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 \sim 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 \pm 0.0020 M _ { \odot } ; M _ { s } = 0.2098 \pm 0.0014 M _ { \odot } ) and radii ( R _ { p } = 0.363 \pm 0.008 R _ { \odot } ; R _ { s } = 0.272 \pm 0.012 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 \lesssim 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 \sim 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 .