A unified spin-harmonic framework for correlating pulsar timing, astrometric deflection, and shimmering gravitational wave observations
Author(s)
Mentasti, Giorgio
Contaldi, Carlo R
Type
Journal Article
Abstract
We present a unified spin-weighted harmonic framework that delivers analytic, diagonal expressions for the overlap (correlation) functions of three low frequency gravitational wave observables-pulsar timing redshifts, astrometric deflections, and time-dependent image distortions (“shimmering”). Writing each response in spin-s spherical harmonics and rotating to a basis in which the wave tensor has definite helicity, we obtain compact closed-form series for every auto- and cross-correlation, recovering the Hellings-Downs curve as the s = 0 limit and deriving its astrometric (s = ± 1) and shimmering (s = ± 2) analogues. The formalism naturally extends to non-standard scalar-breathing, longitudinal, and vector polarisation modes, clarifying when higher-spin observables are (and are not) sourced and providing a complete set of harmonic spectra Cℓ ready for parameter estimation pipelines. These results supply the common theoretical language needed to combine upcoming pulsar timing, Gaia-class astrometric, and high resolution imaging data sets, enabling coherent, multi probe searches for stochastic gravitational wave backgrounds, tests of general relativity and its alternatives across the nano- to micro-hertz gravitational wave band.
Date Issued
2026-02-01
Date Acceptance
2025-12-12
Citation
Journal of Cosmology and Astroparticle Physics, 2026, 2026 (02)
ISSN
1475-7516
Publisher
IOP Publishing
Journal / Book Title
Journal of Cosmology and Astroparticle Physics
Volume
2026
Issue
02
Copyright Statement
© 2026 The Author(s). Published by IOP Publishing Ltd on behalf of Sissa Medialab. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
License URL
Publication Status
Published
Date Publish Online
2026-02-05