The structure of star clusters. I. an empirical density law

New observations make it possible to re-examine the question of the density distribution in globular clusters. Jeans' law is based on insufficient observations and on an incorrect theory. On Palomar Schmidt plates the densities can be followed far enough out to define a limit to a globular cluster. The observed loca- tion of this limit agrees with the limit to be expected as a result of galactic tidal forces. The central regions of all globular clusters are similar, except for the effect of the tidal cutoff. An empirical formula has been found that represents the density from center to edge in globular clusters of all degrees of central concen- tration. The formula has three parameters, which is the minimum number permitted by the physical circum- stances. Globular clusters are therefore as similar in structure as they could possibly be. Galactic clusters and Sculptor-type dwarf galaxies also appear to follow the same density law. From dynamical considerations it would appear that all these stellar systems are subject to two types of relaxation, which produce nearly identical effects. The first relaxation is produced by the initial mixing of the system. Thereupon stellar encounters slowly change the density parameters without affecting the basic law. Relative to globular clusters, giant elliptical galaxies have an excess of brightness near the center. This difference can be explained as a result of relaxation, equipartition, and an excess of dwarf stars.