Fast and Accurate Sensitivity Estimation for Continuous-Gravitational-Wave Searches

TL;DR

This paper introduces a fast, accurate numerical method for estimating the sensitivity of continuous-gravitational-wave searches, applicable to various F-statistic-based methods, validated against simulations and past search results.

Contribution

The authors extend an analytic sensitivity estimation approach to a broad class of F-statistic-based methods, providing a practical tool for rapid sensitivity assessment in gravitational-wave searches.

Findings

Estimates agree within a few percent at high detection thresholds.

Deviations increase at lower detection thresholds due to approximation limitations.

Sensitivity depths from past searches align within 10% of estimates, accounting for uncertainties.

Abstract

This paper presents an efficient numerical sensitivity-estimation method and implementation for continuous-gravitational-wave searches, extending and generalizing an earlier analytic approach by Wette [1]. This estimation framework applies to a broad class of F-statistic-based search meth- ods, namely (i) semi-coherent StackSlide F-statistic (single-stage and hierarchical multi-stage), (ii) Hough number count on F-statistics, as well as (iii) Bayesian upper limits on (coherent or semi-coherent) F-statistic search results. We test this estimate against results from Monte-Carlo simulations assuming Gaussian noise. We find the agreement to be within a few % at high (i.e. low false-alarm) detection thresholds, with increasing deviations at decreasing (i.e. higher false- alarm) detection thresholds, which can be understood in terms of the approximations used in the estimate. We also provide an extensive summary of sensitivity depths achieved in past continuous- gravitational-wave searches (derived from the published upper limits). For the F-statistic-based searches where our sensitivity estimate is applicable, we find an average relative deviation to the published upper limits of less than 10%, which in most cases includes systematic uncertainty about the noise-floor estimate used in the published upper limits.