  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 and
cooler than predicted by theory by several percent. In an on-going effort to
elucidate this issue, we examine the double-lined Kepler eclipsing binary star
system KIC 8736245. We supplement the near-continuous 4-year Kepler light curve
with ground-based multicolor photometry from Mount Laguna Observatory and
spectroscopy 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 $0.804 \pm
0.004\,\text{R}_\odot$, respectively, and an estimated age of 7-9 Gyr. We find
that the stellar radii are consistent with theoretical models within the
uncertainties, whereas the temperature of the secondary star is $\sim$6% cooler
than predicted. An important aspect of this work is that the uncertainties
derived from a single epoch (individual night of observations) underestimates
the overall system parameter uncertainties due to the effect of the 1-4%
fluctuations caused by stellar activity. Our error estimates come from the
spread in parameters measured at 8 epochs. From the periodicities in the light
curve and from the eclipse times, we measure candidate spin periods to be
approximately 4.98 and 5.87 days for the primary and secondary star.
Surprisingly, these imply super- and sub-synchronous rotation compared to the
orbital period. Thus KIC 8736245 serves as an interesting case study for the
exchange of angular momentum and general stellar astrophysics as stars in
binaries evolve off the main sequence.
