Computationally efficient models for the dominant and subdominant harmonic modes of precessing binary black holes

We present imrphenomxphm, a phenomenological frequency-domain model for the gravitational-wave signal emitted by quasicircular precessing binary black holes, which incorporates multipoles beyond the dominant quadrupole in the precessing frame. The model is a precessing extension of imrphenomxhm, [C. Garc\'{\i}a-Quir\'os et al., Phys. Rev. D 102, 064002 (2020)] based on approximate maps between aligned-spin waveform modes in the coprecessing frame and precessing waveform modes in the inertial frame, which is commonly referred to as ``twisting up'' the nonprecessing waveforms. imrphenomxphm includes imrphenomxp as a special case, the restriction to the dominant quadrupole contribution in the coprecessing frame. We implement two alternative mappings, one based on a single-spin post-Newtonian approximation, as used in imrphenompv2 [M. Hannam et al., Phys. Rev. Lett. 113, 151101 (2014).], and one based on the double-spin multiple scale analysis approach of [K. Chatziioannou et al., Phys. Rev. D 95, 104004 (2017).]. We include a detailed discussion of conventions used in the description of precessing binaries and of all choices made in constructing the model. The computational cost of imrphenomxphm is further reduced by extending the interpolation technique of [C. Garc\'{\i}a-Quir\'os et al., Classical Quant. Grav. 38, 015006 (2021).] to the Euler angles. The accuracy, speed, robustness, and modularity of the imrphenomx family will make these models productive tools for gravitational wave astronomy in the current era of greatly increased number and diversity of detected events.