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It has recently been discovered that sunspots scatter intermediate and high-degree p-modes. The scattering may be characterized by a shift in phase between modes travelling toward and away from the spot. These observations offer the hope that suitable models of the scattering may yield important clues about the subsurface evolution and structure of magnetic regions.
We model the scattering of p-mode waves in a polytropic atmosphere by localized inhomogeneities in compressibility (the wave speed), density and pressure of the media. The effect of the inhomogeneities is to introduce a source term in the pressure wave equation. We solve this inhomogeneous equation for the scattered wave amplitudes using standard Green's function techniques under the simplification of the Born approximation. We found that with reasonable strength (or contrast) of the imhomogeneities we can obtain phase shifts between the outgoing and the in-going waves similar to observations of p-modes in both the magnitude and degree ($\ell$) dependence. We discuss how the strength of the scattered waves may depend on the depth distribution of the inhomogeneities.
This work is supported by a NSF grant AST-9496171 and NASA grant NAGW-4143 awarded to DCB. YF is supported by ONR grant N00014-91-J-1040.
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