2 The limb-darkening coefficients and the colors

The stellar models are those of (Claret 1995). We have selected a representative chemical composition corresponding to (X,  Z) = (0.70, 0.02). In fact, such a chemical composition seems to fit well, as average, the properties of double-lined eclipsing binaries compiled by Andersen (1991) including the apsidal motion analysis.

The limb-darkening coefficients are computed using the stellar atmospheres models generated with the ATLAS code (Kurucz 1993). A few modifications were introduced in the method to compute the coefficients with respect to our recent publications (Díaz-Cordovés et al. 1995; Claret et al. 1995). A curve of sensitivity for a CCD detector was introduced in order to cover all bands investigated (from about 3500 Å up to 22000 Å). The limb-darkening coefficients were computed for most usual photometric systems used in investigations of eclipsing binaries covering 12 bands: uvby, U B V and R I J H K. For the J H K bands the sensitivity of the In-Sb detector was included.

  

Figure 1: Linear limb-darkening coefficients for the photometric bands R I J H K for a 2 $M_{\odot}$ model as a function of the surface gravity

  

Figure 2: Mv as a function of B-V for a 2 $M_{\odot}$ model

In Fig. 1 we present an example of such a calculation showing the "evolution" of the linear limb-darkening coefficients for a 2 $M_{\odot}$ model. The main-sequence phase and the giant branches are perfectly distinguishable. Coefficients are available for each point of each track, allowing an analysis of the light curves that is both coherent and consistent with the usual final products of double-lined eclipsing binary systems: the masses, radii and effective temperatures.

In the recent years we have shown the non-linearity of the distribution of the intensities across the stellar disk (Díaz-Corbobés et al. 1995; Claret et al. 1995). For very low effective temperatures the non-linear effect is still larger (Claret 1998). Since many people still use the linear approximation, we urge such users to consider the adoption of non-linear coefficients.

When working with stellar evolution models, some basic information related directly to observations is desirable. This is the case of stellar colors. In order to carry out the computation of such parameters, we have considered the following semi-empirical calibrations: for luminosity class V the relationship between $T_{\rm eff}$ and B-V (5000 K $\le$ $T_{\rm eff}$ $\le$ 8000 K) was that of Arribas & Martínez Roger (1988) while for hotter stars we used the Böhm-Vitense (1981) data. For luminosity classes I and III we used the data by Flower (1977). The bolometric corrections were taken from Malagnini et al. (1986). To transform colors from the Johnson to Strömgren, we used the equations by Penprase (1992). Figure 2 shows a sample of such calculations: the $B{-}V \times M_v$ diagram for a 2 $M_{\odot}$ model.