Sensitivity to a stochastic background

6.4 Sensitivity to a stochastic background

A stochastic background of low-frequency GWs, potentially detectable with single or multiple spacecraft Doppler tracking, has been discussed by [49 , 27 , 55 , 79 , 6 , 29 , 41 , 7 , 51 , 19

]. The level of stochastic GWs is conventionally expressed either as the energy density in GWs relative to closure density, $Ω$ , as a characteristic rms strain, or as spectrum of strain. The best directly observational upper bounds on stochastic GWs in the low-frequency band come from the Cassini data. Details of how the upper limits were produced are given in [19

]. Figure 23

shows limits to $Ω$ as a function of Fourier frequency (upper limits expressed as spectrum of strain are given in [19

]). The lowest bound is at 1.2 $×$ 10^–6 Hz : $Ω <$ 0.025. Between 1.2 $×$ 10^–6 and $≃$ 10^–5 Hz, $Ω <$ 0.1, while between about 10^–5 – 10^–4 Hz the upper bounds are between 0.1 to about 1.0. For f $>$ 10^–4 Hz the limits to $Ω$ are larger than 1. The Cassini data improved limits to $Ω$ in the 10^–6 to 10^–4 Hz band by factors of 500 – 1200 (depending on Fourier frequency) compared with earlier Doppler experiments.

Figure 23:

Upper limits to the energy density of GWs in bandwidth equal to center frequency, relative to closure energy density. This assumes an isotropic GW background, H₀ = 75 km s^–1 Mpc^–1, and is computed from the Cassini 2001–2002 data [19 ].

Predictions for an astrophysical GW background in the low-frequency band, e.g., from an ensemble of galactic binary stars or an ensemble of massive black hole binaries, have mainly been aimed at the design sensitivity of future dedicated GW missions [24 ]. The galactic binary star background is much too weak to be seen with spacecraft Doppler tracking. At lower frequencies (10^–9 – 10^–6 Hz) the strength of a GW background from an ensemble of coalescing black hole binaries has been estimated [87 , 66 , 125 ] mostly in the context of a pulsar timing array. Extrapolations or predictions in the low-frequency band [66 , 125 ] give strengths substantially lower than spacecraft Doppler tracking can presently observe (see Figure 20 ).