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M. Swisdak, E. G. Zweibel (U. Colorado)
While the correspondence between observed and predicted p-mode frequencies is good, it is clear that the detailed effects of convection are not adequately treated by contemporary solar models. Even models of simple convective structures which ignore the difficulties inherent in realistically modelling solar convection encounter difficulties in determining their effects on global oscillations. However, under the WKB approximation p modes may be treated as rays and their propagation described using the formalism of Hamiltonian systems. This is an adequate approximation for large-scale convection and modes of large spherical harmonic degree \ell.
Only simple stellar models (polytropes, for example) have eigenfrequencies which may be found analytically. However, a computer program we have written using a method known as adiabatic switching allows us to determine the eigenfrequencies of modes in the ray approximation. The motion of a ray is governed by a dispersion relation which may account for several effects, including variations in the local sound speed as well as advective motions of the underlying fluid.
Our investigations have shown that simple models of convective cells produce downshifts in the eigenfrequencies which are of second-order in the strength of the perturbation. At the minimum, this result is of the proper sign to explain the observed discrepancy although it is unclear if the correction is large enough to account for the entire effect.
In addition, we demonstrate the dependence of the shift on the radial order n and degree \ell of the mode and show that they roughly agree with our analytic estimates predicting a frequency shift which varies as a/\ell + b\ell where a and b are constants. Finally, we consider the case of a ray interacting with a thermal plume such as those observed at the edges of granules and supergranules.
The author(s) of this abstract have provided an email address for comments about the abstract: swisdak@solarz.colorado.edu