The possible role of high-frequency waves in heating solar coronal loops

Abstract

We investigate the role of high-frequency waves in the heating of solar active region coronal loops. We assume a uniform background magnetic field, and we introduce a density stratification in a direction perpendicular to this field. We focus on ion compressive viscosity as the damping mechanism of the waves. We incorporate viscosity self-consistently into the equations, and we derive a dispersion relation by adopting a slab model, where the density inside the slab is greater than that outside. Such a configuration supports two types of modes: surface waves and trapped body waves. In order to determine under what conditions these waves may contribute to the heating of active regions, we solve our dispersion relation for a range of densities, temperatures, magnetic field strengths, density ratios, wavevector magnitudes, wavevector ratios, and slab widths. We find that surface waves exhibit very small damping, but body waves can potentially damp at rates needed to balance radiative losses. However, the required frequencies of these body waves are very high. For example, the wave frequency must be at least 5.0/s for a slab density of 10(exp 9,5)/cc, a slab temperature of 10(exp 6,5) K, a field strength of 100 G, and a density ratio of 5. For a slab density of 10(exp 10)/cc, this frequency increases to 8.8/s. Although these frequencies are very high, there in no observational evidence to rule out their existence, and they may be generated both below the corona and at magnetic reconnection sites in the corona. However, we do find that, for slab densities of 10(exp 10)/cc or less, the dissipation of high-frequency waves will be insufficient to balance the radiative losses if the magnetic field strength exceeds roughly 200 G. Because the magnetic field is known to exceed 200 G in many active region loops, particularly low-lying loops and loops emanating from sunspots, it is unlikely that high-frequency waves can provide sufficient heating in these regions.