Parameterisation of coronal heating: spatial distribution and observable consequences

Abstract

Aims. We investigate the difference in the spatial distribution of the energy input for parameterisations of different mechanisms to heat the corona of the Sun and possible impacts on the coronal emission. Methods. We use a 3D magneto-hydrodynamic (MHD) model of a solar active region as a reference and compare the Ohmic-type heating in this model to parameterisations for alternating current (AC) and direct current (DC) heating models; in particular, we use Alfven wave and MHD turbulence heating. We extract the quantities needed for these two parameterisations from the reference model and investigate the spatial distribution of the heat input in all three cases, globally and along individual field lines. To study differences in the resulting coronal emission, we employ 1D loop models with a prescribed heat input based on the heating rate we extracted along a bundle of field lines. Results. On average, all heating implementations show a rough drop of the heating rate with height. This also holds for individual field lines. While all mechanisms show a concentration of the energy input towards the low parts of the atmosphere, for individual field lines the concentration towards the foot points is much stronger for the DC mechanisms than for the Alfven wave AC case. In contrast, the AC model gives a stronger concentration of the emission towards the foot points. This is because the more homogeneous distribution of the energy input leads to higher coronal temperatures and a more extended transition region. Conclusions. The significant difference in the concentration of the heat input towards the foot points for the AC and DC mechanisms and the pointed difference in the spatial distribution of the coronal emission for these cases show that the two mechanisms should be discriminable by observations. Before drawing final conclusions, these parameterisations should be implemented in new 3D models in a more self-consistent way.