First Digit Distributions of Gamma-Ray Bursts

Abstract

The occurrence of the first significant digits from real world sources is usually not equally distributed, but is consistent with a logarithmic distribution instead, known as Benford's law. In this work, we perform a comprehensive investigation on the first digit distributions of the duration, fluence, and energy flux of gamma-ray bursts (GRBs) for the first time. For a complete GRB sample detected by the Fermi satellite, we find that the first digits of the duration and fluence adhere to Benford's law. However, the energy flux shows a significant departure from this law, which may be due to the fact that a considerable part of the energy flux measurements are restricted by lack of spectral information. Based on the conventional duration classification scheme, we also check if the durations and fluences of long and short GRBs (with duration $T_{90}>2$ s and $T_{90}\leq2$ s, respectively) obey Benford's law. We find that the fluences of both long and short GRBs still agree with the Benford distribution, but their durations do not follow Benford's law. Our results hint that the long--short GRB classification scheme does not directly represent the intrinsic physical classification scheme.