The Effect of Density on the Thermal Structure of   Gravitationally-Darkened Be Star Disks
  The effects of gravitational darkening on the thermal structure of Be star disks of differing densities are systematically examined. Gravitational darkening is the decrease of the effective temperature near the equator and the corresponding increase near the poles of a star caused by rapid rotation. We also include the rotational distortion of the star using the Roche Model. Increasing the disk density increases the optical depths in the equatorial plane, resulting in the formation of an inner cool region near the equatorial plane of the disk. High rotation rates result in disks that have temperatures similar to those of a denser disk, namely cooler overall. However the effect of increasing rotation produces additional heating in the upper disk due to the hotter stellar pole. Cool regions in the equatorial plane normally associated with high density are seen in low density models at high rotation rates. Gravitational darkening increases the amount of very cool and very hot material in the disk and decreases the amount of disk material at moderate temperatures. We also present models which study the effect of gravitational darkening on hydrostatically-converged disks, in which the temperature structure is consistent with vertical hydrostatic equilibrium. Because the equatorial regions become cooler, hydrostatically converged models that include gravity darkening have smaller vertical scale heights, and $H/R$ is smaller by as much as 56% near $v_{\rm crit}$. Finally we explore differences in disk temperatures when alternate formulations of gravitational darkening, which lower the temperature difference between the pole and the equator, are used. 
M. A. McGill, T. A. A. Sigut, and C. E. Jones
astro-ph.SR