A relaxation model of coronal heating in multiple interacting flux ropes

¹ School of Mechanical, Aerospace, and Civil Engineering, University of Manchester, Manchester M13 9PL, UK
e-mail: asad.hussain@postgrad.manchester.ac.uk
² Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
³ School of Mathematics and Statistics, University of St. Andrews, St. Andrews, Fife, KY16 9SS, UK

Received: 28 August 2016
Accepted: 22 December 2016

Abstract

Context. Heating the solar corona requires dissipation of stored magnetic energy, which may occur in twisted magnetic fields. Recently published numerical simulations show that the ideal kink instability in a twisted magnetic thread may trigger energy release in stable twisted neighbours, and demonstrate an avalanche of heating events.

Aims. We aim to construct a Taylor relaxation model for the energy release from two flux ropes and compare this with the outcomes of the simulations. We then aim to extend the model to large numbers of flux ropes, allowing the possibility of modelling a heating avalanche, and calculation of the energy release for ensembles of twisted threads with varying twist profiles.

Methods. The final state is calculated by assuming a helicity-conserving relaxation to a minimum energy state. Multiple scenarios are examined, which include kink-unstable flux ropes relaxing on their own, as well as stable and unstable flux ropes merging into a single rope as a result of magnetic reconnection. We consider alternative constraints that determine the spatial extent of the final relaxed state.

Results. Good agreement is found between the relaxation model and the magnetohydrodynamic simulations, both for interactions of two twisted threads and for a multi-thread avalanche. The model can predict the energy release for flux ropes of varying degrees of twist, which relax individually or which merge through reconnection into a single flux rope. It is found that the energy output of merging flux ropes is dominated by the energy of the most strongly twisted rope.

Conclusions. The relaxation approach provides a very good estimate of the energy release in an ensemble of twisted threads of which one is kink-unstable.