Orbital content and velocity fields of triaxial galaxies

Abstract

We discuss the properties of the thin tube orbit dynamical models with triaxial potentials of Stäckel form. We calculate the dependence of orbital content and internal kinematic misalignment on model shape and their variation as a function of radius within a model. As particular examples we present four families of models with a variety of shapes: the self-consistent perfect ellipsoid, two triaxial generalizations of the modified Hubble profile, with and without a massive dark halo, and a self-consistent logarithmic dark halo. We find that the orbital content and the distribution of mass over the four families are strongly influenced by the shape of the isodensity contours, and by whether or not the model becomes rounder with increasing radius. We discuss the projection on to the sky of the velocity fields, and the distributions of various observables. In particular we show that, for a wide range of shapes in our models, the angular deviation of the projected angular momentum vector from the minor axis Ψkin is well approximated by the observed kinematic misalignment |${\Psi }_\text {obs}=\text {tan}^{-1}({v}_\text {minor}/{v}_\text {major})$| Thin orbit models have the maximum internal streaming in a given potential, and place a physical upper bound on observable projected velocity amplitudes. Although no elliptical galaxy is made exclusively of thin tube orbits, the velocity fields of our models can be smoothly rescaled to resemble those of realistic models containing thick tube orbits. The projected velocity fields (though not the dispersions) of our models and of thick tube orbit models have the same structures, and are derived by placing the correct dynamical constraints on the orbital content.