Nonlinear Effect on the Gravitational Instability for the Adiabatically Deformed Case Compared with the Isothermal One
Abstract
An attempt is made to report on an analysis performed to investigate some nonlinear aspect of a gravitational wave in a onedimensional collisionless stellar system. Attention is given to the frequency function, the adiabatically invariant action variable, Poisson's equation in one dimension, an analytical method of solution, and firstorder, secondorder, and higherorder terms. Some numerical results are obtained and discussed, particularly in relation to the critical wavelength for gravitational instability. These results are compared with those determined for the purely isothermal case.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 December 1977
 Bibcode:
 1977A&A....61..609A
 Keywords:

 Gravitational Waves;
 Jeans Theory;
 Stellar Models;
 Stellar Systems;
 Adiabatic Conditions;
 Elliptic Functions;
 Galactic Radio Waves;
 Gravitational Effects;
 Invariance;
 Isothermal Processes;
 Liouville Equations;
 Particle Collisions;
 PhaseSpace Integral;
 Poisson Equation;
 Wavelengths;
 Astrophysics