Relativistic cross sections of mass stripping and tidal disruption of a star by a super-massive rotating black hole

Aims. We consider the problem of tidal disruption of a star by a super-massive rotating black hole. Methods. Using a numerically fast Lagrangian model of a tidally disrupted star developed in our previous works, we survey the parameter space of the problem and find regions where the total disruption of the star or a partial mass loss from the star takes place as a result of fly-by around the black hole. Our treatment is based on General Relativity, and we consider a range of black hole masses where the tidal disruption competes with the relativistic effect of direct capture of stars by the black hole. We model the star as a full polytrope with n = 1.5 with the solar mass and radius. We show that our results can also be used to obtain the amount of mass lost by stars with different stellar masses and radii. Results. We find that the results can be conveniently represented on the plane of specific orbital angular momenta of the star (j θ , j Φ ). We calculate the contours of a given mass loss of the star on this plane, for a given black hole mass M, rotational parameter a and inclination of the trajectory of the star with respect to the black hole equatorial plane. In the following such contours are referred to as the tidal cross sections. It is shown that the tidal cross sections can be approximated as circles symmetric above the axis j Φ = 0, and shifted with respect to the origin of the coordinates in the direction of negative j θ . The radii and shifts of these circles are obtained numerically for the black hole masses in the range 5 × 10 5 M Θ -10 9 M Θ and different values of a. It is shown that when a = 0 tidal disruption takes place for M < 5 x 10 7 M Θ and when a ≈ 1 tidal disruption is possible for M < 10 9 M Θ .