Parameter Estimation of Gravitational Waves from Nonprecessing BH-NS Inspirals with higher harmonics: Comparing MCMC posteriors to an Effective Fisher Matrix

TL;DR

This study uses MCMC and Fisher matrix methods to analyze gravitational wave parameter estimation for nonprecessing BH-NS binaries, finding higher harmonics offer limited additional information at expected detection levels.

Contribution

It compares MCMC posteriors with an effective Fisher matrix approach for BH-NS inspirals, providing tools to assess potential new physics and parameter measurement accuracy.

Findings

Higher harmonics provide minimal extra information about source geometry.

Results favor the effective Fisher matrix approach for parameter estimation.

Masses can be measured with high confidence, constraining astrophysical models.

Abstract

Using the \texttt{lalinference} Markov-chain Monte Carlo parameter estimation code, we examine two distinct nonprecessing black hole-neutron star (BH-NS) binaries with and without higher-order harmonics. Our simulations suggest that higher harmonics provide a minimal amount of additional information, principally about source geometry. Higher harmonics do provide disproportionately more information than expected from the signal power. Our results compare favorably to the "effective Fisher matrix" approach. Extrapolating using analytic scalings, we expect higher harmonics will provide little new information about nonprecessing BH-NS binaries at the signal amplitudes expected for the first few detections. Any study of subdominant degrees of freedom in gravitational wave astronomy can adopt the tools presented here ($V/V_{\rm prior}$ and $D_{KL}$) 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. For astrophysicists, we provide a concrete illustration of how well parameters of a BH-NS binary can be measured, relevant to the astrophysical interpretation of coincident EM and GW events (e.g., short GRBs). For our fiducial initial-detector example, the individual masses can be determined to lie between $7.11-11.48 M_\odot$ and $1.77-1.276M_\odot$ at greater than 99% confidence, accounting for unknown BH spin. Assuming comparable control over waveform systematics, future measurements of BH-NS binaries can constrain the BH and perhaps NS mass distributions.