Innermost stable circular orbit of arbitrary-mass compact binaries at fourth post-Newtonian order

TL;DR

This paper calculates the innermost stable circular orbit (ISCO) for arbitrary-mass compact binaries at 4PN order using two methods, showing results consistent with numerical relativity and gravitational self-force calculations, without resummation techniques.

Contribution

It provides a gauge-invariant 4PN order calculation of the ISCO for arbitrary-mass binaries using harmonic and ADM coordinates, including tail effects, with results matching other approaches.

Findings

ISCO location at 4PN order matches GSF and numerical relativity results.

The gauge transformation between harmonic and ADM coordinates is explicitly computed.

The 4PN ISCO result is close to numerical and self-force predictions.

Abstract

We compute by means of post-Newtonian (PN) methods the innermost stable circular orbit (ISCO) of arbitrary-mass (in particular, comparable-mass) compact binaries. Two methods are used with equivalent results: dynamical perturbation of the conservative equations of motion in harmonic coordinates, and dynamical perturbation of the conservative Hamiltonian in ADM coordinates. The perturbation of the non-local tail term at 4PN order in both approaches is carefully investigated. Our final gauge invariant result for the location of the ISCO at 4PN order is close to the numerical value of the ISCO shift computed by the gravitational self-force (GSF) approach in the small mass-ratio limit, and is also in good agreement with the full numerical-relativity calculation in the case of equal masses. The PN method followed here is considered in standard Taylor-expanded form, without any resummation techniques applied. As a complement, we also compute explicitly the gauge transformation from harmonic coordinates to ADM coordinates up to 4PN order, including the tail contribution therein.