Self organized criticality in an one dimensional magnetized grid. Application to GRB X-ray afterglows

Abstract

A simplified one dimensional grid is used to model the evolution of magnetized plasma flow. We implement diffusion laws similar to those so-far used to model magnetic reconnection with Cellular Automata. As a novelty, we also explicitly superimpose a background flow. The aim is to numerically investigate the possibility that Self-Organized Criticality appears in a one dimensional magnetized flow. The cellular automaton's cells store information about the parameter relevant to the evolution of the system being modelled. Under the assumption that this parameter stands for the magnetic field, the magnetic energy released by one volume during one individual relaxation event is also computed. Our results show that indeed in this system Self-Organized Criticality is established. The possible applications of this model to the study of the X-ray afterglows of GRBs is also briefly considered.

Statistical Distributions of Optical Flares from Gamma-Ray Bursts

“…Besides, they also studied the peak times, rising times and decay times of GRB X-ray flares, and found all of them show the power-law distributions. These similar statistical distributions between solar flares and GRB X-ray flares suggest both of them could be produced by magnetic reconnection, and also could be explained by a fractal diffusive, self-organized criticality model (Aschwanden 2011;Wang & Dai 2013;Harko et al 2015;Dȃnilȃ et al 2015;Yi et al 2016). Interestingly, some theoretical models have been proposed that GRB X-ray flares could be powered by magnetic reconnection events (Giannios 2006;Dai et al 2006;Zhang & Yan 2011;Mu et al 2016b).…”

Comprehensive study of the X-ray flares from gamma-ray bursts observed by Swift

“…They found the energy, duration, and waiting-time distributions of X-ray flares are similar to those of solar flares, which suggest a similar physical origin of the both events. This result is supported by later numerical simulations (Harko et al 2015). Harko et al (2015) numerically investigated the possibility that self-organized criticality (SOC) appears in a one-dimensional magnetized flow, which can be applied to GRB X-ray flares.…”

“…This result is supported by later numerical simulations (Harko et al 2015). Harko et al (2015) numerically investigated the possibility that self-organized criticality (SOC) appears in a one-dimensional magnetized flow, which can be applied to GRB X-ray flares. Wang et al (2015) studied the energy, duration and waiting time distributions of X-ray flares from Swift J1644+57 (Burrows et al 2011), Galactic center black hole Sgr A * (Neilsen et al 2013), and M87 (Harris et al 2009;Abramowski et al 2012).…”

天体物理中自组织临界现象的观测和模拟

“…笔者基于以往研究工 作, 倾向于如下定义: SOC 描述了一个非线性动力学 系统或复杂系统在不依赖于外部参数调节的情况下, 由能量驱动并通过自组织过程演化到某个临界点, 随 之产生无标度的、分形耗散的、且满足幂律分布的能 量释放或"雪崩"现象 [1,28,29,30,31,32] . 最初它被用来解 释自然界中无处不在的粉红噪声或闪烁噪声(功率谱 为幂律形式且谱指数为 1), 之后被广泛应用于解释 诸多非线性动力学系统的幂律频数分布, 例如人类社 会中的人口分布 [2] 和金融危机 [3,4] 、生物学中的物种灭 绝 [5] 和病毒扩散 [6] 、地球物理中的板块运动 [7] 和地震活 动 [8] 、地磁物理中的磁层亚暴 [9] 和极光辐射 [10] 、天体物 理中的太阳爆发 [11,12,13,14,15,16] 、恒星耀斑 [17,18,19,20,21] 、伽 马射线暴 [22,23,24] 和磁陀星爆发 [25,26,27] 等. 图 1 自组织临界沙堆模型示意图(左)和雪崩能量释放率随时间的演化(右) [41] .…”