Self-Organized Braiding and the Structure of Coronal Loops

Abstract

The Parker model for heating of the solar corona involves reconnection of braided magnetic flux elements. Much of this braiding is thought to occur at as yet unresolved scales, for example, braiding of threads within an extremeultraviolet or X-ray loop. However, some braiding may be still visible at scales accessible to TRACE or Hinode. We suggest that attempts to estimate the amount of braiding at these scales must take into account the degree of coherence of the braid structure. In this paper, we examine the effect of reconnection on the structure of a braided magnetic field. We demonstrate that simple models of braided magnetic fields which balance the input of topological structure with reconnection evolve to a self-organized critical state. An initially random braid can become highly ordered, with coherence lengths obeying power-law distributions. The energy released during reconnection also obeys a power law. Our model gives more frequent (but smaller) energy releases nearer to the ends of a coronal loop.

The extreme solar storm of May 1921: observations and a complex topological model

“…The linking numbers are closely related to the average crossing number, which is an algebraic measure of the link complexity in space (Ricca, 2002). Interestingly it is also found (Berger and Asgari-Targhi, 2009) that the energy released due to reconnection of the braids in the coronal loops follows a powerlaw distribution, i.e. is fractal.…”

Self-organized braiding in solar coronal loops

“…Delaying rapid reconnection allows the build up of substantial energy reserves in the magnetic field lines. As the magnetic field becomes more and more braided and twisted, its energy will generally increase quadratically in time (Parker 1983; Self-organized braiding in solar coronal loops 3 Berger 1991Berger , 1993. If reconnection occurs too early, there will not be enough energy stored to power flares or coronal heating.…”

THE STORAGE AND DISSIPATION OF MAGNETIC ENERGY IN THE QUIET SUN CORONA DETERMINED FROM SDO /HMI MAGNETOGRAMS

“…The complex evolution of these magnetic features on the photosphere may significantly heat the low corona through braiding and reconnection of the magnetic fields connecting them (e.g., Parnell & Galsgaard 2004;Berger & Asgari-Targhi 2009;Pontin et al 2011).…”