2026ApJ...996..144G

Current models of binary black hole distributions are difficult to interpret because inferences hinge on modeling choices, which can mask or mimic real structure. The maximum population likelihood “ formalism” provides a means to investigate features in the distribution of binary black holes using only data-no model required. It tells us whether inferred features are truly present in the data or whether they arise from model misspecification. It also provides guidance for developing new models by highlighting previously unnoticed features. We utilize the formalism to examine the binary black hole population in the LIGO-Virgo-KAGRA (LVK) Gravitational-Wave Transient Catalog (GWTC-4). Our analysis supports the existence of a gap around 45 M_⊙ in the secondary black hole mass distribution and identifies a widening in the distribution of the effective inspiral spin parameter χ_eff at ≈45 M_⊙ as recently reported by H. Tong et al. We find support for a previously reported anticorrelation between χ_eff and mass ratio. However, this may be a spurious correlation arising from misspecification of the joint distribution of black hole masses. Furthermore, we identify support for dimensionless black hole spin magnitudes at χ ≈ 0.2 and χ ≈ 0.7. The data support the existence of a correlation between spin magnitudes χ₁ and χ₂, though subsequent study is required to determine whether this is statistically significant. The accompanying data release includes samples, which can be used to compare theoretical predictions to LVK data and to assess assumptions in parameterized models.