Scaling law for the heating of solar coronal loops

Abstract

We report preliminary results from a series of numerical simulations of the reduced magnetohydrodynamic equations, used to describe the dynamics of magnetic loops in active regions of the solar corona. A stationary velocity field is applied at the photospheric boundaries to imitate the driving action of granule motions. A turbulent stationary regime is reached, characterized by a broadband power spectrum $E_k\simeq k^{-3/2}$ and heating rate levels compatible with the heating requirements of active region loops. A dimensional analysis of the equations indicates that their solutions are determined by two dimensionless parameters: the Reynolds number and the ratio between the Alfven time and the photospheric turnover time. From a series of simulations for different values of this ratio, we determine how the heating rate scales with the physical parameters of the problem, which might be useful for an observational test of this model.