Numerically stable equations for the orbital evolution of compact object binaries

TL;DR

This paper introduces a numerically stable and efficient method for evolving compact object binaries under gravitational wave emission by rewriting Peters' equations in logarithmic space, improving convergence and reducing computational cost.

Contribution

The authors reformulate Peters' equations in log-space, enabling standard numerical solvers to converge reliably and efficiently for binary orbital evolution calculations.

Findings

Reduces function evaluations by 60-70% in tests.

Enhances numerical stability of orbital evolution simulations.

Provides a more robust method for gravitational wave-driven binary evolution.

Abstract

The orbital and eccentricity evolution for compact object binaries through gravitational wave emission first derived by Peters and Mathews are used extensively throughout the gravitational wave community for calculating the orbital evolution and merger time of compact binaries. While improved calculations of the binary merger time have been the focus of several investigations since, the orbital evolution has not received the same attention. As the equations lack a closed form solution, a numerical integrator is required, but standard methods typically break when the point of merger is overstepped. We present a rewrite of Peters' equations in $\ln$-space, which allows common numerical solvers to converge. This leads to a more numerically robust and computationally efficient method for evolving compact binaries due to gravitational wave emission, reducing the number of function evaluations by 60\% to 70\% in our tests.