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 Eiso, 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: $$\alpha_E^d=1.54\pm0.09, \alpha_T^d=1.82\pm_{0.15}^{+0.14}\;and\;\alpha_P^d=2.09_{-019}^{+0.18}$$ , while the power-law indices in the cumulative frequency distributions are: $$\alpha_E^c=1.44_{-0.10}^{+0.08}, \alpha_T^c=1.75_-{0.13}^{+0.141}\;and\;\alpha_P^c=1.99_{-019}^{+0.16}$$ . 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 I²=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.