Evolution of Thin Discs with Partial Accretion

TL;DR

This paper develops an approximate self-similar solution for the viscous evolution of thin accretion discs with partial mass inflow, validated by numerical simulations, advancing understanding of intermediate asymptotic states.

Contribution

It introduces a novel approximate solution for partial accretion in thin discs, bridging the gap between full and no accretion models.

Findings

The approximate solution accurately describes the intermediate asymptotic stage.

Numerical simulations confirm the validity of the solution.

The method extends modeling capabilities for partially accreting discs.

Abstract

The viscous evolution of a thin disc around a central object is considered. Such discs are described by self-similar solutions in which either all or none of the inflowing mass accretes. An approximate solution for the partial accretion regime is constructed by employing a prescription recently introduced for nonlinear heat conduction. The solution is compared with numerical simulations demonstrating that the approximate solution describes the intermediate asymptotic stage for partially accreting discs.