*Astron. Astrophys. 361, 340-348 (2000)*
## Radial stellar oscillations under the influence of the dynamics of the atmosphere - a one-dimensional approach
### I. Linear adiabatic oscillations of a special model
**
M.P. Geyer**^{ 1} and
F. Schmitz^{ 2}
^{1} Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
^{2} Institut für Theoretische Physik und Astrophysik der Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
*Received 10 May 2000 / Accepted 14 July 2000*
**Abstract**
The dynamics of the quiet solar atmosphere are highly nonlinear.
Both the standing waves of solar oscillations and acoustic waves
generated in the upper convection zone become nonlinear in the
atmosphere and transform into shock waves. Interactions of shock
waves, the formation of contact discontinuities, and interactions of
shocks with these discontinuities will occur. The strong nonlinear
dynamics of the atmosphere should influence high order *p*-modes
of the Sun. In this series of papers we shall deal with fundamental
properties of the interaction of the interior of a star with its
atmosphere. According to the state of numerical techniques, we must
restrict ourselves to radial oscillations or to the vertical dynamics
of the atmosphere, respectively. As the nonlinear dynamics of the
atmosphere governs the problem, we use a simple equilibrium model of
the Sun or a star. For simplicity, we do not take a radial model but a
plane layer model. Our particular "standard model" is a layer with
nearly constant density in the interior and a smoothly matched
isothermal atmosphere. The structure of this configuration is fitted
to the structure of the Sun. In the present paper we present the
equilibrium model and solutions of its linear adiabatic wave equation.
The equilibrium configuration has been selected so, that the wave
equation can be transformed to the equation of the associated Legendre
functions. We determine the discrete eigenfrequencies, the modes, and
the eigenfunctions of the continuous frequency spectrum. Resonances of
the continuum are discussed. Also a set of discrete complex
frequencies exists. The corresponding waves are not damped modes but
limiting cases of instationary waves. The influence of an isothermal
corona with a discontinuous transition layer on the frequency spectrum
is investigated. We find strong resonances at frequencies between the
discrete frequencies of the corona-free model.
**Key words:** hydrodynamics
waves
Sun: atmosphere
Sun:
oscillations
stars: oscillations
*Send offprint requests to:* F. Schmitz
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### Contents
© European Southern Observatory (ESO) 2000
Online publication: September 5, 2000
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