Effects of the energy equation in studies of limit-cycle behaviors of black hole accretion disks

Abstract

The inconsistency of the energy equation used in the literature is pointed out and a new consistent energy equation is given. With this new energy equation, calculations are made for the limit-cycle behaviors of thermally unstable accretion disks around black holes. From the comparison of our numerical results with those obtained using the inconsistent energy equation, it is found that the inconsistent energy equation undervalues the temperature and overvalues the effective optical depth when the accreted gas becomes effectively optically thin. Thus, it is dangerous if the inconsistent energy equation is used in the studies of very hot and optically thin accretion flows such as advection-dominated accretion flows (ADAFs), and our new energy equation is likely to be a better alternative.