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 methods, 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 falsealarm) 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 continuousgravitational-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.
I.with the incorrect N 1/4 seg scaling in Eq. 2 would result in an overestimate by a factor of two of the sensitivity of the first Einstein@Home search on LIGO S5 data [36].These limitations of previous sensitivity estimates were eventually overcome by the analytic sensitivityestimation method developed by Wette [1] for semicoherent StackSlide F-statistic searches. In this work we simplify and extend this framework by employing a simpler direct numerical implementation. This further improves the estimation accuracy by requiring fewer approximations. It also allows us to generalize the framework to multi-stage hierarchical StackSlide-F searches, Hough-F searches (such as [36]), as well as to Bayesian upper limits based on F-statistic searches.
Plan of this paperSec. II provides a description of the CW signal model and introduces different F-statistic-based search methods. In Sec. III we present the sensitivity-estimation framework and its implementation, for both frequentist and Bayesian upper limits. Section IV discusses how (frequentist) upper limits are typically measured using Monte-Carlo injection-recovery simulations. Section V provides comparisons of our sensitivity estimates to simulated upper limits in Gaussian noise, while in Sec. VI we provide a comprehensive summary of published sensitivities of past CW searches (translated into sensitivity depth), and a comparison to our sensitivity estimates where applicable. We summarize and discuss the results in Sec. VII. Further details on the referenced searches and upper limits are given in appendix A. More technical details on the signal model can be found in appendix B. Finally, appendix C contains a discussion of the distribution of the maximum F-statistic over ...