Non-Parametric 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 non-parametrically determine the mass density profiles and isotropic phase-space distribution functions $f(E)$ for the globular clusters M15 (NGC7078), 47~Tuc (NGC104), 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. In the two centrally-concentrated clusters, M15 and 47~Tuc, we find that the mass-to-light ratios (M/L's) reach minima around 1\arcmin, and increase by more than a factor of four towards the cluster centers. For the two less centrally concentrated clusters, the M/L decreases monotonically all the way into the center. All four clusters exhibit an increase in the M/L's in their outer parts. If the variations in the M/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$<0.3$M$_\odot$). By applying the crude approximation of local thermodynamic equilibrium, we derive the present-day mass function for each cluster. In the central 2--3 parsecs, 0.7--1.5 M$_\odot$ objects provide the bulk of the cluster mass. The paper is in a uuencoded compressed tar file (260kb).