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

Advanced LIGO and Virgo detected ten binary black holes (BBHs) in their first two observing runs (O1 and O2). Analysis of these events found strong evidence for a dearth of BBHs with component masses greater than $\sim45 \ M_\odot$, as would be expected from a pair-instability mass gap. Meanwhile, a standalone analysis of the merger GW170729 found its primary mass $m_1 = {51.2^{+16.2}_{-11.0} \ M_\odot}$, with the majority of its posterior support at $m_1 > 45 \ M_\odot$. Although this appears to be in contradiction with the existence of a limit at $\sim45\ M_\odot$, we argue that individual events cannot be evaluated without reference to the entire population. When GW170729 is analyzed jointly with the rest of the detections, as part of a full hierarchical population analysis, its inferred primary mass tightens considerably, to $m_1 = {38.9^{+7.3}_{-4.5} \ M_\odot}$. For a large sample of events in the presence of noise, apparent outliers in the detected distribution are inevitable, even if the underlying population forbids outliers. We discuss methods of distinguishing between statistical fluctuations and population outliers using posterior predictive tests. Applying these tests to the primary mass distribution in O1 and O2, we find that the ten detections are consistent with even the simplest power-law plus maximum-mass model considered by the LVC. This supports 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 $m_1 > 45 \ M_\odot$ at $2.8^{+5.4}_{-2.0}\%$ of the total merger rate. After 100 detections like those of O1 and O2 from a population with a maximum primary mass of $45 \, M_\odot$, it would be common for the most massive system to have an observed maximum-likelihood mass $m_1 \gtrsim 70 \, M_\odot$.