Probing Multiple Populations of Compact Binaries with Third-generation Gravitational-wave Detectors

Third-generation (3G) gravitational-wave detectors will be able to observe binary black hole mergers (BBHs) up to a redshift of ∼30. This gives unprecedented access to the formation and evolution of BBHs throughout cosmic history. In this paper, we consider three subpopulations of BBHs originating from the different evolutionary channels: isolated formation in galactic fields, dynamical formation in globular clusters, and mergers of black holes formed from Population III (Pop III) stars at very high redshift. Using input from population synthesis analyses, we create 2 months of simulated data of a network of 3G detectors made of two Cosmic Explorers and one Einstein Telescope consisting of ∼16,000 field and cluster BBHs, as well as ∼400 Pop III BBHs. First, we show how one can use a nonparametric model to infer the existence and characteristics of a primary and secondary peak in the merger rate distribution as a function of redshift. In particular, the location and height of the secondary peak around z ≈ 12, arising from the merger of Pop III remnants, can be constrained at the ${ \mathcal O }(10 \% )$ level (95% credible interval). Then we perform a modeled analysis using phenomenological templates for the merger rates of the three subpopulations and extract the branching ratios and characteristic parameters of the merger rate densities of the individual formation channels. With this modeled method, the uncertainty on the measurement of the fraction of Pop III BBHs can be improved to ≲10%, while the ratio between field and cluster BBHs can be measured with an uncertainty of ∼100%.