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 \pm 0.009 and 0.782 \pm 0.009 \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 .