Dust distribution in circumstellar disks harboring multi-planet systems. I. Sub-thermal mass planets

TL;DR

This study analyzes how embedded sub-thermal mass planets sculpt dust distributions in circumstellar disks, using 2D hydrodynamic simulations with dust treated as Lagrangian particles across a multi-size distribution. By varying disk properties and planetary architectures, the authors identify two dominant gap-opening channels: gas outflows that deplete tightly coupled dust ($St \lesssim 10^{-2}$) and tidal torques that carve gaps for weakly coupled dust ($St \gtrsim 1$), with intermediate coupling showing limited gap formation. Multi-planet systems produce dust substructures that cannot be inferred from single-planet models, including inner cavities, common gaps, and gaps overlapping Lindblad resonances, and the outcome is strongly modulated by disk viscosity (e.g., $\alpha=10^{-4}$) and thermodynamics. The results have direct implications for interpreting ALMA disk observations, indicating that dust gaps do not uniquely reveal planetary masses or gas pressure bumps and that disk conditions and dust size distributions must be accounted for when linking substructures to planet formation. The work lays a baseline for future studies including dust evolution, 3D structure, and radiative effects to more accurately connect observed dust rings and gaps to the underlying planetary architectures.

Abstract

We investigate the formation of dust gaps in circumstellar disks driven by the presence of multiple low-mass planets, focusing on the distinct physical mechanisms that operate across different gas-dust coupling regimes. We performed 2D hydrodynamical simulations of multiple planets embedded in a circumstellar disk using the PLUTO code, with the addition of dust treated as Lagrangian particles with a multi-size distribution. We carried out a large parameter space analysis to check the influence of disk and planetary properties on the dust component. Planets with $m \gtrsim 1 \, M_{\oplus}$ can open dust gaps for small grains in dense and warm disks (strong coupling) and for large grains in thin and cold disks (weak coupling), without significantly perturbing the gas. In the strong coupling regime, rapid Type I migration can shift the gap location inward or outward with respect to the planetary orbit, depending on the direction of migration. We also find dust gaps that overlap with Lindblad resonances. In the weak coupling regime, planets can create an inner dust cavity, multiple dust rings, or hide inside a common gap. Our results show how low-mass multi-planet systems perturb the dust distribution, which cannot be explained by considering each planet in isolation and has a crucial dependence on local disk conditions and dust grain sizes.

Figures (18)

• Figure 1: Schematic representation of the proposed dominant gap opening mechanism for a sub-thermal mass planet, as a function of planetary mass and Stokes number of the dust particles. Black dots (crosses) indicate the dust sizes considered in our models for which we found (no) dust gaps.
• Figure 2: Dust distribution in Model 1. From left to right, the dust particle distributions in the $(r, \phi)$ plane for 200 $\mu$m, 1.6 mm, and 2.6 cm dust sizes in Model 1, respectively. The black lines show radial density distribution of the gas normalized between (0, 2$\pi$), while the filled green circles mark the position of the planets. The plots are zoomed in the inner region (0.5,6) au and the width of the density profile is multiplied by a constant for readability.
• Figure 3: Histogram illustrating the number density of dust particles in Model 1 as a function of radial distance from the star. The number density is computed in 100 radial bins with logarithmic spacing. Filled green circles mark the positions of the planets. The black line represents 200-micron particles, while the red and blue lines represent 1.6-mm and 2.6-cm grains, respectively.
• Figure 4: Dust distribution in Model 2. From left to right, the dust particle distributions in the $(r, \phi)$ plane for 200 $\mu$m, 3.2 mm, and 1.3 cm dust sizes in Model 2, respectively. The black lines show radial density distribution of the gas normalized between (0, 2$\pi$), while the filled green circles mark the position of the planets. The plots are zoomed in the inner region (0.5,5) au and the width of the density profile is multiplied by a constant for readability.
• Figure 5: Same as Fig. \ref{['model1_hist']}, but for Model 2. The black line represents 200-micron particles, while the red and blue lines represent 3.2-mm and 1.3-cm grains, respectively.