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

202 Generalities on the stochastic GW backgroundTable 12.5. Minimum values of h 2 0 gw for the correlation VIRGO–VIRGO for one yearof observation and different values of the pair (δ, α) (different values of SNR), for the threepossible locations of the second VIRGO considered in section 12.3.1.Correlation (0.95, 0.05) (0.95, 0.10) (0.90, 0.10)A 2.4 × 10 −7 2.1 × 10 −7 1.8 × 10 −7B 2.5 × 10 −7 2.2 × 10 −7 1.9 × 10 −7C 2.8 × 10 −7 2.5 × 10 −7 2.2 × 10 −7Table 12.6. Minimum values of h 2 0 gw(100 Hz) for the correlation VIRGO–VIRGO(T = 1 year, SNR = 1), for different values of the exponent β in equation (12.53). The rowsrefer to the three different locations of the second VIRGO considered in section 12.3.1.Correlation β = 0 β = 1 β =−1 β = 3A 7.2 × 10 −8 1.1 × 10 −7 3.0 × 10 −8 2.0 × 10 −8B 7.6 × 10 −8 1.3 × 10 −7 3.1 × 10 −8 9.7 × 10 −8C 8.5 × 10 −8 1.6 × 10 −7 3.2 × 10 −8 2.5 × 10 −7approximately 40 Hz. This calculation has been performed also for the othertwo geographical locations of the second VIRGO interferometer considered insection 12.3.1. Although the range of frequency where γ(f ) has a sensible valueis very different in the three cases (see figure 12.2), it is evident from table 12.5that, for fixed values of (δ, α), the corresponding sensitivities to a frequencyindependentbackground are practically the same, and approximately one order ofmagnitude better than the ones achievable with the two LIGO detectors [7].Let us now consider the case of a frequency-dependent stochasticbackground, that in the VIRGO frequency band can be parametrized in thefollowing way( gw ( f ) = gw (100 Hz)f100 Hz) β. (12.53)The same procedure applied to obtain equation (12.52) gives, in the cases β =±1, 3, the minimum detectable values for h 2 0 gw(100 Hz) reported in table 12.6(T = 1 year, SNR = 1). For the sake of comparison, we also reported theanalogous quantities in the case of a frequency-independent background (β = 0).Some comments about this table are necessary. First, to compare thesensitivities of a correlation to backgrounds with different frequency behaviour,we have to take into account that in the case β ̸= 0 the spectrum will exhibit apeak within the VIRGO band: at low frequency for β