The Minimum Energy Principle Applied to Parker's Coronal Braiding and Nanoflaring Scenario

TL;DR

This paper applies the minimum energy principle to Parker's coronal braiding model, showing it prevents large misalignments and nanoflares in the corona, suggesting nanoflares are more likely in lower solar atmospheric layers.

Contribution

It demonstrates that the minimum energy principle causes bifurcation in force-free magnetic fields, limiting free energy buildup and preventing nanoflares in the corona.

Findings

Magnetic field lines remain nearly parallel with small misalignment angles.

No nanoflares are expected in the force-free, divergence-free corona.

Nanoflares are more probable in the chromosphere and transition region.

Abstract

Parker's coronal braiding and nanoflaring scenario predicts the development of tangential discontinuities and highly misaligned magnetic field lines, as a consequence of random buffeting of their footpoints due to the action of sub-photospheric convection. The increased stressing of magnetic field lines is thought to become unstable above some critical misalignment angle and to result into local magnetic reconnection events, which is generally referred to as Parker's `nanoflaring scenario'. In this study we show that the {\sl minimum (magnetic) energy principle} leads to a bifurcation of force-free field solutions for helical twist angles at $|\varphi(t)| = \pi$, which prevents the build-up of arbitrary large free energies and misalignment angles. The minimum energy principle predicts that neighbored magnetic field lines are almost parallel (with misalignment angles of $\Delta \mu \approx 1.6^\circ-1.8^\circ$), and do not reach a critical misalignment angle prone to nanoflaring. Consequently, no nanoflares are expected in the divergence-free and force-free parts of the solar corona, while they are more likely to occur in the chromosphere and transition region.