Instantaneous and average tidal radii of globular clusters

The main aim of this paper is an extension of the heuristic concept of the tidal radii of globular clusters to the case of very non-circular orbits, i.e. with large differences between the peri- and apogalactic distances. We had found earlier that perigalactic tidal radii do clearly not represent the observed limiting photometric radii. For 16 globular clusters with orbits based on absolute proper motions we derived instantaneous tidal radii along the orbit. We computed four kind of averages of the instantaneous values. The comparison between average tidal radii and observed limiting radii relies on the ratios between the two, since the equations for the theoretical values may need the inclusion of an additional constant factor. In case that the said ratios do not depend on the shape of the orbits, we consider the underlying method of averaging as satisfying. In a quantitative approximation, this non-dependence can be assumed for all methods within 3 sigma-limits; but one method stands out in that it fulfils it within 1 sigma. This method or way consists in forming the reciprocal squares of the instantaneous tidal radii and their mean along the orbit. (C) 1999 Elsevier Science B.V. All rights reserved.