Distribution of proper motions in spherical star clusters

Abstract

Along with data on radial velocities, more and more data on proper motions of individual stars in globular clusters are becoming available. Their usage was until now rather limited. It was mostly restricted to determining cluster membership of individual stars and to determining the spatial velocity of the cluster. We study the two dimensional distribution of the proper motions, in order to clarify the relation between the projection of the velocities and the dynamical structure. Obviously some assumptions on the dynamics of the system have to be made. In this study we chose a Plummer model. This complements an earlier study about line profiles. The three velocity dispersions in the main directions are determined and compared with the three spherical velocity dispersions. Two parameters analogous to Binney's anisotropy parameter $β$ are defined. Moreover, since the proper motion components are distance dependent and the line of sight velocity dispersion is distance independent, we show explicitly how to determine distances.