Innermost Stable Circular Orbit of Coalescing Neutron Star-Black Hole Binary: Generalized Pseudo-Newtonian Potential Approach

The innermost stable circular orbits (ISCO) of coalescing neutron star-blackhole binary are studied taking into account both the tidal and relativisticeffects. We adopt the generalized pseudo-Newtonian potential to mimic thegeneral relativistic effects of gravitation. It is found that the separation ofthe neutron star and the black hole at the ISCO is greater than that obtainedby using either the Newtonian potential or the second post-Newtonian equationof motion of point mass. In equal mass cases, it is found that for $\bar{a}/m_1> 3.5$ with $\bar{a}$ and $m_1$ being the mean radius and the mass of theneutron star, the tidal effect dominates the stability of the binary systemwhile for $\bar{a}/m_1 < 3.5$, the relativistic effect, i.e. the fact that theinteraction potential has unstable orbit, does.Comment: 31 pages, revtex, 8 figures(eps). To appear in Progress of Theoretical Physics, Vol.96 No.