Tides, Rotation Or Anisotropy? 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 general analytical models would allow to address the long-standing issue of the physical origin of the deviations from spherical symmetry of the globular clusters, that now can be properly measured. In fact, it remains to be established which is the cause of the observed flattening, among external tides, internal rotation, and pressure anisotropy. In this paper we focus on the first two physical ingredients. We start by briefly describing a recently studied family of triaxial models that incorporate in a self-consistent way the tidal effects of the host galaxy, as a collisionless analogue of the Roche problem (Varri & Bertin ApJ 2009). We then present two new families of axisymmetric models in which the deviations from spherical symmetry are induced by the presence of internal rotation. 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. 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. For possible application to globular clusters, models of interest should be those, in both families, characterized by low values of the rotation strength parameter and quasi-spherical shape. For general interest in stellar dynamics, we show that, for high values of that parameter, the differentially rotating models may exhibit unexpected morphologies, even with a toroidal core.