On the exceptionality of exceptional gravitational-wave events

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.

Figures (4)

• Figure 1: Distribution of exceptional events in a catalog of $N_{\mathrm{obs}}=100$ using the toy population of Eq. \ref{['eq:ppop']} and Gaussian measurement errors. The parameter $\sigma$ controls the importance of measurement errors compared to the width of the population. The top panel compares the measured parameter $\hat{\theta}^\star$ to the true value $\theta^\star$; the black dashed line corresponds to $\Delta \theta^\star=0$. The bottom panel shows the distribution of measurement errors.
• Figure 2: Exceptional events' total mass distribution using the GWTC-4.0 population as described in the main text. Catalogs of different sizes $N_{\mathrm{obs}}$ are shown as colored histograms. The thin grey distribution shows the detected population $p(M_{\rm tot} | {\rm det}, \{d\})$. The scatter point indicates the total mass of GW231123 obtained under agnostic priors $\mathcal{I}_{\rm ag}$ from Ref. LIGOScientific:2025rsn.
• Figure 3: Deviation of the maximum measured total mass $\hat{M}_{\rm tot}^\star$ with respect to the true parameter $M_{\rm tot}^\star$ in units of $\delta M_{\rm tot}= 40 \mathrm{M}_{\odot}$. Results related to exceptional events from catalogs of sizes $N_{\rm obs}$ are shown with curves and markers. The thin grey curve indicates the corresponding distribution for the entire population $p(M_{\rm tot} | {\det}, \{d\})$ (i.e. without maximizing). This analysis illustrates the putative "exceptionality" of GW231123's total mass.
• Figure 4: Deviation of the largest aligned/anti-aligned spin components $\hat{\chi}_{1\mathrm{z}}^\star$ with respect to the true parameter $\chi_{1\mathrm{z}}^\star$. In the top (bottom) panel, we maximize (minimize) $\hat{\chi}_{1\mathrm{z}}$, which is indicative of GW241011 (GW241110) and use units of $\delta\chi_{1\mathrm{z}}=0.08$ ($\delta\chi_{1\mathrm{z}}=0.35$); see main text. Results related to exceptional events from catalogs of sizes $N_{\rm obs}$ are shown with curves and markers. The thin grey curves indicate the corresponding distribution for the entire population $p(\chi_{1\mathrm{z}} | {\det}, \{d\})$ (i.e. without extremizing). Grey areas correspond to cases where BH binaries with aligned spins are recovered with anti-aligned spins, and viceversa.