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Abstract

We present a new method and implementation to obtain Bayesian posteriors on
the amplitude parameters $\{h_0, \cos \iota, \psi, \phi_0\}$ 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 $\phi_0$, which avoids signal degeneracy
problems in the $\psi$-$\phi_0$ 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 $7 \times 10^{-27}$, consistent with a previous frequentist upper
limit.