Template lattices for a cross-correlation search for gravitational waves from Scorpius X-1

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 xray 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 LetticeTiling 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.

Automated summary

This study applies lattice covering problem to template placement in the search for continuous gravitational waves from the low-mass xray binary Scorpius X-1. By defining a shearing coordinate transformation, potential correlations are minimized and the lattices constructed have fewer templates with improved sensitivity.