All-sky analysis of astrochronometric signals induced by gravitational waves

TL;DR

This paper develops a unified spin-weighted spherical harmonic formalism to analyze astrochronometric signals from gravitational waves, enhancing interpretation, simulation, and correlation analysis of anisotropies in astrophysical observations.

Contribution

It introduces a novel formalism using spin-weighted spherical harmonics to analyze gravitational wave-induced signals in astrophysical data, linking polarization, chirality, and correlation functions.

Findings

Simplifies analysis of anisotropies in astrochronometric signals.

Derives angular cross-spectra and their relation to Hellings-Downs functions.

Calculates expected signal-to-noise ratios for timing and deflection observables.

Abstract

We introduce a unified formalism to describe both timing and astrometric perturbations induced on astrophysical point sources by gravitational waves using a complex spin field on the sphere. This allows the use of spin-weighted spherical harmonics to analyse "astrochronometric" observables. This approach simplifies the interpretation and simulation of anisotropies induced in the observables by gravitational waves. It also allows a simplified derivation of angular cross-spectra of the observables and their relationship with generalised Hellings-Downs correlation functions. The spin-weighted formalism also allows an explicit connection between correlation components and the spin of gravitational wave polarisations and any presence of chirality. We also calculate expected signal-to-noise ratios for observables to compare the utility of timing and deflection observables.