Absolute dimensions of the M-type eclipsing binary YY Geminorum (Castor C): A challenge to evolutionary models in the lower main sequence

We present new spectroscopic observations of the detached late-type double-lined eclipsing binary YY Geminorum (P=0.814 day), a member of the Castor sextuple system and one of the benchmarks for the comparison between observations and stellar evolution theory in the lower main sequence. In addition, we have reanalyzed existing light curves in several passbands using modern techniques that account for the conspicuous presence of spots. This, combined with the spectroscopy, has yielded a very precise determination of the absolute dimensions of the components, which are virtually identical to each other. We obtain for the mean mass, radius, and effective temperature the values M=0.5992+/-0.0047 M-circle dot, R=0.6191+/-0.0057 R-circle dot, and T-eff = 3820+/-100 K, respectively. Both the mass and the radius determinations are good to better than 1%, which in the case of the radius represents a fourfold improvement over previous results and signifintly enhances the value of this quantity for testing the models. We discuss the importance of systematic effects in these measurements by comparison with another high-precision determination of the mass by Segransan and coworkers. A reanalysis of the Hipparcos transit data for Castor AB that accounts for the relative motion of the pair in its 467 yr period orbit has yielded an improved parallax for the system of 66.90+/-0.63 mas. With this, we have estimated the age (similar to370 Myr) and metal abundance ([Fe/H]similar to0.0) of YY Gem from isochrone fits to Castor A and B under the assumption of a common origin. This, along with the other physical properties, allow for an unusually stringent test of the models for low-mass stars. We have compared the observations of YY Gem with a large number of recent theoretical calculations, and we show that all models underestimate the radius by up to 20% and that most overestimate the effective temperature by 150 K or more. Both of these trends are confirmed by observations of another similar system in the Hyades (V818 Tau). Consequently, theoretical ages for relatively low mass objects such as T Tauri stars derived by placing them on the H-R diagram may be considerably biased. If the radius is used directly as a measure of evolution, ages could be underestimated by as much as a factor of 10 in this mass regime. In view of these discrepancies, absolute ages from essentially all current models for the lower main sequence must be viewed with at least some measure of skepticism. Finally, we derive a new and very accurate ephemeris based on all available times of eclipse, and we lay to rest previous claims of sudden changes in the orbital period of the binary, which we show to be spurious.