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We search for features in the mass distribution of detected compact binary coalescences which signify the transition between neutron stars (NSs) and black holes (BHs). We analyze all gravitational-wave (GW) detections by the LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration (LVK) made through the end of the first half of the third observing run, and find clear evidence for two different populations of compact objects based solely on GW data. We confidently (99.3%) find a steepening relative to a single power law describing NSs and low-mass BHs below${2.4}_{-0.5}^{+0.5}{M}_{\odot }$, which is consistent with many predictions for the maximum NS mass. We find suggestions of the purported lower mass gap between the most massive NSs and the least massive BHs, but are unable to conclusively resolve it with current data. If it exists, we find the lower mass gap’s edges to lie at${2.2}_{-0.5}^{+0.7}{M}_{\odot }$and${6.0}_{-1.4}^{+2.4}{M}_{\odot }$. We reexamine events that have been deemed “exceptional” by the LVK collaborations in the context of these features. We analyze GW190814 self-consistently in the context of the full population of compact binaries, finding support for its secondary to be either a NS or a lower mass gap object, consistent with previous claims. Our models are the first to accommodate this event, which is an outlier with respect to the binary BH population. We find that GW200105 and GW200115 probe the edges of, and may have components within, the lower mass gap. As future data improve global population models, the classification of these events will also improve.

As catalogs of gravitational-wave transients grow, new records are set for the most extreme systems observed to date. The most massive observed black holes probe the physics of pair-instability supernovae while providing clues about the environments in which binary black hole systems are assembled. The least massive black holes, meanwhile, allow us to investigate the purported neutron star–black hole mass gap, and binaries with unusually asymmetric mass ratios or large spins inform our understanding of binary and stellar evolution. Existing outlier tests generally implement leave-one-out analyses, but these do not account for the fact that the event being left out was by definition an extreme member of the population. This results in a bias in the evaluation of outliers. We correct for this bias by introducing a coarse-graining framework to investigate whether these extremal events are true outliers or whether they are consistent with the rest of the observed population. Our method enables us to study extremal events while testing for population model misspecification. We show that this ameliorates biases present in the leave-one-out analyses commonly used within the gravitational-wave community. Applying our method to results from the second LIGO–Virgo transient catalog, we find qualitative agreement with the conclusions of Abbott et al. GW190814 is an outlier because of its small secondary mass. We find that neither GW190412 nor GW190521 is an outlier.