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 starblack 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 innermost stable circular orbit is greater than that obtained by using either the Newtonian potential (i.e. the case in which only the tidal interaction is included.) or the second postNewtonian equation of motion of point mass (i.e. the case in which the effect of general relativity is taken into account but the tidal force is neglected.). In equal mass cases, it is found that for ā/m1 >∼ 3.5 with ā and m1 being the mean radius and the mass of the neutron star, the tidal effect dominates the stability of the binary system while for ā/m1 <∼ 3.5, the relativistic effect, i.e. the fact that the interaction potential has unstable orbit, does. The effect of the circulation is also studied by comparing the Roche ellipsoids (REs) with ∗ e-mail: [email protected] the irrotational Roche-Riemann ellipsoids (IRREs). In the IRREs case, which are believed to be the case of coalescing binary neutron stars, it is found that in the equal mass binary case, the orbital frequency is 495Hz at the ISCO. PACS number(s): 04.30.Db Typeset using REVTEX 2