Tuning into Scorpius X-1: adapting a continuous gravitational-wave search for a known binary system

We describe how the TwoSpect data analysis method for continuous gravitational waves (GWs) has been tuned for directed sources such as the Low Mass X-ray Binary (LMXB), Scorpius X-1 (Sco X-1). A comparison of five search algorithms generated simulations of the orbital and GW parameters of Sco X-1. Where that comparison focused on relative performance, here the simulations help quantify the sensitivity enhancement and parameter estimation abilities of this directed method, derived from an all-sky search for unknown sources, using doubly Fourier- transformed data. Sensitivity is shown to be enhanced when the source sky location and period are known, because we can run a fully-templated search, bypassing the all-sky hierarchical stage using an incoherent harmonic sum. The GW strain and frequency as well as the projected semi-major axis of the binary system are recovered and uncertainty estimated, for simulated signals that are detected. Upper limits on GW strain are set for undetected signals. Applications to future GW observatory data are discussed. Robust against spin-wandering and computationally tractable despite unknown frequency, this directed search is an important new tool for finding gravitational signals from LMXBs.