HAT-TR-318-007: A Double-lined M Dwarf Binary with Total Secondary Eclipses Discovered by HATNet and Observed by K2

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 ± 0.011M_⊙^N, M_B 0.2721_-0.0042^+0.0041 M_⊙^N, R_A 0.4548_-0.0036^+0.0035R_⊙^N, and R_B 0.2913_-0.0024^+0.0023R_⊙^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 HATTR-318-007, that contain M dwarfs with 0.2M_⊙^N < M < 0.5M_⊙^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.