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

Achievable sensitivities to the SGWB 205Table 12.8. Minimum values of h 2 0 gw for one year of observation, for(δ, α) = (0.95, 0.05), for the optimal combination of cross-correlation measurementsbetween multiple detector pairs, taken from all possible triples of interferometerscontaining VIRGO.VIRGO ⋆ LIGO-WA ⋆ LIGO-LAVIRGO ⋆ LIGO-LA ⋆ GEO-600VIRGO ⋆ LIGO-WA ⋆ GEO-600VIRGO ⋆ LIGO-LA ⋆ TAMA-300VIRGO ⋆ LIGO-WA ⋆ TAMA-300VIRGO ⋆ GEO-600 ⋆ TAMA-3002.6 × 10 −64.2 × 10 −64.8 × 10 −65.4 × 10 −66.6 × 10 −67.3 × 10 −6Table 12.9. The same as table 12.8 for the case of quadruples.VIRGO ⋆ LIGO-WA ⋆ LIGO-LA ⋆ GEO-600VIRGO ⋆ LIGO-WA ⋆ LIGO-LA ⋆ TAMA-300VIRGO ⋆ LIGO-LA ⋆ GEO-600 ⋆ TAMA-300VIRGO ⋆ LIGO-WA ⋆ GEO-600 ⋆ TAMA-3002.4 × 10 −62.6 × 10 −64.2 × 10 −64.8 × 10 −6and, therefore, all the measurements can be considered uncorrelated;the authors of [7] show that the optimal SNR turns out to be 7SNR 4 =M∑i=1M∑n ij (SNR (ij) ) 4 (12.54)j>iwhere SNR (ij) is given in equation (12.12). Thus, in the case of a frequencyindependentspectrum gw ( f ) = gw , the minimum value of gw for givendetection (δ) and false alarm (α) rates turns out to be:( )1 2= gw (δ, α)M∑i=1( ) 2 M∑ 1 (ij) . (12.55)gw (δ, α)where (ij)gw (δ, α) are the analogous quantities for the ij detector pairs (seeequation (12.50)). In the case (δ, α) = (0.95, 0.05), the minimum values ofh 2 0 gw obtained considering all triples and quadruples of interferometers havingin common VIRGO, are reported in tables 12.8 and 12.9, respectively.7 Remember that we defined the SNR as the square root of the SNR defined in [7].j>i