  We consider the cross-correlation search for periodic GWs and its potential
application to the LMXB Sco X-1. This method coherently combines data from
different detectors at the same time, as well as different times from the same
or different detectors. By adjusting the maximum time offset between a pair of
data segments to be coherently combined, one can tune the method to trade off
sensitivity and computing costs. In particular, the detectable signal amplitude
scales as the inverse fourth root of this coherence time. The improvement in
amplitude sensitivity for a search with a coherence time of 1hr, compared with
a directed stochastic background search with 0.25Hz wide bins is about a factor
of 5.4. We show that a search of 1yr of data from Advanced LIGO and Advanced
Virgo with a coherence time of 1hr would be able to detect GWs from Sco X-1 at
the level predicted by torque balance over a range of signal frequencies from
30-300Hz; if the coherence time could be increased to 10hr, the range would be
20-500Hz. In addition, we consider several technical aspects of the
cross-correlation method: We quantify the effects of spectral leakage and show
that nearly rectangular windows still lead to the most sensitive search. We
produce an explicit parameter-space metric for the cross-correlation search in
general and as applied to a neutron star in a circular binary system. We
consider the effects of using a signal template averaged over unknown amplitude
parameters: the search is sensitive to a combination of the intrinsic signal
amplitude and the inclination of the neutron star rotation axis, and the peak
of the expected detection statistic is systematically offset from the true
signal parameters. Finally, we describe the potential loss of SNR due to
unmodelled effects such as signal phase acceleration within the Fourier
transform timescale and gradual evolution of the spin frequency.
