Radial and Non-Radial Oscillations of Spherically Symmetric Stellar Systems

Abstract

In an expansion scheme in velocity space, the first order perturbations of a stellar system bear close resemblance to those of a fluid. This feature is exploited to study the structure of the Hilbert space of the linear perturbations of a stellar system, to provide a classification for the modes, and to construct ansatz for variational calculations. The first order non-radial modes appear to be trispectral in that they are predominantly derived from a scalar potential, a toroidal vector potential, or a poloidal vector potential. The eigenfrequencies and the eigenfunctions of radial (ℓ = O) and non-radial (ℓ = l) modes of polytropes and of truncated isothermal distributions are calculated. The density waves associated with these modes are also reported.