Template Lattices for a Cross-Correlation Search for Gravitational Waves from Scorpius X-1

Understand

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.