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

Akcay, Sarp; Gamba, Rossella; Bernuzzi, Sebastiano

We introduce \texttt{TEOBResumSP}: an efficient yet accurate hybrid scheme for generating gravitational waveforms from spin-precessing compact binaries. Our approach Euler-rotates aligned-spin \texttt{TEOBResumS} effective-one-body waveforms from a precessing frame to an inertial frame. We obtain the Euler angles by solving the post-Newtonian precession equations expanded to (next-to)$^4$ leading (second post-Newtonian) order and use them in the waveform mode rotations to extend non-precessing \texttt{TEOBResumS} waveforms to generic spin configurations. The scheme is compared to current state-of-the-art precessing approximants \texttt{NRSur7dq4} and \texttt{SEOBNRv4PHM} in terms of frequency-domain matches of the $\ell=2$ gravitational-wave strain for 200 and 1100 binaries, respectively, with the initial gravitational-wave frequencies between 20 and 50 Hz and the precessing spin parameter $\chi_p$ ranging up to one. The matches are better than $0.965$ for 85\% of the \texttt{NRSur7dq4} and 75\% of the \texttt{SEOBNRv4PHM} sets. The largest disagreements occur for large mass ratios and for large spin components along the orbital plane quantified in terms of a new parameter, $S_{\perp,\text{max}}$, that we introduce. The disagreements stem from Euler-rotating non-precessing waveforms with constant spins, which can be replaced by time-varying $z$-components of spins. Our scheme provides a robust alternative precessing approximant to be employed in the parameter estimation of generic-spin compact binaries with \texttt{TEOBResumSP} waveforms.