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Abstract

We generalize the targeted $\mathcal{B}$-statistic for continuous
gravitational waves by modeling the $h_0$-prior as a half-Gaussian distribution
with scale parameter $H$. This approach retains analytic tractability for two
of the four amplitude marginalization integrals and recovers the standard
$\mathcal{B}$-statistic in the strong-signal limit ($H\rightarrow\infty$). By
Taylor-expanding the weak-signal regime ($H\rightarrow0$), the new prior
enables fully analytic amplitude marginalization, resulting in a simple,
explicit statistic that is as computationally efficient as the
maximum-likelihood $\mathcal{F}$-statistic, but significantly more robust.
Numerical tests show that for day-long coherent searches, the weak-signal Bayes
factor achieves sensitivities comparable to the $\mathcal{F}$-statistic, though
marginally lower than the standard $\mathcal{B}$-statistic (and the Bero-Whelan
approximation). In semi-coherent searches over short (compared to a day)
segments, this approximation matches or outperforms the weighted
dominant-response $\mathcal{F}_{\mathrm{ABw}}$-statistic and returns to the
sensitivity of the (weighted) $\mathcal{F}_{\mathrm{w}}$-statistic for longer
segments. Overall the new Bayes-factor approximation demonstrates
state-of-the-art or improved sensitivity across a wide range of segment lengths
we tested (from 900s to 10days).