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The new model of a tidally disrupted star: further development and relativistic calculations

In this paper we develop a new semi-analytical model of a tidally perturbed or tidally disrupted star proposed recently by two of us. This model is effectively a one-dimensional Lagrangian model and it can be evolved numerically much faster than the conventional three-dimensional (3D) models. A self-consistent derivation of dynamical equations of the model is performed and several important theorems concerning the dynamics of the model are proved without any particular assumptions concerning the equation of state of the stellar gas. The dynamical equations are solved numerically for the case of an n = 1.5 polytropic star evolving in the relativistic tidal field of a 10 7 -M O . Kerr black hole. Some results of these calculations are compared with the results of calculations based on finite-difference 3D simulations. The comparison shows a very good agreement between both approaches to the problem. Then we show that the strength of the tidal encounter depends significantly on the relative orientation of the orbital angular momentum of the star and the spin of the black hole.