Radiation Pressure-supported Accretion Disks: Vertical Structure, Energy Advection, and Convective Stability

By taking into account the local energy balance per unit volume between the viscous heating and the advective cooling plus the radiative cooling, we investigate the vertical structure of radiation pressure-supported accretion disks in spherical coordinates. Our solutions show that the photosphere of the disk is close to the polar axis and therefore the disk seems to be extremely thick. However, the profile of density implies that most of the accreted matter exists in a moderate range around the equatorial plane. We show that the well-known polytropic relation between the pressure and the density is unsuitable for describing the vertical structure of radiation pressure-supported disks. More importantly, we find that the energy advection is significant even for slightly sub-Eddington accretion disks. We argue that the non-negligible advection may help to understand why the standard thin disk model is likely to be inaccurate above \sim 0.3 Eddington luminosity, which was found by some works on the black hole spin measurement. Furthermore, the solutions satisfy the Solberg-Hoiland conditions, which indicates the disk to be convectively stable. In addition, we discuss the possible link between our disk model and ultraluminous X-ray sources.