RELATIVISTIC TIDAL INTERACTION OF STARS WITH A ROTATING BLACK-HOLE

The tidal interaction of n = 1.5 poly-tropic stars with a massive rota ting black hole is studied numerically. The general relativistic tidal potential for the Kerr metric is used to evaluate tidal forces exerte d on a star. The hydrodynamic response of a star to these forces is tr eated in the Newtonian approximation using a three-dimensional, Euleri an, PPM hydrodynamical code. We compute the energy, Delta E, and angul ar momentum, Delta L, transferred into a star and the mass, Delta M, l ost by the star during the interaction. The quantities Delta E, Delta L, and Delta M depend on the stellar orbit, stellar structure, and the black hole's mass and angular momentum in a complicated way. We show that the dependence can be factorized by introducing a single dimensio nless parameter (C) over cap proportional to the integral of the squar e of the trace of the tidal tensor along the stellar trajectory. The e nergy and angular momentum transfer, and the mass loss as functions of (C) over cap are found in hydrodynamical simulations. Analytical appr oximations to Delta E((C) over cap) and Delta M((C) over cap) are cons tructed. The value of (C) over cap does not depend on the stellar stru cture. It is a universal function on the parameters of the orbit and c an tabulated once and for ah. Tables of (C) double under bar are prese nted. The results of this paper allow one to easily determine the outc ome of tidal interaction for every possible combination of the input p arameters. We find that the final energy of a star or a stellar remnan t (if mass is lost) and its internal angular momentum as well depend m ost strongly on the angle between the initial orbital angular momentum and the angular momentum of the black hole.