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

174 Detection of scalar gravitational wavesTable 11.3. Eigenfrequencies, sizes and distances at which coalescing binaries can be seenby monitoring of their emitted JBD GWs. Figures correspond to a 100 ton CuAl hollowsphere.ς (m) ν 10 (Hz) ν 12 (Hz) r(ν 10 ) (kpc) r(ν 12 ) (kpc)0.00 2.94 1655 807 − 29.80.25 2.96 1562 771 − 30.30.50 3.08 1180 578 55 31.10.75 3.5 845 375 64 330.90 4.5 600 254 80 40JBD theory, as a short pulse of amplitude b, whose value can be estimated as [27]( )( )( )500b ≃ 10 −23 M∗ 10 Mpc(11.114) BD M ⊙ rwhere M ∗ is the collapsing mass.The minimum value of the Fourier transform of the amplitude of the scalarwave, for a quantum limited detector at unit SNR, is given by( ) 1/24¯h|b(ω nl )| min =MvS 2ω (11.115)nl K nwhere K n = 2H n for the mode with l = 0 and K n = F n /3 for the mode withl = 2, m = 0.The duration of the impulse, τ ≈ 1/f c , is much shorter than the decay timeof the nl mode, so that the relationship between b and b(ω nl ) isb ≈|b(ω nl )| f c at frequency ω nl = 2π f c (11.116)so that the minimum scalar wave amplitude detectable is|b| min ≈(4¯hω nlπ 2 Mv 2 S K n) 1/2. (11.117)Let us now consider a hollow sphere made of molybdenum, for which thespeed of sound is as high as v S = 5600 m s −1 . For a given detector massand diameter, equation (11.117) tells us which is the minimum signal detectablewith such a detector. For example, a solid sphere of M = 31 tons and 1.8 m indiameter, is sensitive down to b min = 1.5 × 10 −22 . Equation (11.114) can thenbe inverted to find which is the maximum distance at which the source can beidentified by the scalar waves it emits. Taking a reasonable value of BD = 600,one finds that r(ν 10 ) ≈ 0.6 Mpc.