Where did Heavy Binaries Go? Gravitational-wave Populations Using Delaunay Triangulation with Optimized Complexity

Abstract We investigate the joint mass–redshift evolution of the binary black hole (BBH) merger rate in the latest Gravitational-Wave Transient Catalog (GWTC-4.0). We present and apply a novel nonparametric framework for modeling multidimensional, correlated distributions based on Delaunay triangulation. Crucially, the complexity of the model—namely, the number, positions, and weights of triangulation nodes—is inferred directly from the data, resulting in a highly efficient approach that requires about 1 to 2 orders of magnitude fewer parameters and significantly less calibration than current state-of-the-art methods. We find no evidence for a peak at M tot ∼ 70 M ⊙ at low redshifts ( z ∼ 0.2), where it would correspond to the m 1 ∼ 35 M ⊙ feature reported in redshift-independent mass spectrum analyses, and we infer an increased merger rate at high redshifts ( z ∼ 1) around those masses, compatible with such a peak. When related to the time-delay distribution from progenitor formation to a BBH merger, our results suggest that sources contributing to the m 1 ∼ 35 M ⊙ feature follow a steeper (shallower) time-delay distribution at high (low) redshifts. This hints at contributions from different formation channels—for example, dense environments and isolated binary evolution, respectively—although firm identification of specific formation pathways will require further observations and analyses.