Validity of common modeling approximations for precessing binary black holes with higher-order modes

The current paradigm for constructing waveforms from precessing compact binaries is to first construct a waveform in a noninertial, coprecessing binary source frame followed by a time-dependent rotation to map back to the physical, inertial frame. A key insight in the construction of these models is that the coprecessing waveform can be effectively mapped to some equivalent aligned spin waveform. Secondly, the time-dependent rotation implicitly introduces m-mode mixing, necessitating an accurate description of higher-order modes in the coprecessing frame. We assess the efficacy of this modeling strategy in the strong field regime using numerical relativity simulations. We find that this framework allows for the highly accurate construction of (2,±2) modes in our dataset, while for higher order modes, especially the (2,|1|),(3,|2|) and (4,|3|) modes, we find rather large mismatches. We also investigate a variant of the approximate map between coprecessing and aligned spin waveforms, where we only identify the slowly varying part of the time domain coprecessing waveforms with the aligned-spin one, but find no significant improvement. Our results indicate that the simple paradigm to construct precessing waveforms does not provide an accurate description of higher order modes in the strong-field regime and demonstrate the necessity for modeling mode asymmetries and mode-mixing to significantly improve the description of precessing higher order modes.