Alternative statistical interpretation for the apparent plateaus in the duration distributions of gamma-ray bursts

Abstract

The existence of a plateau in the short-duration tail of the observed distribution of cosmological long-soft gamma ray bursts (LGRBs) is posited to be the first direct evidence of collapsars. A similar plateau in the short-duration tail of the observed duration distribution of short-hard gamma ray bursts (SGRBs) has been suggested as evidence of compact binary mergers. We present an equally plausible alternative interpretation for this evidence, based on a purely statistical approach. Specifically, we show that the observed plateau in the short-duration tail of the duration distribution of LGRBs can naturally occur in the statistical distributions of strictly positive physical quantities, exacerbated by the effects of mixing with the duration distribution of SGRBs, observational selection effects, and data aggregation (e.g., binning) methodologies. The observed plateau in the short-duration tail of the observed distributions of SGRBs may likewise result from a combination of sample incompleteness and inhomogeneous binning of data. We further confirm the impact of these factors on the observation of a plateau in the duration distributions of GRBs through extensive numerical Monte Carlo simulations. This analysis corroborates and strengthens a purely statistical and sample-incompleteness interpretation of the observed plateau in the duration distribution of LGRBs and SGRBs, without invoking the physics of collapsars or jet-propagation through the stellar envelope.