Hubble Space Telescope proper motion (HSTPROMO) catalogs of Galactic
  globular clusters. III. Dynamical distances and mass-to-light ratios
  We present dynamical distance estimates for 15 Galactic globular clusters and
use these to check the consistency of dynamical and photometric distance
estimates. For most of the clusters, this is the first dynamical distance
estimate ever determined. We extract proper-motion dispersion profiles using
cleaned samples of bright stars from the Hubble Space Telescope proper-motion
catalogs recently presented in Bellini et al. (2014) and compile a set of
line-of-sight velocity-dispersion profiles from a variety of literature
sources. Distances are then estimated by fitting spherical, non-rotating,
isotropic, constant mass-to-light (M/L) dynamical models to the proper-motion
and line-of-sight dispersion profiles together. We compare our dynamical
distance estimates with literature photometric estimates from the Harris (1996,
2010 edition) globular cluster catalog and find that the mean fractional
difference between the two types is consistent with zero at just $-1.9 \pm 1.7
\%$. This indicates that there are no significant biases in either estimation
method and provides an important validation of the stellar-evolution theory
that underlies photometric distance estimates. The analysis also estimates
dynamical M/L ratios for our clusters; on average, the dynamically-inferred M/L
ratios agree with existing stellar-population-based M/L ratios that assume a
Chabrier initial mass function (IMF) to within $-8.8 \pm 6.4 \%$, implying that
such an IMF is consistent with our data. Our results are also consistent with a
Kroupa IMF, but strongly rule out a Salpeter IMF. We detect no correlation
between our M/L offsets from literature values and our distance offsets from
literature values, strongly indicating that our methods are reliable and our
results are robust.
