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 from its equilibrium position. Let and denote the corresponding Eulerian changes in the density, , the pressure, p and the gravitational potential, , respectively. The linearized Euler's equation of motion is
All terms in Eq. (1) are expressed in terms of the vector field . The second equality in this equation is the definition for the operator whose properties will be discussed shortly.
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998