The Mass-Radius Relation of Young Stars. I. USco 5, an M4.5 Eclipsing Binary in Upper Scorpius Observed by K2

We present the discovery that UScoCTIO 5, a known spectroscopic binary in the Upper Scorpius star-forming region (P = 34 days, {M}_{tot}{sin}(i)=0.64 {M}_⊙ ), is an eclipsing system with both primary and secondary eclipses apparent in K2 light curves obtained during Campaign 2. We have simultaneously fit the eclipse profiles from the K2 light curves and the existing RV data to demonstrate that UScoCTIO 5 consists of a pair of nearly identical M4.5 stars with {M}_A=0.329+/- 0.002 {M}_⊙ , {R}_A=0.834+/- 0.006 {R}_⊙ , {M}_B=0.317+/- 0.002 {M}_⊙ , and {R}_B=0.810+/- 0.006 {R}_⊙ . The radii are broadly consistent with pre-main-sequence ages predicted by stellar evolutionary models, but none agree to within the uncertainties. All models predict systematically incorrect masses at the 25%-50% level for the HR diagram position of these mid-M dwarfs, suggesting significant modifications to mass-dependent outcomes of star and planet formation. The form of the discrepancy for most model sets is not that they predict luminosities that are too low, but rather that they predict temperatures that are too high, suggesting that the models do not fully encompass the physics of energy transport (via convection and/or missing opacities) and/or a miscalibration of the SpT-{T}_{eff} scale. The simplest modification to the models (changing {T}_{eff} to match observations) would yield an older age for this system, in line with the recently proposed older age of Upper Scorpius (τ ∼ 11 Myr).