Measuring orbital eccentricity and periastron advance in quasi-circular black hole simulations

TL;DR

This paper evaluates various methods for measuring orbital eccentricity and periastron advance in binary black hole simulations, highlighting the effectiveness of gravitational wave phase analysis for low eccentricities and identifying deviations from post-Newtonian predictions.

Contribution

It introduces a reliable method using gravitational wave phase for measuring low eccentricities and compares numerical results with post-Newtonian approximations for periastron advance.

Findings

Gravitational wave phase provides a clean measurement of low eccentricity.

Orbital eccentricity decay agrees with post-Newtonian predictions.

Detected deviations between numerical simulations and post-Newtonian calculations for periastron advance.

Abstract

We compare different methods of computing the orbital eccentricity of quasi-circular binary black hole systems using the orbital variables and gravitational wave phase and frequency. For eccentricities of about a per cent, most methods work satisfactorily. For small eccentricity, however, the gravitational wave phase allows a particularly clean and reliable measurement of the eccentricity. Furthermore, we measure the decay of the orbital eccentricity during the inspiral and find reasonable agreement with post-Newtonian results. Finally, we measure the periastron advance of non-spinning binary black holes, and we compare them to post-Newtonian approximations. With the low uncertainty in the measurement of the periastron advance, we positively detect deviations between fully numerical simulations and post-Newtonian calculations.