Gravitational waves from BH-NS binaries: Effective Fisher matrices and parameter estimation using higher harmonics

TL;DR

This paper introduces a method to compute effective Fisher matrices from gravitational wave signals of BH-NS binaries, analyzing how higher harmonics influence parameter estimation, especially in precessing systems.

Contribution

It presents a novel approach to approximate Fisher matrices from ambiguity functions and assesses the impact of higher harmonics on parameter measurement accuracy.

Findings

Higher harmonics marginally improve parameter estimation for non-precessing binaries.

Precessing binaries benefit more from higher harmonics in measuring parameters.

The method provides concrete estimates for measurement accuracy using adapted coordinates.

Abstract

Inspiralling black hole-neutron star (BH-NS) binaries emit a complicated gravitational wave signature, produced by multiple harmonics sourced by their strong local gravitational field and further modulated by the orbital plane's precession. Some features of this complex signal are easily accessible to ground-based interferometers (e.g., the rate of change of frequency); others less so (e.g., the polarization content); and others unavailable (e.g., features of the signal out of band). For this reason, an ambiguity function (a diagnostic of dissimilarity) between two such signals varies on many parameter scales and ranges. In this paper, we present a method for computing an approximate, effective Fisher matrix from variations in the ambiguity function on physically pertinent scales which depend on the relevant signal to noise ratio. As a concrete example, we explore how higher harmonics improve parameter measurement accuracy. As previous studies suggest, for our fiducial BH-NS binaries and for plausible signal amplitudes, we see that higher harmonics at best marginally improve our ability to measure parameters. For non-precessing binaries, these Fisher matrices separate into intrinsic (mass, spin) and extrinsic (geometrical) parameters; higher harmonics principally improve our knowledge about the line of sight. For the precessing binaries, the extra information provided by higher harmonics is distributed across several parameters. We provide concrete estimates for measurement accuracy, using coordinates adapted to the precession cone in the detector's sensitive band.