Coronal heating by the partial relaxation of twisted loops

Abstract

Context. Relaxation theory offers a straightforward method for estimating the energy that is released when continual convective driving causes a magnetic field to become unstable. Thus, an upper limit to the heating caused by ensembles of nanoflaring coronal loops can be calculated and checked against the level of heating required to maintain observed coronal temperatures (T 10 6 K). Aims. We present new results obtained from nonlinear magnetohydrodynamic (MHD) simulations of idealised coronal loops. All of the initial loop configurations discussed are known to be linearly kink unstable. The purpose of this work is to determine whether or not the simulation results agree with Taylor relaxation, which will require a modified version of relaxation theory applicable to unbounded field configurations. In addition, we show for two cases how the relaxation process unfolds. Methods. A three-dimensional (3D) MHD Lagrangian-remap code is used to simulate the evolution of a line-tied cylindrical coronal loop model. This model comprises three concentric layers surrounded by a potential envelope; hence, being twisted locally, each loop configuration is distinguished by a piecewise-constant current profile, featuring three parameters. Initially, all configurations carry zero-net-current fields and are in ideally unstable equilibrium. The simulation results are compared with the predictions of helicityconserving relaxation theory. Results. For all simulations, the change in helicity is no more than 2% of the initial value; also, the numerical helicities match the analytically-determined values. Magnetic energy dissipation predominantly occurs via shock heating associated with magnetic reconnection in distributed current sheets. The energy release and final field profiles produced by the numerical simulations are in agreement with the predictions given by a new model of partial relaxation theory: the relaxed field is close to a linear force free state; however, the extent of the relaxation region is limited, while the loop undergoes some radial expansion. Conclusions. The results presented here support the use of partial relaxation theory, specifically, when calculating the heating-event distributions produced by ensembles of kink-unstable loops. The energy release increases with relaxation radius; but, once the loop has expanded by more than 50%, further expansion yields little more energy. We conclude that the relaxation methodology may be used for coronal heating studies.

Physical role of topological constraints in localized magnetic relaxation

“…Only once the kink instability had led to the onset of a turbulent relaxation, did it become clear that the extent of the turbulent region would be about 1.8 times the diameter of the initial loop. It was suggested by Bareford et al [11] that, due to the presence of zero net vertical current, their relaxation region was more localized than previous simulations by Browning et al [9] in which turbulence filled the whole domain. However, our simulations with a net vertical current still have a localized turbulent region (e.g.…”

Shock heating in numerical simulations of kink-unstable coronal loops

“…Another important difference is in the way Ohmic heating is handled. Bareford et al [17] found that regions of Ohmic heating appeared more or less at the same locations (and times) as shock heating, although the latter was far stronger than the former. By contrast, the use of a variable critical current employed here produces small pockets of Ohmic heating scattered near the footpoints and around the midplane.…”

Soft X-ray emission in kink-unstable coronal loops

“…The flux-rope field is purely toroidal (B z = 0) for this limiting value of λ. The threshold for the kink instability depends both on the specific transverse twist profile considered and on geometrical parameters such as the flux-rope aspect ratio (Bareford et al 2013). In our case, and for an aspect ratio L 0 /r 0 = 10, the kink instability is prone to develop for λ > ∼ 1.6.…”