Principle of Minimum Energy in Magnetic Reconnection in a Self-Organized Critical Model for Solar Flares

Abstract

Solar flares are an abrupt release of magnetic energy in the Sun's atmosphere due to reconnection of the coronal magnetic field. This occurs in response to turbulent flows at the photosphere which twist the coronal field. Similar to earthquakes, solar flares represent the behavior of a complex system, and expectedly their energy distribution follows a power law. We present a statistical model based on the principle of minimum energy in a coronal loop undergoing magnetic reconnection, which is described as an avalanche process. We show the distribution of peaks for the flaring events in this self-organized critical system is scale-free. The obtained power law index 1.84 $ \pm $ 0.02 for the peaks is in good agreement with satellite observations of soft X-ray flares. The principle of minimum energy can be applied for general avalanche models to describe many other phenomena.