Analysis of the duration--hardness ratio plane of gamma-ray bursts using skewed distributions

Abstract

The two widely accepted classes of gamma-ray bursts (GRBs), short and long, are with confidence ascribed to mergers of compact objects and collapse of massive stars, respectively. A third, intermediate/soft class, remains putative. Its existence was claimed based on univariate and bivariate analyses of GRB observables modeled with Gaussian distributions. This, however, may not be the appropriate approach, as it has been already shown that the univariate distributions of durations are better described by mixtures of two skewed components rather than three Gaussian ones. This paper investigates whether data in the duration--hardness ratio plane is better modeled by mixtures of skewed bivariate distributions than by normal ones. The archival data set of the Compton Gamma-Ray Observatory/BATSE and Fermi/GBM data from the most recent catalogue release are examined. The preferred model is chosen based on two information criteria, Akaike ($AIC$) and Bayesian ($BIC$). It is found that the best description is given by a two-component mixture of skewed Student-$t$ distributions, which outperforms any other model considered. This implies that the distribution of the studied parameters is intrinsically skewed, introducing spurious Gaussian components, and hence the third class is unlikely to be a real phenomenon. Its existence, based on statistical inference, is therefore rejected as unnecessary to explain the observations.