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Abstract We describe the application of the lattice covering problem to the placement of templates in a search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1. Efficient placement of templates to cover the parameter space at a given maximum mismatch is an application of the sphere covering problem, for which an implementation is available in the LatticeTiling software library. In the case of Sco X-1, potential correlations, in both the prior uncertainty and the mismatch metric, between the orbital period and orbital phase, lead to complications in the efficient construction of the lattice. We define a shearing coordinate transformation which simultaneously minimizes both of these sources of correlation, and allows us to take advantage of the small prior orbital period uncertainty. The resulting lattices have a factor of about three fewer templates than the corresponding parameter space grids constructed by the prior straightforward method, allowing a more sensitive search at the same computing cost and maximum mismatch. 

Abstract Improved observational constraints on the orbital parameters of the low-mass X-ray binary Scorpius X-1 were recently published in Killestein et al. In the process, errors were corrected in previous orbital ephemerides, which have been used in searches for continuous gravitational waves from Sco X-1 using data from the Advanced LIGO detectors. We present the results of a reanalysis of LIGO detector data from the third observing run of Advanced LIGO and Advanced Virgo using a model-based cross-correlation search. The corrected region of parameter space, which was not covered by previous searches, was about 1/3 as large as the region searched in the original O3 analysis, reducing the required computing time. We have confirmed that no detectable signal is present over a range of gravitational-wave frequencies from 25 to 1600 Hz, analogous to the null result of Abbott et al. Our search sensitivity is comparable to that of Abbott et al., who set upper limits corresponding, between 100 and 200 Hz, to an amplitudeh₀of about 10⁻²⁵when marginalized isotropically over the unknown inclination angle of the neutron star’s rotation axis, or less than 4 × 10⁻²⁶assuming the optimal orientation.