Intermediate mass-ratio black hole binaries: Applicability of small mass-ratio perturbation theory

TL;DR

This paper assesses the accuracy of small mass-ratio perturbation theory in modeling black hole binaries by comparing theoretical predictions with numerical relativity simulations, finding good agreement even for nearly equal masses.

Contribution

It provides the first three terms of the post-adiabatic expansion for small mass-ratio binaries and evaluates the applicability of perturbation theory to nearly comparable mass systems.

Findings

The leading term matches SMR perturbation theory predictions.

The 1-post-adiabatic term is robustly predicted.

The 2-post-adiabatic term is small, indicating high accuracy of 1PA approximation.

Abstract

The dynamics of merging black hole binaries with small mass-ratios (SMR) can be expressed as a series in the symmetric mass-ratio, the post-adiabatic expansion. Using numerical relativity simulations, we compute the first three terms in this series for quasicircular non-spinning binaries. We recover the leading term predicted by SMR perturbation theory, and obtain a robust prediction of the 1-post-adiabatic term. The 2-post-adiabatic term is found to be small, indicating that the 1PA approximation may be quite accurate even for nearly comparable mass binaries. We also estimate the range of applicability for SMR and post-Newtonian series for non-spinning, quasi-circular inspirals.