The search for continuous gravitational waves: metric of the multi-detector F-statistic
arXiv:gr-qc/0606088 · doi:10.1103/PhysRevD.75.023004 10.1103/PhysRevD.75.069901
Abstract
We develop a general formalism for the parameter-space metric of the multi-detector F-statistic, which is a matched-filtering detection statistic for continuous gravitational waves. We find that there exists a whole family of F-statistic metrics, parametrized by the (unknown) amplitude parameters of the gravitational wave. The multi-detector metric is shown to be expressible in terms 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 detectors of similar sensitivity is therefore the computationally cheapest way to improve the sensitivity of coherent wide-parameter searches for continuous gravitational waves. We explicitly compute the F-statistic metric family for signals from isolated spinning neutron stars, and we numerically evaluate the quality of different metric approximations in a Monte-Carlo study. The metric predictions are tested against the measured mismatches and we identify regimes in which the local metric is no longer a good description of the parameter-space structure.
arXiv comment20 pages, 15 figures, revtex4; v2: some edits of style and notation, fixed minor typos
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