Bayesian $\mathcal{F}$-statistic-based parameter estimation of continuous gravitational waves from known pulsars

Abstract

We present a new method and implementation to obtain Bayesian posteriors on the amplitude parameters $\{h_0,\cos {\hat{I}}^1,\ddot{I}ˆ,\ddot{I}{•}_0\}$ 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 $\ddot{I}{•}_0$, which avoids signal degeneracy problems in the $\ddot{I}ˆ$-$\ddot{I}{•}_0$ subspace. The method is tested on simulated signals, hardware injections in Advanced-LIGO detector data, and by performing percentile-percentile (PP) 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.

15 pages, 17 figures, updated to match published version