Time-dependent accretion disks around compact objects. I - Theory and basic equations. II - Numerical models and instability of inner region

We consider accretion disks around compact stars and black holes, generalizing the stationary disk models of various authors to allow time dependence on the radial-flow time scale. The structure and evolution of the disk are governed by an 'evolution equation' for matter surface density, plus a set of implicit algebraic equations determining various thermodynamic and radiation variables in terms of surface density. The analytic structure of these equations is studied. It is shown that there exists a maximum permissible value of the surface density at which gas and radiation pressure are approximately equal, and beyond which viscosity generates more energy than radiative transport can remove.