The Factory and the Beehive III: PTFEB132.707+19.810, a Low-Mass Eclipsing Binary in Praesepe Observed by PTF and K2

Theoretical models of stars constitute a fundamental bedrock upon which much of astrophysics is built, but large swaths of model parameter space remain uncalibrated by observations. The best calibrators are eclipsing binaries in clusters, allowing measurement of masses, radii, luminosities, and temperatures, for stars of known metallicity and age. We present the discovery and detailed characterization of PTFEB132.707+19.810, a P=6.0 day eclipsing binary in the Praesepe cluster ($\tau$~600--800 Myr; [Fe/H]=0.14$\pm$0.04). The system contains two late-type stars (SpT$_P$=M3.5$\pm$0.2; SpT$_S$=M4.3$\pm$0.7) with precise masses ($M_p=0.3953\pm0.0020$~$M_{\odot}$; $M_s=0.2098\pm0.0014$~$M_{\odot}$) and radii ($R_p=0.363\pm0.008$~$R_{\odot}$; $R_s=0.272\pm0.012$~$R_{\odot}$). Neither star meets the predictions of stellar evolutionary models. The primary has the expected radius, but is cooler and less luminous, while the secondary has the expected luminosity, but is cooler and substantially larger (by 20%). The system is not tidally locked or circularized. Exploiting a fortuitous 4:5 commensurability between $P_{orb}$ and $P_{rot,prim}$, we demonstrate that fitting errors from the unknown spot configuration only change the inferred radii by <1--2%. We also analyze subsets of data to test the robustness of radius measurements; the radius sum is more robust to systematic errors and preferable for model comparisons. We also test plausible changes in limb darkening, and find corresponding uncertainties of ~1%. Finally, we validate our pipeline using extant data for GU Boo, finding that our independent results match previous radii to within the mutual uncertainties (2--3%). We therefore suggest that the substantial discrepancies are astrophysical; since they are larger than for old field stars, they may be tied to the intermediate age of PTFEB132.707+19.810.