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

The early inspiral phase of a compact binary coalescence is well modeled 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 the PN energy equals the energy of the (post-Newtonian expanded) exact Kerr solution. However, for comparable-mass systems the MECO of the PN energy does not exist when bodies have large spins and no analytical solution to the end of the inspiral is known. By including the exact Kerr limit, 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.