Near-infrared interferometers have recently imaged a number of rapidly rotating A-type stars , finding levels of gravity darkening inconsistent with theoretical expectations .
Here , we present new imaging of both a cooler star \beta Cas ( F2IV ) and a hotter one \alpha Leo ( B7V ) using the CHARA array and the MIRC instrument at the H band .
Adopting a solid-body rotation model with a simple gravity darkening prescription , we modeled the stellar geometric properties and surface temperature distributions , confirming both stars are rapidly rotating and show gravity darkening anomalies .
We estimate the masses and ages of these rapid rotators on \emph { L - R } _ { pol } and HR diagrams constructed for non-rotating stars by tracking their non-rotating equivalents .
The unexpected fast rotation of the evolved sub-giant \beta Cas offers a unique test of the stellar core-envelope coupling , revealing quite efficient coupling over the past \sim 0.5 Gyr .
Lastly we summarize all our interferometric determinations of the gravity darkening coefficient for rapid rotators , finding none match the expectations from the widely used von Zeipel gravity darkening laws .
Since the conditions of the von Zeipel law are known to be violated for rapidly rotating stars , we recommend using the empirically-derived \beta = 0.19 for such stars with radiation-dominated envelopes .
Furthermore , we note that no paradigm exists for self-consistently modeling heavily gravity-darkened stars that show hot radiative poles with cool convective equators .