  The nearby star Alpha Oph (Ras Alhague) is a rapidly rotating A5IV star
spinning at ~89% of its breakup velocity. This system has been imaged
extensively by interferometric techniques, giving a precise geometric model of
the star's oblateness and the resulting temperature variation on the stellar
surface. Fortuitously, Alpha Oph has a previously known stellar companion, and
characterization of the orbit provides an independent, dynamically-based check
of both the host star and the companion mass. Such measurements are crucial to
constrain models of such rapidly rotating stars. In this study, we combine
eight years of Adaptive Optics imaging data from the Palomar, AEOS, and CFHT
telescopes to derive an improved, astrometric characterization of the companion
orbit. We also use photometry from these observations to derive a model-based
estimate of the companion mass. A fit was performed on the photocenter motion
of this system to extract a component mass ratio. We find masses of
2.40^{0.23}_{0.37} solar masses and 0.85^{0.06}_{0.04} solar masses for Alpha
Oph A and Alpha Oph B, respectively. Previous orbital studies of this system
found a mass too high for this system, inconsistent with stellar evolutionary
calculations. Our measurements of the host star mass are more consistent with
these evolutionary calculations, but with slightly higher uncertainties. In
addition to the dynamically-derived masses, we use IJHK photometry to derive a
model-based mass for Alpha Oph B, of 0.77 +/- 0.05 solar masses marginally
consistent with the dynamical masses derived from our orbit. Our model fits
predict a periastron passage on 2012 April 19, with the two components having a
~50 milliarcsec separation from March to May 2012. A modest amount of
interferometric and radial velocity data during this period could provide a
mass determination of this star at the few percent level.
