Resonant stellar orbits in spiral galaxies. VI. The equilibrium of a stellar disk in regions of the Lindblad resonances.
Abstract
The epicyclic theory of resonant stellar orbits is incorporated into a representation of the equilibrium of a spiral galaxy in the regions of the Lindblad resonances. This is accomplished by generalizing the epicyclic theory of the equilibrium of an axisymmetric stellar disk. In the axisymmetric case, the distribution function giving the density of stars in the fourdimensional phase space is a function of the wellknown epicyclic integrals. The present generalization consists of writing the distribution function as the same function of perturbed epicyclic integrals. Thus the paper deals mainly with the construction of suitable forms of the perturbed integrals. It is found that there are two pairs of perturbed epicyclic integrals; this ambiguity arises in the manner in which the resonant perturbation couples two distinct solutions of the unperturbed equations of motion. The two pairs of perturbed integrals are equivalent, and they are symmetrically related. The two distribution functions constructed from these pairs of integrals differ significantly in the manners in which they populate the resonant orbits with stars.
 Publication:

The Astrophysical Journal
 Pub Date:
 April 1978
 DOI:
 10.1086/156055
 Bibcode:
 1978ApJ...221..539V
 Keywords:

 Galactic Rotation;
 Orbital Mechanics;
 Orbital Resonances (Celestial Mechanics);
 Resonance;
 Spiral Galaxies;
 Stellar Motions;
 Stellar Orbits;
 Distribution Functions;
 Epicycloids;
 Mathematical Models;
 Orbit Perturbation;
 Astrophysics;
 Spiral Galaxies:Internal Motions;
 Spiral Galaxies:Stellar Orbits