Effects of gravity and density stratification on the asymptotic representation of p-modes in stars.

Details Effects of gravity and density stratification on the asymptotic representation of p-modes in stars. Effects of gravity and density stratification on the asymptotic representation of p-modes in stars.

Oct 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997a%26a...326.1055w&link_type=abstract

Astronomy and Astrophysics, v.326, p.1055-1065

Astronomy and Astrophysics

Astrophysics

1

Stars: Oscillations, Stars: Interiors, Sun: Oscillations, Methods: Analytical

Scientific paper

The second-order asymptotic theory for low-degree p-modes in a star developed by Smeyers et al. (1996A&A...307..105S) is reconsidered, especially for lower-frequency modes. The investigation is undertaken in analogy with an earlier investigation of Roxburgh and Vorontsov (1994MNRAS.267..297R), in which a generalization of the first Born approximation for the scattering, by the stellar core, of acoustic waves modified by gravity and buoyancy is applied. A frequency-dependent velocity of propagation of acoustic waves is introduced that is affected by gravity and density gradient, mainly in the central region of the star. The time needed for an acoustic wave to propagate from the centre of the star to a given radial distance is increased, and, in the first asymptotic approximation, the oscillation frequency of a p-mode is decreased. The differences are larger for lower-frequency p-modes. The asymptotic theory is applied to a polytropic model with index equal to 3. The relative errors on the scaled frequency separations D_n,l_ for degrees l=0,1,2 are reduced in comparison to those resulting from the usual asymptotic theory, but still amount to about 30% for modes of radial order n=20 and to about 18% for modes of radial order n=30. For a normal solar model, the second asymptotic approximations of the eigenfrequencies do not lead to satisfactory results. The failure is ascribed to the behaviour of the second derivative of the mass density in the partial ionization zone of hydrogen near the solar surface. This behaviour introduces a sharp and high peak in the propagation diagram, which is not taken into account in the present asymptotic analysis.

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