Cross-correlating Astrometric and Timing Residuals to Constrain Stochastic Gravitational-Wave Backgrounds

TL;DR

This paper develops a formalism to analyze cross-correlations between astrometric and timing residuals for distant sources, aiming to detect or constrain the stochastic gravitational-wave background with improved sensitivity and reduced systematics.

Contribution

It introduces a unified spin-weighted formalism and generalized Hellings-Downs curves for mixed observables, enabling new cross-correlation methods for gravitational-wave detection.

Findings

Derived angular correlation functions for mixed observables.

Estimated signal-to-noise ratios for future measurements.

Highlighted the potential of high-precision astrometry in gravitational-wave studies.

Abstract

We investigate the cross-correlation between astrometric and timing-residual observables for distant sources, such as pulsars and galaxies, and equivalent observables for nearby solar system bodies. Using the unified spin-weighted formalism introduced in [1], we derive the angular correlation functions-generalised Hellings-Downs curves-that describe the response of these mixed observables to a stochastic, unpolarised gravitational-wave background (SGWB). We compute the expected signal-to-noise ratio (SNR) and sensitivity for such measurements, focusing on cross-correlations between pulsar timing array (PTA) redshift signals and astrometric or distortion (shimmering) effects induced in solar system objects such as asteroids. Although the current astrometric precision of asteroid tracking does not yet provide competitive constraints relative to PTA-only surveys, the method offers a complementary probe with enhanced sensitivity at higher frequencies. Future wide-field surveys capable of sub-milliarcsecond precision could make this approach a viable tool for detecting or constraining the SGWB. A key advantage of the technique is its reduced susceptibility to correlated systematics across different measurement domains, providing an independent cross-check of PTA detections and a potential observational bridge between PTA and LISA frequency bands.