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 ${\mathrm{\Omega }}_{\mathrm{GW}}\sim 7.5\times {10}^{-10}$ at the reference frequency of 25 Hz for population I/II only, making the background detectable after $\sim 5.5\mathrm{years}$ 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 ${\mathrm{\Omega }}_{\mathrm{GW}}\sim 1.4\times {10}^{-8}$, and also modifies the shape of the spectrum which starts deviating from the usual power law ${\mathrm{\Omega }}_{\mathrm{GW}}(f)\sim f^{2/3}$ after $\sim 10\mathrm{Hz}$. 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.

Figure 1

Energy density for the total population of sources that coalesce within the Hubble time. The upper panel is for Population I/II stars and the lower panel for Population III stars. The three different types of binaries BBHs, BHNSs, and BNSs are shown separately in red, green and blue, with a null eccentricity (dashed line) and accounting for harmonics $n=2–5$ (continuous). The dotted lines indicate the Power Integrated curves of the different networks of terrestrial detectors (see text) and LISA.

Figure 2

Energy density from binaries which do not merge in a Hubble time. The three different types of binaries BBHs, BHNSs, and BNSs are shown separately in red, green, and blue, with a null eccentricity (dashed line) and accounting for harmonics $n=2–5$ (continuous).

Figure 3

Energy density for the residual population I/II and III of sources that coalesce within the Hubble time. The upper panel is for 2G detector networks HLV (dashed lines) and HLVIK (solid lines) and the lower panel for 3G detector networks ET (dashed lines) and $\mathrm{ET}+2\mathrm{CE}$ (solid lines). The black lines describe the residual energy densities for the total population and the green/blue ones for respectively the population I/II and III.

Figure 4

Ratios $r_{\mathrm{Count}}$ (blue) and $r_{\mathrm{\Omega }}$ (orange) for the terrestrial detector residual backgrounds for the total population I/II and III.

Figure 5

Energy density of ET (left panel) and $\mathrm{ET}+2\mathrm{CE}$ (right panel) residual populations, at frequencies between 1 Hz–2 kHz. The solid lines indicate the contribution of the different types of binaries: BBH in red, BNS in blue and BHNS in green. The dotted lines show the power integrated curves for ET (in purple on the left panel) and $\mathrm{ET}+2\mathrm{CE}$ (in pink on the right panel).