Extreme value distribution for gamma-ray-burst prompt data

How unexpected was the BOAT event?

¹ INAF – Osservatorio Astronomico di Brera, via E. Bianchi 46, 23807 Merate, Italy
² Como Lake centre for AstroPhysics (CLAP), DiSAT, Università dell’Insubria, via Valleggio 11, 22100 Como, Italy

^★ Corresponding author: stefano.covino@inaf.it

Received: 7 April 2025
Accepted: 15 July 2025

Abstract

Context. Gamma-ray bursts (GRBs) are known to be unpredictable in time and position. A few (observationally) exceptional events have been observed, such as GRB 221009A, which stands out for having a fluence and peak flux orders of magnitude higher than what has been measured so far.

Aims. Analysing the observed fluence, peak flux, or duration distributions typically requires one to assume some scenarios, and the consistency of the observed data with the predictions turns out to be an important model diagnostic. However, it is also of interest to model these distributions using general statistical properties that do not rely on specific model assumptions, allowing one to derive inferences only based on the consistency of the observed distributions with the hypothesis of one single population of events that generate them.

Methods. We obtained fluences, peak fluxes, and durations from the catalogues of GRBs observed by the CGRO-BATSE and Fermi-GBM instruments. We selected the extreme values in slots of equal duration and modelled their distributions using the generalised extreme value (GEV) formalism. The GEV distribution is a limit distribution naturally arising when the number of observations is large and is essentially independent of the phenomena producing the observed data.

Results. The distributions of extreme values for fluences, peak fluxes, and durations are consistent with being extracted from a single population of events, but the fluence and peak flux recorded for GRB 221009A constitute a striking exception. The probability of observing such an event, assuming it is a cosmological GRB, is low, with a median value of about one event per millennium for the fluence and about one event per century for the peak flux.