2011ApJ...743..111M

The effect of gravitational darkening on models of the thermal structure of Be star disks is systematically studied for a wide range of Be star spectral types and rotation rates. Gravitational darkening causes a reduction of the stellar effective temperature toward the equator and a redirection of energy toward the poles. It is an important physical effect in these star-disk systems because the photoionizing radiation from the central B star is the main energy source for the disk. We have added gravitational darkening to the BEDISK code to produce circumstellar disk models that include both the variation in the effective temperature with latitude and the non-spherical shape of the star in the calculation of the stellar photoionizing radiation field. The effect of gravitational darkening on global measures of disk temperature is generally significant for rotation rates above 80% of critical rotation. For example, a B0V model rotating at 95% of critical has a density-averaged disk temperature ~2500 K cooler than its non-rotating counterpart. However, detailed differences in the temperature structure of disks surrounding rotating and non-rotating stars reveal a complex pattern of heating and cooling. Spherical gravitational darkening, an approximation that ignores the changing shape of the star, gives good results for disk temperatures for rotation rates less than ~80% of critical. However for the highest rotation rates, the distortion of the stellar surface caused by rotation becomes important.