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

TL;DR

This paper introduces a lattice-based template placement method for gravitational wave searches from Scorpius X-1, reducing the number of templates needed and increasing search sensitivity by addressing parameter correlations.

Contribution

It presents a novel shearing coordinate transformation that minimizes correlations, enabling more efficient lattice template placement for gravitational wave searches from Scorpius X-1.

Findings

Lattices with about 3 times fewer templates than traditional grids.

Enhanced search sensitivity at the same computational cost.

Effective handling of parameter correlations in template placement.

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 3 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.