Approximate helical symmetry in compact binaries

TL;DR

This paper investigates the approximate helical symmetry in binary inspirals, quantifies its breakdown due to eccentricity and precession using post-Newtonian theory, and confirms predictions with numerical relativity data.

Contribution

It analytically predicts the order at which helical symmetry breaks in binary systems and validates this with numerical relativity waveforms.

Findings

Helical symmetry breaks at about 5PN order for quasi-circular non-precessing binaries.

Analytical predictions agree well with numerical relativity results.

Eccentric orbits exhibit non-vanishing helical flux at 0PN order.

Abstract

The inspiral of a circular, non-precessing binary exhibits an approximate helical symmetry. The effects of eccentricity, precession, and radiation reaction break the exact symmetry. We estimate the failure of this symmetry using the flux of the BMS charge corresponding to helical symmetry carried away by gravitational waves. We analytically compute the helical flux for binaries moving on eccentric orbits and quasi-circular orbits without precession using post-Newtonian theory. The helical flux is non-vanishing at the 0PN order for eccentric orbits as expected. We analytically predict the helical flux to be at a relative 5PN order for quasi-circular non-precessing binaries. This prediction is compared with 113 quasi-circular non-precessing numerical relativity waveforms from the SXS catalog. We find good agreement between analytical and numerical results for quasi-circular non-precessing binaries establishing that helical symmetry starts to break at 5PN for these binaries.