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Velocity anisotropy in tidally limited star clusters

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.