R3 fluids

The current paper is aimed in getting more insight on three main points concerning large-scale astrophysical systems, namely: (i) formulation of tensor virial equations from the standpoint of analytical mechanics; (ii) investigation on the role of systematic and random motions with respect to virial equilibrium configurations; (iii) extent to which systematic and random motions are equivalent in flattening or elongating the shape of a mass distribution. The tensor virial equations are formulated regardless from the nature of the system and its constituents, by generalizing and extending a procedure used for the scalar virial equations, in presence of discrete subunits (Landau & Lifchitz 1966). In particular, the self potential-energy tensor is shown to be symmetric with respect to the exchange of the indices, (Epot)pq = (Epot)qp. Then the results are extended to continuous mass distributions. The role of systematic and random motions in collisionless, ideal, self-gravitating fluids, is analysed in detail including radial and tangential velocity dispersion on the equatorial plane, and the related mean angular velocity, Ω, is conceived as a figure rotation. R3 fluids are defined as ideal, self-gravitating fluids in virial ∗Dipartimento di Astronomia, Università di Padova, Vicolo Osservatorio 2, I-35122 Padova, Italy email: [email protected]