MULTIPLE-SCATTERING OF ACOUSTIC-WAVES BY A PAIR OF UNIFORMLY MAGNETIZED FLUX TUBES

Motivated by the outstanding question of whether sunspot seismology can distinguish between the competing monolithic flux-tube and spaghetti sunspot models, we consider the interaction of an acoustic plane wave with a pair of uniformly magnetized flux tubes of circular cross section. We demonstrate that this interaction falls within one of three distinct categories depending upon the separation of the magnetic flux tubes and their individual scattering strengths. At the largest flux-tube separations the scattering is incoherent, with the net scattering cross section being just the sum of the scattering cross sections of the individual flux tubes. At intermediate separations phase coherence between the acoustic waves scattered by the individual flux tubes leads to net scattering cross sections that deviate considerably from the incoherent scattering cross section. Finally, a multiple scattering regime can exist at the smallest flux-tube separations, where the acoustic field scattered by a particular flux tube differs significantly from that which would be obtained in the absence of its companion magnetic flux tube. Our estimates suggest that the interaction of the solar acoustic oscillations with a spaghetti sunspot will almost certainly show coherent phasing of the scattered waves and will most likely also exhibit multiple scattering effects. Accordingly, much of our attention is focused on the novel features pertinent to the multiple scattering regime. Of these novel features a new class of scattering resonances deserves special mention. The thin fluid channel that separates two magnetic flux tubes in close proximity to one another is essential for the existence of these scattering resonances-or, equivalently, tube modes-which obviously have no counterpart on an isolated magnetic flux tube. Unlike the tube modes of an isolated slender magnetic flux tube, these channel modes travel rapidly along the pair of flux tubes with phase velocities that can be comparable to the Alfven speed within the individual flux tubes. Our results offer much preliminary encouragement that sunspot seismology will be able to distinguish between the monolithic flux-tube and the spaghetti sunspot models, although any definitive conclusions must await the extension of this present work to flux-tube bundles containing several individual flux tubes which are embedded in gravitationally stratified atmospheres.