Fundamental physics behind solar flares

Amir Jafari, Ethan Vishniac

Published 2019-09-16Version 1

Differential rotation, shear and thermal convection, among other things, produce complex patterns of turbulent flows in magnetized astrophysical systems. The corresponding magnetic fields are consequently entangled in an extremely complicated way. Once the field becomes very entangled, it should slip through the fluid to reduce its spatial complexity level, otherwise the observed large scale fields in astrophysical objects could never be generated and evolved over cosmological time scales. Such a spontaneous slippage of magnetic fields launching jets of fluid-magnetic reconnection-is usually interpreted and described as a change in the topology of the stochastic magnetic fields. However, neither magnetic topology nor its stochasticity level is usually given a precise mathematical definition, and such technical terms are usually used rather loosely. We show that in fact magnetic topology is well-defined only in the phase space corresponding to a dynamical system governed by the induction equation. Hence the field's topology and stochasticity should be studied in terms of the corresponding phase space trajectories rather than the field lines in real Euclidean space. It is shown that the phase space topology is preserved in time for a magnetic field which, besides satisfying few continuity conditions, solves a time reversal invariant induction equation. What breaks the time symmetry in the induction equation is the presence of non-ideal plasma effects at small scales such as resistivity, which results from random collisions between diffusing electrons and other particles. This suggests that reconnection is rooted in the second law of thermodynamics that dictates entropy increase which in turn breaks the time symmetry.