Anisotropy and rotation

With regard to homeoidally striated Jacobi ellipsoids (Caimmi & Marmo 2005), a unified theory of systematically rotating and peculiar motions is developed, where both real and imaginary rotation (around a fixed axis) 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 (Wiegandt 1982a,b; Caimmi & Marmo 2005). The reasons of the above mentioned discrepancy are also explained. ∗Astronomy Department, Padua Univ., Vicolo Osservatorio 2, I-35122 Padova, Italy email: [email protected]