First Results from the CHARA Array. III. Oblateness, Rotational Velocity and Gravity Darkening of Alderamin

We present observations of the A7IV-V star Alderamin ($\alpha$ Cep, HR 8162, HD 203280) from the Georgia State University CHARA Array. These infrared interferometric angular size measurements indicate a non-circular projected disk brightness distribution for this known rapid rotator. The interferometric observations are modeled as arising from an elongated rigid atmosphere, with apparent polar and equatorial radii of $r_p=0.6753^{+0.0119}_{-0.0135}$ milliarcseconds (mas) and $r_e=0.8767^{+0.0293}_{-0.0183}$ mas, respectively, for a difference of $201\pm 32$ microarcseconds ($\mu$as), and with an axial ratio of $r_e/r_p =1.298\pm 0.051$. Using the Hipparcos distance of $14.96\pm 0.11$ pc, these angular measures translate to $2.18\pm0.05$ and $2.82\pm0.10$ $R_\odot$. The inclination of Alderamin to the line of sight indicated by this modeling is effectively edge-on ($i=88.2^{+1.8}_{-13.3}$). The star has a true rotational velocity of $283\pm 10$ km/s ($\sim83$% of breakup velocity), and a polar temperature of roughly 8400 K. Significantly, a necessary aspect of this modeling is a determination of the gravity darkening coefficient, which at a value of $\beta=0.084^{+0.026}_{-0.049}$ is consistent with a convective photosphere, as expected for an A7IV-V star. Our detailed characterization of this object allows us to investigate various scenarios for the angular momentum history of Alderamin and the appropriateness of certain stellar evolution models.