Dust-void evolution driven by turbulent dust flux can induce runaway migration of Earth-mass planets

¹ Charles University, Faculty of Mathematics and Physics, Astronomical Institute. V Holešovičkách 747/2, 180 00 Prague 8, Czech Republic
² Instituto de Ciencias Físicas, Universidad Nacional Autonoma de México. Av. Universidad s/n, 62210 Cuernavaca, Mor., Mexico
³ Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
⁴ Department of Space Studies, Southwest Research Institute, 1050 Walnut St., Suite 300, Boulder, CO 80302, USA

^★ Corresponding author: raul@sirrah.troja.mff.cuni.cz

Received: 12 August 2024
Accepted: 27 March 2025

Abstract

Torques from asymmetric dust structures (so-called dust-void and filamentary structures) formed around low-mass planets embedded in a nonturbulent dust-gas disk can exceed the torques produced by the gas disk component and then go on to dominate the planet’s orbital dynamics. Here, we investigate how these structures (hence the dust torque) change when the effect of turbulent dust diffusion and dust feedback are included, along with the direct implications on the migration of Earth-like planets. Using the FARGO3D code, we performed 2D and 3D multifluid hydrodynamic simulations, focusing on a non-migrating planet with a mass of M_p = 1.5 M_⊕ in 2D and on migrating planets with M_p ∈ [1.5, 12] M_⊕ in 3D. We varied the δ-dimensionless diffusivity parameter in the range [0, 3 × 10⁻³] and considered three different Stokes numbers, St = {0.04, 0.26, 0.55}, which are representative of the gas-dominated, the transitional, and the gravity-dominated regimes, respectively. In our 2D models, we find that turbulent diffusion of dust prevents the formation of the dust-void and filamentary structures when δ > 3 × 10⁻⁴. Otherwise, dust structures survive turbulent diffusion flow. However, dust and total torques become positive only in transitional and gravity-dominated regimes. In our 3D models, we find that the dust-void is drastically modified and the high-density ring-shaped barrier delineating the dust-void disappears if δ ≳ 10⁻⁴, due to the effect of dust turbulent diffusion along with the back-reaction of the dust. For all values of δ, the filament in front of the planet is replaced by a low-density trench. Remarkably, as we have allowed the planets to migrate, the evolving dust-void can drive either runaway migration or outward (inward) oscillatory-torque migration. Our study thus suggests that low-mass Earth-like planets can undergo runaway migration in dusty disks.