used. This will be the subject of the next section.

Figure 9. The observed spectrum of the elliptical galaxies (thick line) is compared with a SSP spectrum of the BC99 model (thin line) with an age of 12 Gyr and solar metallicity. The upper panel shows the full spectrum, the four lower panels show enlargements in the optical and in the three near-IR bands. The shape of the spectrum is very well reproduced in all the range between 0.2 and 2.4 µm, and this is true for the optical absorption features too. In the near-IR large discrepancies can be noted, especially in J and H. The reason of these differences are explained in the text.