Post-Newtonian analysis of a precessing convention for spinning compact binaries

A precessing source frame, constructed using the Newtonian orbital angular momentum $L_N$, 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 $L$, to evolve the $L_N$-based precessing source frame. This influenced us to develop inspiral waveforms for spinning compact binaries in a precessing convention that explicitly employ $L$ 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 $L_N$-based implementation of the precessing convention. We examine the practical implications of these additional terms by computing the match between inspiral waveforms that employ $L$ and $L_N$-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. (paper)