Studies on stellar rotation: II. Gravity-darkening: The effects of the input physics and differential rotation. New results for very low mass stars

In the second paper of this series we present the calculations of the gravity-darkening exponent for low mass stars. Such calculations are based on a modified version of the method developed by us and published in an earlier paper. The corresponding apsidal motion constants for VLMS are also presented. The mass range for which both parameters are available is now extended from 0.08 up to 40 M⊙. The derived β1 is compared with the results of the radiation hydrodynamics simulations. Although a systematic difference with decreasing effective temperature is detected, the interagreement can be considered as good (maximum discrepancy around 10%). The local maximum for log Teff ≈ 3.7 is not detected in the RHD formalism, although calculations for lower effective temperatures are needed to draw a more definitive conclusion. It is pointed out that the gravity-darkening phenomenon is related not only with atmospheric parameters but also with the internal stellar structure and with details of the rotation law. The influence of changing the input physics on the gravity-darkening exponent is investigated and it is found that they depend slightly on the chemical composition mainly in the zone of the radiative/convective phase transition. For deep convective envelopes, it is found no significant differences in β1's computed for different mixing-length parameter. It is emphazised that at the actual level of light curve quality of eclipsing binaries it is not possible to discriminate effects of third order in the gravity-darkening exponents such as chemical composition, theory of convection, irradiation, etc. On the other hand, the role of the differential rotation is discussed in the light of its possible relation with moderately anomalous gravity-darkening exponents for some particular cases. Concerning the high values of the gravity-darkening exponent reported by some authors, this is not supported by very recent simultaneous uvby observations, at least in the case of VV Uma.