Inspiral waveforms for spinning compact binaries in a new precessing convention

TL;DR

This paper introduces a new precessing convention for inspiral gravitational waveforms from spinning binaries that explicitly uses the orbital angular momentum ${f L}$, leading to more accurate modeling of waveform modulations.

Contribution

The authors develop inspiral waveforms based on ${f L}$ instead of ${f L}_{ m N}$, adding 3PN order terms and analyzing their impact on waveform accuracy.

Findings

Match between ${f L}$ and ${f L}_{ m N}$-based waveforms is often below 0.97.

New convention captures additional physical effects in orbital phase evolution.

Impacts parameter estimation accuracy for spinning binary systems.

Abstract

It is customary to use a precessing convention, based on Newtonian orbital angular momentum ${\bf L}_{\rm N}$, to model inspiral gravitational waves from generic spinning compact binaries. A key feature of such a precessing convention is its ability to remove all spin precession induced modulations from the orbital phase evolution. However, this convention usually employs a post-Newtonian (PN) accurate precessional equation, appropriate for the PN accurate orbital angular momentum ${\bf L}$, to evolve the ${\bf L}_{\rm N}$-based precessing source frame. This motivated us to develop inspiral waveforms for spinning compact binaries in a precessing convention that explicitly use ${\bf L}$ to describe the binary orbits. Our approach introduces certain additional 3PN order terms in the orbital phase and frequency evolution equations with respect to the usual ${\bf L}_{\rm N}$-based implementation of the precessing convention. The implications of these additional terms are explored by computing the match between inspiral waveforms that employ ${\bf L}$ and ${\bf L}_{\rm N}$-based precessing conventions. We found that the match estimates are smaller than the optimal value, namely 0.97, for a non-negligible fraction of unequal mass spinning compact binaries.