The Disk Substructures at High Angular Resolution Project (DSHARP). V. Interpreting ALMA Maps of Protoplanetary Disks in Terms of a Dust Model

Abstract

The Disk Substructures at High Angular Resolution Project (DSHARP) is the largest homogeneous high-resolution (∼0. 035, or ∼ 5 au) disk continuum imaging survey with ALMA so far. In the coming years, many more disks will be mapped with ALMA at similar resolution. Interpreting the results in terms of the properties and quantities of the emitting dusty material is, however, a very non-trivial task. This is in part due to the uncertainty in the dust opacities, an uncertainty which is not likely to be resolved any time soon. It is also partly due to the fact that, as the DSHARP survey has shown, these disk often contain regions of intermediate to high optical depth, even at millimeter wavelengths and at relatively large radius in the disk. This makes the interpretation challenging, in particular if the grains are large and have a large albedo. On the other hand, the highly structured features seen in the DSHARP survey, of which strong indications were already seen in earlier observations, provide a unique opportunity to study the dust growth and dynamics. To provide continuity within the DSHARP project, its follow-up projects, and projects by other teams interested in these data, we present here the methods and opacity choices used within the DSHARP collaboration to link the measured intensity I ν to dust surface density Σ d .

A Multifrequency ALMA Characterization of Substructures in the GM Aur Protoplanetary Disk

“…Of course, as illustrated in Birnstiel et al (2018), different assumptions about the dust grain composition and structure will affect how multi-wavelength intensities are translated to grain sizes. For example, unlike the compact DSHARP grains, the β curves of highly porous grains are nearly flat as a function of a max (e.g., Kataoka et al 2014).…”

“…A comparison of the dust absorption opacity index β between 1.1 and 2.1 mm to the β nominal values derived for GM Aur. The β curves are computed as a function of amax and p using the "DSHARP dust opacities" fromBirnstiel et al (2018). From top to bottom, the dark gray horizontal lines show the β values from the best-fit GM Aur model at D67, D145, and B168, respectively.…”

Effects of Scattering, Temperature Gradients, and Settling on the Derived Dust Properties of Observed Protoplanetary Disks

“…Other authors have also studied the inclusion of the scattering effects in the radiative transfer. For example, Birnstiel et al (2018) found an analytic solution for vertically isothermal slabs with the Eddington-Barbier approximation. Using their solution, Liu (2019) found spectral indices below of 2, consistent with the results discussed in this section.…”

“…This solution was used by D' Alessio et al (2001) to obtain the source function S ν and integrate the radiative transfer equation in models of accretion disks around T Tauri stars. Recently, the Miyake solution was included in radiative transfer models of the complex substructures observed in dust continuum images with high angular resolution of disks from the DSHARP project (Birnstiel et al 2018). Liu (2019) also used the Miyake solution together with Monte Carlo simulations to explain the anomalous spectral indices reported in some optically thick protoplanetary disks.…”

Hints on the origins of particle traps in protoplanetary disks given by the Mdust – M⋆ relation

“…Information obtained about the dusty material in disks from observations is, however, prone to uncertainties as well since it is based on several assumptions, such as the disk temperature (which is typically assumed to be 20 K but could vary depending on disk size; Hendler et al 2017), and the dust opacity. The dust opacity is the major source of uncertainty because it depends on the grain size and composition, which are unknown in protoplanetary disks (e.g., Birnstiel et al 2018). Nevertheless, when comparing millimeter-observations of protoplanetary disks with models of disk evolution, the same assumptions can be taken in order to facilitate the comparison and understand the effect of different crucial physical processes in the formation of planets, such as grain growth and drift.…”