Tides, rotation, and anisotropy : new self-consistent nonspherical models for globular clusters

Spherical models of quasi-relaxed stellar systems provide a successful zeroth-order description of globular clusters. Yet, the great progress made in recent years in the acquisition of detailed information of the structure of these stellar systems calls for a renewed effort on the side of modeling. In particular, more realistic analytical models would allow to address a number of key issues on both the theoretical and observational side, such as the effects induced by different tidal environments, the dynamical interplay between internal rotation and two-body relaxation processes, and the physical origin of the deviations from spherical symmetry. External tides, internal rotation and anisotropy in the velocity space are therefore the physical ingredients that should be added to the traditional paradigm in order to achieve a proper understanding of the internal dynamics of globular clusters. In this contribution, I will describe a recently presented family of triaxial models that incorporate in a self-consistent way the tidal effects of the host galaxy. I will then introduce two new families of axisymmetric rotating models, studied in collaboration with G. Bertin. The first one is an extension of the well-known family of King models to the case of axisymmetric equilibria flattened by solid-body rotation, while the second family is characterized by differential rotation, designed to be rigid in the center and to vanish in the outer parts, where the imposed truncation in phase space becomes effective. Preliminary results of an extensive survey of N-body simulations carried out in collaboration with E. Vesperini and S. McMillan to explore the dynamical stability and the long-term evolution of these models will also be presented along with the comparison with observational data for selected Galactic globular clusters.