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Astron. Astrophys. 321, 1024-1026 (1997)

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2. Normal modes of a star

The formalism below is parallel to that of Beiki and Sobouti (1990) who studied excitation of the oscillation of a binary member by its companion. Consider a non rotating spherical star in hydrostatic equilibrium. Let a mass element at r adiabaticlly undergo an infinitesimal lagrangian displacement [FORMULA] from its equilibrium position. Let [FORMULA] and [FORMULA] denote the corresponding Eulerian changes in the density, [FORMULA], the pressure, p and the gravitational potential, [FORMULA], respectively. The linearized Euler's equation of motion is

[EQUATION]

where

[EQUATION]

[EQUATION]

[EQUATION]

All terms in Eq. (1) are expressed in terms of the vector field [FORMULA]. The second equality in this equation is the definition for the operator [FORMULA] whose properties will be discussed shortly.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
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