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 ( \langle M _ { d } \rangle ) 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 _ { \odot } , respectively .
Viscous disks have similar mean masses ( \overline { M } _ { d } = 0.10 - 0.11 ~ { } M _ { \odot } ) 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 _ { \odot } ) .
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 .
The difference is especially large for Class II disks , for which we find \overline { M } _ { d,CII } = 0.06 - 0.12 ~ { } M _ { \odot } but Andrews and Williams report median masses of order 3 \times 10 ^ { -3 } ~ { } M _ { \odot } .
When Class 0/I/II systems are considered altogether , a least-squares best fit yields the following relation between the time-averaged disk and stellar masses , \langle M _ { d } \rangle = \left ( 0.2 \pm 0.05 \right ) \langle M _ { \ast } \rangle ^ { 1.3 % \pm 0.15 } .
The dependence of \langle M _ { d } \rangle on \langle M _ { \ast } \rangle becomes progressively steeper along the sequence of stellar evolution phases , with exponents 0.7 \pm 0.2 , 1.3 \pm 0.15 , and 2.2 \pm 0.2 for Class 0 , Class I , and Class II systems , respectively .