Gravitational wave background from Population III black hole formation

We study the generation of a stochastic gravitational wave (GW) background produced from a population of core-collapse supernovae, which form black holes in scenarios of structure formation. We obtain, for example, that the formation of a population (Population III) of black holes, in cold dark matter scenarios, could generate a stochastic GW background with a maximum amplitude of $h_{\rm BG} \simeq 10^{-24}$ and corresponding closure energy density of $\Omega_{\rm{GW}}\sim 10^{-7}$, in the frequency band $\nu_{\rm{obs}} \simeq 30-470 {\rm Hz}$ (assuming a maximum efficiency of generation of GWs, namely, $\epsilon_{\rm GW_{\rm max}} = 7\times 10^{-4}$) for stars forming at redshifts $z\simeq 30-10.$ We show that it will be possible in the future to detect this isotropic GW background by correlating signals of a pair of `advanced' LIGO observatories (LIGO III) at a signal-to-noise ratio of $\simeq 40$. We discuss what astrophysical information could be obtained from a positive (or even a negative) detection of such a GW background generated in scenarios such as those studied here. One of them is the possibility of obtaining the initial and final redshifts of the emission period from the observed spectrum of GWs.