NONPARAMETRIC DYNAMICAL ANALYSIS OF GLOBULAR-CLUSTERS - M15, 47-TUC, NGC-362, AND NGC-3201

We use radial velocities of member stars and cluster surface brightness profiles to nonparametrically determine the mass density profiles and isotropic phase-space distribution functions f(E) for the globular clusters M15 (NGC 7078), 47 Tuc (NGC 104), NGC 362, and NGC 3201. Assuming isotropy and using the velocity dispersion and surface brightness profiles, the Jeans equation uniquely determines the mass density profile. For M15 and 47 Tuc, the slopes of the mass density profiles beyond 2.0′ are similar to the theoretical predictions for core collapse, whereas the density profiles for NGC 362 and NGC 3201 are steeper than the predicted slope. In the two centrally concentrated clusters, M15 and 47 Tuc, we find that the mass-to-light ratios (script M sign.L's) reach minima around 1′, and increase by more than a factor of 4 towards the cluster centers. For the two less centrally concentrated clusters, the script M sign/L decreases monotonically all the way into the center. All four clusters exhibit an increase in the script M sign/L's in their outer parts. If the variations in the script M sign/L's are due to equipartition of energy between different mass stars, then we attribute the central increases to massive remnants and the outer increases to low-mass stars (m<0.3script M sign⊙). By applying the crude approximation of local thermodynamic equilibrium, we derive the present-day mass function for each cluster. In the central 2-3 pc, 0.7-1.5script M sign⊙ objects provide the bulk of the cluster mass. These results may be sensitive to the assumption of isotropy in the stellar velocities. We derive phase-space distribution functions f(E) for the clusters and find significant disagreement with the best-fit King distribution functions. For NGC 362 and NGC 3201, there are significantly more low E objects than predicted by King models. The f(E) for M15 and 47 Tuc are similar to each other but show differences from the King models. The techniques described in this paper can be used for other dynamical systems, such as galactic nuclei and clusters of galaxies.