Self-organized criticality in multi-pulse gamma-ray bursts

The variability in multi-pulse gamma-ray bursts (GRBs) may help to reveal the mechanism of underlying processes from the central engine. To investigate whether the self-organized criticality (SOC) phenomena exist in the prompt phase of GRBs, we statistically study the properties of GRBs with more than 3 pulses in each burst by fitting the distributions of several observed physical variables with a Markov Chain Monte Carlo approach, including the isotropic energy E_iso, the duration time T, and the peak count rate P of each pulse. Our sample consists of 454 pulses in 93 GRBs observed by the CGRO/BATSE satellite. The best-fitting values and uncertainties for these power-law indices of the differential frequency distributions are: {\alpha }_E^d=1.54\pm 0.09, {\alpha }_T^d={1.82}_{-0.15}^{+0.14} and {\alpha }_P^d={2.09}_{-0.19}^{+0.18}, while the power-law indices in the cumulative frequency distributions are: {\alpha }_E^c={1.44}_{-0.10}^{+0.08}, {\alpha }_T^c={1.75}_{-0.13}^{+0.11} and {\alpha }_P^c={1.99}_{-0.19}^{+0.16}. We find that these distributions are roughly consistent with the physical framework of a Fractal-Diffusive, Self-Organized Criticality (FD-SOC) system with the spatial dimension S = 3 and the classical diffusion β=1. Our results support that the jet responsible for the GRBs should be magnetically dominated and magnetic instabilities (e.g., kink model, or tearing-model instability) lead the GRB emission region into the SOC state.