A family of models of partially relaxed stellar systems

I. Dynamical properties

¹ Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy e-mail: m.trenti@sns.it
² Dipartimento di Fisica, Università di Milano, via Celoria 16, 20133 Milano, Italy e-mail: Giuseppe.Bertin@unimi.it

Received: 5 April 2004
Accepted: 27 August 2004

Abstract

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. Ψ, measuring the depth of the galaxy potential, and ν, 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 Ψ. The projected density profiles are well fitted by the law, with n ranging from 2.5 to 8.5, dependent on Ψ, 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 . At fixed values of ν, models with lower Ψ are more anisotropic; at fixed values of Ψ, models with lower ν are more concentrated and more anisotropic. When the global amount of anisotropy, measured by , 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 Ψ, for ) is covered by models that are dynamically stable; for these, the line profiles (line-of-sight velocity distribution) are Gaussian at the level, with a general trend of positive values of h₄ at radii larger than the effective radius R_e.