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Power law size distributions are the hallmarks of nonlinear energy dissipation processes governed by self-organized criticality. Here we analyze 75 data sets of stellar flare size distributions, mostly obtained from the {sl Extreme Ultra-Violet Explorer (EUVE)} and the {sl Kepler} mission. We aim to answer the following questions for size distributions of stellar flares: (i) What are the values and uncertainties of power law slopes? (ii) Do power law slopes vary with time ? (iii) Do power law slopes depend on the stellar spectral type? (iv) Are they compatible with solar flares? (v) Are they consistent with self-organized criticality (SOC) models? We find that the observed size distributions of stellar flare fluences (or energies) exhibit power law slopes of $alpha_E=2.09pm0.24$ for optical data sets observed with Kepler. The observed power law slopes do not show much time variability and do not depend on the stellar spectral type (M, K, G, F, A, Giants). In solar flares we find that background subtraction lowers the uncorrected value of $alpha_E=2.20pm0.22$ to $alpha_E=1.57pm0.19$. Furthermore, most of the stellar flares are temporally not resolved in low-cadence (30 min) Kepler data, which causes an additional bias. Taking these two biases into account, the stellar flare data sets are consistent with the theoretical prediction $N(x) propto x^{-alpha_x}$ of self-organized criticality models, i.e., $alpha_E=1.5$. Thus, accurate power law fits require automated detection of the inertial range and background subtraction, which can be modeled with the generalized Pareto distribution, finite-system size effects, and extreme event outliers.
Stars produce explosive flares, which are believed to be powered by the release of energy stored in coronal magnetic field configurations. It has been shown that solar flares exhibit energy distributions typical of self-organized critical systems. Th
The original concept of self-organized criticality (Bak et al.~1987), applied to solar flare statistics (Lu and Hamilton 1991), assumed a slow-driven and stationary flaring rate, which warrants time scale separation (between flare durations and inter
We explore upper limits for the largest avalanches or catastrophes in nonlinear energy dissipation systems governed by self-organized criticality (SOC). We generalize the idealized straight power low size distribution and Pareto distribution function
Self-organized criticality (SOC) refers to the ability of complex systems to evolve towards a 2nd-order phase transition at which interactions between system components lead to scale-invariant events beneficial for system performance. For the last tw
The shape of clouds has proven to be essential for classifying them. Our analysis of images from fair weather cumulus clouds reveals that, besides by turbulence they are driven by self-organized criticality (SOC). Our observations yield exponents tha