Calculating energy storage due to topological changes in emerging active region NOAA AR 11112

The Minimum Current Corona (MCC) model provides a way to estimate stored coronal energy using the number of field lines connecting regions of positive and negative photospheric flux. This information is quantified by the net flux connecting pairs of opposing regions in a connectivity matrix. Changes in the coronal magnetic field, due to processes such as magnetic reconnection, manifest themselves as changes in the connectivity matrix. However, the connectivity matrix will also change when flux sources emerge or submerge through the photosphere, as often happens in active regions. We have developed an algorithm to estimate the changes in flux due to emergence and submergence of magnetic flux sources. These estimated changes must be accounted for in order to quantify storage and release of magnetic energy in the corona. To perform this calculation over extended periods of time, we must additionally have a consistently labeled connectivity matrix over the entire observational time span. We have therefore developed an automated tracking algorithm to generate a consistent connectivity matrix as the photospheric source regions evolve over time. We have applied this method to NOAA Active Region 11112, which underwent a GOES M2.9 class flare around 19:00 on Oct.16th, 2010, and calculated a lower bound on the free magnetic energy buildup of ~8.25 x 10^30 ergs over 3 days.Comment: 36 pages, 14 figures. Published in 2012 ApJ, 749, 64. Published version available at http://stacks.iop.org/0004-637X/749/64 Animation available at http://solar.physics.montana.edu/tarrl/data/AR11112.mp

The Role of fast magnetosonic waves in the release and conversion via reconnection of energy stored by a current sheet

Using a simple two-dimensional, zero-beta model, we explore the manner by which reconnection at a current sheet releases and dissipates free magnetic energy. We find that only a small fraction (3%-11% depending on current sheet size) of the energy is stored close enough to the current sheet to be dissipated abruptly by the reconnection process. The remaining energy, stored in the larger-scale field, is converted to kinetic energy in a fast magnetosonic disturbance propagating away from the reconnection site, carrying the initial current and generating reconnection-associated flows (inflow and outflow). Some of this reflects from the lower boundary (the photosphere) and refracts back to the X-point reconnection site. Most of this inward wave energy is reflected back again, and continues to bounce between X-point and photosphere until it is gradually dissipated, over many transits. This phase of the energy dissipation process is thus global and lasts far longer than the initial purely local phase. In the process a significant fraction of the energy (25%-60%) remains as undissipated fast magnetosonic waves propagating away from the reconnection site, primarily upward. This flare-generated wave is initiated by unbalanced Lorentz forces in the reconnection-disrupted current sheet, rather than by dissipation-generated pressure, as some previous models have assumed. Depending on the orientation of the initial current sheet the wave front is either a rarefaction, with backward directed flow, or a compression, with forward directed flow

A viscoelastic theory of turbulent fluid permeated with fibril magnetic fields

The solar convection zone is a turbulent plasma interacting with a magnetic field. Its magnetic field is often described as fibrillar since it consists of slender flux tubes occupying a small fraction of the total volume. It is well known that plasma flow will exert a force on these magnetic fibrils, but few models have accounted for the back-reaction of the fibrils on the flow. We present a model in which the back-reaction of the fibrils on the flow is manifest as viscoelastic properties. On short timescales the fibrils react elastically with a shear modulus proportional to their overall magnetic energy density. On longer timescales they produce an effective viscosity resulting from collective aerodynamic drag. The viscosity due to flux tubes in the solar convection zone can be comparable to that attributed to turbulence there. These forces might have observable effects on the convection zone flows

Relating magnetic reconnection to coronal heating

It is clear that the solar corona is being heated and that coronal magnetic fields undergo reconnection all the time. Here we attempt to show that these two facts are in fact related - i.e. coronal reconnection generates heat. This attempt must address the fact that topological change of field lines does not automatically generate heat. We present one case of flux emergence where we have measured the rate of coronal magnetic reconnection and the rate of energy dissipation in the corona. The ratio of these two, $P/\dot{\Phi}$, is a current comparable to the amount of current expected to flow along the boundary separating the emerged flux from the pre-existing flux overlying it. We can generalize this relation to the overall corona in quiet Sun or in active regions. Doing so yields estimates for the contribution to corona heating from magnetic reconnection. These estimated rates are comparable to the amount required to maintain the corona at its observed temperature.Comment: To appear in Phil. Trans. Royal Soc.