Aligned Spins: Orbital Elements, Decaying Orbits, and Last Stable Circular Orbit to high post-Newtonian Orders

TL;DR

This paper extends the quasi-Keplerian parameterisation for aligned-spin compact binaries to high post-Newtonian orders, providing detailed expressions for orbital decay, energy loss, and the last stable circular orbit.

Contribution

It introduces high-order post-Newtonian corrections for aligned-spin binary systems, including spin-orbit, spin(1)-spin(2), and spin-squared effects, and computes related radiation losses.

Findings

Derived 3PN orbital elements for aligned spins.

Calculated energy and angular momentum loss due to gravitational radiation.

Provided an expression for the last stable circular orbit in terms of orbital velocity.

Abstract

In this article the quasi-Keplerian parameterisation for the case that spins and orbital angular momentum in a compact binary system are aligned or anti-aligned with the orbital angular momentum vector is extended to 3PN point-mass, next-to-next-to-leading order spin-orbit, next-to-next-to-leading order spin(1)-spin(2), and next-to-leading order spin-squared dynamics in the conservative regime. In a further step, we use the expressions for the radiative multipole moments with spin to leading order linear and quadratic in both spins to compute radiation losses of the orbital binding energy and angular momentum. Orbital averaged expressions for the decay of energy and eccentricity are provided. An expression for the last stable circular orbit is given in terms of the angular velocity type variable $x$.