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 \textbf{\textit{StarTrack}} binary population code. We include Population I/II stars as well as metal-free Population III stars. Merging and non-merging 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 $\Omega_{GW} \sim 2.7 \times 10^{-9}$ at the reference frequency of 10 Hz for population I/II only, making the background detectable by 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 $\Omega_{GW} \sim 1.4 \times 10^{-8}$, and also modifies the shape of the spectrum that deviates from the usual power law after $\sim 10$ Hz. The contribution from the population of non merging 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.