2012ApJ...761..157B

KIC 6131659 is a long-period (17.5 days) eclipsing binary discovered by the Kepler mission. We analyzed six quarters of Kepler data along with supporting ground-based photometric and spectroscopic data to obtain accurate values for the mass and radius of both stars, namely, M₁= 0.922±0.007 M_☉, R₁= 0.8800±0.0028 R_☉, and M₂= 0.685±0.005 M_☉, R₂= 0.6395±0.0061 R_☉. There is a well-known issue with low-mass (M ≲ 0.8 M_☉) stars (in cases where the mass and radius measurement uncertainties are smaller than 2% or 3%) where the measured radii are almost always 5% to 15% larger than expected from evolutionary models, i.e., the measured radii are all above the model isochrones in a mass-radius plane. In contrast, the two stars in KIC 6131659 were found to sit on the same theoretical isochrone in the mass-radius plane. Until recently, all of the well-studied eclipsing binaries with low-mass stars had periods of less than about three days. The stars in such systems may have been inflated by high levels of stellar activity induced by tidal effects in these close binaries. KIC 6131659 shows essentially no evidence of enhanced stellar activity, and our measurements support the hypothesis that the unusual mass-radius relationship observed in most low-mass stars is influenced by strong magnetic activity created by the rapid rotation of the stars in tidally locked, short-period systems. Finally, using short cadence data, we show that KIC 6131657 has one of the smallest measured non-zero eccentricities of a binary with two main-sequence stars, where ecos ω = (4.57±0.02)x10^–5.