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Disk masses in the embedded and T Tauri phases of stellar evolution

(Abridged). Motivated by a growing concern that masses of circumstellar disks may have been systematically underestimated by conventional observational methods, we present a numerical hydrodynamics study of time-averaged disk masses (<M_d>) around low-mass Class 0, Class I, and Class II objects. Mean disk masses (\overline{M}_d}) are then calculated by weighting the time-averaged disk masses according to the corresponding stellar masses using a power-law weight function with a slope typical for the Kroupa initial mass function of stars. Two distinct types of disks are considered: self-gravitating disks, in which mass and angular momentum are redistributed exclusively by gravitational torques, and viscous disks, in which both the gravitational and viscous torques are at work. We find that self-gravitating disks have mean masses that are slowly increasing along the sequence of stellar evolution phases. More specifically, Class 0/I/II self-gravitating disks have mean masses \overline{M}_d=0.09, 0.10, and 0.12 M_sun, respectively. Viscous disks have similar mean masses (\overline{M}_d=0.10-0.11 M_sun) in the Class 0/I phases but almost a factor of 2 lower mean mass in the Class II phase (\overline{M}_d,CII=0.06 M_sun). In each evolution phase, time-averaged disk masses show a large scatter around the mean value. Our obtained mean disk masses are larger than those recently derived by Andrews & Williams and Brown et al., regardless of the physical mechanisms of mass transport in the disk.