Stellar capture by an accretion disc

The long-term evolution of a stellar orbit captured by a massive galactic centre via successive interactions with an accretion disc has been examined. An analytical solution describing the evolution of the stellar orbital parameters during the initial stage of the capture has been found. Our results are applicable to thin Keplerian discs with an arbitrary radial distribution of density and a rather general prescription for the star-disc interaction. Temporal evolution is given in the form of quadrature which can be carried out numerically.