We present a new method and implementation to obtain Bayesian posteriors on the amplitude parameters $\{h_0,\cos \iota ,\psi ,{\varphi }_0\}$ of continuous gravitational waves emitted by known pulsars. This approach leverages the well-established $\mathcal{F}$-statistic framework and software. We further explore the benefits of employing a likelihood function that is analytically marginalized over ${\varphi }_0$, which avoids signal degeneracy problems in the $\psi \text{−}{\varphi }_0$ subspace. The method is tested on simulated signals, hardware injections in Advanced-LIGO detector data, and by performing percentile-percentile self-consistency tests of the posteriors via Monte-Carlo simulations. We apply our methodology to PSR J1526-2744, a recently discovered millisecond pulsar. We find no evidence for a signal and obtain a Bayesian upper limit $h_0^{95\%}$ on the gravitational-wave amplitude of approximately $7\times {10}^{-27}$, comparable with a previous frequentist upper limit.

• Received 30 January 2024
• Accepted 26 March 2024

DOI:https://doi.org/10.1103/PhysRevD.109.104002

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. Open access publication funded by the Max Planck Society.

Published by the American Physical Society