An anisotropic turbulent model for solar coronal heating

Context. We present a self-consistent model of solar coronal heating in which we include the dynamical effect of the background magnetic field along a coronal structure by using exact results from wave MHD turbulence. Aims. We evaluate the heating rate and the microturbulent velocity for comparison with observations in the quiet corona, active regions and also coronal holes. Methods. The coronal structures are assumed to be in a turbulent state maintained by the slow erratic motion of the magnetic footpoints. A description of the large-scale and the unresolved small-scale dynamics are given separately. From the latter, we compute exactly (or numerically for coronal holes) turbulent viscosites used in the former to self-consistently close the system and derive the heating flux expression. Results. We show that the heating rate and the turbulent velocity compare favorably with coronal observations. Conclusions. Although the Alfvén wave turbulence regime is strongly anisotropic, and could reduce a priori the heating efficiency, it provides a unexpected satisfactory model of coronal heating for both magnetic loops and open magnetic field lines.