最近三个太阳活动周期间太阳的自组织临界性状态。II。理论模型
The State of Self-Organized Criticality of the Sun During the Last Three Solar Cycles. II. Theoretical Model
摘要：
观测到的太阳耀斑参数的幂律分布可以用一个处于自组织临界性（SOC）状态的非线性耗散系统来解释。我们提出了一个通用的分析模型的SOC过程，是由三个条件：（i）乘法或指数增长阶段，（ii）随机中断终止的增长阶段，和（iii）线性衰减阶段。这个基本概念近似地再现了所观察到的频率分布。我们将其推广到一个随机的指数增长模型，其中还包括一个（对数正态）分布的阈值能量不稳定开始之前，以及随机衰减时间，它可以重现所观察到的发生频率分布和相关parameters的分散更现实。利用该解析模型，我们可以有效地进行SOC过程频率分布和参数相关性的蒙特卡罗模拟，这比元胞自动机模型的迭代模拟更简单、更快速。太阳活动周期对耀斑频率分布幂律斜率的调制可以用来诊断引起太阳耀斑的磁不稳定性的阈值和增长率。
英文摘要：
The observed powerlaw distributions of solar flare parameters can be interpreted in terms of a nonlinear dissipative system in the state of self-organized criticality (SOC). We present a universal analytical model of a SOC process that is governed by three conditions: (i) a multiplicative or exponential growth phase, (ii) a randomly interrupted termination of the growth phase, and (iii) a linear decay phase. This basic concept approximately reproduces the observed frequency distributions. We generalize it to a randomized exponential-growth model, which includes also a (log-normal) distribution of threshold energies before the instability starts, as well as randomized decay times, which can reproduce both the observed occurrence frequency distributions and the scatter of correlated parametyers more realistically. With this analytical model we can efficiently perform Monte-Carlo simulations of frequency distributions and parameter correlations of SOC processes, which are simpler and faster than the iterative simulations of cellular automaton models. Solar cycle modulations of the powerlaw slopes of flare frequency distributions can be used to diagnose the thresholds and growth rates of magnetic instabilities responsible for solar flares.
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