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

• Published in: arXiv.org
• Main Authors: Wagner, Katelyn J, Whelan, John T, Wofford, Jared K, Wette, Karl
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 30.06.2021
• Subjects: Coordinate transformations; Cross correlation; Gravitational waves; Lattices; Orbits; Parameters; Physics - General Relativity and Quantum Cosmology; Physics - High Energy Astrophysical Phenomena; Placement; Searching; Shearing; Uncertainty; X ray binaries; X ray stars
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2106.16142

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.