We derive simple analytic expressions for the (coherent and semi-coherent) phase metrics of continuous-wave sources in low-eccentricity binary systems, for the two regimes of long and short segments compared to the orbital period. The resulting expressions correct and extend previous results found in the literature. We present results of extensive Monte-Carlo studies comparing metric mismatch predictions against the measured loss of detection statistic for binary parameter offsets. The agreement is generally found to be within ∼ 10% − 30%. As an application of the metric template expressions, we estimate the optimal achievable sensitivity of an Einstein@Home directed search for Scorpius X-1, under the assumption of sufficiently small spin wandering. We find that such a search, using data from the upcoming advanced detectors, would be able to beat the torquebalance level [1,2] up to a frequency of ∼ 500 − 600 Hz, if orbital eccentricity is well-constrained, and up to a frequency of ∼ 160 − 200 Hz for more conservative assumptions about the uncertainty on orbital eccentricity.
Plan of this paperSec. II provides a general introduction of the concepts and notation of semi-coherent StackSlide methods, parameter-space metric and template banks. Secs. III-V build on the work of [27], rectifying some of the results and extending them to the case of a general orbital refer-arXiv:1502.00914v2 [gr-qc] 9 Apr 2015 1 This form of the "ideal" StackSlide statistic is not directly used for actual searches. For reasons of computational cost, the coherent statistics across segments are computed on coarser template banks, and are combined on a fine template bank by summing across segments using interpolation on the coarse grids. This is discussed in detail in [20], but is not relevant for the present investigation.