Hubble Space Telescope Astrometry of the Metal-Poor Visual Binary $\mu$
  Cassiopeiae: Dynamical Masses, Helium Content, and Age
  $\mu$ Cassiopeiae is a nearby, high-velocity, metal-poor ($\rm[Fe/H]=-0.81$)
visual binary. We have used high-resolution imaging with the Hubble Space
Telescope (HST), obtained over nearly two decades, to determine the period
(21.568 yr) and precise orbital elements. Combining these with published
ground- and space-based astrometry, we determined dynamical masses for both
components of $\mu$ Cas: $0.7440\pm0.0122\,M_\odot$ for the G5 V primary, and
$0.1728\pm0.0035\,M_\odot$ for its faint dM companion. We detect no significant
perturbations in the HST astrometry due to a third body in the system. The
primary aim of our program was to determine, with the aid of stellar models,
the helium content and age of the metal-deficient primary star, $\mu$ Cas A.
Although we now have a precise mass, there remain uncertainties about other
parameters, including its effective temperature. Moreover, a re-examination of
archival interferometric observations leads to a suspicion that the angular
diameter was overestimated by a few percent. In the absolute magnitude versus
color plane, $\mu$ Cas A lies slightly cooler and more luminous than the main
sequence of the globular cluster 47 Tucanae; this may imply that the star has a
lower helium content, and/or is older, and/or has a higher metallicity, than
the cluster. Our best estimates for the helium content and age of $\mu$ Cas A
are $Y=0.255\pm0.014$ and $12.7\pm2.7$ Gyr--making $\mu$ Cas possibly the
oldest star in the sky visible to the naked eye. Improved measurements of the
absolute parallax of the system, the effective temperature of $\mu$ Cas A, and
its angular diameter would provide tighter constraints.
