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

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 Mtot similar to 70 M circle dot at low redshifts (z similar to 0.2), where it would correspond to the m1 similar to 35 M circle dot feature reported in redshift-independent mass spectrum analyses, and we infer an increased merger rate at high redshifts (z similar to 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 m1 similar to 35 M circle dot 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.