Parameter estimation of gravitational waves from nonprecessing black hole-neutron star inspirals with higher harmonics: Comparing Markov-chain Monte Carlo posteriors to an effective Fisher matrix

Most calculations of the gravitational wave signal from merging compact binaries limit attention to the leading-order quadrupole when constructing models for detection or parameter estimation. Some studies have claimed that if additional ``higher harmonics'' are included consistently in the gravitational wave signal and search model, binary parameters can be measured much more precisely. Using the lalinference Markov-chain Monte Carlo parameter estimation code, we construct posterior parameter constraints associated with two distinct nonprecessing black hole--neutron star (BH-NS) binaries, each with and without higher-order harmonics. All simulations place a plausible signal into a three-detector network with Gaussian noise. Our simulations suggest that higher harmonics provide little information, principally allowing us to measure a previously unconstrained angle associated with the source geometry well but otherwise improving knowledge of all other parameters by a few percent for our loud fiducial signal ($\ensuremath{\rho}=20$). Even at this optimistic signal amplitude, different noise realizations have a more significant impact on parameter accuracy than higher harmonics. We compare our results with the ``effective Fisher matrix'' introduced previously as a method to obtain robust analytic predictions for complicated signals with multiple significant harmonics. We find generally good agreement with these predictions, confirm that intrinsic parameter measurement accuracy is nearly independent of detector network geometry, and show that uncertainties in extrinsic and intrinsic parameters can, to a good approximation, be separated. For our fiducial example, the individual masses can be determined to lie between $7.11--11.48{M}_{\ensuremath{\bigodot}}$ and $1.77--1.276{M}_{\ensuremath{\bigodot}}$ at greater than 99% confidence level, accounting for unknown BH spin. Assuming comparable control over waveform systematics, measurements of BH-NS binaries can constrain the BH and perhaps NS mass distributions. Using analytic arguments to guide extrapolation, we anticipate that higher harmonics should provide little new information about nonprecessing BH-NS binaries, for the signal amplitudes expected for the first few detections. Though our study focused on one particular example---higher harmomics---any study of subdominant degrees of freedom in gravitational wave astronomy can adopt the tools presented here ($V/{V}_{\text{prior}}$ and ${D}_{\mathrm{KL}}$) to assess whether new physics is accessible (e.g., modifications of gravity, spin-orbit misalignment) and if so precisely what information those new parameters provide.