Accurate frequencies of polytropic models

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Abstract
Observations of solar oscillations are already yielding frequencies with a relative accuracy exceeding 10–5; new experiments will increase this accuracy by about an order of magnitude during the coming decade. Full utilization of such data requires comparable accuracy in the computation of frequencies of stellar models. A very convenient test of the calculation of adiabatic oscillation frequencies is provided by the polytropic models: the models are completely well defined and can easily be computed with the required precision; hence their frequencies can serve as references against which to test oscillation codes before these are applied to more realistic models. Here we analyse the computation of such frequencies. Their accuracy is tested in different ways, including the comparison of two independently derived sets of results, and tables of frequencies are given. More extensive sets of frequencies can be obtained directly from the authors, in computer-readable form. The analysis of the polytropic models provides interesting illustrations of a problem in the labelling of dipolar modes, as well as of the effects on the frequencies of the perturbation in the gravitational potential.

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