Equilibria, Dynamics and Current Sheets Formation in Magnetically Confined Coronae

Abstract

The dynamics of magnetic fields in closed regions of solar and stellar coronae are investigated with a reduced magnetohydrodynamic (MHD) model in the framework of Parker scenario for coronal heating. A novel analysis of reduced MHD equilibria shows that their magnetic fields have an asymmetric structure in the axial direction with variation length-scale $z_\ell \sim \ell B_0/b$, where $B_0$ is the intensity of the strong axial guide field, $b$ that of the orthogonal magnetic field component, and $\ell$ the scale of $\mathbf{b}$. Equilibria are then quasi-invariant along the axial direction for variation scales larger than approximatively the loop length $z_\ell \gtrsim L_z$, and increasingly more asymmetric for smaller variation scales $z_\ell \lesssim L_z$. The $critical$ $length$ $z_\ell \sim L_z$ corresponds to the magnetic field intensity threshold $b \sim \ell B_0/L_z$. Magnetic fields stressed by photospheric motions cannot develop strong axial asymmetries. Therefore fields with intensities below such threshold evolve quasi-statically, readjusting to a nearby equilibrium, without developing nonlinear dynamics nor dissipating energy. But stronger fields cannot access their corresponding asymmetric equilibria, hence they are out-of-equilibrium and develop nonlinear dynamics. The subsequent formation of current sheets and energy dissipation is $necessary$ for the magnetic field to relax to equilibrium, since dynamically accessible equilibria have variation scales larger than the loop length $z_\ell \gtrsim L_z$, with intensities smaller than the threshold $b \lesssim \ell B_0/L_z$. The dynamical implications for magnetic fields of interest to solar and stellar coronae are investigated numerically and the impact on coronal physics discussed.