The Age of the Directly-Imaged Planet Host Star $\kappa$ Andromedae Determined From Interferometric Observations

$\kappa$ Andromedae, an early type star that hosts a directly imaged low mass companion, is expected to be oblate due to its rapid rotational velocity ($v\sin i$ = $\sim$162 $\mathrm{km~s^{-1}}$). We observed the star with the CHARA Array's optical beam combiner, PAVO, measuring its size at multiple orientations and determining its oblateness. The interferometric measurements, combined with photometry and this $v\sin i$ value are used to constrain an oblate star model that yields the fundamental properties of the star and finds a rotation speed that is $\sim$85\% of the critical rate and a low inclination of $\sim$30$^\circ$. Three modeled properties (the average radius, bolometric luminosity, and equatorial velocity) are compared to MESA evolution models to determine an age and mass for the star. In doing so, we determine an age for the system of 47$^{+27}_{-40}$ Myr. Based on this age and previous measurements of the companion's temperature, the BHAC15 evolution models imply a mass for the companion of 22$^{+8}_{-9}$ M$_\mathrm{J}$.