Post-newtonian analysis of precessing convention for spinning compact binaries

TL;DR

This paper develops inspiral gravitational waveforms for spinning compact binaries using a precessing convention based on the Newtonian orbital angular momentum, incorporating additional post-Newtonian order terms, and evaluates their impact on waveform accuracy.

Contribution

It introduces a new approach employing the orbital angular momentum ${f L}$ in the precessing convention, adding 3PN order terms and analyzing their effects on waveform matches.

Findings

Match between ${f L}$ and ${f L_{ m N}}$-based waveforms can be below 0.97

Additional 3PN terms influence waveform accuracy for unequal mass binaries

The new approach affects the modeling of inspiral gravitational waves from spinning binaries

Abstract

A precessing source frame, constructed using the Newtonian orbital angular momentum ${\bf L_{\rm N}}$, can be invoked to model inspiral gravitational waves from generic spinning compact binaries. An attractive 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 influenced us to develop inspiral waveforms for spinning compact binaries in a precessing convention that explicitly employ ${\bf L}$ to describe the binary orbits. Our approach introduces certain additional 3PN order terms in the evolution equations for the orbital phase and frequency with respect to the usual ${\bf L_{\rm N}}$-based implementation of the precessing convention. We examine the practical implications of these additional terms by computing the match between inspiral waveforms that employ ${\bf L}$ and ${\bf L_{\rm N}}$-based precessing conventions. The match estimates are found to be smaller than the optimal value, namely $0.97$, for a non-negligible fraction of unequal mass spinning compact binaries.