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

Abstract

The innermost stable circular orbits (ISCO) of coalescing neutron star-black hole binary are studied taking into account both the tidal and relativistic effects. We adopt the generalized pseudo-Newtonian potential to mimic the general relativistic effects of gravitation. It is found that the separation of the neutron star and the black hole at the ISCO is greater than that obtained by using either the Newtonian potential or the second post-Newtonian equation of 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 the neutron star, the tidal effect dominates the stability of the binary system while for $\bar{a}/m_1 < 3.5$, the relativistic effect, i.e. the fact that the interaction potential has unstable orbit, does.