Anisotropic Inhomogeneous Riemann S-Ellipsoids in Spheroidal Halos. I.

The classical Riemann S-ellipsoids are generalized to account for a Ferrers inhomogeneity in the mass distribution, a three-dimensional anisotropy of the velocity dispersions, and the gravitation of a spheroidal halo. The Ferrers inhomogeneity does not affect the equilibrium and stability conditions for the ellipsoids, but only changes the numerical coefficients in the equilibrium parameters. The anisotropy of the velocity dispersions changes both the equilibrium conditions and the criterion for stability of the ellipsoids, either extending or limiting the region in which the ellipsoids exist. A halo extends this region in all cases and stabilizes the ellipsoids. The observed of the velocity dispersions of stars in the neighborhood of the sun are obtained using the inhomgeneous model. __________ Translated from Astrofizika, Vol. 48, No. 4, pp. 613–632 (November 2005).