Newtonian models for black hole-gaseous star close binary systems
  Circularly orbiting black hole-gaseous star close binary systems are examined by using numerically exact stationary configurations in the framework of Newtonian gravity. We have chosen a polytropic star for the fluid component of the binary system and considered two ideal situations: 1) a synchronously rotating star and 2) an irrotationally rotating star. They correspond to a rotating star under the influence of viscosity and to that in the inviscid limit, respectively. By analyzing the stationary sequences of binary systems with small separations, we can discuss the final stages of black hole-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 due to tidal force for a large parameter range of the mass ratio and the polytropic index. It is very likely that such stable Roche(-Riemann) limits or Roche lobe filling states survive even under the general relativistic effect. Therefore, at the final stage of the evolution which is caused by the emission of gravitational waves, the Roche overflow will occur instead of merging of a black hole and a star. 
Koji Uryu (ICTP, SISSA), Yoshiharu Eriguchi (Univ. Tokyo)