Dust back reaction on gas around planets modifies the cold thermal torque

¹ Charles University, Faculty of Mathematics and Physics, Astronomical Institute, V Holešovičkách 747/2, 180 00 Prague 8, Czech Republic
² Instituto de Astronomía, Universidad Nacional Autónoma de México, Apt. Postal 70-264, C.P. 04510, Mexico City, Mexico
³ Instituto de Astronomía, Universidad Nacional Autónoma de México, Ensenada, B.C. 22800, Mexico
⁴ IRAP, Université de Toulouse, CNRS, UPS, 31400 Toulouse, France
⁵ Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, Göttingen 37077, Germany
⁶ Division of Space Research & Planetary Sciences, Physics Institute, University of Bern, Sidlerstr. 5, 3012 Bern, Switzerland
⁷ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁸ Fakultät für Physik, Universität Duisburg-Essen, Lotharstraße 1, 47057 Duisburg, Germany
⁹ Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA

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

Received: 12 November 2024
Accepted: 3 November 2025

Abstract

Context. A nascent planet in a gas disk experiences radial migration due to the different torques that act on it (e.g., Lindblad and corotation torques). It has recently been shown that the torques produced by the gas and dust density variations around a non-accreting low-mass planet, the so-called cold thermal and dust streaming torques, can surpass each of the other torque components.

Aims. We investigate how the total torque acting on the planet is affected by the presence of dust grains and their aerodynamic back reaction on gas, while taking into account the cold thermal torque produced by thermal diffusion in the gas component.

Methods. We performed high-resolution local and global three-dimensional two-fluid simulations within the pressureless-fluid dust approximation using the Fargo3D code. We explored the influence of different dust species parameterized by the Stokes number, focusing on non-accreting protoplanets with masses from one-third the mass of Mars to one Earth mass.

Results. The dust feedback has a substantial impact on the asymmetry of the cold thermal lobes (which produce the cold thermal torque). However, the total torque is dominated by the dust torque when St > 10⁻². The dust torque becomes more negative over time due to the formation of dust lobes that resemble the cold thermal lobes that form in the gas component. Therefore, the dust streaming torque prevails over the cold thermal torque. On the other hand, when St = 10⁻², the dust streaming torque is negligible and thus, the total torque on the planet comes from the gaseous component of the disk.

Conclusions. Our results suggest that a planet embedded in a gas-dust disk may experience stagnant migration or inward runaway migration in regions of the protoplanetary disk where the dust is not fully coupled to the gas. However, this behavior could change in regions with strong dust-gas coupling or in the inner transition region of the disk, where the cold thermal torque may become relevant.