An Analytic Approximation to the Bayesian Detection Statistic for Continuous Gravitational Waves

Understand

We consider the Bayesian detection statistic for a targeted search for continuous gravitational waves, known as the $\mathcal{B}$-statistic.

• This is a Bayes factor between signal and noise hypotheses, produced by marginalizing over the four amplitude parameters of the signal.
• We show that by Taylor-expanding to first order in certain averaged combinations of antenna patterns (elements of the parameter space metric), the marginalization integral can be performed analytically, producing a closed-form approximation in terms of confluent hypergeometric functions.
• We demonstrate using Monte Carlo simulations that this approximation is as powerful as the full $\mathcal{B}$-statistic, and outperforms the traditional maximum-likelihood $\mathcal{F}$-statistic, for several observing scenarios which involve an average over sidereal times.