# Stochastic gravitational-wave background as a tool for investigating multi-channel astrophysical and primordial black-hole mergers

### Autors:

Bavera, Fragos, Zapartas et al. (2022)

### Abstract:

The formation of merging binary black holes can occur through multiple astrophysical channels such as, e.g., isolated binary evolution and dynamical formation or, alternatively, have a primordial origin. Increasingly large gravitational-wave catalogs of binary black-hole mergers have allowed for the first model selection studies between different theoretical predictions to constrain some of their model uncertainties and branching ratios. We show how one could add an additional and independent constraint to model selection by using the stochastic gravitational-wave background. In contrast to model selection analyses that have discriminating power only up to the gravitational-wave detector horizons ($z \lesssim 1$), the stochastic gravitational-wave background accounts for the redshift integration of all gravitational-wave signals in the Universe. As a working example, we consider the branching ratio results from a model selection study that includes potential contribution from astrophysical and primordial channels. We renormalize the relative contribution of each channel to the detected event rate to compute the total stochastic gravitational-wave background energy density. The predicted amplitude lies below the current observational upper limits of GWTC-3 by LIGO-Virgo. Even though the predicted background will not be detectable by current generation gravitational-wave detectors, it will be accessible by third-generation detectors such as the Einstein Telescope and space-based detectors such as LISA.

Stochastic gravitational-wave background energy density spectrum of merging astrophysical and primordial BBHs (black). The fiducial model assumes combined BBH event rate normalized against LIGO and Virgo GWTC-2 events and branching ratios of each channel inferred by the model selection analysis of Franciolini et al. (2021). We show with individual lines the partial contribution of each considered channel: common envelope (CE, orange), stable mass transfer (SMT, green), globular cluster (GC, pink) and primordial black holes (PBH, blue). The upper constraint to the SGWB from GWTC-3 is indicated with a blue bar marker and an arrow. For comparison, we indicate with dashed lines the power-law integrated sensitivity curves of different detectors for corresponding continuous observation time. The detector configurations include LIGO-Virgo at design sensitivity (HLV), the same configuration including KAGRA with auto-correlations (HLVK auto-corr.), Einstein Telescope (ET) and the Laser Interferometer Space Array (LISA).