ORBITAL-PHASE DEPENDENCE OF GLOBULAR-CLUSTER TIDAL RADII

The tidal radii of 21 globular clusters are studied using positions an d spatial velocities based on recent compilations as well as new measu rements of their proper motions. The calculation of the perigalactic p osition of each cluster gives the possibility to determine their tidal radii using the classical formula of King (1962). Previous papers hav e claimed that the present tidal radius is approximately the same as t he radius at the perigalactic position. We show here that this hypothe sis is not verified and that there is in fact a discrepancy between th eoretical and observed tidal radii. We also show that this difference depends on the relative orbital position of the cluster, leading to an orbital phase dependence. For this phase, which reflects complex rela xation processes in the core cluster, we give an empirical linear equa tion. However, no evident relation has been found between relaxation t ime and the difference between classical theory and observations. The present work shows that a rigorous estimation of the tidal radii of th e globular clusters requires not only good kinematical data for the cl usters themselves, but also a good understanding of the internal relax ation processes.