The Mass-Radius Relation of Young Stars, I: UScoCTIO 5, An M4.5 Eclipsing Binary in Upper Scorpius Observed By K2

Evolutionary models of pre-main sequence stars remain largely uncalibrated, especially for masses below that of the Sun, making each new dynamical mass and radius measurement a valuable test of theoretical models. Stellar mass dependent features of star formation (such as disk evolution, planet formation, and even the IMF) are fundamentally tied to these models, which implies a systematic uncertainty that can only be improved with precise measurements of calibrator stars. We present the discovery that UScoCTIO 5, a known spectroscopic binary (P = 34 days, Mtot sin(i) = 0.64 Msun), 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 Msun, R_A = 0.834 +/- 0.006 Rsun, M_B = 0.317 +/- 0.002 Msun, and R_B = 0.810 +/- 0.006 Rsun. 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 for any trend of other properties that vary with stellar mass. 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-Teff scale. The simplest modification to the models (changing Teff to match observations) would yield an older age for this system, in line with the recently proposed older age of Upper Scorpius (~11 Myr).