Gravitational-wave stochastic background detection with resonant-mass detectors

In this paper we discuss how the standard optimal Wiener filter theory can be applied, within a linear approximation, to the detection of an isotropic stochastic gravitational-wave background with two or more detectors. We apply then the method to the AURIGA-NAUTILUS pair of ultralow temperature bar detectors, soon to operate in coincidence in Italy, obtaining an estimate for the sensitivity to the background spectral density of ≈${10}^{\mathrm{-}49}$ ${\mathrm{Hz}}^{\mathrm{-}1}$, that converts to an energy density per unit logarithmic frequency of $\approx 8\times {10}^{-5}\times {\rho }_c$, with ${\rho }_c\approx 1.9\times {10}^{-26}$ ${\mathrm{k}\mathrm{g}/\mathrm{m}}^3$ the closure density of the Universe. We also show that by adding the VIRGO interferometric detector under construction in Italy to the array, and by properly reorienting the detectors, one can reach a sensitivity of $\approx 6\times {10}^{-5}\times {\rho }_c$. We then calculate that the pair formed by VIRGO and one large mass spherical detector properly located in one of the nearby available sites in Italy can reach a sensitivity of $\approx 2\times {10}^{-5}\times {\rho }_c$ while a pair of such spherical detectors at the same sites of AURIGA and NAUTILUS can achieve sensitivities of $\approx 2\times {10}^{-6}\times {\rho }_c$.