Bayesian F -statistic-based parameter estimation of continuous gravitational waves from known pulsars

We present a new method and implementation to obtain Bayesian posteriors on the amplitude parameters <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mo stretchy="false">{</a:mo><a:msub><a:mi>h</a:mi><a:mn>0</a:mn></a:msub><a:mo>,</a:mo><a:mi>cos</a:mi><a:mi>ι</a:mi><a:mo>,</a:mo><a:mi>ψ</a:mi><a:mo>,</a:mo><a:msub><a:mi>ϕ</a:mi><a:mn>0</a:mn></a:msub><a:mo stretchy="false">}</a:mo></a:math> of continuous gravitational waves emitted by known pulsars. This approach leverages the well-established <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi mathvariant="script">F</e:mi></e:math>-statistic framework and software. We further explore the benefits of employing a likelihood function that is analytically marginalized over <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msub><h:mi>ϕ</h:mi><h:mn>0</h:mn></h:msub></h:math>, which avoids signal degeneracy problems in the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mrow><j:mi>ψ</j:mi><j:mtext>−</j:mtext><j:msub><j:mrow><j:mi>ϕ</j:mi></j:mrow><j:mrow><j:mn>0</j:mn></j:mrow></j:msub></j:mrow></j:math> 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 <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msubsup><l:mi>h</l:mi><l:mn>0</l:mn><l:mrow><l:mn>95</l:mn><l:mo>%</l:mo></l:mrow></l:msubsup></l:math> on the gravitational-wave amplitude of approximately <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mn>7</n:mn><n:mo>×</n:mo><n:msup><n:mn>10</n:mn><n:mrow><n:mo>−</n:mo><n:mn>27</n:mn></n:mrow></n:msup></n:math>, comparable with a previous frequentist upper limit.