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Description
We report the discovery by the HATNet survey of HAT-TR-318-007, a P=3.34395390+/-0.00000020 day period detached double-lined M dwarf binary with total secondary eclipses. We combine radial velocity (RV) measurements from TRES/FLWO 1.5 m and time-series photometry from HATNet, FLWO 1.2 m, BOS 0.8 m, and NASA K2 Campaign 5, to determine the masses and radii of the component stars: M_A_=0.448+/-0.011 M_{sun}_^N^, M_B_=0.2721_-0.0042_^+0.0041^ M_{sun}_^N^, R_A_=0.4548_-0.0036_^+0.0035^ R_{sun}_^N^, and R_B_=0.2913_-0.0024_^+0.0023^ R_{sun}_^N^. We obtained a FIRE/Magellan near-infrared spectrum of the primary star during a total secondary eclipse, and we use this to obtain disentangled spectra of both components. We determine spectral types of ST_A_=M3.71+/-0.69 and ST_B_=M5.01+/-0.73 and effective temperatures of T_eff,A_=3190+/-110 K and T_eff,B_=3100+/-110 K for the primary and secondary star, respectively. We also measure a metallicity of [Fe/H]=+0.298+/-0.080 for the system. We find that the system has a small, but significant, nonzero eccentricity of 0.0136+/-0.0026. The K2 light curve shows a coherent variation at a period of 3.41315_-0.00032_^+0.00030^ days, which is slightly longer than the orbital period, and which we demonstrate comes from the primary star. We interpret this as the rotation period of the primary. We perform a quantitative comparison between the Dartmouth stellar evolution models and the seven systems, including HAT-TR-318-007, that contain M dwarfs with 0.2 M_{sun}_^N^<M<0.5 M_{sun}_^N^, have metallicity measurements, and have masses and radii determined to better than 5% precision. Discrepancies between the predicted and observed masses and radii are found for three of the systems.
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