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

Achievable sensitivities to the SGWB 203Table 12.7. Minimum values of h 2 0 gw for cross-correlation measurements between twobars and between one bar and VIRGO for one year of observation and SNR = 1.AURIGA ⋆ NAUTILUSAURIGA ⋆ VIRGONAUTILUS ⋆ VIRGO2.0 × 10 −41.6 × 10 −42.8 × 10 −4β>0. For example, in the case of the correlation A, according to table 12.6 andfrom equation (12.53), we find that a spectrum with β = 1 will be detected, atSNR=1,ifh 2 0 gw(1 kHz) = 1.1 × 10 −6 , while a spectrum with β =−1 willbe detected if h 2 0 gw(2 Hz) = 1.5 × 10 −6 . So, both for increasing or decreasingspectra, to be detectable in one year at SNR = 1, h 2 0 gw must have a peak value,within the VIRGO band, of the order of a few 10 −6 in the case β =±1. Underthe same conditions, a frequency-dependent spectrum can be detected at the level7 × 10 −8 (see the first column of table 12.6). Clearly, for detecting increasing(decreasing) spectra, the upper (lower) part of the frequency band becomes moreimportant, and this is the reason why the sensitivity degrades compared to flatspectra, since for increasing or decreasing spectra the maximum of the signal is atthe edges of the accessible frequency band, where the interferometer sensitivityis worse. Second, for each β the sensitivity on h 2 0 gw( f ) always degrades goingfrom A to C. Relatively to A, the size of this decay for B and C increases with β,and for β = 3 the correlation C show a sensitivity one order of magnitude lowerthan the sensitivity of A. This means that in order to have the same sensitivity, thein case C has to be two orders of magnitude lower than in case A(see equation (12.50)). The case β = 3 is particularly important, because this isthe frequency dependence of the spectrum predicted by the string cosmology.product S n (1) S n(2)Resonant masses and resonant mass-interferometerResonant mass detectors includes bars like NAUTILUS, EXPLORER andAURIGA (see, e.g., [15, 21] for reviews). Spherical [16, 22] and truncatedicosahedron (TIGA) [23] resonant masses are also being developed or studied.The correlation between two resonant bars and between a bar and aninterferometer has been extensively considered in [19, 24–26]. The resultsobtained in [19] for the minimum values of h 2 0 gw in the case of a backgroundhaving constant frequency spectrum, for one year of integration and SNR = 1, aresummarized in table 12.7.Using resonant optical techniques, it is possible to improve the sensitivityof interferometers at special values of the frequency, at the expense of theirbroadband sensitivity. Since bars have a narrow band anyway, narrow-bandingthe interferometer improves the sensitivity of a bar-interferometer correlation by