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Searching for gravitational waves with Gaia and its cross-correlation with PTA: Absolute vs differential astrometry

Massimo Vaglio1,2,*, Mikel Falxa3,4,†, Giorgio Mentasti5,‡, Arianna I. Renzini3,4,§, Adrien Kuntz6,∥, Enrico Barausse1,2,¶, Carlo R. Contaldi5,**, and Alberto Sesana3,4,††

  • *Contact author: mvaglio@sissa.it
  • †Contact author: mikel.falxa@unimib.it
  • ‡Contact author: g.mentasti21@imperial.ac.uk
  • §Contact author: arianna.renzini@unimib.it
  • ∥Contact author: adrien.kuntz@tecnico.ulisboa.pt
  • Contact author: barausse@sissa.it
  • **Contact author: c.contaldi@imperial.ac.uk
  • ††Contact author: alberto.sesana@unimib.it
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Phys. Rev. D 113, 124003 – Published 2 June, 2026

DOI: https://doi.org/10.1103/cg1z-2r29

Abstract

Astrometric missions like Gaia provide exceptionally precise measurements of stellar positions, parallaxes, and proper motions. Gravitational waves traveling between the observer and distant stars can induce small, correlated shifts in their apparent positions, a phenomenon known as astrometric deflection. The precision and scale of astrometric datasets make them well suited for searching for a stochastic gravitational-wave background, whose signature appears in the two-point correlation function of the deflection field across the sky. In space-based astrometry, the ultimate sensitivity of such measurements is reduced by systematic uncertainties in the satellite’s absolute attitude reconstruction, which constrain the accuracy of absolute astrometry. These orientation errors can be mitigated by focusing on relative angular separation between pairs of stars, which effectively cancel out common-mode orientation noise. In this work, we compute the astrometric response and the overlap reduction functions for this differential approach, correcting previous expressions presented in the literature. We use a Fisher matrix analysis to compare the sensitivity of differential astrometry to that of conventional absolute astrometry. Our analysis shows that while the differential method is theoretically sound, its sensitivity is limited for closely spaced star pairs. Pairs with large angular separations provide competitive sensitivity, but, when considered in connection with Gaia, it is unclear whether the differential strategy would be effective, since instrumental systematics are not expected to remain correlated on such scales. Finally, we demonstrate that combining astrometric data with observations from pulsar-timing arrays leads to slight improvements in sensitivity at frequencies ≳10−7  Hz.

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Phys. Rev. D 113, 124003– Published 2 June, 2026
  • Received 24 July 2025
  • Accepted 8 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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