On the exceptionality of exceptional gravitational-wave events

TL;DR

This paper critically examines the concept of 'exceptionality' in gravitational-wave events, emphasizing the importance of measurement uncertainties and prior assumptions in interpreting extreme astrophysical observations.

Contribution

It provides a quantitative analysis showing that claims of exceptionality are often influenced by measurement errors and prior choices, especially when uncertainties are large.

Findings

The total mass of GW231123 is unlikely to be overestimated due to measurement error.

The spin of GW241110 is less anti-aligned than initially thought, with 70% of realizations consistent with aligned or nonspinning.

Claims of exceptionality should be carefully scrutinized considering measurement uncertainties and priors.

Abstract

In gravitational-wave astronomy, as in other scientific disciplines, ``exceptional'' sources attract considerable interest because they challenge our current understanding of the underlying (astro)physical processes. Crucially, ``exceptionality'' is defined only relative to the rest of the detected population. For instance, among all gravitational-wave events detected so far, GW231123 is the binary black hole with the largest total mass, while GW241110 is the binary black hole with the most strongly misaligned spin relative to the orbital angular momentum. Mandel [Astrophys.J.Lett. 996 (2026) 1, L4] argued that apparent ``exceptionality'' may reflect measurement error rather than an extreme true value, and suggested that the total mass of GW231123 may be significantly overestimated. Here we present a quantitative analysis that supports this conceptual point. We find that claims of ``exceptionality'' obtained under agnostic priors should be critically questioned whenever measurement uncertainties are comparable to the width of the underlying population. Specifically, we find that the total mass of GW231123 is unlikely to be meaningfully affected by this effect while the spin of GW241110 is far less likely to be anti-aligned than initially claimed: about 70% of realizations that appear to yield an ``exceptionally anti-aligned'' spin are in fact consistent with either nonspinning or aligned configurations.