Living on the edge: Testing for compact population features at the edges of parameter space

Abstract

Many astrophysical population studies involve parameters that exist on a bounded domain, such as the dimensionless spins of black holes or the eccentricities of planetary orbits, both of which are confined to $[0, 1]$. In such scenarios, we often wish to test for distributions clustered near a boundary, e.g., vanishing spin or orbital eccentricity. Conventional approaches -- whether based on Monte Carlo, kernel density estimators, or machine-learning techniques -- often suffer biases at the boundaries. These biases stem from sparse sampling near the edge, kernel-related smoothing, or artifacts introduced by domain transformations. We introduce a truncated Gaussian mixture model framework that substantially mitigates these issues, enabling accurate inference of narrow, edge-dominated population features. While our method has broad applications to many astronomical domains, we consider gravitational wave catalogs as a concrete example to demonstrate its power. In particular, we maintain agreement with published constraints on the fraction of zero-spin binary black hole systems in the GWTC-3 catalog -- results originally derived at much higher computational cost through dedicated reanalysis of individual events in the catalog. Our method can achieve similarly reliable results with a much lower computational cost. The method is publicly available in the open-source packages gravpop and truncatedgaussianmixtures.