Inconsistency in the Standard Model for Thin Accretion Disks

We analyze the configuration of a thin rotating accretion disk, which is embedded in a magnetic field inducing a backreaction in the gravitating plasma. The aim of this study is to determine the conditions under which the gaseous accretion model of Shakura can be reconciled with the magneto-hydrodynamical picture requested to trigger the underlying turbulent behavior. We focus our attention to the generalized Ohm equation in order to understand if the plasma backreaction is able to provide the proper toroidal current, allowing a non-zero infalling velocity. In the limit of linear plasma backreaction, this analysis shows how the Shakura profile of accretion turns out to be inconsistent. In particular, comparing the azimuthal and the generalized Ohm equilibrium equations, we argue that it is not possible to maintain a constant rate of accretion. A non-stationary scenario for the disk configuration is then outlined and it results into a transient process which is however associated to a vanishing accretion rate.