## Appendix A: lateral heat diffusionHere we show that in a realistic situation the lateral temperature gradient caused by irradiating the secondary anisotropically is negligible compared to the radial temperature gradient in the subphotospheric layers and that, therefore, lateral energy transport by radiation is unimportant. We demonstrate this in the framework of the point source model. In that model we estimate the lateral gradient of to be On the other hand, the radial temperature stratification is given by the Eddington approximation (e.g. Tout et al. 1989) where is the optical depth. Therefore From the definition of the optical depth we have Inserting (A.5) into (A.4) yields the minimum radial temperature gradient in the presence of irradiation: Combining now (A.1) and (A.6) we obtain Now, because and in the subphotospheric layers , we have Because in the stars in question
is so small, the lateral temperature gradient is always much smaller
than the radial one unless and thus
.
However, in the range of interest of © European Southern Observatory (ESO) 2000 Online publication: August 23, 2000 |