# Beyond static torques: Self-consistent migration and dynamical trapping of low-mass planets in dusty disks

**Authors:** Jose L. Gomez, Pablo Benitez-Llambay, Ximena S. Ramos, Octavio M. Guilera  
**arXiv:** [2610.27071](https://arxiv.org/abs/2610.27071)  
**Date:** 2026-10-19  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2610.27071v1/

## Key points

- Purpose: Test whether dust can halt or reverse low-mass planet migration through self-consistent feedback, without pre-existing disk structures.
- Methods: The authors ran 144 two-dimensional gas–dust simulations, varying six planetary and disk parameters and including turbulent dust diffusion and dust back-reaction on gas.
- Outcomes: Planets undergo monotonic inward migration, sustained or runaway outward migration, or bounded oscillatory confinement.
- Favorable conditions: Trapping generally favors dust-rich disks and particles with Stokes number 0.55; particles with Stokes number 0.10 rarely produce trapping or outward migration.
- Confinement: Planets approaching from opposite directions can settle into the same dynamically maintained zone; two representative 4-Earth-mass planets converge near 5.16 reference radii, approximately 15 astronomical units.
- Disk dependence: All trapping cases starting at the inner radius require higher gas surface density and a dust-to-gas ratio of 0.05; lower-density disks can support more distant traps, typically at 14–27 reference radii.
- Mechanism: A leading dust filament and trailing dust cavity drive outward torque. Rapid outward migration disrupts this asymmetry, allowing inward migration until the dust structure rebuilds and the cycle restarts.
- Dust feedback helps sustain confinement against turbulent diffusion, while 10-Earth-mass planets often develop unstable or runaway trajectories.
- Implication: Fixed-orbit torque prescriptions miss important migration feedback, and self-induced dust confinement could help planetary cores survive beyond the water-ice line.
- Limitations: Two-dimensional geometry, simplified thermodynamics, one fixed-Stokes-number dust population, and uncertain long-term stability require further testing with fully stratified three-dimensional simulations.

## Summary

This paper investigates whether dust can prevent the rapid inward migration of low-mass planets in protoplanetary disks when planetary motion is modeled self-consistently. Previous fixed-orbit calculations showed that asymmetric dust distributions can exert positive torques strong enough to counteract negative gas torques. A migrating planet, however, alters the surrounding dust distribution and thus the torque acting on it. The study examines whether this feedback leads to sustained outward migration, inward decay, or stable orbital confinement without pre-existing pressure bumps or other disk substructures. The authors perform 144 two-dimensional, two-fluid hydrodynamical simulations using FARGO3D, modeling gas as locally isothermal and dust as a pressureless fluid. The model includes turbulent dust diffusion and the back-reaction of dust drag on the gas. Six parameters are varied: initial orbital radius, planetary mass, Stokes number, dust-to-gas ratio, turbulent viscosity, and gas surface density. Planetary masses are 2.67, 4, and 10 Earth masses; Stokes numbers are 0.10, 0.26, and 0.55; dust-to-gas ratios are 0.01 and 0.05; and viscosity parameters are 0.0001 and 0.001. Planets begin at either one or ten reference radii. A radially comoving, corotating mesh follows each planet, preserving fine co-orbital structures while reducing numerical diffusion and computational cost. The grid comprises 1,024 radial and 2,048 azimuthal cells. Three broad outcomes emerge: monotonic inward migration, sustained or runaway outward migration, and bounded oscillatory confinement. Strong trapping generally favors dust-rich disks and moderately coupled particles, particularly those with a Stokes number of 0.55. At a Stokes number of 0.10, only seven of 48 simulations produce trapping or outward migration. Of the 72 simulations beginning at one reference radius, 46 show inward migration and 26 initially show outward migration; 11 of the latter become trapped. All trapping cases involving planets starting at the inner radius require the higher gas surface density and a dust-to-gas ratio of 0.05. A central finding is that planets approaching from opposite directions can converge on the same dynamically maintained confinement zone. In a representative configuration, 4-Earth-mass planets starting at one and ten reference radii both settle near 5.16 reference radii, with average eccentricities of approximately 0.004. Lower-density disks can support more distant traps, typically at 14–27 reference radii. For the adopted reference radius of 3 astronomical units, confinement zones near five and twenty reference radii correspond to approximately 15 and 60 astronomical units, respectively. The trapping mechanism relies on the repeated disruption and restoration of dust asymmetry. A dense leading filament and a depleted trailing cavity generate positive torque. During sufficiently rapid outward migration, the filament cannot replenish quickly enough, weakening the dust torque and allowing gas-driven inward migration. The dust asymmetry then rebuilds, restoring the outward torque and restarting the cycle. Dust feedback helps sustain this process against turbulent diffusion, even at the higher viscosity tested. More massive, 10-Earth-mass cores often develop unstable or runaway trajectories, although some remain trapped. The authors conclude that fixed-orbit torque prescriptions cannot capture the diversity of migration outcomes and that self-induced dust trapping could help planetary cores survive beyond the water-ice line. Important limitations include the two-dimensional geometry, simplified thermodynamics, a single dust population with a fixed Stokes number, and uncertain long-term stability. Some integrations end when eccentricity exceeds approximately 0.2 because the planet’s disturbances no longer fit reliably within the computational domain. Fully stratified three-dimensional simulations are needed to determine realistic trapping efficiencies and mass thresholds, while the proposed universality of the oscillatory behavior requires broader testing.