Dynamical Masses and Mass-to-light Ratios of Resolved Massive Star
  Clusters. I. NGC 419 and NGC 1846
  As an introduction of a kinematic survey of Magellanic Cloud (MC) star
clusters, we report on the dynamical masses and mass-to-light ($M/L$) ratios of
NGC 419 (SMC) and NGC 1846 (LMC). We have obtained more than one hundred
high-resolution stellar spectra in and around each cluster using the
multi-object spectrograph M2FS on the $Magellan$/Clay Telescope. Line-of-sight
velocities and positions of the stars observed in each cluster were used as
input to an expectation-maximization algorithm used to estimate cluster
membership probabilities, resulting in samples of 46 and 52 likely members
($P_{M}\geq 50$%) in NGC 419 and NGC 1846, respectively. This process employed
single-mass King models constrained by the structural parameters of the
clusters and provided self-consistent dynamical mass estimates for both
clusters. Our best-fit results show that NGC 419 has a projected central
velocity dispersion of $2.44^{+0.37}_{-0.21}\ {\rm km\,s^{-1}}$, corresponding
to a total mass of $7.6^{+2.5}_{-1.3}\times10^4\ {\rm M}_{\odot}$ and $V$-band
$M/L$ ratio of $0.22^{+0.08}_{-0.05}$ in solar units. For NGC 1846, the
corresponding results are $2.04^{+0.28}_{-0.24}\ {\rm km\,s^{-1}}$,
$5.4^{+1.5}_{-1.4}\times10^4\ {\rm M}_{\odot}$ and $0.32^{+0.11}_{-0.11}$. The
mean metallicities of NGC 419 and NGC 1846 are found to be $\rm
[Fe/H]=-0.84\pm0.19$ and $-0.70\pm0.08$, respectively, based on the spectra of
likely cluster members. We find marginal statistical evidence of rotation in
both clusters, though in neither cluster does rotation alter our mass estimates
significantly. We critically compare our findings with those of previous
kinematic studies of these two clusters in order to evaluate the consistency of
our observational results and analytic tools.
