A viscosity prescription for a self-gravitating accretion disc

A model for treating the transfer of angular momentum within a gaseous differentially rotating disc subject to gravitational instability is discussed in terms of an effective kinematic viscosity. It is assumed that even when matter in the disc is subject to self-gravitation, the instability does not necessarily lead directly to condensation of parts of the disc into self-gravitating bodies. Conditions under which the present model permits a similarity solution are discussed, and it is shown that the general solution tends to the similarity solution at large times.