Alternative Waiting Time Statistics for the Lu and Hamilton Avalanche Model

Abstract

The solar corona hosts many explosive events. Among them, flares are some of the most energetic, rapidly releasing huge amounts of energy and, in the case of the largest ones, producing coronal mass ejections that have the potential to harm life on our planet. Therefore, there is great interest in attempting to foresee the occurrence of extreme solar flares. Avalanche models for solar flares have been used since the beginning of the 1990s to model the flaring corona in a simple and computationally inexpensive way. The pioneering and now most prevalent model in the literature was proposed by Lu and Hamilton. This model has been extremely useful to reproduce most of the main characteristic features observed in solar flares (e.g., the probability density function of a flare’s energy) and, in recent years, has been used as the starting point to predict extreme flaring events. In this work, we revisit Lu and Hamilton’s model and the very definition of waiting time for both extreme and all-sized events. We find that extreme avalanche statistics are well described by a log-normal distribution, in accordance with recent observations of solar flares.