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Kepler Studies of Low-Mass Eclipsing Binaries I. Parameters of the Long-Period Binary KIC 6131659

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 M_1=0.922 +/- 0.007 M_sun, R_1=0.8800 +/- 0.0028 R_sun, and M_2=0.685 +/- 0.005 M_sun, R_2=0.6395 +/- 0.0061 R_sun. There is a well-known issue with low mass (M <<0.8 M_sun) stars (in cases where the mass and radius measurement uncertainties are smaller than two or three percent) where the measured radii are almost always 5 to 15 percent 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 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 e cos omega=(4.57 +/-0.02)*10^-5.