| Abstract : | The theory of self-organization in continuous systems in the presence of dissipation suggests that ideal invariants undergo selective decay. This allows a mathematical formulation in terms of the variational principle to predict the self-organized or relaxed state. The earliest theory of relaxation was put forward by Taylor (1974), wherein total magnetic energy was taken as minimizer and total helicity as an invariant. The corresponding relaxed state was shown by Woltjer (1958) to be linear force-free. An example of one such system is the solar corona, where transients such as solar flares are known to be driven by the process of magnetic reconnection. This suggests the possible applicability of Taylor’s theory and was first adapted for the case of solar flares by Heyvaerts and Priest (1984). Since then, numerical experiments have been conducted to test Taylor’s theory in various contexts, such as the nanoflare heating model and the topological dissipation problem. In this study, we take an alternative approach to understand the relaxation process for a solar flare within the framework of extrapolation model and data-constrained magnetohydrodynamics simulation. For AR 12253, hosting M1.3 class flare, observations are utilized to identify the possible sites of reconnection and extrapolation of coronal magnetic field. Our investigation reveals an overlying hyperbolic flux tube (HFT) where we explore reconnection using magnetohydrodynamics simulations with EULAG-MHD. Using three suitably chosen sub-volumes, we analyze the variation and distribution of parameters such as the magnetic energy, current density, and twist to understand plasma relaxation and to draw our conclusions on the result, limitations, and future scope of this study. Essentially, we find that all the sub-volumes undergo at least partial relaxation in the sense of lowering of twist, and that the size and position of chosen sub-volumes with respect to the boundaries play an important role in governing the dynamics. |
