Description of Stellar Acoustic Modes Using the Local Wave Concept

Abstract

An understanding of stellar acoustic oscillations is attempted, using the local wave concept in semi-analytical calculations. The local homogeneity approximation allows to obtain simplified equations that can nevertheless describe the wave behavior down to the central region, as the gravitational potential perturbation is not neglected. Acoustic modes are calculated as classical standing waves in a cavity, by determining the cavity limits and the wave phases at these limits. The internal boundary condition is determined by a fitting with an Airy function. The external boundary condition is defined as the limit where the spatial variation of the background is important compared to the wavelength. This overall procedure is in accordance with the JWKB approximation. When comparing the results with numerical calculations, some drawbacks of the isothermal atmosphere approximation are revealed. When comparing with seismic observations of the Sun, possible improvements at the surface of solar models are suggested. The present semi-analytical method can potentially predict eigenfrequencies at the precision of +-3microHz in the range 800-5600 microHz, for the degrees l=0-10. A numerical calculation using the same type of external boundary conditions could reach a global agreement with observations better than 1 microHz. This approach could contribute to better determine the absolute values of eigenfrequencies for asteroseismology.