Homeoidally striated density profiles: sequences of virial equilibrium configurations with constant anisotropy parameters

The formulation of the tensor virial equations is generalized to unrelaxed configurations, where virial equilibrium does not coincide with dynamical (or hydrostatic) equilibrium. Homeoidally striated, Jacobi ellipsoids, which generalize classical Jacobi ellipsoids, are studied in detail. Further investigation is devoted to the generation of sequences of virial equilibrium configurations where the anisotropy parameters are left unchanged, including both flattened and elongated, triaxial configurations, and the determination of the related bifurcation points. An application is made to dark matter haloes hosting giant galaxies (M ≈ 1012 m⊙), with regard to assigned initial and final configuration, following and generalizing to many respects a procedure conceived by Thuan & Gott (1975). The dependence of the limiting axis ratios, below which no configuration is allowed for the sequence under consideration, on the change in mass, total energy, and angular momentum, during the evolution, is illustrated in some representative situations. The dependence of the axis ratios, ε31 and ε21, on a parameter, related to the initial conditions of the density perturbation, is analysed in connection with a few special cases. The same is done for the rotation parameters. Within the range of the rotation parameter, λ, deduced from high-resolution numerical simulations, the shape of dark matter haloes is mainly decided by the amount of anisotropy in residual velocity distribution. On the other hand, the contribution of rotation has only a minor effect on the meridional plane, and no effect on the equatorial plane, as bifurcation points occur for larger values of λ. To this respect, dark matter haloes are found to resemble giant elliptical galaxies. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)