The true shapes of globular clusters

The basic relations between the distributions of true and apparent axial ratios for oblate and prolate objects with random orientations are inverted. Several properties of these formulae are examined, including the relations between the first two moments of the distributions. The results are then applied to measurements of the axial ratios of globular clusters in the Large Magellanic Cloud and the Galaxy from a previous investigation. It is found that the clusters in the LMC with ages smaller than their relaxation time scales are as flat on average as elliptical galaxies, whereas the older clusters in the LMC and in the Galaxy are much rounder. On the reasonable assumption that the older clusters have isotropic velocity distributions and oblate forms, their kinematic properties are simply related to the observed axial ratios. The available evidence suggests that globular clusters have a smaller fraction of their kinetic energy in rotation than faint elliptical galaxies and a larger fraction than bright elliptical galaxies. The results have several interesting consequences for the formation and evolution of the two types of stellar systems.