Non-linear effects at tidal capture of stars by a massive black hole -I. Incompressible affine model

Non-linear effects of the tidal interaction of a star with a massive black hole are discussed on the basis of an ellipsoidal 'affine' stellar model proposed by Carter & Luminet. The effects are considered for an incompressible stellar model. We compute the amount of energy deposited into the star from the orbital motion by tidal forces and determine an effective Roche limit of tidal disruption for a parabolic orbit. A comparison between the non-linear affine model and a linear theory of small perturbations is made, and the limits of their applicability are found. The dynamics of the tidal interactions at subsequent pericentre passages after the tidal capture are considered, and it is shown that the non-linear effects significantly reinforce the absorption of the orbital energy by the star, and result in tidal disruptions far beyond the Roche limit.