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

We introduce $\mathtt{\text{TEOBResumSP}}$: 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 $\mathtt{\text{TEOBResumS}}$ 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 $\mathtt{\text{TEOBResumSP}}$ produces precessing waveforms through the inspiral phase up to the onset of the merger. We compare $\mathtt{\text{TEOBResumSP}}$ to current state-of-the-art precessing approximants $\mathtt{\text{NRSur7dq4}}$, $\mathtt{\text{SEOBNRv4PHM}}$, and $\mathtt{\text{IMRPhenomPv3HM}}$ 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 $\mathtt{\text{SEOBNRv4PHM}}$ involving 1030 more inspirals with ${\chi }_p\le 1$ and mass ratios up to 10. We find that 91% of the $\mathtt{\text{TEOBResumSP}}$-$\mathtt{\text{NRSur7dq4}}$ matches, 85% of the $\mathtt{\text{TEOBResumSP}}$-$\mathtt{\text{SEOBNRv4PHM}}$ matches, and 77% of the $\mathtt{\text{TEOBResumSP}}$-$\mathtt{\text{IMRPhenomPv3HM}}$ 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 $\mathtt{\text{TEOBResumSP}}$ is on its way to becoming a robust precessing approximant to be employed in the parameter estimation of generic-spin compact binaries.