Analytical model of static coronal loops

Abstract

By solving the energy-equilibrium equation in the stationary case, we derive analytical formulae in the form of scaling laws for non-uniformly heated and gravitationally stratified coronal loops. The heating is assumed to be localized in the chromosphere and to exponentially decrease with increasing distance along the loop strand. This exponential behavior of the heating and pressure profiles implies that we need to use the mean-value theorem, and in turn fit the mean-value parameters of the scaling laws to the results of the numerical simulations. The radiative-loss function is approximated by a power-law function of the temperature, and its effect on the resulting scaling laws for coronal loops is studied. We find that this effect is more important than the effect of varying loop geometry. We also find that the difference in lengths of the different loop strands in a loop with expanding cross-section does not produce differences in the EUV emission of these strands significant enough to explain the observed narrowness of the coronal loops.