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 ω Centauri. We solve the spherical anisotropic Jeans equation for a given density profile to predict the projected profiles of the rms velocity σ-bar(R), in each of the three orthogonal coordinate directions (line of sight, proper motion radial, and proper motion tangential). The models allow for the presence of a central dark mass, such as a possible intermediate-mass black hole (IMBH). We fit the models to new Hubble Space Telescope star count and proper motion data near the cluster center presented in the companion paper, which is Paper I in this series, combined with existing ground-based measurements at larger radii. The projected density profile is consistent with being flat near the center, with an upper limit γ ∼< 0.07 on the central logarithmic slope. The rms proper motion profile is also consistent with being flat near the center. The velocity anisotropy profile, distance, and stellar mass-to-light ratio are all tightly constrained by the data and found to be in good agreement with previous determinations by van de Ven et al. To fit the kinematics, we consider anisotropic models with either a flat core (γ = 0) or a shallow cusp (γ = 0.05). Core models provide a good fit to the data with MBH = 0; cusp models require a dark mass. If the dark mass in cusp models is an IMBH, then MBH = (8.7 ± 2.9) x 103 Msun; if it is a dark cluster, then its extent must be ∼<0.16 pc. Isotropic models do not fit the observed proper motion anisotropy and yield spuriously high values for any central dark mass. These models do provide a good fit to the Gauss-Hermite moments of the observed proper motion distributions (h4 = -0.023 ± 0.004, h6 = 0.001 ± 0.004). There are no unusually fast-moving stars observed in the wings of the proper motion distribution, but we show that this does not strongly constrain the mass of any possible IMBH. The overall end result of the modeling is an upper limit to the mass of any possible IMBH in ω Centauri: MBH ∼< 1.2 x 104 Msun at ∼1σ confidence (or ∼<1.8 x 104 Msun at ∼3σ confidence). The 1σ 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. to suspect an IMBH in ω Centauri are not confirmed by our study; the value of MBH they suggested is firmly ruled out.