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

Scalar–tensor cross sections 171monopole and quadrupole modes of the sphere happen at different frequencies,sothat cross sections for them only make sense if defined separately. More precisely,σ n0 (ω) = 10πη n0c 2ω 2 Ɣ 2 n0 /4(ω − ω n0 ) 2 + Ɣ 2 n0 /4 (11.105)σ n2 (ω) = 10πη n2c 2ω 2 Ɣ 2 n2 /4(ω − ω n2 ) 2 + Ɣ 2 n2 /4 (11.106)where η n0 and η n2 are defined as in (11.101), with all terms referring to thecorresponding modes. After some algebra one finds thatGMvS2 Ɣn0 2 σ n0 (ω) = H /4n(ω BD + 2)c 3 (ω − ω n0 ) 2 + Ɣn0 2 /4 (11.107)GMvS2 Ɣn2 2 σ n2 (ω) = F /4n(ω BD + 2)c 3 (ω − ω n2 ) 2 + Ɣn2 2 (11.108)/4.Here, we have defined the dimensionless quantities4π 2H n =9(1 + σ P ) (k n0b n0 ) 2 (11.109)8π 2F n =15(1 + σ P ) (k n2b n2 ) 2 (11.110)where σ P represents the sphere material’s Poisson ratio (most often very close toa value of 1/3), and b nl are defined in (11.96); v S is the speed of sound in thematerial of the sphere.In tables 11.1 and 11.2 we give a few numerical values of the above crosssection coefficients.As already stressed in [25], one of the main advantages of a hollow sphereis that it enables us to reach good sensitivities at lower frequencies than in a solidsphere. For example, a hollow sphere of the same material and mass as a solidone (ς = 0) has eigenfrequencies which are smaller byω nl (ς) = ω nl (ς = 0)(1 − ς 3 ) 1/3 (11.111)for any mode indices n and l. We now consider the detectability of JBD GWcoming from several interesting sources with a hollow sphere.The values of the coefficients F n and H n , together with the expressions(11.105) for the cross sections of the hollow sphere, can be used to estimatethe maximum distances at which a coalescing compact binary system and agravitational collapse event can be seen with such detector. We consider thesein turn.By taking as a source of GWs a binary system formed by two neutronstars, each of them with a mass of m 1 = m 2 = 1.4M ⊙ . The chirp mass