On the 3D time evolution of the dust size distribution in protostellar envelopes

TL;DR

This work tackles the problem of following the 3D time evolution of the dust size distribution during protostellar collapse by coupling a full dust coagulation solver (Smoluchowski equation) with a non-ideal MHD framework (RAMSES). The authors integrate the COALA dust-growth module into RAMSES, enabling polydisperse dust growth across $s_{ m min}=5~\mathrm{nm}$ to $s_{ m max}=1~\mathrm{cm}$ with $N=40$ bins and simultaneous dust dynamics in the terminal velocity regime. They perform the first 3D simulations that self-consistently account for dust growth and gas/dust dynamics in protostellar envelopes and disks, finding rapid growth to micron sizes in envelopes and larger grains in disk regions, with strong anisotropy driven by turbulence and outflow structures and measurable dust-to-gas enrichment. The method increases computational cost by about a factor of $1.7$ compared to gas-only runs, offering a scalable route to study dust evolution in diverse astrophysical environments and informing how early grain growth impacts disk formation, chemistry, and magnetic coupling; fragmentation and more kernels remain as important future extensions.

Abstract

Dust plays a fundamental role during protostellar collapse, disk and planet formation. Recent observations suggest that efficient dust growth may begin early, in the protostellar envelopes, potentially even before the formation of the disk. Three-dimensional models of protostellar evolution, addressing multi-size dust growth, gas and dust dynamics and magnetohydrodynamics, are required to characterize the dust evolution in the embedded stages of star formation. We aim to establish a new framework for dust evolution models, following in 3D the dust size distribution both in time and space, in MHD models describing the formation and evolution of star-disk systems, at low numerical cost. We present our work coupling the COALA dust evolution module into the code RAMSES, performing the first 3D MHD simulation of protostellar collapse including simultaneously polydisperse dust growth modeled by the Smoluchowski equation as well as dust dynamics in the terminal velocity approximation. Ice-coated micron-sized grains can rapidly grow in the envelope and survive by not entering the fragmentation regime. The evolution of the dust size distribution is highly anisotropic due to the turbulent nature of the collapse and the development of favorable locations such as outflow cavity walls, which enhance locally the dust-to-gas ratio. We analyzed the first 3D non-ideal MHD simulations that self-consistently account for the dust dynamics and growth during the protostellar stage. Very early in the lifetime of a young embedded protostar, micron-sized grains can grow, and locally the dust size distribution deviates significantly from the MRN initial shape. This new numerical method opens the perspective to treat simultaneously gas/dust dynamics and dust growth in 3D simulations at a low numerical cost for several astrophysical environments.

Figures (9)

• Figure 1: Snapshots taken from the RAMSES MHD models ($\mathcal{M}_0$ and $\mathcal{M}_1$) of a collapsing protostellar envelope (initial parameters can be found in the text) with dust grain size evolution computed by COALA. The maps show a 2000-au zoom-in of the model when the central star has accreted 0.4$M_\odot$ from the initial 2.5$M_\odot$ core. The red cross represents the position of the star. The left column shows the total column gas density $\Sigma$. The middle column shows the average grain size at the peak of the size distribution $a_{\mathrm{peak}}$, weighted by the gas density along the line of sight (see text for further details). Similarly, the right column shows the average dust enrichment (ratio between the evolved dust-to-gas ratio $\epsilon$ and the initial dust-to-gas ratio $\epsilon_0$) weighted by the gas density along the line of sight. On the top row, the square patterns near the sink are not numerical artifacts but result from the weighted average of the quantities along the line of sight.
• Figure 2: Snapshots and histograms of the dust enrichment at two given times of the model $\mathcal{M}_1$ with (top row) and without (bottom row) dust growth. The histograms are obtained with the dust enrichment calculated in each cell in a box of side 2000 au around the star. The two times are chosen when $M_{\bigstar}=0.06\, M_{\odot}$ (orange) and $M_{\bigstar}=0.4\, M_{\odot}$. Dust growth and dynamics enhance larger local variations of the dust enrichment, greater than 2 in the envelope compared to the dust dynamics alone. The black line shows the histograms for the $\mathcal{M}_1$ model with dust growth and 60 dust bins, highlighting the numerical convergence reached with 40 bins simulations. The red cross represents the position of the star. The variance value $\sim 0.01$ of the histogram explains the low variation observed on the map for the model $\mathcal{M}_1$ when $M_{\bigstar}=0.4\, M_{\odot}$.
• Figure 3: Comparison of the computational time between three simulations for the model $\mathcal{M}_0$: gas only (black), gas with 40 dust sizes (blue), gas with 40 dust sizes and dust growth (orange). Using COALA in RAMSES only increases the global execution time by a factor $1.7$.
• Figure 4: Radial profiles of the dust grain size at the peak of the size distribution $a_{\rm{peak}}$ (see text for further details), and the grain-grain differential velocity of grains with size $a_{\rm{peak}}$ from turbulence model (see Sect. \ref{['sec:dust_dv_turb']}), noted $\delta \mathrm{v}_{a_{\mathrm{peak}}}$ , for the two snapshots shown in Fig.\ref{['fig:maps']}, models $\mathcal{M}_0$ and $\mathcal{M}_1$ at $t_{0.4 M_{\odot}}$. The radial profiles shown in the left panels are built by computing the mean $a_{\rm{peak}}$ in concentric shells from the $a_{\rm{peak}}$ map (for further details, see Fig. \ref{['fig:shells']} and text), they show a clear increase of the mean dust grains size with decreasing envelope radius, up to sizes $\sim 10$$\mu$m. The power-law in model $\mathcal{M}_1$ is higher than for model $\mathcal{M}_0$. This shows that the grain grow faster in model $\mathcal{M}_1$, since the gas turbulence tends to slow down the collapse letting more time for grains to grow. The right panels show the dust grain populations (colored by $a_{\rm{peak}}$ ) at all envelope radii, and plotted against the $\delta \mathrm{v}_{a_{\mathrm{peak}}}$ they experience at this envelope location (in individual cells in the model). A grey vertical line represents the 100 au radius, approximating the ice-line expected in such solar-type protostars. On each side of this line, orange and blue shaded areas represent the locations where the dust grains are expected to fragment (see text for further details).
• Figure 5: Time evolution of the fraction of the total dust mass in the envelope represented by each grain size bin. Initially the grains from 0.19 to 0.27 µm represent $\sim 20\%$ of the total dust mass. After 100 kyrs, these grains account for $\sim 13\%$ of the total dust mass. A part of the mass is represented by larger grains, such as the grains with size $\sim 3-5$µm which represent steady-state value of $\sim 1\%$ of the total dust mass (white lines).