Annu. Rev. Astron. Astrophys. 1991. 29:
239-274
Copyright © 1991 by Annual Reviews. All rights reserved |

2.3.2 *f* = *f (E, I*_{2},
*I*_{3}). Direct calculation of distribution function(s)
*f (E, I*_{2}, *I*_{3}) consistent with a
given triaxial density (*x, y, z*) by
solving the fundamental integral equation - which gives as a triple
integral of *f* over the velocities - is a rather intimidating task
(49,
74,
75,
110).
The individual orbit densities in a separable model are known
explicitly (80),
however, so that building
self-consistent models by means of Schwarzschild's method is
straightforward. Statler
(320)
used this approach, and constructed a large variety of different
equilibrium models for a set of 21 triaxial separable models, all with the
same density profile and with axial ratios covering all possible shapes.
He found that the presence of four major orbit families, each of which can
contribute density at any point, provides ample opportunity for exchanging
orbits of different shapes while keeping the model density the same. As a
result, the distribution functions for self-consistent separable
triaxial models are highly non-unique (cf
Section 2.2.2), and this is reflected
in the variety of kinematic properties displayed by Statler's models: The mean
streaming motions range up to values that are comparable to those found for
the fastest rotating ellipticals
(Section 3.2), showing that ample mean streaming
(``rotation'') can occur in triaxial systems without figure rotation. Models
with a large fraction of stars on box orbits show differences between the
velocity dispersion profiles along the major and minor axes. Detailed
kinematic observations may therefore help constrain the distribution functions
of elliptical galaxies.