The Level of Chaos in N-Body Models of Elliptical Galaxies

Abstract

This paper presents a combination of methods that estimate reliably the level of chaos (proportion of particles in chaotic orbits and the corresponding values of the Lyapunov Characteristic Numbers) in self-consistent N-body models of elliptical galaxies. A careful simultaneous use of several numerical tools can induce the proportion of particles in chaotic orbits dynamically important within one Hubble time. In models with smooth centers the mass component in chaotic motion is less than about 30% of the total mass. In models with central black holes this percentage increases up to 70%. Typical Lyapunov characteristic numbers are below 0.1 in units of the inverse crossing time. A remarkable property of the chaotic mass component is that it has a different surface density profile than that of the ordered component. The superposition of the two profiles causes observable humps in the overall profile, which are suggested as a possible observational ‘signature’ of chaos in elliptical galaxies.