Chaos and the Shapes of Elliptical Galaxies

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-consistent, strongly triaxial equilibrium. Most elliptical galaxies may therefore be nearly axisymmetric, either oblate or prolate. Information about the three-dimensional shape of a galaxy is lost when the galaxy is projected onto the plane of the sky. This loss of information is acute in the case of elliptical galaxies, whose apparent shapes are elliptical but whose intrinsic shapes could be oblate, prolate or fully triaxial. Before about 1975, elliptical galaxies were thought to be rotationally flattened oblate spheroids. The discovery that elliptical galaxies rotate much more slowly than a fluid body with the same shape (1) led to the hypothesis that most of these systems are triaxial ellipsoids, with shapes that are maintained by anisotropic velocity dispersions rather than by centrifugal force (2). The triaxial hypothesis was supported by the successful construction of self-consistent triaxial models on the computer (3). Most of the stars in these numerical models occupied " regular " orbits that respect three isolating integrals, two in addition to the energy; the major families of regular orbits are the short-and long-axis " tubes, " and the " boxes " (4). Box orbits are uniquely associated with the triaxial geometry; they densely fill a box-or bowtie-shaped region, and a star on such an orbit passes arbitrarily close to the galaxy center after many oscillations. The time-averaged shape of a box orbit mimics that of the underlying galaxy, and the potential from a star on a box orbit helps support