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

TL;DR

The study addresses how BBH formation channels imprint mass–spin correlations in gravitational-wave data. It develops physically grounded, parametric spin and redshift models for four channels—isolated (IBH), hierarchical in clusters (HBH), AGN-disk dynamics (AGN), and primordial (PBH)—and applies hierarchical Bayesian inference to GWTC-4.0, allowing comparison across models. The results show a strong mass–spin correlation; dynamical channels HBH or AGN provide the best single-channel explanations, PBH alone is disfavored, and spin orientation information remains weak with current data. These findings support a picture where hierarchical mergers shape the high-mass, high-spin regime, and they demonstrate the power of physics-mmotivated spin modeling to distinguish BBH formation pathways using current and future GW catalogs.

Abstract

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.

Figures (9)

• Figure 1: GWTC-4.0 catalog: Mass-spin scatter plot of the 153 GW candidates used in this analysis, chosen to have at least IFAR=1yr$^{-1}$. The stars represent the median values of the BBH event parameters from the GWTC-4.0 catalog. The x-axis indicates the source-frame masses of the primary (left columns) and secondary (right columns), while the y-axis shows the dimensionless spin magnitudes $\chi$ (first row) or the cosine of the polar angle $\cos \theta$ (second row). Error bars correspond to the $1\sigma$ uncertainties from the official LVK parameter estimation samples for each event. We do not show the non-trivial correlation between parameters in the posterior for simplicity. $m_i$ indicates source frame mass, as in the rest of the text.
• Figure 2: Examples of probability distributions of $\chi$ (first row) and $\cos{\theta}$ (second row), for the different formation channels. The distributions span from 10$M_{\odot}$ (blue) to 100$M_{\odot}$ (red). The model parameters of each scenario are fixed to the maximum likelihood (ML) point obtained when fitting the GWTC-4.0 catalog with our models.
• Figure 3: Left panel: Local merger rate density for the 2-population scenarios considered in this work: IBH+HBH, IBH+AGN, IBH+PBH, and HBH+PBH. The first (second) column corresponds to the first and second subpopulation in each case. Right panel: Local merger rate density for the 3-population scenarios. In both plots, the contours in the 2D-posteriors denote the 68% and 95% credible regions.
• Figure 4: Marginalized 1D PPDs of the spin magnitudes $\chi$ for different mass ranges, from $10$ to $100\,M_{\odot}$. Continuous colored lines represent the median value for each subpopulation, while the shaded region shows the $90\%$ credible interval. The black line shows the mixture of all channels. Each plot corresponds to Model I, in which all populations share the same merger-rate redshift evolution. We do not show the AGN case, which yields very similar results to the HBH PPDs, as observed when comparing IBH+HBH with IBH+AGN.
• Figure 5: Marginalized 1D PPDs of the polar angle $\cos \theta$ for different mass ranges, from $10$ to $100\,M_{\odot}$. The color notation is the same used in Fig. \ref{['fig:GWTC-4_posterior_predictive']}. In the second column, we show the AGN model instead of the HBH model, as the latter force the distribution to be $p(\cos \theta) = 1/2$.