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There is a well-known stellar parameter discrepancy for late K and M dwarfs,in that the observed radii and temperatures are often respectively larger andcooler than predicted by theory by several percent. In an on-going effort toelucidate this issue, we examine the double-lined Kepler eclipsing binary starsystem KIC 8736245. We supplement the near-continuous 4-year Kepler light curvewith ground-based multicolor photometry from Mount Laguna Observatory andspectroscopy from the Hobby-Eberly Telescope. The binary has an edge-on,circular 5.07 day orbit with stellar masses equal to $0.987\pm0.009$ and$0.782\pm0.009\,\text{M}_\odot$ and radii of $1.311 \pm 0.006$ and $0.804 \pm0.004\,\text{R}_\odot$, respectively, and an estimated age of 7-9 Gyr. We findthat the stellar radii are consistent with theoretical models within theuncertainties, whereas the temperature of the secondary star is $\sim$6% coolerthan predicted. An important aspect of this work is that the uncertaintiesderived from a single epoch (individual night of observations) underestimatesthe overall system parameter uncertainties due to the effect of the 1-4%fluctuations caused by stellar activity. Our error estimates come from thespread in parameters measured at 8 epochs. From the periodicities in the lightcurve and from the eclipse times, we measure candidate spin periods to beapproximately 4.98 and 5.87 days for the primary and secondary star.Surprisingly, these imply super- and sub-synchronous rotation compared to theorbital period. Thus KIC 8736245 serves as an interesting case study for theexchange of angular momentum and general stellar astrophysics as stars inbinaries evolve off the main sequence.

Stellar Properties of KIC 8736245: An Eclipsing Binary with a Solar-type Star Leaving the Main Sequence