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#### Search for continuous gravitational waves: metric of the multi-detector F-statistic

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Erratum275785.pdf

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prd75_023004.pdf

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0606088.pdf

(Preprint), 1005KB

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##### Citation

Prix, R. (2007). Search for continuous gravitational waves: metric of the multi-detector
F-statistic.* Physical Review D,* *75*: 023004. doi:10.1103/PhysRevD.75.023004.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-48A1-1

##### Abstract

We derive the parameter-space metric of the multi-detector F-statistic, which is the optimal detection statistic for continuous gravitational waves in stationary Gaussian noise. We find that there is a family of F-statistic metrics, parametrized by the (unknown) amplitude parameters. We explicitly derive the maximal mismatch-range of this metric family, and we introduce a corresponding "average" F-metric. We show that the multi-detector metric consists of noise-weighted averages of single-detector contributions, which implies that the number of templates required to cover the parameter space does not scale with the number of detectors. Contrary to using a longer observation time, combining more detectors (of similar sensitivity) is therefore the computationally cheapest way to improve the sensitivity of a coherent wide-parameter search for continuous gravitational waves. We explicitly compute the F-statistic metric (family) for signals from isolated spinning neutron stars, and we evaluate the quality of different metric approximations in a Monte-Carlo study. We also compare the metric predictions to the measured mismatches and identify two regimes in which the metric is not a good description of the parameter-space structure.
Comment of the Author: Erratum-ibid. D75 (2007) 069901