The Most Massive Binary Black Hole Detections and the Identification of Population Outliers

Advanced LIGO and Virgo detected 10 binary black holes (BBHs) in their first two observing runs (O1 and O2). Analysis of these events found evidence for a dearth of BBHs with component masses greater than ∼45 M⊙, as would be expected from pair-instability supernovae. Meanwhile, a standalone analysis of the merger GW170729 found its primary mass to be ${m}_{1}={51.2}_{-11.0}^{+16.2}\ {M}_{\odot }$, which appears to be in contradiction with the existence of a limit at ∼45 M⊙. In this work, we argue that the masses of individual events can only be evaluated with reference to the full population. When GW170729 is analyzed jointly with the remaining detections, its inferred primary mass tightens considerably, to ${m}_{1}={38.9}_{-4.5}^{+7.3}\ {M}_{\odot }$. In the presence of noise, apparent outliers in the detected distribution are inevitable. We discuss methods of distinguishing between statistical fluctuations and true population outliers using posterior predictive tests. Applying these tests to O1 and O2, we find that the 10 detections are consistent with even the simplest power-law plus maximum-mass model considered by the LIGO–Virgo Collaboration, supporting the claim that GW170729 is not a population outlier. We also provide non-parametric constraints on the rate of high-mass mergers and conservatively bound the rate of mergers with m1 > 45 M⊙ at ${2.8}_{-2.0}^{+5.4} \% $ of the total merger rate. After 100 detections like those of O1 and O2 from a population with a maximum primary mass of 45 M⊙, it would be common for the most massive system to have an observed maximum-likelihood mass m1 ≳ 70 M⊙.