  Rapidly-rotating neutron stars are the only candidates for persistent
high-frequency gravitational wave emission, for which a targeted search can be
performed based on the spin period measured from electromagnetic (e.g. radio
and X-ray) observations. The principal factor determining the sensitivity of
such searches is the measurement precision of the physical parameters of the
system. Neutron stars in X-ray binaries present additional computational
demands for searches due to the uncertainty in the binary parameters. We
present the results of a pilot study with the goal of improving the measurement
precision of binary orbital parameters for candidate gravitational wave
sources. We observed the optical counterpart of Sco X-1 in 2011 June with the
William Herschel Telescope, and also made use of Very Large Telescope
observations in 2011, to provide an additional epoch of radial-velocity
measurements to earlier measurements in 1999. From a circular orbit fit to the
combined dataset, we obtained an improvement of a factor of two in the orbital
period precision, and a factor of 2.5 in the epoch of inferior conjunction
$T_0$. While the new orbital period is consistent with the previous value of
Gottllieb et al. (1975), the new $T_0$ (and the amplitude of variation of the
Bowen line velocities) exhibited a significant shift, which we attribute to
variations in the emission geometry with epoch. We propagate the uncertainties
on these parameters through to the expected Advanced LIGO & VIRGO detector
network observation epochs, and quantify the improvement obtained with
additional optical observations.
