Self-Similar Temporal Behavior of Gamma-Ray Bursts

Abstract

We apply Fourier analysis to 214 light curves of long gamma-ray bursts and study the statistical properties of their power density spectra (PDSs). The averaged PDS is found to follow a power law of index -5/3 over almost 2 decades of frequency with a break at about 2 Hz. Individual PDSs are exponentially distributed around the power law. It provides evidence that the diversity of the bursts is due to random realizations of the same process which is self-similar over the full range of time-scales. The -5/3 slope of the average spectrum may indicate that gamma-ray bursts are related to a phenomenon well studied in hydrodynamics - fully developed turbulence.