Hybrid post-Newtonian effective-one-body scheme for spin-precessing compact-binary waveforms up to merger

We introduce TEOBResumSP: an efficient yet accurate hybrid scheme for generating gravitational waveforms from spin-precessing compact binaries. The precessing waveforms are generated via the established technique of Euler rotating aligned-spin (nonprecessing) waveforms from a precessing frame to an inertial frame. We employ the effective-one-body approximant TEOBResumS to generate the aligned-spin waveforms. We obtain the Euler angles by solving the post-Newtonian precession equations expanded to ${(\mathrm{next}\text{\ensuremath{-}}\mathrm{to})}^{4}$ leading (second post-Newtonian) order. Current version of TEOBResumSP produces precessing waveforms through the inspiral phase up to the onset of the merger. We compare TEOBResumSP to current state-of-the-art precessing approximants NRSur7dq4, SEOBNRv4PHM, and IMRPhenomPv3HM in terms of frequency-domain matches of the $\ensuremath{\ell}=2$ gravitational-wave strain 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 ${\ensuremath{\chi}}_{p}$ up to 0.75. We further provide an extended comparison with SEOBNRv4PHM involving 1030 more inspirals with ${\ensuremath{\chi}}_{p}$ ranging up to one and mass ratios up to 10. We find that 91% of the TEOBResumSP-NRSur7dq4 matches, 85% of the TEOBResumSP-SEOBNRv4PHM matches, and 77% of the TEOBResumSP-IMRPhenomPv3HM matches are greater than 0.965. Most of the significant disagreements occur for large mass ratios and ${\ensuremath{\chi}}_{p}\ensuremath{\gtrsim}0.6$. We identify the mismatch of the non-precessing (2,1) mode as one of the leading causes of disagreements. We also introduce a new parameter, ${\ensuremath{\chi}}_{\ensuremath{\perp},\mathrm{max}}$, to measure the strength of precession and hint that the strain mismatch between the above waveform approximants shows an exponential dependence on ${\ensuremath{\chi}}_{\ensuremath{\perp},\mathrm{max}}$ though this requires further study. Our results indicate that TEOBResumSP is on its way to becoming a robust precessing approximant to be employed in the parameter estimation of generic-spin compact binaries.