An Angular Diameter Measurement of $\beta$ UMa via Stellar Intensity Interferometry with the VERITAS Observatory

We use the VERITAS imaging air Cherenkov Telescope (IACT) array to obtain the first measured angular diameter of $\beta$ UMa at visual wavelengths using stellar intensity interferometry (SII) and independently constrain the limb-darkened angular diameter. The age of the Ursa Major moving group has been assessed from the ages of its members, including nuclear member Merak ($\beta$ UMa), an A1-type subgiant, by comparing effective temperature and luminosity constraints to model stellar evolution tracks. Previous interferometric limb-darkened angular-diameter measurements of $\beta$ UMa in the near-infrared (CHARA Array, $1.149 \pm 0.014$ mas) and mid-infrared (Keck Nuller, $1.08 \pm 0.07$ mas), together with the measured parallax and bolometric flux, have constrained the effective temperature. This paper presents current VERITAS-SII observation and analysis procedures to derive squared visibilities from correlation functions. We fit the resulting squared visibilities to find a limb-darkened angular diameter of $1.07 \pm 0.04 {\rm (stat)} \pm 0.05$ (sys) mas, using synthetic visibilities from a stellar atmosphere model that provides a good match to the spectrum of $\beta$ UMa in the optical wave band. The VERITAS-SII limb-darkened angular diameter yields an effective temperature of $9700\pm200\pm 200$ K, consistent with ultraviolet spectrophotometry, and an age of $390\pm 29 \pm 32$ Myr, using MESA Isochrones and Stellar Tracks (MIST). This age is consistent with $408 \pm 6$ Myr from the CHARA Array angular diameter.