Nonradial adiabatic oscillations of stars

Abstract

The classication scheme of mode oscillations in stars is investigated mathematically and physically by using a new phase diagram representation. This technique is presented in order to study the basic equation of motion for linear adiabatic nonradial oscillations, and leads us to obtain an unambiguous scheme classication of modes. The order number introduced by this classication scheme only depends on the boundary conditions at the endpoints, the centre and the surface of the star. Furthermore, this classication is independent of the number of nodes of the eigenfunction used to characterize the oscillatory motion. Consequently, the sequence of ordinate eigenfrequencies becomes the signature of the oscillatory system itself. Provided that the equation of motion of linear adiabatic nonradial stellar oscillations has been reduced to a second-order dierential equation, this technique allows us to obtain a more reliable classication scheme of modes in stars. Although this phase analysis method has been presented to characterize the propagation of acoustic-gravity waves with one or two propagative regions, it can be nevertheless successfully applied to perturbative motions with more than three propagative regions, provided that a propagation diagram can be built.