| Summary: | 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^N⊙, M_B = 0.2721^(+0.0041)_(-0.0042) M^N⊙, R_A = 0.4548^(+0.0035)_(-0.0036) R^N⊙, and R_B = 0.2913^(+0.0023)_(-0.0024) R^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^(+0.00030)_(-0.00032) 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 0.0 M^N⊙ < M < 0.5 M^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. © 2018 The American Astronomical Society. Received 2017 November 17; revised 2018 January 9; accepted 2018 January 10; published 2018 February 14. Based in part on observations made with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, ...
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