Post-newtonian analysis of precessing convention for spinning compact binaries

A precessing source frame, constructed using the Newtonian orbital angular momentum ${\mathbf{L}}_{\mathrm{N}}$, 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 $\mathbf{L}$, 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 $\mathbf{L}$ 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 $\mathbf{L}$ and ${\mathbf{L}}_{\mathrm{N}}$-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.