Turbulence and dust fragility in protoplanetary discs

Abstract

Dust growth from micron- to planet-size in protoplanetary discs involves multiple physical processes, including dust collisions, the streaming instability, and pebble accretion. Disc turbulence and dust fragility matter at almost every stage. Previous studies typically vary one of them while fixing the other, failing to provide a complete picture. Here, we use analytical models and numerical dust evolution models DustPy to study the combinations of gas turbulence and dust fragility that can reproduce multi-wavelength ALMA observables. We find that only appropriate combinations -- fragile dust (fragmentation velocity $v_\mathrm{frag}$= 1-2 m/s) in discs with viscous $α=10^{-4}$ or resilient dust ($v_\mathrm{frag}$= 6-10 m/s) in discs with viscous $α=10^{-3}$ -- can reproduce observations. Our result is robust to two widely used opacities (DSHARP and Ricci opacities). Regardless of the strength of disc turbulence, reproducing observations requires observed dust rings to be optically thick at $λ=1.3$ and $3$ mm. As only small dust can be lifted above the midplane to reach the emitting layers, SED analysis probably yields lower limits on the maximum grain sizes. We highlight the challenge of creating detectable dust rings at large radii when incorporating bouncing in models, and the need for earlier formation of dust rings at smaller radii to reproduce the decreasing ring brightness with radius observed across ALMA wavelengths.

Figures (15)

• Figure 1: Correlations of disc turbulence and dust fragility for two most prominent dust rings of three MAPS samples (GM Aur, HD 163296 and MWC 480). Each ribbon represents a dust ring and is labelled with the disc name and the radius of the dust ring (R plus the radius in parentheses). The shaded regions arise from consideration of dust porosity, with is not consistently accounted for when deriving $a_\mathrm{max,frag}$2021ApJS..257...14S but included as demonstrated in Section \ref{['subsec:ana_method']}.
• Figure 2: Azimuthally averaged relative intensity profiles of HD 169142 (upper panel) and GM Aur (lower panel) at Bands 6 (blue) and 3/4 (orange). The shaded regions show the relative standard deviation. The coloured bars at the left corner show the beam size of observations encoded in the same colour. The profiles are obtained after deprojecting targets on the image plane by their position angles and inclination 2006AJ....131.2290R2020ApJ...891...48H. The upper panel is created with data from 2019ApJ...881..159M (Band 3) and data retrieved from the ALMA science archive (Band 6). The resolution and sensitivity are $0.^{\prime\prime}22\times 0.^{\prime\prime}10$ (PA$=-88^{\circ}$) and $17~\mu\mathrm{Jy~beam}^{-1}$ for the Band 3 observation, and $0.^{\prime\prime}19\times 0.^{\prime\prime}13$ (PA$=63^{\circ}$) and $108~\mu\mathrm{Jy~beam}^{-1}$ for the Band 6 observation. The lower panel is created based on data from 2020ApJ...891...48H. The resolution and sensitivity are $0.^{\prime\prime}057\times 0.^{\prime\prime}034$ (PA$=-13^{\circ}$) and $12~\mu\mathrm{Jy~beam}^{-1}$ for the Band 4 observation, and $0.^{\prime\prime}045\times 0.^{\prime\prime}025$ (PA$=2^{\circ}$) and $10~\mu\mathrm{Jy~beam}^{-1}$ for the Band 6 observation.
• Figure 3: Continuum images of GM Aur in ALMA Bands 6 ($\lambda=1.3$ mm, upper panels) and 4 ($\lambda=2.1$ mm, lower panels). The left columns are for sky-plane images adopted from 2020ApJ...891...48H, and the right columns are for corresponding deprojected images. Beam sizes are denoted as ellipses at the left corners in panels of the sky plane images. Resolution and sensitivity of these data are reported in the caption of Fig. \ref{['fig:brightness']}. We remind the readers that GM Aur is shown as a representative example of multiple-ringed discs seen in multi-wavelength observations, and reproducing the GM Aur disc is not the aim of this study.
• Figure 4: Overview of numerical models: blue indicates valid combinations that can fulfil the criteria in Section \ref{['subsec:setup']}; white indicates invalid models and grey indicates combinations that have not been tested due to extreme values of parameters.
• Figure 5: Valid numerical models (columns 1 and 4) and corresponding synthetic observations (columns 2-3 and 5-6). For each model, Bands 6 and 3 continuum synthetic observations are plotted at $t=1$ and $3~\mathrm{Myr}$. A representative beam size ($0.053$ arcsec $\times$ 0.045 arcsec, $15.^{\circ}28$) for the synthetic observations is indicated in the left lower corner of the panel in row 1, column 2. Synthetic images are plotted in the linear colour scale. The dotted lines plotted over the numerical models indicate the grain size $a=0.1~\mathrm{cm}$.