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Template banks based on Zn and An∗ lattices

Allen, B., & Shoom, A. A. (2021). Template banks based on Zn and An∗ lattices. Physical Review D, 104 (2): 122007. doi:10.1103/PhysRevD.104.122007.

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Creators:
Allen, Bruce1, Author
Shoom, Andrey A.1, Author
Affiliations:
1Observational Relativity and Cosmology, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society, ou_24011

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Free keywords: Astrophysics, Instrumentation and Methods for Astrophysics, astro-ph.IM,General Relativity and Quantum Cosmology, gr-qc
Abstract: Matched filtering is a traditional method used to search a data stream for signals. If the source (and hence its $n$ parameters) are unknown, many filters must be employed. These form a grid in the $n$-dimensional parameter space, known as a template bank. It is often convenient to construct these grids as a lattice. Here, we examine some of the properties of these template banks for $\mathbb{Z}^n$ and $A_n^*$ lattices. In particular, we focus on the distribution of the mismatch function, both in the traditional quadratic approximation and in the recently-proposed spherical approximation. The fraction of signals which are lost is determined by the even moments of this distribution, which we calculate. Many of these quantities we examine have a simple and well-defined $n\to\infty$ limit, which often gives an accurate estimate even for small $n$. Our main conclusions are the following: (i) a fairly effective template-based search can be constructed at mismatch values that are shockingly high in the quadratic approximation; (ii) the minor advantage offered by an $A_n^*$ template bank (compared to $\mathbb{Z}^n$) at small template separation becomes even less significant at large mismatch. So there is little motivation for using template banks based on the $A_n^*$ lattice.

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Dates: 2021-02-232021
Publication Status: Published in print
Pages: 17 pages, 8 figures
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Rev. Type: -
Identifiers: arXiv: 2102.11631
DOI: 10.1103/PhysRevD.104.122007
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Title: Physical Review D
Source Genre: Journal
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Pages: - Volume / Issue: 104 (2) Sequence Number: 122007 Start / End Page: - Identifier: -