Homeoidally striated density profiles. II. Anisotropy and rotation

TL;DR

This paper develops a comprehensive theory of rotating and anisotropic homeoidally striated Jacobi ellipsoids, analyzing their equilibrium configurations, bifurcation points, and implications for galaxy shapes and stability.

Contribution

It introduces a unified framework considering both real and imaginary rotation, and establishes new constraints on velocity anisotropy and shape limits of elliptical galaxies.

Findings

Bifurcation points from axisymmetric to triaxial configurations match classical results.

No lower limit to elongation of prolate-like configurations, explaining observed galaxy shapes.

A lower limit to flattening of oblate-like configurations is identified.

Abstract

With regard to homeoidally striated Jacobi ellipsoids, a unified theory of systematically rotating and peculiar motions is developed, where both real and imaginary rotation are considered. The effect of positive or negative residual motion excess, is shown to be equivalent to an additional real or imaginary rotation, respectively. Then it is realized that a homeoidally striated Jacobi ellipsoid with assigned velocity distribution, always admits an adjoint configuration i.e. a classical Jacobi ellipsoid of equal mass and axes. In addition, further constraints are established on the amount of residual velocity anisotropy along the principal axes, for triaxial configurations. Special effort is devoted to investigating sequences of virial equilibrium configurations in terms of normalized parameters, including the effects of both density and velocity profile. In particular, it is shown that bifurcation points from axisymmetric to triaxial configurations occur as in classical Jacobi ellipsoids, contrary to earlier results. The reasons of the above mentioned discrepancy are also explained. An interpretation of recent results from numerical simulations on stability (Meza 2002), is provided in the light of the model. A physical interpretation of the early Hubble sequence is shortly reviewed and discussed from the standpoint of the model, according if elliptical galaxies are considered as isolated systems or embedded within dark matter haloes. In any case, a lower limit to the flattening of oblate-like configurations is established. On the other hand, it is found no lower limit to the elongation of prolate-like configurations, and observed lack of elliptical galaxies more elongated than E7 needs a different physical interpretation, such as the fully investigated bending instabilities.