Nanoflare Theory Revisited

At any scale l in the turbulent inertial range, the magnetic field can be divided up into a large-scale component and a small-scale, high spatial frequency component which undergoes magnetic reversals. Such local reconnections, i.e., on any inertial scale l, seem to be an inseparable part of magnetohydrodynamic (MHD) turbulence, whose collective outcome can lead to global reconnection with a rate independent of the small-scale physics dominant at dissipative scales. We show that this picture, known as stochastic reconnection, is intimately related to nanoflare theory, proposed long ago to explain solar coronal heating. We argue that, due to stochastic flux freezing, a generalized version of magnetic flux freezing in turbulence, the field follows the flow in a statistical sense. Turbulence bends and stretches the field, increasing its spatial complexity. Strong magnetic shears associated with such a highly tangled field can trigger local reversals and field annihilations on a wide range of inertial scales which convert magnetic energy into kinetic and thermal energy. The former may efficiently enhance turbulence and the latter heat generation. We support this theoretical picture using scaling laws of MHD turbulence and also recent analytical and numerical studies which suggest a statistical correlation between magnetic spatial complexity and energy dissipation. Finally, using an MHD numerical simulation, we show that the time evolution of the magnetic complexity is statistically correlated with the rate of kinetic energy injection and/or magnetic-to-thermal energy conversion, in agreement with our proposed theoretical picture.