New prospects for continuous gravitational wave detection from binary systems in the advanced detector era

Gravitational wave detection is eagerly expected as one of the major discoveries of the next decade. A worldwide effort is currently underway, building ever-more-sensitive detectors and developing more powerful data-analysis tools. Continuous gravitational waves (CWs) are a promising class of signals for advanced detectors, and a particularly interesting type of CW sources are neutron stars in low-mass X-ray binaries, with Scorpius X-1 being the most remarkable representative. We describe the details of a project aimed to perform directed searches for CWs from binary systems. We use a search algorithm based on coherently computing a maximum likelihood statistic for a bank of signal templates, and then incoherently summing this statistic over the segments in which the entire data set has been previously split. The current strategy strongly relies on the derivation of precise analytic expressions for the (coherent and semicoherent) phase metrics of CW sources in low-eccentricity binary systems, for the two regimes of long and short segments compared to the orbital period. 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, and using data from the upcoming advanced detectors. We find that such a search would be able to beat the torque-balance level 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.