R fluids

A theory of collisionless fluids is developed in a unified picture, where nonrotating (Ω̃1 = Ω̃2 = Ω̃3 = 0) figures with anisotropic (σ11 = σ22 = σ33) random velocity component distributions and rotating (Ω̃1 6= Ω̃2 6= Ω̃3) figures with isotropic (σ11 6= σ22 6= σ33) random velocity component distributions, make adjoints configurations to the same system. R fluids are defined as ideal, self-gravitating fluids satisfying the virial theorem assumptions, in presence of systematic rotation around each principal axis of inertia. To this aim, mean and rms angular velocities and mean and rms tangential velocity components are expressed, by weighting on the moment of inertia and the mass, respectively. The figure rotation is defined as the mean angular velocity, weighted on the moment of inertia, with respect to a selected axis. The generalized tensor virial equations (Caimmi & Marmo 2005) are formulated for R fluids and further attention is devoted to axisymmetric configurations where, for selected coordinate axes, a variation in figure rotation has to be counterbalanced by a variation in anisotropy excess and vice versa. A microscopical analysis of systematic and random motions is performed under a few general ∗Dipartimento di Astronomia, Università di Padova, Vicolo Osservatorio 2, I-35122 Padova, Italy email: [email protected]