  We test whether the radii of circumstellar disks can be reliably determined
in observations applying the results of a numerical simulation. Firstly, we
execute a core collapse simulation which starts from a rotating magnetized
spherical core, and continue the calculation until the protostellar mass
reaches 0.5 Msun. Then, for each set of simulation data, we calculate the
radiative transfer to generate the data cube for the synthetic observation. The
spatial and velocity resolutions of the synthetic observation are 0.15 arcsec
(20 au) and 0.1 km/s, respectively. We define seven different disk radii. Four
radii are estimated from the synthetic observation, using the continuum image,
continuum visibility, C18O channel map, and C18O position velocity (PV)
diagram. The other three radii are taken from the simulation and use the disk
rotation, infall motion, and density contrast around the protostar to identify
the disk. Finally, we compare the disk radii estimated from the systemic
observation with those from the simulation. We find that the disk radius
defined using the PV diagram can reliably trace the Keplerian disk when the
protostellar mass is larger than M_*>~ 0.2 Msun independent of the inclination
angle to the line of sight. In addition, the PV diagram provides an accurate
estimate of the central stellar mass through the whole protostellar evolution.
The simulation also indicates that the circumstellar disk is massive enough to
be gravitationally unstable through the evolution. Such an unstable disk can
show either a circular or spiral morphology on a similar timescale.
