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

Continuous gravitational wave (CW) signals from spinning, deformed neutron stars are yet to be detected. Searches targeted at known pulsars use pulsar timing observations to infer the phase evolution parameters of the CW signals they emit. We present a new method and implementation to obtain Bayesian posteriors on the amplitude parameters {h₀, cos ι, Ψ, φ_o} of continuous-gravitational waves from known pulsars. The method combines modern Bayesian parameter estimation techniques with the well-established $\mathcal{F}$-statistic framework. 

We further explore the benefits of a likelihood function that is analytically marginalized over φ_o, which avoids signal degeneracy problems in the Ψ-φ_o subspace and improves overall accuracy. The method is tested on simulated signals, CW hardware injections in Advanced-LIGO detector data, and using percentile-percentile (PP) self-consistency tests of the posteriors. As a first application, we use the method on CW emission from PSR J1526-2744, a recently discovered millisecond pulsar. 

We find no evidence for a signal and obtain a Bayesian 95% upper limit on the gravitational-wave amplitude that is consistent with a previous frequentist upper limit.