Multiple scattering and resonant absorption of p-modes by fibril sunspots

Abstract

We investigate the scattering and absorption of sound waves by bundles of magnetic flux tubes. The individual flux tubes within the bundle have thin nonuniform boundary layers where the thermodynamic and magnetic properties change continuously to their photospheric levels. In these nonuniform layers, resonant absorption converts some of the incident acoustic wave energy into heat and thus the flux-tube bundle appears as a sink of acoustic power. For a fixed amount of magnetic flux, we find that composite ('spaghetti') sunspots absorb much more wave energy than their monolithic counterparts, although both sunspots scatter comparable amounts of the incident acoustic wave energy. The extra energy drainage results from the interplay of the wave scattering back and forth between the tubes and the incremental loss of acoustic power at each interaction with an individual tube due to the resonant absorption in its boundary layer. The scattering cross section is not similarly enhanced because the multiply scattered waves generally interfere destructively in the far field. Another interesting consequence of the lack of axisymmetry is that composite sunspots may show acoustic emission for some multipole components, and absorption for others. The net absorption cross section is however never negative, and is nonzero only when the projection of the wave phase speed along the flux-tube bundle is less than the maximal value of the Alfven speed. Whereas composite sunspots composed of uniformly magnetized flux tubes posses narrow scattering resonances, the analogous bundle of nonuniform fibrils instead exhibits corresponding broad absorption resonances, resulting from the incremental loss of power on successive scatters. These broad absorption resonances correspond to leaky (MHD radiating) eigenmodes of the composite structure. When progressively more flux tubes are clustered, additional oscillation eigenmodes appear grouped in a complicated band structure characterized by a (nearly) common speed of propagation along the bundle.