A family of models of partially relaxed stellar systems : 1. Dynamical properties

Recently we have found that a family of models of partially relaxed, anisotropic stellar systems, inspired earlier by studies of incomplete violent relaxation, exhibits some interesting thermodynamic properties. Here we present a systematic investigation of its dynamical characteristics, in order to establish the basis for a detailed comparison with simulations of collisionless collapse, planned for a separate paper. For a full comparison with the observations of elliptical galaxies, the models should be extended to allow for the presence a sizable dark halo and of significant rotation. In the spherical limit, the family is characterized by two dimensionless parameters, i.e. Psi, measuring the depth of the galaxy potential, and nu, defining the form of a third global quantity Q, which is argued to be approximately conserved during collisionless collapse (in addition to the total energy and the total number of stars). The family of models is found to have the following properties. The intrinsic density profile beyond the half-mass radius r_M is basically universal and independent of Psi. The projected density profiles are well fitted by the R^(1/n) law, with n ranging from 2.5 to 8.5, dependent on Psi, with n close to 4 for concentrated models. All models exhibit radial anisotropy in the pressure tensor, especially in their outer parts, already significant at r ~ r_M. At fixed values of nu, models with lower Psi are more anisotropic; at fixed values of Psi, models with lower nu are more concentrated and more anisotropic. When the global amount of anisotropy, measured by 2K_r/K_T, is large, the models are unstable with respect to the radial-orbit instability; still, a wide region of parameter space (i.e., sufficiently high values of Psi, for nu > 3/8) is covered by models that are dynamically stable; for these, the line profiles (line-of-sight velocity distribution) are Gaussian at the 5% level, with a general trend of positive values of h_4 at radii larger than the effective radius R_e.