  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.
