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2 The model library


2.1 Construction of a combined library

Proceeding with the work undertaken in LCB97, we have built a more extensive library providing now almost complete coverage of the stellar parameter ranges in $T_{\mathrm{eff}}$, $\log g$, [M/H] which are required for population and evolutionary synthesis studies. This new grid is complementing the previous version by the addition of M dwarf model spectra. Different basic libraries have been assembled: the Kurucz (1995, [K95]) models provide wide coverage in $T_{\mathrm{eff}}$ (50000 K $\sim$ 3500 K), $\log g$ (5.0 $\sim$ 0.0), and [M/H] (+1.0 $\sim$ -5.0), whereas in the temperature range 3500 K $\sim$ 2500 K the M giants spectra are represented by the hybrid ``B+F'' models constructed from spectra of Fluks et al. (1994) and Bessell et al. (1989, 1991 [BBSW]) (LCB97). For the M dwarf models, we introduced the synthetic spectra of cool stars originating from the Allard & Hauschildt (1995, [AH95]) grid. Thus, the previous library is extended by models within the following parameter ranges: 3500 K > $T_{\mathrm{eff}}$ $\geq$ 2000 K, 5.5 $\geq$ $\log g$ $\geq$ 3.5 and +0.5 $\geq$ [M/H] $\geq$ -4.0. Figure 1 gives a 3-D representation of the new combined library.

\epsffile {fig1.eps}\end{figure} Figure 1: Coverage of the final combined library in the stellar parameter space. ``B+F'' models are those constructed for M giants from Fluks et al. and BBSW spectra (see LCB97)

The ``base model grid'' of AH95 atmosphere models (referred to hereafter as the ``Extended'' models) used here present several improvements compared to the previous generation models of Allard (1990). In particular, new molecular opacities have been incorporated and the opacity sampling technique has been introduced in order to improve the treatment of some of the atomic and molecular lines. For solar metallicity, we used an upgraded version (referred to as the ``NextGen'' models version) of the ``base model grid''. In these new models a more extensive list of 12 million TiO lines (Jørgensen 1994) has also been included, with a more rigourous line-by-line treatment instead of the Just Overlapping Line Approximation (JOLA) previously used. The main effect is the reduction of the derived effective temperature by $\sim$ 150 K (Jones et al. 1996). We also found that these new models provide more realistic UBV colors than the previous generations (see Sect. 4.2). Because the ``NextGen'' model grid is still incomplete, only solar-abundance spectra can be included in order to cover the whole range of $T_{\mathrm{eff}}$ and $\log g$ provided by the hybrid library. For other metallicities, we still use the ``Extended'' models.

In the combined library, all the original spectra were rebinned on the same K95 wavelength grid, from 9.1 nm to 160 $\mu$m, with a mean resolution of $\sim$ 10 Å in the ultraviolet and $\sim$ 20 Å in the visible. Recall that the M giant model spectra ``B+F'' are metallicity-independent blueward of 4900 Å owing to the introduction of the Fluks et al. models in this spectral range, and that a black-body tail was attached for $\lambda \geq$ 4070 nm (see LCB97). The AH95 spectra stop at 20 $\mu$m, and for $\lambda$ > 3 $\mu$m the resolution is not sufficient for an accurate description of the synthetic spectrum. In order to cover the whole K95 wavelength range, we then connected a black-body to the synthetic spectra beyond $\sim$ 5 $\mu$m (M band).

These model spectra - except for the updated NextGen models used in this work for solar metallicity - are available on a CD-ROM[*] collecting various materials for galaxy evolution modelling (Leitherer et al. 1996), or by request on anonymous ftp, and have been used for single stellar populations models (Bruzual 1996; Bruzual et al. 1997; Lejeune 1997).

2.2 Model colors and bolometric corrections

Synthetic UBVRIJHKLL'M colors and bolometric corrections have also been computed from the theoretical stellar energy distributions (SEDs) over the whole range of parameters available in the grid, using the filter transmission functions given by Buser (1978) for UBV, Bessell (1979) for $(RI)_{\rm C}$, and Bessell & Brett (1988) for JHKLL'M. The zero-points were defined from the Vega model spectra of Kurucz (1991) by fitting to the observed values from Johnson (1966) (U-B = B-V = 0.0), Bessell & Brett (1988) (J-H = H-K = K-L = K-L' = K-M = 0.0), and Bessell (1983) (V-I = 0.005, R-I = -0.004). For the bolometric corrections, we followed the zero-pointing procedure described in Buser & Kurucz (1978). We first (arbitrarily) set the smallest bolometric correction for the ($T_{\mathrm{eff}}$ = 7000 K, $\log g$ = 1.0) model to zero. This produces BC'V = -0.190 for the solar model, $T_{\mathrm{eff}}$ = 5777 K, $\log g$ = 4.44 (LCB97). The zero-point is then defined,  
BC_{{V}} = BC'_{{V}} + 0.082 \, ,\end{displaymath} (1)
in order for the present theoretical calculations to provide the best fit of the empirical bolometric-correction scale of Flower (1996). Adopting these definitions and the standard value of the solar radius (Allen 1973) we find $L = 3.845\ 10^{33}$ erg/s, MV = 4.854 and BCV = -0.108 for the solar model. Tables of theoretical colors and bolometric corrections for the whole range of stellar parameters in the grid are available in electronic form.

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