  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.

General Relativity and Quantum Cosmology;High Energy Astrophysical Phenomena