Radial and nonradial pulsations of polytropes - High precision eigenvalues and the approach of p-modes to asymptotic behavior

Statistics – Computation

Scientific paper

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Asymptotic Properties, Eigenvalues, Polytropic Processes, Pulsed Radiation, Solar Oscillations, Stellar Oscillations, Computational Astrophysics, Frequency Measurement, Gravitational Effects, Helioseismology, Surface Properties

Scientific paper

In order to extract eigenfrequencies of high-order p-modes with precisions of one part in 500,000, a careful numerical treatment is necessary for both the input stellar model and the oscillation code. Here, polytropes are used to avoid uncertainties associated with the input model. Eigenfrequencies were obtained in a number of polytropes for l-values of 0-3 and radial orders up to about 40. It was that, in order to have the frequencies converge with the necessary precision, the input model must contain several thousand shells, and the oscillation code must contain at least several dozen grid points in each loop of the eigenfunction. The outermost loop requires many more points: the converged models contain several hundred grid points between the last node and the surface. An important check on the results is provided by a comparison of the asymptotic behavior of adjacent mode separations with the limiting behavior predicted by Tassoul (1980). The present oscillation code is based on the Cowling (1941) approximation (as assumed by Tassoul).

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