A Survey of Four Precessing Waveform Models for Binary Black Hole Systems

Angular momentum and spin precession are expected to be generic features of a significant fraction of binary black hole systems. As such, it is essential to have waveform models that faithfully incorporate the effects of precession. Here, we assess how well the current state of the art models achieve this for waveform strains constructed only from the $\mathrm{\ell }=2$ multipoles.Specifically, we conduct a survey on the faithfulness of the waveform models %(approximants) $\mathtt{\text{SEOBNRv5PHM}}$, $\mathtt{\text{TEOBResumS}}$, $\mathtt{\text{IMRPhenomTPHM}}$, $\mathtt{\text{IMRPhenomXPHM}}$ to the numerical relativity (NR) surrogate $\mathtt{\text{NRSur7dq4}}$ and to NR waveforms from the $\mathtt{\text{SXS}}$ catalog. The former assessment involves systems with mass ratios up to six and dimensionless spins up to 0.8. The latter employs $317$ short and $23$ long $\mathtt{\text{SXS}}$ waveforms. For all cases, we use reference inclinations of zero and ${90}^{\circ }$. We find that all four models become more faithful as the mass ratio approaches unity and when the merger-ringdown portion of the waveforms are excluded. We also uncover a correlation between the co-precessing $(2,\pm 2)$ multipole mismatches and the overall strain mismatch. We additionally find that for high inclinations, precessing $(2,\pm 1)$ multipoles that are more faithful than their $(2,\pm 2)$ counterparts, and comparable in magnitude, improve waveform faithfulness. As a side note, we show that use of uniformly-filled parameter spaces may lead to an overestimation of precessing model faithfulness. We conclude our survey with a parameter estimation study in which we inject two precessing $\mathtt{\text{SXS}}$ waveforms (at low and high masses) and recover the signal with $\mathtt{\text{SEOBNRv5PHM}}$, $\mathtt{\text{IMRPhenomTPHM}}$ and $\mathtt{\text{IMRPhenomXPHM}}$. As a bonus, we present preliminary multidimensional fits to model unfaithfulness for Bayesian model selection in parameter estimation studies.