Parameter estimation of gravitational waves from precessing black hole-neutron star inspirals with higher harmonics

Precessing black hole-neutron star (BH-NS) binaries produce a rich gravitational wave signal, encoding the binary's nature and inspiral kinematics. Using the lalinference_mcmc Markov chain Monte Carlo parameter estimation code, we use two fiducial examples to illustrate how the geometry and kinematics are encoded into the modulated gravitational wave signal, using coordinates well adapted to precession. Extending previous work, we demonstrate that the performance of detailed parameter estimation studies can often be estimated by ``effective'' studies: comparisons of a prototype signal with its nearest neighbors, adopting a fixed sky location and idealized two-detector network. Using a concrete example, we show that higher harmonics provide nonzero but small local improvement when estimating the parameters of precessing BH-NS binaries. We also show that higher harmonics can improve parameter estimation accuracy for precessing binaries by breaking leading-order discrete symmetries and thus ruling out approximately degenerate source orientations. Our work illustrates quantities gravitational wave measurements can provide, such as the orientation of a precessing short gamma ray burst progenitor relative to the line of sight. More broadly, ``effective'' estimates may provide a simple way to estimate trends in the performance of parameter estimation for generic precessing BH-NS binaries in next-generation detectors. For example, our results suggest that the orbital chirp rate, precession rate, and precession geometry are roughly independent observables, defining natural variables to organize correlations in the high-dimensional BH-NS binary parameter space.