Free Magnetic Energy in Solar Active Regions above the Minimum-Energy Relaxed State

TL;DR

This paper estimates the free magnetic energy in solar active regions by comparing nonlinear force-free fields to minimum-energy states, providing insights into flare processes and improving energy estimates over traditional potential field comparisons.

Contribution

It introduces a method to estimate free magnetic energy using the minimum-energy state, enhancing understanding of solar flare energetics.

Findings

Free magnetic energy above the minimum-energy state correlates better with flare activity.

Reconstructed nonlinear force-free fields provide more accurate energy estimates.

The method improves understanding of energy release during solar flares.

Abstract

To understand the physics of solar flares, including the local reorganisation of the magnetic field and the acceleration of energetic particles, we have first to estimate the free magnetic energy available for such phenomena, which can be converted into kinetic and thermal energy. The free magnetic energy is the excess energy of a magnetic configuration compared to the minimum-energy state, which is a linear force-free field if the magnetic helicity of the configuration is conserved. We investigate the values of the free magnetic energy estimated from either the excess energy in extrapolated fields or the magnetic virial theorem. For four different active regions, we have reconstructed the nonlinear force-free field and the linear force-free field corresponding to the minimum-energy state. The free magnetic energies are then computed. From the energy budget and the observed magnetic activity in the active region, we conclude that the free energy above the minimum-energy state gives a better estimate and more insights into the flare process than the free energy above the potential field state.