Adding electromagnetic birefringence to pulsar timing and astrometry to detect gravitational waves

TL;DR

This work leverages the total-angular-momentum (TAM) formalism to derive cross-correlations between electromagnetic birefringence and pulsar timing as a probe of gravitational-wave chirality, and extends the framework to astrometry. By decomposing GWs into TAM waves and computing the timing residuals and polarization rotation, the authors obtain compact, mode-by-mode expressions for $z$ and $\psi$ and show how chirality parameters $\Delta\chi_T$ and $\Delta\chi_V$ shape the cross-spectra. The analysis unifies spin-2 (GR) and spin-1 (alternative theories) GW content and provides harmonic- and configuration-space prescriptions for parity-conserving and parity-violating cross-correlations with astrometric observables. The approach enables multi-messenger, sky-wide probes of GW chirality using pulsar timing, polarization rotation measurements, and astrometry, with clear pathways to include anisotropies. Overall, the TAM formalism offers a efficient and versatile toolkit for testing parity violation in the SGWB across multiple observables. $\Delta\chi_T$ and $\Delta\chi_V$ quantify the degree of parity breaking, and the formalism delivers explicit relations between $z$, $\psi$, and astrometric deflections for both spin-1 and spin-2 GWs.

Abstract

It was recently shown that the time variation of the polarization of electromagnetic waves from pulsars can be used, in cross-correlation with pulsar timing, to probe the chirality of an isotropic gravitational wave background. Here, we show that the expression for the cross-correlation is derived efficiently with the total-angular-momentum formalism and use this framework to extend the formulation to cross-correlation with astrometry. We do so for spin-1 gravitational waves (that may arise in alternative-gravity theories) as well as the general-relativistic spin-2 gravitational waves.