Study of Globular Clusters

Abstract In the study of globular clusters, the King distribution function has been the standard for modeling the velocity dispersion, luminosity and surface density profiles. However, based on star count analysis developed by Grillmair et al. [5], it is apparent that there exist stars outside of the King tidal radius (while the model predicts that stars should no longer be bound to the globular cluster). Moreover, the star counts depart from the King model even at radii considerably less than the tidal radius. In this paper, we use the star count data developed by Grillmair et al. [5] and fit them to a Michie model (an extension of the King model that considers an extra parameter: the anisotropic radius of the cluster). Our results show that the Michie distribution function is more accurate than the more popular King distribution function. This result validates the belief that the velocity dispersions of stars in a globular cluster are not isotropic at all radii. Furthermore, I will consider the possibility that the deviation in star counts from the King model is attributed to the presence of dark matter. However, our results imply that adding dark matter to a Michie model does not improve the fit, largely because the model does not permit the dark matter to extend beyond the tidal radius. Due to this limitation in the models, no statements about the amount of dark matter in a globular cluster can be made