Analytical model of precessing binaries using post-Newtonian theory in the extreme mass-ratio limit I: General Formalism

We develop a fully analytical waveform model for precessing binaries with arbitrary spin vectors using post-Newtonian~(PN) theory in the extreme mass-ratio limit and a hierarchical multi-scale analysis. The analytical model incorporates leading PN order spin precession dynamics from spin-orbit, spin-spin, and quadrupole-monopole couplings, and 2PN order dissipative dynamics truncated to first order in the mass ratio $q \ll 1$. Due to the pure analytic nature of the model, the framework developed herein can readily be extended to both higher PN and higher-$q$ order. Although the PN series is asymptotic to this limit, our results can be used to estimate how precession affects the measurability of certain binary parameters, and to inform and compare with other waveform approximants, such as effective-one-body models, hybrid waveforms, and self-force calculations.
Comment: 29 pages, 10 figures, published version