We explore the long-term evolution of the anisotropy in the velocity space of star clusters starting with different structural and kinematical properties. We show that the evolution of the radial anisotropy strength and its radial variation within a cluster contain distinct imprints of the cluster initial structural properties, dynamical history, and of the external tidal field of its host galaxy. Initially isotropic and compact clusters with small initial values of the ratio of the half-mass to Jacobi radius, r h /r J , develop a strong radial anisotropy during their long-term dynamical evolution. Many clusters, if formed with small values of r h /r J , should now be characterized by a significant radial anisotropy increasing with the distance from the cluster centre, reaching its maximum at a distance between 0.2 r J and 0.4 r J , and then becoming more isotropic or mildly tangentially anisotropic in the outermost regions. A similar radial variation of the anisotropy can also result from an early violent relaxation phase. In both cases, as a cluster continues its evolution and loses mass, the anisotropy eventually starts to decrease and the system evolves toward an isotropic velocity distribution. However, in order to completely erase the strong anisotropy developed by these compact systems during their evolution, they must be in the advanced stages of their evolution and lose a large fraction of their initial mass. Clusters that are initially isotropic and characterized by larger initial values of r h /r J , on the other hand, never develop a significant radial anisotropy.

The presence of an external tidal field often induces significant dynamical evolutionary effects on the internal kinematics of star clusters. Previous studies investigating the restricted three-body problem with applications to star cluster dynamics have shown that unbound stars on retrograde orbits (with respect to the direction of the cluster's orbit) are more stable against escape than prograde orbits, and predicted that a star cluster might acquire retrograde rotation through preferential escape of stars on prograde orbits. In this study we present evidence of this prediction, but we also illustrate that there are additional effects that cannot be accounted for by the preferential escape of prograde orbits alone. Specifically, in the early evolution, initially underfilling models increase their fraction of retrograde stars without losing significant mass, and acquire a retrograde angular velocity. We attribute this effect to the development of preferentially eccentric/radial orbits in the outer regions of star clusters as they are expanding into their tidal limitation.We explore the implications of the evolution of the fraction of prograde and retrograde stars for the evolution of the cluster internal rotation, and its dependence on the initial structural properties. Although all the systems studied here evolve towards an approximately solidbody internal rotation with angular velocity equal to about half of the angular velocity of the cluster orbital motion around the host galaxy, the evolutionary history of the radial profile of the cluster internal angular velocity depends on the cluster initial structure.

In the context of the ESO-VLT Multi-Instrument Kinematic Survey (MIKiS) of Galactic globular clusters (GGCs), we present the line-of-sight rotation curve and velocity dispersion profile of M5 (NGC 5904), as determined from the radial velocity of more than 800 individual stars observed out to 700″ (∼5 half-mass radii) from the center. We found one of the cleanest and most coherent rotation patterns ever observed for globular clusters, with a very stable rotation axis (having constant position angle of 145°at all surveyed radii) and a well-defined rotation curve. The density distribution turns out to be flattened in the direction perpendicular to the rotation axis, with a maximum ellipticity of ∼0.15. The rotation velocity peak (∼3 km s −1 in projection) is observed at ∼0.6 half-mass radii, and its ratio with respect to the central velocity dispersion (∼0.3-0.4 at 4 projected half-mass radii) indicates that ordered motions play a significant dynamical role. This result strengthens the growing empirical evidence of the kinematic complexity of GGCs and motivates the need of fundamental investigations of the role of angular momentum in collisional stellar dynamics.

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We present the results of a suite of N-body simulations aimed at understanding the fundamental aspects of the long-term evolution of the internal kinematics of multiple stellar populations in globular clusters. Our models enable us to study the cooperative effects of internal, relaxation-driven processes and external, tidally-induced perturbations on the structural and kinematic properties of multiple-population globular clusters. To analyse the dynamical behaviour of the multiple stellar populations in a variety of spin-orbit coupling conditions, we have considered three reference cases in which the tidally perturbed star cluster rotates along an axis oriented in different directions with respect to the orbital angular momentum vector. We focus specifically on the characterisation of the evolution of the degree of differential rotation and anisotropy in the velocity space, and we quantify the process of spatial and kinematic mixing of the two populations. In light of recent and forthcoming explorations of the internal kinematics of this class of stellar systems by means of line-of sight and astrometric measurements, we also investigate the implications of projection effects and spatial distribution of the stars adopted as tracers. The kinematic and structural richness emerging from our models further emphasises the need and the importance of observational studies aimed at building a complete kinematical picture of the multiple population phenomenon.1 Although we use the terms first-and second-generation to refer to the different populations, we point out that according to some formation models (see, e.g., Bastian et al. 2013, Gieles et al. 2018) all the populations form at the same time, and in those cases the two populations are more properly referred to as first-and second-population.