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Title:
Mode Mixing by a Shallow Sunspot
Authors:
Barnes, G.; Cally, P. S.
Affiliation:
AA(Department of Mathematics, Monash University, Clayton, Vic 3168 Australia), AB(Department of Mathematics, Monash University, Clayton, Vic 3168 Australia)
Publication:
SOHO-9 Workshop "Helioseismic Diagnostics of Solar Convection and Activity", Stanford, California, July 12-15, 1999, meeting abstract.
Publication Date:
00/1999
Origin:
AUTHOR
Bibliographic Code:
1999soho....9E..35B

Abstract

In a polytropic atmosphere, the oscillation modes are described by well-known special functions. However, the presence of a magnetic field inside a sunspot makes the mode structure much more complex, so that analytic expressions are not available. Recent observations of sunspots suggest that most of the scattering and absorption due to the spots occurs in a layer immediately below the surface of the sun. We have therefore modelled the acoustic modes inside a sunspot by assuming that the effect of the magnetic field is concentrated right at the surface. Instead of imposing the conventional upper boundary condition, that the divergence of the velocity vanish, we require that the horizontal component of the velocity vanish, which allows us to write down analytic expressions for the acoustic modes inside the spot. This may be justified by arguing that a vertical magnetic field will tend to inhibit horizontal fluid motions. In effect, we are introducing a purely scattering disk to the surface of the sun. More realistic models, in which the disk both scatters and absorbs energy are also possible. We consider the scattering of an incident p-mode off our "sunspot," matching the pressure and horizontal velocity across the boundary. The result is a mixing of the incident mode into outgoing external p-modes and internal p-modes, as well as jacket modes both inside and outside the spot. We find that the inclusion of the jacket modes is crucial to satisfying the matching conditions, and we present results indicating the spectrum of outgoing and internal modes that are present.
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