Damping of Slow Surface Sausage Modes in Photospheric Waveguides

Abstract

There has been considerable interest in sausage modes in photospheric waveguides such as pores and sunspots, and slow surface sausage modes (SSSMs) have been suggested to damp sufficiently rapidly to account for chromospheric heating. Working in the framework of linear resistive magnetohydrodynamics, we examine how efficient electric resistivity and resonant absorption in the cusp continuum can be for damping SSSMs in a photospheric waveguide with equilibrium parameters compatible with recent measurements of a photospheric pore. For SSSMs with the measured wavelength, we find that the damping rate due to the cusp resonance is substantially less strong than theoretically expected with the thin-boundary approximation. The damping-time-to-period ratio ( τ / P ) we derive for standing modes, equivalent to the damping-length-to-wavelength ratio for propagating modes given the extremely weak dispersion, can reach only ∼180. However, the accepted values for electric resistivity ( η ) correspond to a regime where both the cusp resonance and resistivity play a role. The values for τ / P attained at the largest allowed η may reach ∼30. We conclude that electric resistivity can be considerably more efficient than the cusp resonance for damping SSSMs in the pore in question, and needs to be incorporated into future studies on the damping of SSSMs in photospheric waveguides in general.