Evidence for the Self-organized Criticality Phenomenon in the Prompt Phase of Short Gamma-Ray Bursts

Abstract

The prompt phase of gamma-ray bursts (GRBs) contains essential information regarding their physical nature and central engine, which are as yet unknown. In this paper, we investigate the self-organized criticality phenomenon in GRB prompt phases as done in X-ray flares of GRBs. We obtain the differential and cumulative distributions of 243 short GRB pulses, such as peak flux, FWHM, rise time, decay time, and peak time in the fourth BATSE Time-Tagged Event Catalog with the Markov Chain Monte Carlo technique. It is found that these distributions can be well described by power-law models. In particular, comparisons are made with 182 short GRB pulses in the third Swift GRB Catalog from 2004 December to 2019 July. The results are essentially consistent with the BATSE ones. We notice that there is no obvious power-law index evolution across different energy bands for either BATSE or Swift short GRBs. The joint analysis suggests that the GRB prompt phase can be explained by a fractal-diffusive self-organized criticality system with the spatial dimension S = 3 and the classical diffusion β = 1. Our findings show that GRB prompt phases and X-ray flares possess the very same magnetically dominated stochastic process and mechanism.

Signatures of the Self-organized Criticality Phenomenon in Precursors of Gamma-Ray Bursts

“…Likewise, the same spatial dimension S = 3 can be determined by the quite same mean values of the power-law indexes of the main bursts, indicating that precursors and main bursts might share similar physical processes. Moreover, we find that the results of main bursts are consistent with those reported by our Paper I (Li et al 2023) and Lyu et al (2020) in spite of different GRB samples, involving short or long or mixed GRBs samples, suggesting that the similar processes are responsible for producing the main bursts in two classes of GRBs. In particular, under the assumption that there is no correlation between the sizes of two events, an exact relation between the index α of the avalanche size distribution and the q value of the appropriate q-Gaussian function has been obtained as (Caruso et al 2007;Celikoglu & Tirnakli 2010;Wei et al 2021)…”

“…given by Paper I for the BATSE and Swift short GRBs (Li et al 2023). Similar scale-invariant behaviors of main bursts are shown in Figure 4.…”

“…It can be seen that the results of main bursts tend to be similar to those of the precursors. In other words, the signatures of the SOC behaviors in main bursts are also legible, which are essentially consistent with the GRBs without precursors (Lyu et al 2020;Li et al 2023). The mean values of α of differential and cumulative distributions of peak fluxes, durations, rise times, and decay times are α mean = 2.00 ± 0.09, 1.75 ± 0.10, 1.84 ± 0.07, and 1.75 ± 0.09, respectively.…”

“…Moreover, they found that the energetic initial impulses in the magnetohydrodynamic flow can cause onedimensional signatures when a two-dimensional SOC regime has been established. Owing to the radial component of magnetic fields decaying with the radius, the early prompt phases are in a three-dimensional form while the later X-ray flares are closer to one-dimension (Wang & Dai 2013;Lyu et al 2020;Li et al 2023). Thus, the same Euclidean dimensions of SOC systems between precursor and main burst near to the central engine are reasonable.…”

Constraints on the Cosmological Parameters with Three-Parameter Correlation of Gamma-Ray Bursts

“…If the central engine of a GRB is powered by a newly-born fast spinning neutron star with a high magnetic field, then the energy injection from the magnetar could cause the plateau phase in the X-ray light curves (Dai & Lu 1998b;Zhang & Mészáros 2001;Metzger et al 2011). Based on the observations of Swift (Gehrels et al 2004), a significant fraction of GRBs show a plateau phase in the X-ray light curves that is followed by a decay phase in the afterglows (Nousek et al 2006;O'Brien et al 2006;Zhang et al 2006;Liang et al 2007;Yi et al 2015Yi et al , 2016Li et al 2023b). This characteristic of the light curve may be explained by the possibility that the energy injection from the magnetar causes a shallow decline phase in the afterglow (Dai & Lu 1998b;Zhang & Mészáros 2001).…”