The role of advection in the accreting corona model for active galactic nuclei and Galactic black holes

We consider the role of advection in the two-temperature accreting corona with an underlying optically thick disc. The properties of coronal solutions depend significantly on the description of advection. Local parameterization of advection by a constant coeficient $\delta$ replacing the radial derivatives lead to complex topology of solutions, similar to some extent to other advection-dominated accretion flow solutions. One, radiatively cooled branch exists for low accertion rates. For higher accretion rates two solutions exist in a broad range of radii: one is radiatively cooled and the other one is advection-dominated. With further increase of accretion rate the radial extensions of the two solutions shrink and no solutions are found above certain critical value. However, these trends change if the local parameterization of advection is replaced by proper radial derivatives computed iteratively from the model. Only one, radiatively cooled solution remains, and it exists even for high accretion rates. The advection-dominated branch disappears during the iteration process which means that a self-consistently described advection-dominated flow cannot exist in the presence of an underlying cold disc.