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

198 Generalities on the stochastic GW backgroundFigure 12.4. The overlap reduction function for the correlation of VIRGO with the fivemodes of a sphere located at (43.2 ◦ N, 10.9 ◦ E) (d = 58.0 km).[14]:S n ( f ) = S 1(f0f) 5 ( ) [ ( ) ]f0f2+ S 2 + S 3 1 +ff 0(12.49)where S 1 = 3.46 × 10 −50 Hz −1 , S 2 = 6.60 × 10 −46 Hz −1 , S 3 = 3.24 ×10 −46 Hz −1 and f 0 = 500 Hz. Figure 12.5 shows also the minimum detectablevalue of h 2 0 gw for the NAUTILUS detector (target sensitivity ˜h f = 8.6 ×10 −23 Hz −1/2 at f = 907 Hz) [15], and for a hollow sphere, made of Al 5056,with a mass of 200 ton, an outer radius of 3 m, and an inner radius of 2.1 m (targetsensitivity ˜h f = 4.3 × 10 −24 Hz −1/2 at 273 Hz; ˜h f = 3.4 × 10 −24 Hz −1/2 at935 Hz) [16].Unfortunately, all these sensitivity levels are not interesting. As we shall findin section 2, an interesting sensitivity level for h 2 0 gw is at least of order 10 −7 –10 −6 . To reach such a level with a single interferometer we need, for example,˜h f