Stability of a Self Gravitating System with Phase Space Density Function of Energy and Angular Momentum
Abstract
Summary. We consider a self gravitating stellar system with spherical symmetry and a phase space density function of the two invariants: energy and angular momentum. The paper is divided into two parts. In Part I, we treat the special case of a "WaterBag" model and show that this model is stable for radical perturbation. For this proof we consider layers of constant angular momentum. This decomposition provides an infinite set of equations for the fields and the eigenvalues can be shown to be positive. In Part II, we approximate a function F of the two integrals of motion e, I, by a succession of steps corresponding to a multiple "WaterBag". The method developed in Part I is extended to this case. We deduce that a model with 8F/ <0 is stable for radial perturbations. Key words: self gravitating system  spherical symmetry  multiple "WaterBag"  stability criterium
 Publication:

Astronomy and Astrophysics
 Pub Date:
 December 1973
 Bibcode:
 1973A&A....29..401D