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 merger rate in the latest Gravitational-Wave Transient Catalog, GWTC-4.0. We present and apply a novel non-parametric framework for modeling multi-dimensional, 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 one to two orders of magnitude fewer parameters and significantly less calibration than current state-of-the-art methods. We find no evidence for a peak at $M_{\mathrm{tot}} \sim 70\,\mathrm{M}_{\odot}$ at low redshifts ($z \sim 0.2$), where it would correspond to the $m_1 \sim 35\,\mathrm{M}_{\odot}$ feature reported in redshift-independent mass spectrum analyses, and we infer an increased merger rate at high redshifts ($z \sim 1$) around those masses, compatible with such a peak. When related to the time-delay distribution from progenitor formation to binary black-hole merger, our results suggest that sources contributing to the $m_1 \sim 35\,\mathrm{M}_{\odot}$ 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.