Inferring black hole formation channels in GWTC-4.0 via parametric mass-spin correlations derived from first principles

We investigate the differences between several proposed formation scenarios for binary black holes (BBHs), including isolated stellar evolution, dynamical assembly in dense clusters and AGN disks, and primordial BHs. Our approach exploits the predicted spin features of each formation channel, and adopts parameterized models of the predicted correlations between the spin magnitudes (and orientations) and mass, inspired by first principles. Using hierarchical Bayesian inference on the recent GWTC-4.0 dataset, we compare these features across all models and assess how well each scenario explains the data. We find that the data strongly favor the presence of a positive correlation between mass and spin magnitude, in agreement with previous studies. Furthermore, the hierarchical scenario provides a better fit to the observations, due to the inclusion of second-generation mergers leading to higher spins at larger masses. The current dataset is not informative enough about spin orientation: the cluster (random orientations) and AGN (aligned orientations) scenarios have comparable Bayesian evidence. Finally, the mass-spin correlation predicted by the primordial scenario gives a poor fit to the data, and this scenario can only account for a subset of the observed events.