Energy Balance in Avalanche Models for Solar Flares

Abstract

The distributions of solar flare energies and waiting times have not been described simultaneously by a single physical model, yet. In this research, we investigate whether recent avalanche models can describe the distributions for both the released energies and waiting times of flares in an active region. Flaring events are simulated using the modified Lu and Hamilton model (Lu and Hamilton (1991), ApJ, 380, 89) and also the optimized model (Farhang et al. (2018), ApJ, 859, 41). Applying a probability balance equation approach, we study the statistics of the simulated flaring events and investigate the origin of the observed power law in the flare frequency-size distribution. The results indicate that the power law originates in the distribution of transition rates (the distribution of the probabilities of transitions between different energies) rather than the distribution of the energy of the active region. It is also observed that the waiting-time distribution of simulated flaring events follows a q-exponential function which approximates a simple Poisson distribution.

References in corpus (15)

• An Observational Overview of Solar Flares
• Power Laws in Solar Flares: Self-Organized Criticality or Turbulence?
• 25 Years of Self-Organized Criticality: Solar and Astrophysics
• Statistical properties of superflares on solar-type stars based on 1-min cadence data
• Nonextensive statistical mechanics: A brief introduction
• Global Energetics of Solar Flares: V. Energy Closure in Flares and Coronal Mass Ejections
• Solar Flares as Cascades of Reconnecting Magnetic Loops
• Reconciliation of Waiting Time Statistics of Solar Flares Observed in Hard X-Rays
• A simple algorithm for optimization and model fitting: AGA (asexual genetic algorithm)
• Solar Flares Complex Networks
• The Energetics of a Flaring Solar Active Region, and Observed Flare Statistics
• A simplified numerical model of coronal energy dissipation based on reduced MHD
• Influence of the definition of dissipative events on their statistics
• Deterministically Driven Avalanche Models of Solar Flares
• Principle of Minimum Energy in Magnetic Reconnection in a Self-Organized Critical Model for Solar Flares

Cited by in corpus (7)

• Automatic detection of small-scale EUV brightenings observed by the Solar Orbiter/EUI
• Synchronization of Small-scale Magnetic Features, Blinkers, and Coronal Bright Points
• Do Cellular Automaton Avalanche Models Simulate the Quasi-Periodic Pulsations of Solar Flares?
• A statistical search for a uniform trigger threshold in solar flares from individual active regions
• Solar Flare Prediction Using Long Short-term Memory (LSTM) and Decomposition-LSTM with Sliding Window Pattern Recognition
• Energy Definition and Minimization in Avalanche Models for Solar Flares
• Forecasting Solar Flares by Data Assimilation in Sandpile Models