Nonlinear Dynamics of the Parker Scenario for Coronal Heating

Abstract

The Parker or field line tangling model of coronal heating is studied comprehensively via long-time high-resolution simulations of the dynamics of a coronal loop in cartesian geometry within the framework of reduced magnetohydrodynamics (RMHD). Slow photospheric motions induce a Poynting flux which saturates by driving an anisotropic turbulent cascade dominated by magnetic energy. In physical space this corresponds to a magnetic topology where magnetic field lines are barely entangled, nevertheless current sheets (corresponding to the original tangential discontinuities hypothesized by Parker) are continuously formed and dissipated. Current sheets are the result of the nonlinear cascade that transfers energy from the scale of convective motions ($\sim 1,000 km$) down to the dissipative scales, where it is finally converted to heat and/or particle acceleration. Current sheets constitute the dissipative structure of the system, and the associated magnetic reconnection gives rise to impulsive ``bursty'' heating events at the small scales. This picture is consistent with the slender loops observed by state-of-the-art (E)UV and X-ray imagers which, although apparently quiescent, shine bright in these wavelengths with little evidence of entangled features. The different regimes of weak and strong MHD turbulence that develop, and their influence on coronal heating scalings, are shown to depend on the loop parameters, and this dependence is quantitatively characterized: weak turbulence regimes and steeper spectra occur in {\it stronger loop fields} and lead to {\it larger heating rates} than in weak field regions.