TY - JOUR

T1 - Spherical ansatz for parameter-space metrics

AU - Allen, Bruce

PY - 2019/12/15

Y1 - 2019/12/15

N2 - A fundamental quantity in signal analysis is the metric gab 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 λ1,λ2,... (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 dλa between two points in parameter space, the traditional ansatz for the mismatch is a non-negative quadratic form m=gabdλadλb. This is a good approximation for small separations mâ‰1, but at larger separations it diverges, whereas the actual mismatch is bounded above. Here, we introduce and discuss a simple "spherical" ansatz for the mismatch m=sin2(gabdλadλb). This agrees with the metric ansatz for small separations mâ‰1, but we show that in simple cases it provides a better (and bounded) approximation for larger separations and argue that this is also true in the generic case. This ansatz should provide a more accurate approximation of the mismatch for semicoherent searches and may also be of use when creating grids for hierarchical searches that (in some stages) operate at a relatively large mismatch.

AB - A fundamental quantity in signal analysis is the metric gab 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 λ1,λ2,... (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 dλa between two points in parameter space, the traditional ansatz for the mismatch is a non-negative quadratic form m=gabdλadλb. This is a good approximation for small separations mâ‰1, but at larger separations it diverges, whereas the actual mismatch is bounded above. Here, we introduce and discuss a simple "spherical" ansatz for the mismatch m=sin2(gabdλadλb). This agrees with the metric ansatz for small separations mâ‰1, but we show that in simple cases it provides a better (and bounded) approximation for larger separations and argue that this is also true in the generic case. This ansatz should provide a more accurate approximation of the mismatch for semicoherent searches and may also be of use when creating grids for hierarchical searches that (in some stages) operate at a relatively large mismatch.

UR - http://www.scopus.com/inward/record.url?scp=85076794937&partnerID=8YFLogxK

U2 - 10.48550/arXiv.1906.01352

DO - 10.48550/arXiv.1906.01352

M3 - Article

AN - SCOPUS:85076794937

VL - 100

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 12

M1 - 124004

ER -