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I would like to learn, if possible, an estimate of the total time-averaged power of gravitational wave emission at frequencies below GHz by the Milky Way. For example the value might be something like $$ (\mbox{number of mergers per unit time}) \times (\mbox{mean energy emitted per merger}) + (\mbox{number of binaries with long-lasting orbits}) \times (\mbox{mean power per binary}) $$ I tried to extract an estimate from the following figure (from "Upper Limits on the Stochastic Gravitational-Wave Background from Advanced LIGO’s First Observing Run", https://arxiv.org/pdf/1612.02029)

plot of main contributions to grav wave spectral energy density

It looks like most of the energy is from BBH and BNS so I did a rough integral of the shown curves. However I'm not sure if I am doing it right. That integral gave an energy density about $2 \times 10^{-9}\,\rho_{\rm crit}$, but I'm not sure if I did that right, and I'm not sure how to convert it into a "total power per galaxy". (Here $\rho_{\rm crit} = 3 c^2 H_0^2/8\pi G$, the cosmological critical energy density).

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  • $\begingroup$ Over what time scale are you willing to average? Mergers are very rare, and if averaging over a century the number of mergers is typically zero. Of course, if you average over a long enough time mergers will contribute (and because of their immense intensity contribute significantly). On the scale of millions of years, you also need to account for EMRIs into sagitarius A*. If you wait even longer, you will have to account for the merger of the Milky Way with Andromeda and the potential merger of the supermassive black holes at their centers. $\endgroup$
    – TimRias
    Commented Oct 15 at 7:45
  • $\begingroup$ Thanks for this comment which goes some way to answering. I think a good answer would start with an average without mergers, and then bring in the mergers and EMRI. $\endgroup$
    – Andrew Steane
    Commented Oct 15 at 18:05

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