A Constrained Tectonics Model for Coronal Heating

TL;DR

This paper develops a constrained tectonics model for coronal heating, demonstrating that energy dissipation becomes independent of plasma resistivity under certain conditions, with implications for understanding solar corona heating mechanisms.

Contribution

It introduces a simplified, non-reconnecting version of the tectonics model, revealing resistivity-independent heating rates in coronal plasma.

Findings

Heating rate is independent of resistivity when footpoint motion coherence time is short.

Scaling relations suggest reconnection does not affect resistivity independence.

Energy dissipation remains steady over long timescales despite geometric constraints.

Abstract

An analytical and numerical treatment is given of a constrained version of the tectonics model developed by Priest, Heyvaerts, & Title [2002]. We begin with an initial uniform magnetic field ${\bf B} = B_0 \hat{\bf z}$ that is line-tied at the surfaces $z = 0$ and $z = L$. This initial configuration is twisted by photospheric footpoint motion that is assumed to depend on only one coordinate ($x$) transverse to the initial magnetic field. The geometric constraints imposed by our assumption precludes the occurrence of reconnection and secondary instabilities, but enables us to follow for long times the dissipation of energy due to the effects of resistivity and viscosity. In this limit, we demonstrate that when the coherence time of random photospheric footpoint motion is much smaller by several orders of magnitude compared with the resistive diffusion time, the heating due to Ohmic and viscous dissipation becomes independent of the resistivity of the plasma. Furthermore, we obtain scaling relations that suggest that even if reconnection and/or secondary instabilities were to limit the build-up of magnetic energy in such a model, the overall heating rate will still be independent of the resistivity.