Ring sequence decomposition of an accretion disk: the viscoresistive approach

We analyze a two-dimensional viscoresistive magnetohydrodynamical (MHD) model for a thin accretion disk which reconciles the crystalline structure outlined in Coppi B., Phys. Plasmas, 12 (2005) 7302 and Coppi B. et al., Astrophys. J., 641 (2006) 458, with real microscopic and macroscopic features of astrophysical accreting systems. In particular, we consider small dissipative effects (viscosity and resistivity, characterized by a magnetic Prandtl number of order unity), poloidal matter fluxes and a toroidal component of the magnetic field. These new ingredients allow us to set up the full equilibrium profile including the azimuthal component of the momentum conservation equation and the electron force balance relation. These two additional equations, which were identically satisfied in the original model, permit us to deal with non-zero radial and vertical matter fluxes, and the solution we construct for the global equilibrium system provides a full description of the radial and vertical dependence within the plasma disk. The main issue of our analysis is outlining a modulation of the matter distribution in the disk which corresponds to the formation of a ring-like sequence, here associated with a corresponding radial oscillation of the matter flux.