Knowing the masses and sizes of protoplanetary disks is of fundamental importance for the contemporary theories of planet formation. However, their measurements are associated with large uncertainties. In this proof of concept study, we focus on the very early stages of disk evolution, concurrent with the formation of the protostellar seed, because it is then that the initial conditions for subsequent planet formation are likely established. Using three-dimensional hydrodynamic simulations of a protoplanetary disk followed by radiation transfer postprocessing, we constructed synthetic disk images at millimeter wavelengths. We then calculated the synthetic disk radii and masses using an algorithm that is often applied to observations of protoplanetary disks with ALMA, and compared the resulting values with the actual disk mass and size derived directly from hydrodynamic modeling. We paid specific attention to the effects of dust growth on the discrepancy between synthetic and intrinsic disk masses and radii. We find that the dust mass is likely underestimated in Band 6 by factors of 1.4–4.2 when Ossenkopf Henning opacities and typical dust temperatures are used, but the discrepancy reduces in Band 3, where the dust mass can be even overestimated. Dust growth affects both disk mass and size estimates via the dust-size-dependent opacity, and extremely low values of dust temperature ( ≈ several Kelvin) are required to recover the intrinsic dust mass when dust has grown to mm-sized grains and its opacity has increased. Dust mass estimates are weakly sensitive to the distance to the source, while disk radii may be seriously affected. We conclude that the accuracy of measuring the dust mass and disk radius during the formation of a protoplanetary disk also depends on the progress in dust growth. The same disk, but observed at different stages of dust growth and with different linear resolutions, can have apparent radii that differ from the intrinsic value by up to a factor of two. Multi-wavelength observations that can help to constrain the maximum dust size would be useful when inferring the disk masses and sizes.
Vorobyov et al. (Wed,) studied this question.