A hybrid post-Newtonian -- effective-one-body scheme for spin-precessing compact-binary waveforms

We introduce \texttt{TEOBResumSP}: an efficient, accurate hybrid scheme for generating gravitational waveforms from spin-precessing compact binaries. The precessing waveforms are generated via the established technique of Euler rotating the non-precessing \texttt{TEOBResumS} waveforms from a precessing frame to an inertial frame. We obtain the Euler angles by solving the post-Newtonian precession equations expanded to second post-Newtonian order. Current version of \texttt{TEOBResumSP} produces precessing waveforms through the inspiral phase up to the onset of the merger. We compare \texttt{TEOBResumSP} to current state-of-the-art precessing approximants \texttt{NRSur7dq4}, \texttt{SEOBNRv4PHM}, and \texttt{IMRPhenomPv3HM} for 200 cases of precessing compact binary inspirals with orbital inclinations up to 90 degrees, mass ratios up to four, and the effective precession parameter $\chi_p$ up to 0.75. We further provide an extended comparison with \texttt{SEOBNRv4PHM} involving 1030 more inspirals with $\chi_p\le 1$ and mass ratios up to 10. We find that 91\% of the \texttt{TEOBResumSP}-\texttt{NRSur7dq4} matches, 85\% of the \texttt{TEOBResumSP}-\texttt{SEOBNRv4PHM} matches, and 77\% of the \texttt{TEOBResumSP}-\texttt{IMRPhenomPv3HM} matches are greater than $0.965$. Most disagreements occur for large mass ratios and $\chi_p \gtrsim 0.6$. We identify the mismatch of the \emph{non}-precessing $(2,1)$ mode as one of the leading causes of disagreements. We also introduce a new parameter, $\chi_{\perp,\text{max}}$, to measure the strength of precession and hint that the mismatch between the above approximants shows an exponential dependence on $\chi_{\perp,\text{max}}$ though this requires further study. Our results indicate that \texttt{TEOBResumSP} is on its way to becoming a robust precessing approximant to be employed in the parameter estimation of generic-spin compact binaries.