Nonradial adiabatic oscillations of stars

Mode classification of acoustic-gravity waves

¹ Department of Physics, Nuclear and Astrophysics Laboratory, Keble Road, Oxford OX1 3RH, UK
² Instituto Superior Técnico, Av. Rovisco Pais, Centro Multidisciplinar de Astrofísica, 1049-001 Lisboa, Portugal

Corresponding author: I. P. Lopes lopes@astro.ox.ac.uk

Received: 31 May 2000
Accepted: 17 January 2001

Abstract

The classification 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 classification of modes. The order number introduced by this classification scheme only depends on the boundary conditions at the endpoints, the centre and the surface of the star. Furthermore, this classification 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 differential equation, this technique allows us to obtain a more reliable classification 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.