A unified spin-harmonic framework for correlating pulsar timing, astrometric deflection, and shimmering gravitational wave observations
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| Format: | Preprint |
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2025
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| _version_ | 1866914120724381696 |
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| author | Mentasti, Giorgio Contaldi, Carlo R. |
| author_facet | Mentasti, Giorgio Contaldi, Carlo R. |
| contents | 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 ($s=\pm 1$) and shimmering ($s=\pm 2$) 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 $C_\ell$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_16906 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A unified spin-harmonic framework for correlating pulsar timing, astrometric deflection, and shimmering gravitational wave observations Mentasti, Giorgio Contaldi, Carlo R. Cosmology and Nongalactic Astrophysics Instrumentation and Methods for Astrophysics General Relativity and Quantum Cosmology 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 ($s=\pm 1$) and shimmering ($s=\pm 2$) 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 $C_\ell$ 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. |
| title | A unified spin-harmonic framework for correlating pulsar timing, astrometric deflection, and shimmering gravitational wave observations |
| topic | Cosmology and Nongalactic Astrophysics Instrumentation and Methods for Astrophysics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2507.16906 |