Transition from regular motion to chaos in a logarithmic potential

Department of Physics, Section of Astrophysics, Astronomy and Mechanics, University of Thessaloniki, 54006 Thessaloniki, Greece

Corresponding author: N. D. Caranicolas, caranic@helios.astro.auth.gr

Received: 12 October 2000
Accepted: 1 December 2000

Abstract

We investigate the properties of motion in a logarithmic galactic potential. The model can be considered to describe the motion in the meridian, plane, of an elliptical galaxy with a dense nucleus or bulge of radius c. For a given value of c, there is a critical value of the angular momentum L_zc such as for , stars, moving near the galactic plane, are scattered to higher scale z heights displaying chaotic motion. Our numerical calculations show that there exists a linear relationship between the radius of the nucleus and the critical value of the angular momentum. This linear relationship can be found using some elementary theoretical arguments. We use the distribution of radial velocities in order to distinguish ordered from chaotic motion. Comparison with previous work is also made.