AN ANALYTICAL MODEL FOR A KEPLERIAN DISK AND A BOUNDARY-LAYER AROUND A RAPIDLY ROTATING STAR

We present an analytical model for a disc accreting on to a rapidly rotating star through a boundary layer. The disc is isothermal along the radial direction, and a polytropic equation of state is used to model the transport of energy along the vertical direction; the kinematic viscosity of the fluid is constant. If the star rotates near breakup, the disc angular velocity close to the stellar surface has no maximum, but it settles smoothly to the stellar value, the flow always remaining subsonic. The process is accompanied by a negligible transfer of angular momentum from the disc to the star: both features are general and do not depend on the model assumptions. We are able to determine the analytical relation between the specific angular momentum accreted by the star j* and the stellar angular velocity OMEGA*, for our isothermal model. The comparison with the recent calculations of Paczynski and Popham & Narayan has then shown that the magnitude of j* (OMEGA*) and its functional form depend rather sensitively on the way energy is transported in the disc along the radial direction, and on the viscosity law. The result might be relevant for models of neutron star formation from accretion induced collapse of massive rapidly rotating white dwarfs.