Density Waves in a Highly Flattened, Rapidly Rotating Galaxy
Abstract
A method is described for flie solution of Liouville's equation guverning the response of a given subsystem of stars in a galaxy of small but finite thickness when the galaxy is perturbed in a manner which does not distort its plane. The method is an adaptation of the method of solution described in the preceding paper. In particular, it involves the use of the adiabatic invariant whose approximate constancy characterizes the perpendicular motions of stars in the unperturbed galaxy. As an illustration and application of the method, the propagation of density waves in a rapidly rotating galaxy of finite thickness is investigated in detail. Poisson's equation governing the perturbed gravitational field is reduced with the aid of the solution of Liouville's equation to a certain characteristic-value problem which determines the dispersion relation for the waves; and that problem is solved with the aid of a variational principle. For practical applications, the dispersion relation obtained does not differ significantly from the dispersion relation derived by Shu on the basis of a heuristic treatment of the perpendicular structure of the perturbed galaxy.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- July 1970
- DOI:
- 10.1086/150514
- Bibcode:
- 1970ApJ...161...87V