Resonant stellar orbits in spiral galaxies. V. Numerical studies of orbits in the region of the inner Lindblad resonance.
Abstract
The epicyclic approximation for the orbits of stars in the region of the inner Lindblad resonance of a spiral galaxy is tested by comparing numerical solutions to the epicyclic and the exact equations of motion. Solutions to the two systems of equations for the orbits are compared in the framework of two models of the prevailing gravitational field near the inner Lindblad resonance of the Galaxy; the pattern of spiral structure in each model has two arms that trail. Surfaces of section are constructed in pairs with one member of each pair derived from the exact equations and the other member derived from the epicyclic equations. It is found that all resonance phenomena are represented, at least qualitatively, in the epicyclic approximation. Quantitatively, the results indicate that the epicyclic approximation is relatively accurate for orbits that do not depart greatly from circles and is rather less accurate for orbits that depart substantially from circles. Two prescriptions are discussed for populating with stars the families of resonant orbits in a spiral galaxy.
 Publication:

The Astrophysical Journal
 Pub Date:
 April 1978
 DOI:
 10.1086/156007
 Bibcode:
 1978ApJ...221...87M
 Keywords:

 Galactic Structure;
 Orbital Resonances (Celestial Mechanics);
 Spiral Galaxies;
 Stellar Motions;
 Stellar Orbits;
 Epicycloids;
 Graphs (Charts);
 Orbits;
 Stellar Models;
 Astronomy;
 Galaxies:Internal Motions;
 Spiral Galaxies:Stellar Orbits