A numerical model for a triaxial stellar system in dynamical equilibrium

Abstract

A sample numerical model has been computed for a triaxial stellar system in dynamical equilibrium. A four-step procedure was employed. (1) A density distribution with a modified Hubble profile - to approximate elliptical galaxies - and axis ratios of 1:25:2 was chosen. This figure was further chosen not to rotate. (2) The potential corresponding to the chosen density distribution was computed. (3) About 1500 orbits were computed with this potential, one at a time, each covering typically 100 oscillations through the system; i.e., about 1 billion years. These orbits belong to two families, viz., box orbits and tube orbits around the long axis of the system. (4) A reproduction of the chosen density distribution - in terms of its mass in 285 cells in each octant - was sought by superposition of a subset of the available orbits, each populated by an appropriate nonnegative number of stars. The application of linear programming led to a numerical solution. The main results are: First, the majority of the orbits computed in step 3 turned out to have three effective integrals; i.e., two nonclassical ones in addition to the energy integral. Second, the existence of the numerical solution found in step 4 suggests the existence of triaxial self-consistent systems in dynamical equilibrium with density profiles fitting elliptical galaxies.