We report the discovery by the HATNet survey of HAT-TR-318-007 , a P = 3.34395390 \pm 0.00000020 { } d 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 \pm 0.011 { } \mathcal { M } ^ { N } _ { \odot } , M _ { B } = 0.2721 ^ { +0.0041 } _ { -0.0042 } { } \mathcal { M } ^ { N } _ { \odot } , R _ { A } = 0.4548 ^ { +0.0035 } _ { -0.0036 } { } \mathcal { R } ^ { N } _ { \odot } , and R _ { B } = 0.2913 ^ { +0.0023 } _ { -0.0024 } { } \mathcal { R } ^ { N } _ { \odot } .
We obtained a FIRE/Magellan near-infrared spectrum of the primary star during a total secondary eclipse , and use this to obtain disentangled spectra of both components .
We determine spectral types of { ST } _ { A } = { M } 3.71 \pm 0.69 and { ST } _ { B } = { M } 5.01 \pm 0.73 , and effective temperatures of T _ { eff,A } = 3190 \pm 110 K and T _ { eff,B } = 3100 \pm 110 K , for the primary and secondary star , respectively .
We also measure a metallicity of [ Fe/H ] = +0.298 \pm 0.080 for the system .
We find that the system has a small , but significant , non-zero eccentricity of 0.0136 \pm 0.0026 .
The K2 light curve shows a coherent variation at a period of 3.41315 ^ { +0.00030 } _ { -0.00032 } d , 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 \hbox { $ \mathcal { M } ^ { N } _ { \odot } $ } < M < 0.5 \hbox { $ \mathcal { M } ^ { N } _ { % \odot } $ } , 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 .