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

We consider the role of advection in a two-temperature accreting corona wit h an underlying optically thick disc. The properties of coronal solutions d epend significantly on the description of advection. Local parametrization of advection by a constant coefficient delta replacing the radial derivativ es leads to complex solution topology, similar to some extent to other adve ction-dominated accretion flow solutions. One radiatively cooled branch exi sts for low accretion rates. For higher accretion rates two solutions exist over a broad range of radii: one is radiatively cooled and the other one i s advection-dominated. With further increase of accretion rate, the radial extensions of the two solutions shrink and no solutions are found above a c ertain critical value. However, these trends change if the local parametriz ation of advection is replaced by proper radial derivatives computed iterat ively from the model. Only one, radiatively cooled solution remains, and it exists even for high accretion rates. The advection-dominated branch disap pears during the iteration process, which means that a self-consistently de scribed advection-dominated flow cannot exist in the presence of an underly ing cold disc.