Minimum energy and the end of the inspiral in the post-Newtonian approximation

TL;DR

This paper refines the definition of the minimum energy circular orbit (MECO) in the post-Newtonian approximation, enabling a more accurate determination of the inspiral's end for highly spinning, comparable-mass binary systems.

Contribution

It introduces a hybrid method incorporating the Kerr limit and recent PN terms to define a well-behaved MECO for diverse binary configurations.

Findings

The hybrid MECO condition exists for high-spin, comparable-mass systems.

It aligns with other definitions in non-spinning cases.

Applicable to any PN order.

Abstract

The early inspiral phase of a compact binary coalescence is well modelled by the post-Newtonian (PN) approximation to the orbital energy and gravitational wave flux. The transition from the inspiral phase to the plunge can be defined by the minimum energy circular orbit (MECO). In the extreme mass-ratio limit, up to the highest PN order known, the PN energy equals the energy of the exact Kerr solution. However, for comparable-mass systems the MECO of the PN energy does not exist when bodies have large spins. By including the exact Kerr limit and recently published post-Newtonian terms we extract a well-defined minimum of the orbital energy beyond which the plunge or merger occurs. We study the hybrid condition for a number of cases of both black hole and neutron stars and compare to other commonly employed definitions. Our method can be used for any known order of the post-Newtonian series and enables the MECO condition to be used to define the end of the inspiral phase for highly spinning, comparable mass systems.