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 ultra low temperature bar detectors, near to operate in coincidence in Italy, obtaining an estimate for the sensitivity to the background spectral density of $\simeq 10^{-49}\ Hz^{-1}$, that converts to an energy density per unit logarithmic frequency of $\simeq 8\times10^{-5}\times\rho_c$ with $\rho_c\simeq1.9 \times 10^{-26}\ kg/m^3$ 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 re- orienting the detectors, one can reach a sensitivity of $\simeq 6 \times10^{-5}\times\rho_c$. 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 reah a sensitivity of $\simeq 2\times10^{-5}\times \rho_c$ while a pair of such spherical detectors at the same sites of AURIGA and NAUTILUS can achieve sensitivities of $\simeq 2 \times10^{-6}\rho_c$.