EFFECTS OF GRAVITY AND DENSITY STRATIFICATION ON THE ASYMPTOTIC REPRESENTATION OF P-MODES IN STARS

The second-order asymptotic theory for low-degree p-modes in a star de veloped by Smeyers et al. (1996) is reconsidered, especially for lower -frequency modes. The investigation is undertaken in analogy with an e arlier investigation of Roxburgh and Vorontsov (1994), in which a gene ralization of the first Born approximation for the scattering, by the stellar core, of acoustic waves modified by gravity and buoyancy is ap plied. A frequency-dependent velocity of propagation of acoustic waves is introduced that is affected by gravity and density gradient, mainl y in the central region of the star. The time needed for an acoustic w ave to propagate from the centre of the star to a given radial distanc e is increased, and, in the first asymptotic approximation, the oscill ation frequency of a p-mode is decreased. The differences are larger f or lower-frequency p-modes. The asymptotic theory is applied to a poly tropic model with index equal to 3. The relative errors on the scaled frequency separations D-n,D-l for degrees l = 0, 1, 2 are reduced in c omparison to those resulting from the usual asymptotic theory, but sti ll amount to about 30% for modes of radial order n = 20 and to about 1 8% for modes of radial order n = 30. For a normal solar model, the sec ond asymptotic approximations of the eigenfrequencies do not lead to s atisfactory results. The failure is ascribed to the behaviour of the s econd derivative of the mass density in the partial ionization zone of hydrogen near the solar surface. This behaviour introduces a sharp an d high peak in the propagation diagram, which is not taken into accoun t in the present asymptotic analysis.