*Astron. Astrophys. 326, 1055-1065 (1997)*
## Effects of gravity and density stratification
on the asymptotic representation of *p* -modes in stars
**
B. Willems
**^{*},
T. Van Hoolst
^{**} and
P. Smeyers
Instituut voor Sterrenkunde, Katholieke Universiteit
Leuven, Celestijnenlaan 200 B, B-3001 Heverlee, Belgium
*Received 11 April 1997 / Accepted 23 May 1997*
**Abstract**
The second-order asymptotic theory for low-degree *p* -modes
in a star developed by Smeyers et al. (1996) is reconsidered,
especially for lower-frequency modes. The investigation is undertaken
in analogy with an earlier investigation of Roxburgh and Vorontsov
(1994), 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
for degrees
are reduced in comparison to those resulting
from the usual asymptotic theory, but still amount to about 30% for
modes of radial order
and to about 18% for modes of radial order
.
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.
**Key words:** stars: oscillations - stars: interiors - Sun:
oscillations - methods: analytical
* Research Assistant of the Fund for Scientific Research - Flanders (Belgium) (F.W.O.)
** Postdoctoral Fellow of the Fund for Scientific Research - Flanders (Belgium) (F.W.O.)
*Send offprint requests to:* P. Smeyers
### Contents
© European Southern Observatory (ESO) 1997
Online publication: April 8, 1998
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