Dynamical mass of the substellar benchmark binary HD 130948BC

We present Keck adaptive optics imaging of the L4+L4 binary HD 130948BC along with archival Hubble Space Telescope and Gemini North observations, which together span ≈ 70% of the binary's orbital period. From the relative orbit, we determine a total dynamical mass of 0.109 ± 0.003 M_⊙ (114 ± 3 M_Jup). The flux ratio of HD 130948BC is near unity, so both components are unambiguously substellar for any plausible mass ratio. An independent constraint on the age of the system is available from the primary HD 130948A (G2V, [M/H] = 0.0). The ensemble of available indicators suggests an age comparable to Hyades, with the most precise age being 0.79 _-0.15^+0.22 Gyr based on gyrochronology. Therefore, HD 130948BC is now a unique benchmark among field L and T dwarfs, with a well-determined mass, luminosity, and age. We find that substellar theoretical models disagree with our observations. (1) Both components of HD 130948BC appear to be overluminous by a factor of ≈ 2-3 times compared to evolutionary models. The age of the system would have to be notably younger than the gyro age to ameliorate the luminosity disagreement. (2) Effective temperatures derived from evolutionary models for HD 130948B and C are inconsistent with temperatures determined from spectral synthesis for objects of similar spectral type. Overall, regardless of the adopted age, evolutionary and atmospheric models give inconsistent results, which indicate systematic errors in at least one class of models, possibly both. The masses of HD 130948BC happen to be very near the theoretical mass limit for lithium burning, and thus measuring the differential lithium depletion between B and C will provide a uniquely discriminating test of theoretical models. The potential underestimate of luminosities by evolutionary models would have wide-ranging implications; therefore, a more refined estimate age for HD 130948A is critically needed.