M. M. Vergne

Chaotic Orbits in Galactic Satellites

In several previous papers we had investigated the orbits of the stars that make up galactic satellites and found that many of those orbits were chaotic. In those investigations we made extensive use of the frequency analysis method of Carpintero and Aguilar (1998) to classify the orbits, because that method is much faster than the use of Lyapunov exponents, allows the classification of the regular orbits and our initial comparison of both methods had shown excellent agreement between their results. More recently, we have found some problems with the use of frequency analysis in rotating systems, so that here we present a new investigation of orbits inside galactic satellites using exclusively Lyapunov exponents. Some of our previous conclusions are confirmed, while others are altered. Besides, the Lyapunov times that are now obtained show that the time scales of the chaotic processes are shorter than, or comparable to, other time scales characteristic of galactic satellites.

Stellar Motions in Galactic Satellites

The study of the motions of the stars that belong to a galactic satellite (i.e. a globular cluster or a dwarf galaxy orbiting a larger one) has some similarities, as well as significant differences, with that of the restricted three-body problem of celestial mechanics. The high percentage of chaotic orbits present in some models is of particular interest because it rises, on the one hand, the question of the origin of those chaotic motions and, on the other hand, the question of whether an equilibrium stellar system can be built when the bulk of the stars that make it up behave chaotically.

Effect of Chaotic Orbits on Dynamical Friction

When a body moves through a medium of smaller particles, it suffers a deceleration due to dynamical friction (Chandrasekhar 1943). Dynamical friction is inversely proportional to the relaxation time, which can be defined as the time needed for the orbits to experiment an energy exchange of the order of their initial energies, as a result of the perturbations produced by stellar encounters. Chaotic orbits, present in non-integrable systems, have exponential sensitivity to perturbations, a feature that makes them to relax in a time much shorter than regular ones, which suggests that dynamical friction would increase in the presence of chaotic orbits (Pfenniger 1986). We present preliminary results of numerical experiments used to check this idea, investigating the orbital decay, caused by dynamical friction, of a rigid satellite which moves within a larger stellar system (a galaxy) whose potential is non-integrable. Triaxial models with similar density distributions but different percentages of chaotic orbits are considered. This last quantity depends on the central concentration of the models. If the potential corresponds to triaxial mass models with smooth cores, the regular orbits have shapes that can be identified with one of the four families of regular orbits in Stackel potentials (box and three types of tubes). Chaotic orbits behave very much like regular orbits for hundreds of oscillations at least. In this case, the galaxy is represented by the triaxial generalization of the γ-models with γ = 0 (Merritt & Fridman 1996). However, the situation is very different in triaxial models with divergent central densities (cusps) or black holes, a feature that is in agreement with the observations.

Dynamical Friction Effects on Sinking Satellites

We investigated the orbital decay, caused by dynamical friction, of a rigid extended satellite which moves within a larger spherical stellar system (a galaxy). In some of our experiments the satellite and the particles that make up the galaxy interact in a fully self consistent way, while in others the the self consistency of the particles that make up the galaxy is neglected. In our simulations the galaxies were represented by Plummer spheres (ρ ∝ r-5) with isotropic velocity distribution. For satellites we used similar models moving along elongated orbits, like those of galactic satellites. Satellites of 1, 4 and 9% of the galaxy mass were considered. We found very good agreement between our numerical results and theoretical predictions obtained from a straightforward application of Chandrasekhar’s dynamical friction equation. We obtained approximate values of the Coulomb logarithm from the best possible fit between numerical and theoretical results. Finally, we investigated the evolution of the structure of the galaxy as a result of the orbital decay of the satellite.