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I've been looking at LIGO figures for gravitational wave sensitivity here and it seem to be displayed in an adimensional strain ratio (which I assume that is more or less equivalent to metric perturbation $h_{\mu \nu}/g_{\mu \nu}$, correct me if I'm wrong)

What I'm wondering is how can I convert this sensitivity measure into something like watts/area, as a measure of energy density flux of gravitational waves.

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There is a nice Figure 6 that I'm afraid to copy and having trouble directly linking to from "Physics, Astrophysics and Cosmology with Gravitational Waves" by Sathyaprakash and Schutz, which gives the corresponding LIGO sensitivity in terms of energy flux.

In section 4.5.2: Sensitivity of interferometers in units of energy flux Sathyaprakash and Schutz explain that there is a $4c^3f^2/\pi G$ conversion factor between the noise power spectrum in units of per hertz and the energy density flux in units of Jansky.

In earlier portions of section 4.5, it is explained that the square root of noise power spectrum is sometimes used, which is the case in the link of the OP.

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