 Flattening–anisotropy virial relation

For a pressure-supported scale-free tracer $\rho \propto (R^2+z^2/q^2{)}^{-\gamma /2}$ in a spherical Newtonian gravitational potential, the tensor virial theorem constrains integrated directional velocity dispersions. Modest oblate flattening and a decreasing radial mass density require greater in-plane random support per direction. The displayed expansion assumes finite global virial integrals; the corresponding ratio of force moments also has a cutoff-independent angular interpretation.