Eccentric binary black holes: Comparing numerical relativity and small mass-ratio perturbation theory

TL;DR

This paper compares numerical relativity and small mass-ratio perturbation theory for eccentric binary black holes, providing tools for better modeling across a range of mass ratios and eccentricities, and quantifying the accuracy of these methods.

Contribution

It introduces a new eccentricity definition based on gravitational wave modes and assesses the applicability of NR and SMR methods across different mass ratios and eccentricities.

Findings

SMR contributions are subdominant in the comparable mass regime.

Developed tools to map NR and SMR inspiral evolutions.

Quantified next-to-leading order SMR effects on fluxes and periastron advance.

Abstract

The modelling of unequal mass binary black hole systems is of high importance to detect and estimate parameters from these systems. Numerical relativity (NR) is well suited to study systems with comparable component masses, $m_1\sim m_2$, whereas small mass ratio (SMR) perturbation theory applies to binaries where $q=m_2/m_1<< 1$. This work investigates the applicability for NR and SMR as a function of mass ratio for eccentric non-spinning binary black holes. We produce $52$ NR simulations with mass ratios between $1:10$ and $1:1$ and initial eccentricities up to $0.7$. From these we extract quantities like gravitational wave energy and angular momentum fluxes and periastron advance, and assess their accuracy. To facilitate comparison, we develop tools to map between NR and SMR inspiral evolutions of eccentric binary black holes. We derive post-Newtonian accurate relations between different definitions of eccentricity. Based on these analyses, we introduce a new definition of eccentricity based on the (2,2)-mode of the gravitational radiation, which reduces to the Newtonian definition of eccentricity in the Newtonian limit. From the comparison between NR simulations and SMR results, we quantify the unknown next-to-leading order SMR contributions to the gravitational energy and angular momentum fluxes, and periastron advance. We show that in the comparable mass regime these contributions are subdominant and higher order SMR contributions are negligible.