StarTrack predictions of the stochastic gravitational-wave background from compact binary mergers

We model the gravitational-wave background created by double compact objects from isolated binary evolution across cosmic time using the StarTrack binary population code. We include Population I/II stars as well as metal-free Population III stars. Merging and nonmerging double compact object binaries are taken into account. In order to model the low frequency signal in the band of the space antenna LISA, we account for the evolution of the redshift and the eccentricity. We find an energy density of Ω_GW∼7.5 ×10^-10 at the reference frequency of 25 Hz for population I/II only, making the background detectable after ∼5.5 years of observation with the current generation of ground based detectors, such as LIGO, Virgo and Kagra, operating at design sensitivity. Adding the contribution from population III increases the energy density to Ω_GW∼1.4 ×10^-8 , and also modifies the shape of the spectrum which starts deviating from the usual power law Ω_GW(f )∼f^{2 /3} after ∼10 Hz . The contribution from the population of nonmerging binaries, on the other hand, is negligible, being orders of magnitude below. Finally, we observe that the eccentricity has no impact in the frequency band of LISA or ground based detectors.