Theory of Stellar Oscillations

Abstract

To evaluate the diagnostic potential of stellar oscillations and develop effective methods to interpret the observations we need an understanding of the possible modes of oscillation and of the dependence of their frequencies on the properties of the stellar interior. This is based on numerical computations of oscillations for different stellar models, but various forms of asymptotic analysis are also highly illuminating for the understanding and form the basis for very efficient techniques to interpret the observations. In the present Chapter we develop the theoretical foundation for the study of stellar oscillations, starting with a brief summary of the relevant aspects of hydrodynamics, and consider some examples of the behaviour of the modes, in terms of numerical calculations and asymptotic analysis. Aspects that are particularly relevant to the Sun and solar-like stars are taken up in Chapter 7.