Time-dependent quasi-spherical accretion

Differentially rotating, "advection-dominated" accretion flows are considered in which the heat generated by viscous dissipation is retained in the fluid. The equations of time-dependent quasi-spherical accretion are solved in a simplified one-dimensional model that neglects the latitudinal dependence of the flow. A self-similar solution is presented that has finite size, mass, angular momentum and energy. This may be expected to be an attractor for the initial-value problem in which a cool and narrow ring of fluid orbiting around a central mass heats up, spreads radially and is accreted. The solution provides some insight into the dynamics of quasi-spherical accretion and avoids many of the strictures of the steady self-similar solution of Narayan & Yi. Special attention is given to the astrophysically important case in which the adiabatic exponent gamma=5/3; even in this case, the flow is found to be differentially rotating and bound to the central object, and accretion can occur without the need for powerful outflows.