We present sensitive, arcsecond-resolution Submillimeter Array observations of the 12CO J=2-1 line emission from the circumstellar disk orbiting the double-lined spectroscopic binary star V4046 Sgr. Based on a simple model of the disk structure, we use a novel Monte Carlo Markov Chain technique to extract the Keplerian velocity field of the disk from these data and estimate the total mass of the central binary. Assuming the distance inferred from kinematic parallax measurements in the literature (d is approximately 73 pc), we determine a total stellar mass M_star = 1.75^{+0.09}_{-0.06} solar masses and a disk inclination i_d = 33.5^{+0.7}_{-1.4} degrees from face-on. These measurements are in excellent agreement with independent dynamical constraints made from multi-epoch monitoring of the stellar radial velocities, confirming the absolute accuracy of this precise (~ few percent uncertainties) disk-based method for estimating stellar masses and reaffirming previous assertions that the disk and binary orbital planes are well aligned (with |i_d - i_star| approx 0.1pm1 degree). Using these results as a reference, we demonstrate that various pre-main sequence evolution models make consistent and accurate predictions for the masses of the individual components of the binary, and uniformly imply an advanced age of ~5-30 Myr. Taken together, these results verify that V4046 Sgr is one of the precious few nearby and relatively evolved pre-main sequence systems that still hosts a gas-rich accretion disk.
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