Antenna patterns of interferometric detectors of gravitational waves - I. Linearly polarized waves

Abstract

The response of a free-mass interferometric gravitational wave detector to plane gravitational waves arriving from an arbitrary direction with an arbitrary linear polarization in the long-wavelength approximation is studied. It is proved that the threshold averaged coincidence probability for two detectors equals the mean of the product of their antenna power patterns, allowing the use of threshold independent criteria for judging the likelihood of coincidences between detectors. Results on the coincidences between detectors located in the U.S.A. and in Europe for random waves from Virgo are obtained, and the implications of these results for the choice of orientation of planned detectors and for the numbers of detectors world-wide are considered.