Precise Age for the Binary Star System 12 Com in the Coma Berenices Cluster

We present measurements of the interferometrically-resolved binary star system 12 Com and the single giant star 31 Com in the cluster Coma Berenices. 12 Com is a double-lined spectroscopic binary system consisting of a G7 giant and an A3 dwarf at the cluster turnoff. Using an extensive radial velocity dataset and interferometric measurements from PTI and the CHARA array, we measured masses $M_1 =2.64 \pm 0.07 M_\odot$ and $M_2 =2.10 \pm 0.03 M_\odot$. Interferometry also allows us to resolve the giant, and measure its size as $R_1 = 9.12 \pm 0.12 \pm 0.01 R_\odot$. With the measured masses and radii, we find an age of $533 \pm 41 \pm 42$ Myr. For comparison, we measure the radius of 31 Com to be $8.36 \pm 0.15 R_\odot$. Based on the photometry and radius measurements, 12 Com A is likely the most evolved bright star in the cluster, large enough to be in the red giant phase, but too small to have core helium burning. Simultaneous knowledge of 12 Com A's mass and photometry puts strong constraints on convective core overshooting during the main sequence phase, which in turn reduces systematic uncertainties in the age. Increased precision in measuring this system also improves our knowledge of the progenitor of the cluster white dwarf WD1216+260.