A nonrotating elliptical galaxy need not have an isotropic velocity ellipsoid: unequal random-motion stresses in different directions can support an oblate or triaxial shape without substantial mean rotation. The tensor virial theorem, for a stationary isolated system with appropriate boundary terms, balances this directional kinetic stress against the directional gravitational stress. Anisotropic random motions can supply the flattening, whereas an isotropic nonrotating equilibrium has much stronger restrictions on its shape.

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