(ed.). Gravitational waves (IOP, 2001)(422s).

Achievable sensitivities to the SGWB 197Figure 12.3. The overlap reduction function for the correlation of VIRGO withNAUTILUS (full curve), AURIGA (broken curve), and EXPLORER (dotted curve) in thecase in which the angles λ, having the values reported in table 12.3, coincide with the angleξ of VIRGO.12.4 Achievable sensitivities to the SGWBIn the following we apply the results of the preceding sections to estimatethe expected sensitivities of the correlation among the various detectors to thestochastic background.12.4.1 Single detectorsTo better appreciate the importance of correlating two detectors, it is instructive toconsider first the sensitivity that can be obtained using only one detector. In thiscase a hypothetical signal would manifest itself as an excess noise, and shouldtherefore satisfy S h ( f ) ² S n ( f ). By imposing this condition to equation (12.28)and introducing the notation ˜h 2 f= S n ( f ), for the minimum detectable value ofh 2 0 gw one hash 2 0 min( ) ()gw ( f ) ≃ 1.3 × f 3 2˜h f10−2100 Hz 10 −22 Hz −1/2 . (12.48)This function in the case of VIRGO is plotted in figure 12.5, where thefollowing analytical approximation for the noise power spectrum has been used