Should Elliptical Galaxies Be Idealised as Collisionless Equilibria?

A review of elliptical galaxy dynamics, with a focus on nonintegrable models. Topics covered include torus construction; modelling axisymmetric galaxies; triaxiality; collisionless relaxation; and collective instabilities.

This talk provides a critical assessment of collisionless galactic dynamics, focusing on the interpretation and limitations of the collisionless Boltzmann equation and the physical mechanisms associated with collisionless relaxation. Numerical and theoretical arguments are presented to motivate the idea that the evolution of a system far from equilibrium should be interpreted as involving nonlinear gravitational Landau damping, which implies a greater overall coherence and re...

Hubble Space Telescope (HST) observations reveal that the density of stars in most elliptical galaxies rises toward the center in a power-law cusp. Many of these galaxies also contain central dark objects,possibly supermassive black holes. The gravitational force from a steep cusp or black hole will destroy most of the box orbits that constitute the ``backbone'' of a triaxial stellar system. Detailed modelling demonstrates that the resulting chaos can preclude a self-consiste...

The present lecture notes are an introduction to selected topics of {\it Galactic Dynamics}. The focus is on topics that we consider more relevant to the main theme of this workshop, {\it Celestial Mechanics}. This is not intended to be a review article. In fact, any of the topics below could be the subject of a separate review. Only the main ideas and notions are introduced, as well as some important currently open problems in each topic. Some relevant results from our own r...

These lectures are intended to provide an introduction to the rich interplay between N-body simulations and stellar-kinematic observations of galaxies. The first section describes the kinematic properties of galaxies that are accessible to observation, and gives a brief introduction to the stellar dynamics that one might wish to infer from such observations. In the next section, the use of N-body simulations in the study of galaxy dynamics is placed in its historical context....

I present various projects to study the halo dynamics of elliptical galaxies. This allows one to study the outer mass and orbital distributions of ellipticals in different environments, and the inner distributions of groups and clusters themselves.

Here I present a review of the work done on the presence and effects of chaos in elliptical galaxies plus some recent results we obtained on this subject. The fact that important fractions of the orbits that arise in potentials adequate to represent elliptical galaxies are chaotic is nowadays undeniable. Alternatively, it has been difficult to build selfconsistent models of elliptical galaxies that include significant fractions of chaotic orbits and, at the same time, are sta...

Recent work on the construction of spherical, Axisymmetric and triaxial dynamical models for elliptical galaxies is reviewed briefly, including their role in providing evidence for dark halos and central black holes. The different orbital structures and shapes of low-mass and giant elliptical galaxies provide essential constraints on scenarios of galaxy formation.

It is shown that the violent relaxation of dissipationless stellar systems leads to universal de Vaucouleurs profiles only outside 1.5 effective radii $R_e$. Inside $1.5 R_e$ the surface density profiles depend strongly on the initial conditions and are in general not in agreement with the de Vaucouleurs law. This result is in contradiction to the observations which show that all elliptical galaxies have de Vaucouleurs profiles inside $1.5 R_e$ and show strong deviations outs...

N-body simulations of collisionless collapse have offered important clues to the construction of realistic stellar dynamical models of elliptical galaxies. Such simulations confirm and quantify the qualitative expectation that rapid collapse of a self-gravitating collisionless system, initially cool and significantly far from equilibrium, leads to incomplete relaxation, that is to a quasi-equilibrium configuration characterized by isotropic, quasi-Maxwellian distribution of s...