2020ApJ...905..174A

We test whether the radii of circumstellar disks can be reliably determined in observations by applying the results of a numerical simulation. First, 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 M_☉. 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 (20 au) and 0.1 km s^–1, 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 M_☉, 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.