Previous abstract Next abstract
Session 74 - The Quiet & Active Sun.
Display session, Friday, January 09
While the correspondence between observed and predicted p-mode frequencies is generally good, it is clear that the detailed effects of the convection zone are not adequately treated by contemporary solar models. Indeed, this discrepancy is to be expected since the effects of simple convective structures on p-mode frequencies and linewidths are not completely understood. While the full problem is difficult to treat, under the WKB approximation p modes may be treated as rays and their propagation can be described using the formalism of Hamiltonian systems.
In general, only simple stellar models such as polytropes have analytic solutions for the eigenfrequencies. However, I have written computer code which uses the method of adiabatic switching (Skodje amp; Cary, 1988) to determine the approximate eigenfrequencies of a ray with a given dispersion relation traveling through a medium with prescribed variations in the local wave velocity.
In this application of the method of adiabatic switching, the initial state is a ray propagating in a polytropic spherical shell. Variations in the properties of the medium (e.g., sound speed perturbations or advective flows) are expressed as time-dependent perturbations to the Hamiltonian. These perturbations are turned on slowly and, consequently, the ray adiabatically adjusts its frequency, eventually yielding the eigenfrequency for the final state. The method is well-suited for describing the effects of time-dependent convection.
This method gives accurate eigenfrequencies for a number of trial simulations, including wave speed perturbations and simple models of convective cells. By coupling this program to snapshots of convective simulations, I can determine both frequency shifts and line widths of p modes and compare them to high-quality data sets such as those taken by the MDI instrument on SOHO.
Skodje, R., amp; Cary, J. 1988, Comp. Phys. Reports, 8, 221.
Program listing for Friday