Model of the stochastic gravitational-wave background due to core collapse to black holes

Superposition of gravitational waves generated by astrophysical sources is expected to give rise to the stochastic gravitational-wave background. We focus on the background generated by the ring-down of black holes produced in the stellar core collapse events, which is one of several mechanisms for gravitational wave production in the stellar core collapse process. We systematically study the parameter space in this model, including the most recent information about the star formation rate and about the population of black holes as a function of redshift and of metallicity. We find that the upcoming second and third generation gravitational-wave detectors will be able to observe this stochastic background if the black hole ring-down efficiency at producing gravitational waves is sufficiently high, namely $\ensuremath{\sim}{10}^{\ensuremath{-}4}$ and $\ensuremath{\sim}{10}^{\ensuremath{-}6}$ of the black hole rest energy, respectively.