Elliptical galaxies are modeled as homeoidally striated Jacobi ellipsoids (Caimmi and Marmo 2005) where the peculiar velocity distribution is anisotropic, or equivalently as their adjoint configurations i.e. classical Jacobi ellipsoids of equal mass and axes, in real or imaginary rotation (Caimmi 2006). Reasons for the coincidence of bifurcation points from axisymmetric to triaxial configurations in both the sequences (Caimmi 2006) contrary to earlier findings (Wiegandt 1982a,b, Caimmi and Marmo 2005) are presented and discussed. The effect of centrifugal support at the ends of the major equatorial axis is briefly outlined. The existence of a lower limit to the attening of elliptical galaxies is investigated in dealing with a number of limiting situations. More specifically, (I) elliptical galaxies are considered as isolated systems, and an allowed region within Ellipsoidland (Hunter and de Zeeuw 1997), related to the occurrence of bifurcation points from ellipsoidal to pear-shaped configurations, is shown to be consistent with observations; (II) elliptical galaxies are considered as embedded within dark matter haloes and, under reasonable assumptions, it is shown that tidal effects from hosting haloes have little inuence on the above mentioned results; (III) dark matter haloes and embedded elliptical galaxies, idealized as a single homeoidally striated Jacobi ellipsoid, are considered in connection with the cosmological transition from expansion to relaxation, by generalizing an earlier model (Thuan and Gott 1975), and the existence of a lower limit to the attening of relaxed (oblate-like) configurations, is established. On the other hand, no lower limit is found to the elongation of relaxed (prolate-like) configurations, and the existence of some sort of instability is predicted, owing to the observed lack of elliptical galaxies more attened or elongated than E7.
Towards a more rigorous treatment of uncertainties on the velocity distribution of dark matter particles for capture in stars
