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

166 Detection of scalar gravitational waveswhere H ( f ) is the Fourier transform of the scalar gravitational waveform h s (t) =Gξ 0 (t).We must now take into account the astrophysical restrictions on the validityof the waveform (11.71) which is obtained in the Newtonian approximation forpoint-like masses. In the following, we will take the point of view that thisapproximation breaks down when there are five cycles remaining to collapse[20, 21].The five-cycles limit will be used to restrict the range of M c over which ouranalysis will be performed. From (11.68), one can obtain√Gmω g (τ) = 2ω 0 = 2d 3( ) 3/815c5 ( )ωBD + 2 3/81= 264G 5/3 12ω BD + 19 M5/8 τ 3/8 . (11.74)cIntegrating (11.74) yields the amount of phase until coalescenceχ(τ) = 16( ) 3/815c5 ( )ωBD + 2 3/8 ( ) τ 5/85 64G 5/3 . (11.75)12ω BD + 19 M cSetting (11.75) equal to the limit period, T 5 cycles = 5(2π), solving for τ andusing (11.74) leads to( )ωBD + 2 3/5M ⊙ω 5 cycles = 2π(6870 Hz). (11.76)12ω BD + 19 M cTaking ω BD = 600, the previous limit readsω 5 cycles = 2π(1547 Hz) M ⊙. (11.77)M cA GW excites those vibrational modes of a resonant body having the propersymmetry. In the framework of JBD theory the spheroidal modes with l = 2 andl = 0 are sensitive to the incoming GW. Thanks to its multimode nature, a singlesphere is capable of detecting GWs from all directions and polarizations. We nowevaluate the SNR of a resonant-mass detector of spherical shape for its quadrupolemode with m = 0 and its monopole mode. In a resonant-mass detector, S h ( f ) isa resonant curve and can be characterized by its value at resonance S h ( f n ) and byits half height width [22]. S h ( f n ) can thus be written asS h ( f n ) = G c 34kTσ n Q n f n. (11.78)Here, σ n is the cross section associated with the nth resonant mode, T is thethermodynamic temperature of the detector and Q n is the quality factor of themode.