Mass estimates from stellar proper motions: The mass of $\omega$ Centauri

A projected mass estimator and a maximum likelihood estimator are developed to best determine the mass of stellar clusters from proper motion data. Both methods effectively account and correct for errors in the velocities, and provide an unbiased and robust estimate of the cluster mass. Using an extensive proper motion study of $\omega$ Centauri by van Leeuwen et al. (2000), we estimate the mass of $\omega$ Centauri using these two different methods to be $2.8 \times 10^{6} M_{\odot} \left[d/5.1 kpc\right]^{3}$. Within this modeling context, the statistical error is $3\%$ and the systematic error is $4\%$.