3 Discussion

Until now the light curve synthesis programs have mostly used non illuminated limb-darkening tables to evaluate the center to limb brightness variation. In fact, the LC models use non-illuminated atmosphere results even to calculate the so-called "reflection effect'', what is not strictly correct since the spectrum of an illuminated atmosphere is different from that of a standard one (Vaz & Nordlund 1992). The effect of the external irradiation on the coefficients themselves is ignored even when it is recognized that the limb-darkening coefficients should vary due to variations of the local effective temperature and surface gravity across the surface of a tidally distorted binary star, as in Van Hamme & Wilson (1994), who calculated position-dependent limb-darkening on computed light curves.

However, it is clear from Fig.7 that the limb-darkening coefficients vary not only with the atmosphere's effective temperature, but show a strong dependence on the characteristics of the external illumination (the incidence angle, the amount of infalling flux, the spectrum of the infalling energy or, in other words, the temperature of the illuminating star), also. This dependence is well represented by the approximating Eqs. (8) to (11) for each of the 9 different limb-darkening laws reviewed in the present work. Even though the effect of the limb-darkening coefficients on the light curve analysis is small, it is large enough to allow attempts of empiric determination of the coefficients from precise observed light curves (as for DMVir, Andersen et al. 1984), while the adoption of incorrect coefficients may affect systematically the determination of the orbital inclination, having also influence on the determination of other parameters (Popper 1984).

As the orbital configuration is fully known during the analysis of an eclipsing binary LC, Eqs. (8) to (11) can be used to calculate the limb-darkening coefficients which are position-dependent on the surface of the components, taking into account not only the variation of $T_{\rm eff}$and $\log g$, but also the effect of the external irradiation. The parametrization attained is very convenient for this purpose, which can be implemented in the existing computer models for eclipsing binary light curve synthesis. This extra calculation will represent a relatively easy task for the modern CPU's and certainly will improve the quality and reliability of the determination of the other parameters as, for instance, the orbital inclination. In fact, the treatment of both the limb-darkening and the gravity brightening, with respect to the effect of the mutual illumination, should be done consistently, and this is our goal. In Alencar et al. (1998) we present the continuation of the work on the gravity brightening exponent (Alencar & Vaz 1997) extended to illuminated atmospheres. The implementation of these results in the WD model (Wilson & Devinney 1921; Wilson 1979; Vaz et al. 1995) is in progress and its application to real systems will be published elsewhere. While this is not the complete integration of atmosphere model calculation with the light curve synthesis programs, yet, a desirable feature of the next generation of the LC programs, this is a significant step towards the improvement of these models with respect to the proximity effects on the theoretical light curves.