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The current paradigm for constructing waveforms from precessing compactbinaries is to first construct a waveform in a non-inertial, co-precessingbinary source frame followed by a time-dependent rotation to map back to thephysical, inertial frame. A key insight in the construction of these models isthat the co-precessing waveform can be effectively mapped to some equivalentaligned spin waveform. Secondly, the time-dependent rotation implicitlyintroduces $m$-mode mixing, necessitating an accurate description ofhigher-order modes in the co-precessing frame. We assess the efficacy of thismodelling strategy in the strong field regime using Numerical Relativitysimulations. We find that this framework allows for the highly accurateconstruction of $(2,\pm 2)$ modes in our data set, while for higher ordermodes, especially the $(2,|1|), (3,|2|)$ and $(4,|3|)$ modes, we find ratherlarge mismatches. We also investigate a variant of the approximate map betweenco-precessing and aligned spin waveforms, where we only identify the slowlyvarying part of the time domain co-precessing waveforms with the aligned-spinone, but find no significant improvement. Our results indicate that the simpleparadigm to construct precessing waveforms does not provide an accuratedescription of higher order modes in the strong-field regime, and demonstratethe necessity for modelling mode asymmetries and mode-mixing to significantlyimprove the description of precessing higher order modes.

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