New Limits on an Intermediate-Mass Black Hole in Omega Centauri. Ii. Dynamical Models

We present a detailed dynamical analysis of the projected density and kinematical data available for the globular cluster Omega Cen. We solve the spherical anisotropic Jeans equation to predict the projected profiles of the RMS velocity in each of the three orthogonal coordinate directions (line of sight, proper motion radial, and proper motion tangential). We fit the models to new HST star count and proper motion data near the cluster center presented in Paper I, combined with existing ground-based measurements. We also derive and model the Gauss-Hermite moments of the observed proper motion distributions. The projected density profile is consistent with being flat near the center, with an upper limit gamma=0.07 on the central logarithmic slope. The RMS proper motion profile is also consistent with being flat near the center, and there are no unusually fast-moving stars. The models provide a good fit and yield a 1-sigma upper limit MBH < 1.2E4 solar masses on the mass of a possible intermediate-mass black hole (IMBH). The inferred upper limit corresponds to MBH/Mtot < 0.43%. We combine this with results for other clusters and discuss the implications for globular cluster IMBH demographics. Tighter limits will be needed to rule out or establish whether globular clusters follow the same black hole demographics correlations as galaxies. The arguments put forward by Noyola et al. (2008) to suspect an IMBH in Omega Cen are not confirmed by our study; the IMBH mass they suggested is firmly ruled out.