Even 25 years after the Shakura-Sunyaev seminal paper on the α-disk, we cannot claim that we have a reliable theory of accretion disks in galactic nuclei. Why? Because the problem is extremely complicated, it is essentially nonlinear and contains a number of parameters (i.e. is many-dimensional). The key point is whether it is possible to determine the magneto-hydrodynamical viscosity self-consistently, i.e. as a function of parameters of the disk - the temperature, matter and radiation densities, magnetic field, radius, etc., both in the radiation dominated and matter dominated regions. Another class of fundamental problems concerns the stability of the disk; Krolik mentioned only one instability - in the radiation dominated region, but there are many other types of instabilities which are quite sensitive to the physical conditions in the disk, for example, to the anisotropy of the ion pressure in the outer regions and possible electron-positron pair production near the inner edge of the disk. The other problems include those of the radiative transfer within the disk in various conditions, Comptonization of the outgoing radiation, radiation reflections by the desk, etc. Therefore it is not suprising that one can ‘explain' almost whatever he wants - spectra, variability, jets, wind, etc., by proper fit of the ‘free’ (which are never free) parameters and ignoring the instabilities and so on.
General Discussion of Accretion Disks
