Hyperdiffusion as a Mechanism for Solar Coronal Heating

TL;DR

This paper develops a theory for coronal heating via hyperdiffusion, showing how magnetic energy from footpoint motions and flux rope fields heats the corona, with a model matching observed cavity properties.

Contribution

It introduces hyperdiffusion as a magnetic dissipation mechanism conserving helicity, and models coronal flux ropes with stochastic magnetic fields to explain temperature and density profiles.

Findings

Flux rope temperature and density are lower than surroundings.

Magnetic fluctuations have a perpendicular scale of about 1000 km.

Hyperdiffusion effectively explains coronal heating in flux ropes.

Abstract

A theory for the heating of coronal magnetic flux ropes is developed. The dissipated magnetic energy has two distinct contributions: (1) energy injected into the corona as a result of granule-scale, random footpoint motions, and (2) energy from the large-scale, nonpotential magnetic field of the flux rope. The second type of dissipation can be described in term of hyperdiffusion, a type of magnetic diffusion in which the helicity of the mean magnetic field is conserved. The associated heating rate depends on the gradient of the torsion parameter of the mean magnetic field. A simple model of an active region containing a coronal flux rope is constructed. We find that the temperature and density on the axis of the flux rope are lower than in the local surroundings, consistent with observations of coronal cavities. The model requires that the magnetic field in the flux rope is stochastic in nature, with a perpendicular length scale of the magnetic fluctuations of order 1000 km.