Newtonian models for black hole gaseous star close binary systems

Circularly orbiting black hole-gaseous star close binary systems are examin ed by using numerically exact stationary configurations in the framework of Newtonian gravity. We have chosen a polytropic star for the fluid componen t of the binary system and considered two ideal situations: (i) a synchrono usly rotating star and (ii) an irrotationally rotating star. They correspon d to a rotating star under the influence of viscosity and to that in the in viscid Limit, respectively. By analysing the stationary sequences of binary systems with small separations, we can discuss the final stages of black h ole-gaseous star close binary systems. Our computational results show that the binary systems reach the Roche(-Riemann) limit states or the Roche lobe filling states without suffering from hydrodynamical instability caused by the tidal force for a certain realistic parameter range of the mass ratio and the polytropic index. Moreover, some of these stable Roche(-Riemann) li mits or Roche lobe filling states survive even under the general relativist ic effect. Therefore, at the final stage of the evolution, which is caused by the emission of gravitational waves, Roche lobe overflow is another poss ibility in addition to the merging of a black hole and a star. For a sufficiently stiff equation of state (the polytropic index N greater than or similar to 0.3-0.7, depending on the mass ratio), the turning point , which corresponds to the secular instability limit for the synchronous bi nary case and the dynamical instability limit for the irrotational binary c ase, disappears on the solution sequence. Therefore, even for a realistic p arameter range, our results are different from the semi-analytic results co mputed by the ellipsoidal approximation in which the turning point always a ppears.