Combining astrometry with pulsar timing: the first joint analysis of very low frequency gravitational waves
Abstract
The pHz to sub-nHz GW regime remains largely unexplored but is crucial for mapping the early inspiral stage of SMBHBs and probing early-Universe physics. Astrometry and pulsar timing offer orthogonal and deeply complementary secular observables to investigate this frequency band. We aim to present the first joint data analysis combining real astrometric proper motions with binary pulsar timing, to search for and constrain continuous gravitational waves (CWs) sourced by SMBHBs in the ultra-low-frequency regime (10−12 ≤ fGW ≤10−9 Hz). We employ a Bayesian model selection and upper limit estimation framework to combine apparent proper motion displacements of ∼ 1.5 × 106 quasars from the Gaia CRF3 catalog with the line-of-sight orbital period derivatives (Ṗb) of 11 high-precision binary pulsars. To prevent spurious detections, we heavily model instrumental and astrophysical systematics: we propagate the Galactic potential uncertainty for pulsars via Monte Carlo simulations and perform a Vector Spherical Harmonics (VSH) decomposition up to the octupole order (l=3) for quasars. We find no statistically significant evidence for a CWs signal in the joint analysis (ln Bjoint = −0.42 ± 0.03). In the absence of detection, we set the tightest constraints to date on CW strain in the pHz band, yielding a 95% upper limit of h0≤6.4x10−11 at a reference frequency of fref = 4 × 10−10 Hz. The combined dataset achieves full sky coverage and improves single-dataset upper limits by 20%-30%. Combining orthogonal observables successfully breaks spatial degeneracies intrinsic to isolated searches. Furthermore, forecasts from inj.-rec. indicate that with the extended temporal baseline and reduced uncertainties of the upcoming Gaia DR4, this joint framework is poised to break the h0 < 10−11 upper limit barrier for sub-nHz CWs.
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BibTeX
@misc{filipello2026combining,
title = {{Combining astrometry with pulsar timing: the first joint analysis of very low frequency gravitational waves}},
author = {Lorenzo Filipello and William Beordo and Volodymyr Akhmetov and Mariateresa Crosta and Mario Gilberto Lattanzi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21606},
eprint = {2609.21606},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21606},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Combining astrometry with pulsar timing: the first joint analysis of very low frequency gravitational waves
AU - Lorenzo Filipello
AU - William Beordo
AU - Volodymyr Akhmetov
AU - Mariateresa Crosta
AU - Mario Gilberto Lattanzi
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21606
UR - https://arxiv.org/abs/2609.21606
AB - The pHz to sub-nHz GW regime remains largely unexplored but is crucial for mapping the early inspiral stage of SMBHBs and probing early-Universe physics. Astrometry and pulsar timing offer orthogonal and deeply complementary secular observables to investigate this frequency band. We aim to present the first joint data analysis combining real astrometric proper motions with binary pulsar timing, to search for and constrain continuous gravitational waves (CWs) sourced by SMBHBs in the ultra-low-frequency regime (10^−12 ≤ f_GW ≤10^−9 Hz). We employ a Bayesian model selection and upper limit estimation framework to combine apparent proper motion displacements of ∼ 1.5 × 10^6 quasars from the Gaia CRF3 catalog with the line-of-sight orbital period derivatives (Ṗ_b) of 11 high-precision binary pulsars. To prevent spurious detections, we heavily model instrumental and astrophysical systematics: we propagate the Galactic potential uncertainty for pulsars via Monte Carlo simulations and perform a Vector Spherical Harmonics (VSH) decomposition up to the octupole order (l=3) for quasars. We find no statistically significant evidence for a CWs signal in the joint analysis (ln B_joint = −0.42 ± 0.03). In the absence of detection, we set the tightest constraints to date on CW strain in the pHz band, yielding a 95% upper limit of h_0≤6.4x10^−11 at a reference frequency of f_ref = 4 × 10^−10 Hz. The combined dataset achieves full sky coverage and improves single-dataset upper limits by 20%-30%. Combining orthogonal observables successfully breaks spatial degeneracies intrinsic to isolated searches. Furthermore, forecasts from inj.-rec. indicate that with the extended temporal baseline and reduced uncertainties of the upcoming Gaia DR4, this joint framework is poised to break the h_0 < 10^−11 upper limit barrier for sub-nHz CWs.
ER -