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

Abstract

A nascent planet in a gas disk experiences radial migration due to the different torques which act on it. 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. 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. We perform high-resolution local and global three-dimensional two-fluid simulations within the pressureless-fluid dust approximation using the Fargo3D code. We explore 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. The dust feedback has 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 $\leq10^{-2}$, the dust streaming torque is negligible and thus, the total torque on the planet comes from the gaseous component of the disk. 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 behaviour 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.