On the accuracy of mass and size measurements of young protoplanetary disks

TL;DR

This paper quantifies how accurately the dust mass and disk radius of a very young protoplanetary disk can be recovered from millimeter-wavelength observations. By coupling 3D hydrodynamic simulations of cloud collapse (via ngFEOSAD) with RADMC-3D radiative transfer and ALMA-like postprocessing, the authors assess how dust growth, opacity choices, and observational configurations bias standard flux-based mass and size estimators. They find that, in Band 6, dust masses are typically underestimated by factors of 1.4–4.2 for common Td ranges and can be overestimated in Band 3; these biases depend strongly on the dust maximum size due to opacity and scattering, and no universal Td yields accurate masses when using size-dependent opacities. Disk radii are particularly susceptible to beam smearing and dust growth, with apparent sizes growing with distance and resolution, while Band 3 can offer improved mass fidelity but may still miss faint spiral structures at large distances. The results highlight the importance of multi-wavelength observations, careful treatment of dust growth and opacities, and consideration of beam effects when inferring the earliest disk properties relevant to planet formation.

Abstract

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. (Abridged)

Figures (16)

• Figure 1: Model disk in the midplane and across a vertical slice. Shown are from top to bottom and from left to right: gas volume density, grown dust volume density, maximum dust size, and temperature.
• Figure 2: Synthetic intensity distributions assuming different maximum size of the dust grains in the disk. From left to right: $a_{\rm max} = 10 \ \mu$m, $100 \ \mu$m, 1 mm, and spatially varying $a_{\rm max}$ distribution, directly taken from simulations. The envelope has $a_{\rm max} = 2 \ \mu$m in all models considered.
• Figure 3: Optical depth in models with different maximum dust sizes in the disk. From left to right are the cases with $a_{\rm max}=10$$\mu$m, $a_{\rm max}=100$$\mu$m, $a_{\rm max}=1.0$ mm, and actual model distribution. The maximum dust size in the envelope is 2.0 $\mu$m in each case.
• Figure 4: Synthetic intensities of the model disk at 1.3 mm obtained with RADMC-3D and postprocessed using the ALMA OST at Band 6. The three columns show, from left to right, the three assumed distances to the object: 140 pc, 350 pc, 700 pc. The rows from top to bottom are models with: $a_{\rm max}^{\rm disk} = 10 \ \mu$m, $100 \ \mu$m, $1$ mm, and actual maximal dust size in the disk. The black and red circles cover the regions of the disk where 90% and 97% of the total radiation flux is contained, defining the disk sizes according to the adopted criteria. In all cases, $a_{\rm max}$ in the cloud is 2.0 $\mu$m. The white circles in the top-right corner of each panel show the linear size of the beam.
• Figure 5: Radial profiles of the radiation intensity in CGS units after postropcessing with ALMA OST. The profiles are obtained by azimuthally averaging the corresponding spatial distributions shown in Fig. \ref{['fig:6alma']}. The vertical dashed and dotted lines indicate the radial positions within which 90% or 97% of the total flux is localizes, respectively. Panels from left to right correspond to different adopted distances to the source.