Gravitational wave phasing for spinning compact binaries in inspiraling eccentric orbits

We present a semi-analytic prescription to obtain gravitational wave (GW) phasing for spinning compact binaries in inspiraling eccentric orbits, while restricting the spin effects to the leading order spin-orbit coupling. We demonstrate that only the radial part of the orbital dynamics is amenable for a Keplerian-type solution that is compatible with the standard post-Newtonian (PN) accurate quasi-Keplerian parametrization for nonspinning compact binaries. We also derive PN-accurate equations governing the evolution of the Eulerian angles that are crucial to obtain temporally evolving GW polarization states and compute the associated fully 1PN accurate amplitude corrected GW polarization states. We show that it is not possible to obtain a Keplerian-type parametric solution for the angular part of the above dynamics in a noninertial frame that follows the precessing orbital plane [N. J. Cornish and J. S. Key, Phys. Rev. D 82, 044028 (2010)]. Further, we point out certain undesirable features present in their approach for doing GW phasing, like the use of precessing polarization vectors to construct the polarization states.