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  Spherical ansatz for parameter-space metrics

Allen, B. (2019). Spherical ansatz for parameter-space metrics. Physical Review D, 100: 124004. doi:10.1103/PhysRevD.100.124004.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0005-5AE8-1 Version Permalink: http://hdl.handle.net/21.11116/0000-0005-5AEC-D
Genre: Journal Article

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

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Free keywords: General Relativity and Quantum Cosmology, gr-qc, Astrophysics, Instrumentation and Methods for Astrophysics, astro-ph.IM
 Abstract: A fundamental quantity in signal analysis is the metric $g_{ab}$ on parameter space, which quantifies the fractional "mismatch" $m$ between two (time- or frequency-domain) waveforms. When searching for weak gravitational-wave or electromagnetic signals from sources with unknown parameters $\lambda$ (masses, sky locations, frequencies, etc.) the metric can be used to create and/or characterize "template banks". These are grids of points in parameter space; the metric is used to ensure that the points are correctly separated from one another. For small coordinate separations $d\lambda^a$ between two points in parameter space, the traditional ansatz for the mismatch is a quadratic form $m=g_{ab} d\lambda^a d\lambda^b$. This is a good approximation for small separations but at large separations it diverges, whereas the actual mismatch is bounded. Here we introduce and discuss a simple "spherical" ansatz for the mismatch $m=\sin^2(\sqrt{g_{ab} d\lambda^a d\lambda^b})$. This agrees with the metric ansatz for small separations, but we show that in simple cases it provides a better (and bounded) approximation for large separations, and argue that this is also true in the generic case. This ansatz should provide a more accurate approximation of the mismatch for semi-coherent searches, and may also be of use when creating grids for hierarchical searches that (in some stages) operate at relatively large mismatch.

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 Dates: 2019-06-042019
 Publication Status: Published in print
 Pages: 8 pages, 2 figures, will be submitted to PRD
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 Rev. Method: -
 Identifiers: arXiv: 1906.01352
DOI: 10.1103/PhysRevD.100.124004
URI: http://arxiv.org/abs/1906.01352
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Title: Physical Review D
  Other : Phys. Rev. D.
Source Genre: Journal
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Publ. Info: Lancaster, Pa. : American Physical Society
Pages: - Volume / Issue: 100 Sequence Number: 124004 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: https://pure.mpg.de/cone/journals/resource/111088197762258