Stochastic Gravitational Wave Measurements with Bar Detectors: Dependence of Response on Detector Orientation

TL;DR

This paper analyzes how the response of resonant bar detectors to stochastic gravitational waves varies with orientation, providing formulas for modulation effects and comparing different detector pairs to optimize measurement strategies.

Contribution

It derives the general form of the response modulation as a function of azimuth for resonant bar detectors, enhancing understanding of detector orientation effects on stochastic gravitational wave measurements.

Findings

Response modulation depends on azimuth and frequency.

Comparison of detector pairs shows varying sensitivities.

Formulas enable optimized detector orientation strategies.

Abstract

The response of a cross-correlation measurement to an isotropic stochastic gravitational-wave background depends on the observing geometry via the overlap reduction function. If one of the detectors being correlated is a resonant bar whose orientation can be changed, the response to stochastic gravitational waves can be modulated. I derive the general form of this modulation as a function of azimuth, both in the zero-frequency limit and at arbitrary frequencies. Comparisons are made between pairs of nearby detectors, such as LIGO Livingston-ALLEGRO, Virgo-AURIGA, Virgo-NAUTILUS, and EXPLORER-AURIGA, with which stochastic cross-correlation measurements are currently being performed, planned, or considered.