The Innermost Stable Circular Orbit in Compact Binaries

TL;DR

This paper reviews the physics and methods used to determine the innermost stable circular orbit (ISCO) in relativistic binary systems, highlighting the effects of finite size and relativity on orbital stability.

Contribution

It provides a comprehensive review of techniques and assumptions used to locate the ISCO in black hole and neutron star binaries, discussing discrepancies and resolutions.

Findings

Different methods yield varying ISCO locations.

Finite size and relativistic effects influence orbital stability.

Discussion on resolving differences in ISCO calculations.

Abstract

Newtonian point mass binaries can be brought into arbitrarily close circular orbits. Neutron stars and black holes, however, are extended, relativistic objects. Both finite size and relativistic effects make very close orbits unstable, so that there exists an innermost stable circular orbit (ISCO). We illustrate the physics of the ISCO in a simple model problem, and review different techniques which have been employed to locate the ISCO in black hole and neutron star binaries. We discuss different assumptions and approximations, and speculate on how differences in the results may be explained and resolved.