Simulations of multiple dust ring formation in a subsolar-metallicity protoplanetary disk

TL;DR

This work investigates dust-ring formation in protoplanetary disks with metallicity as low as 0.1 $Z_{ extodot}$ by performing long-term (750 kyr) 2D thin-disk simulations with self-consistent gas–dust dynamics using the FEOSAD code. Dust is tracked in two populations (small and grown) with size growth to a maximum $a_{ m max}$ via coagulation and fragmentation, and the backreaction of dust on gas is included; the disk forms self-consistently from collapsing cloud material. The main result is that an initially gravitationally unstable disk fragments into clumps and spirals, which later transition into axisymmetric gas substructures due to finite viscosity, creating local gas pressure bumps that trap dust and yield multiple rings within ≈300 au with separations of ≈10 au; these rings host mm–cm-sized dust with Stokes numbers ∼0.01–0.1 and conditions favorable for streaming-instability–driven planetesimal formation. The study highlights a viable pathway for planetesimal formation in metal-poor environments, contingent on having moderate turbulent viscosity (α ∼ 10^{-4}–10^{-3}) and suggests that feedback from photoevaporation and disk winds should be explored to assess ring lifetimes and observability.

Abstract

Super-Earths exist around subsolar-metallicity host stars with a frequency comparable to that around solar-metallicity stars, suggesting efficient assembly of dust grains even in metal-deficient environments. In this study, we propose a pathway for the formation of multiple dust rings that will promote planetesimal formation in a subsolar-metallicity disk. We investigate the long-term evolution of a circumstellar disk with 0.1 $Z_{\odot}$ over 750 kyr from its formation stage using two-dimensional thin-disk hydrodynamic simulations. The motion of dust grains is solved separately from the gas, incorporating dust growth and self-consistent radial drift. The disk is initially gravitationally unstable and undergoes intense fragmentation. By 300 kyr, it tends toward a stable state, leaving a single gravitationally bound clump. This clump generates tightly wound spiral arms through its orbital motion. After the clump dissipates at $\sim$410 kyr, the spiral arms transition into axisymmetric substructures under the influence of viscosity. These axisymmetric substructures create local gas pressure bumps that halt the inward radial drift of dust grains, resulting in the formation of multiple-ring-shaped dust distributions. We observe several rings within $\simeq$200 au of the central star, with separations between them on the order of $\sim$10 au, and dust surface density contrasts with inter-ring gaps by factors of $\sim$10-100. We also demonstrate that turbulent viscosities at observationally suggested levels are essential for converting spiral arms into axisymmetric substructures. We speculate that the physical conditions in the dust rings may be conducive to the development of streaming instability and planetesimal formation.

Figures (11)

• Figure 1: Disk evolution during the first 300 kyr (early phase). The top, middle, and bottom rows show the 2D distributions of the surface density of gas, that of dust, and the maximum dust size at three different epochs, 20, 130, and 300 kyr after the disk formation. The dust density is the sum of grown and small dust densities. In each panel, the white contour line delineates an isosurface density of 0.3 g cm$^{-2}$, indicating the approximate location of the outer edge of the disk.
• Figure 2: Radial profiles of disk structure and dust properties in the early phase. Each row shows the radial profiles of the surface densities (top), the maximum dust size (middle) and the Stokes number (bottom) at the same epochs as in Figure \ref{['Fig:2D_EarlyPhase']}. The lines provide the azimuthally averaged values, and the shaded layers show the ranges of variation of these values at a given radius, with the upper and lower boundaries corresponding to the maximum and minimum values. In the top panels, the lines and colors indicate different components: gas (orange solid), grown dust (green dashed), and small dust (blue dotted). For clarity, the shaded layers are shown only for the gas and grown dust components. The densities of the grown and small dust components are multiplied by 1000 to make comparisons easier. In the middle panels, the lines depict the maximum dust size (red solid line) and the fragmentation barrier (black dashed line).
• Figure 3: Evolution of the gas mass distribution up to the end of the fiducial run. The lines represent three different components, the envelope (solid), the central star (dashed), and the disk (dotted).
• Figure 4: Multiple dust ring formation in the late phase. Each column displays the spatial distributions of the surface densities of dust (upper) and gas (lower) at four different periods, 410, 460, 510, and 750 kyr from left to right.
• Figure 5: Radial distributions of (a) the dust and gas surface densities, (b) the vertically integrated gas pressure, and (c) its radial gradient at 510 kyr. The lines show the azimuthally averaged values, and the shaded regions represent the range between the maximum and minimum values. In Panel (a), the colors depict different components: dust (green) and gas (orange). The dust density is multiplied by 1000 to facilitate easier comparison. In Panel (c), the red solid line depicts negative gradients, and the blue dashed line indicates positive gradients. The dash-dotted vertical lines mark the positions of two examples of dust density peaks, at 50 au (black) and 120 au (gray), among several observed. In Panel (a), the blue dotted line represents the fitting function for the gas density, given by $80\left( r/20\:{\rm au} \right)^{-1.7}$ g cm$^{-2}$, which is used in Section \ref{['Sec:NumericalExperiments']}.