A Toy Model for Advection Dominated Accretion Flows

A toy disk model with advection dominated accretion onto a black hole is presented. The advection dominated accretion flows (ADAFs) are assumed to exist in the inner thick disk with r_in < r < r_out, and the disk is assumed to be geometrically thin for r > r_out. Compared with Paczynski's toy model the thick disk is not limited to be 100% advective. It turns out that the inner radius r_in depends not only on the outer radius r_out but also on the ADAF parameters f and ε. The effects of the inner thick disk on the radiation efficiency and the temperature profile of the outer thin disk are discussed in details.