A semianalytic Fisher matrix for precessing binaries with a single significant spin

TL;DR

This paper introduces a simple semianalytic Fisher matrix approach for precessing binaries with a significant spin, enabling efficient parameter estimation of gravitational wave sources including black hole-neutron star systems.

Contribution

It extends previous nonprecessing binary analyses to include precession effects, providing a straightforward method to estimate measurement precision of binary parameters from gravitational waves.

Findings

The Fisher matrix can be approximated by a weighted average of harmonic channels.

The method effectively incorporates precession effects in parameter estimation.

It offers a simple way to understand measurement capabilities of gravitational wave detectors.

Abstract

Gravitational waves from a binary with a single dynamically significant spin, notably including precessing black hole-neutron star (BH-NS) binaries, let us constrain that binary's properties: the two masses and the dominant black hole spin. Based on a straightforward fourier transform of $h(t)$ enabled by the corotating frame, we show the Fisher matrix for precessing binaries can be well-approximated by an extremely simple semianalytic approximation. This approximation can be easily understood as a weighted average of independent information channels, each associated with one gravitational wave harmonic. Generalizing previous studies of nonprecessing binaries to include critical symmetry-breaking precession effects required to understand plausible astrophysical sources, our ansatz can be applied to address how well gravitational wave measurements can address a wide range of astrophysical and fundamental questions. Our approach provides a simple method to assess what parameters gravitational wave detectors can measure, how well, and why.