Dusty disks as safe havens for terrestrial planets: Effect of the back-reaction of solid material on gas

¹ Konkoly Observatory, HUN-REN, Research Centre for Astronomy and Earth Sciences, 1121 Budapest, Konkoly Thege Miklós út 15–17, Hungary
² CSFK, MTA Centre of Excellence, Konkoly Thege 15–17, 1121 Budapest, Hungary
³ ELTE Eötvös Loránd University, Institute of Physics and Astronomy, Department of Astronomy, 1117 Budapest, Pázmány Péter sétány 1/A, Hungary

^★ Corresponding author; regaly@konkoly.hu

Received: 29 October 2024
Accepted: 13 January 2025

Abstract

Context. Previous studies have shown that there is considerable variation in the dust-to-gas density ratio in the vicinity of low-mass planets undergoing growth. This can lead to a significant change in the planetary momentum exerted by the gas and solid material. However, due to the low dust-to-gas mass ratio of protoplanetary disks (about 1%), the effect of the solid material on the gas dynamics – that is, the back-reaction of the solid material – is often neglected.

Aims. We aim to study the effect of the back-reaction of solid material on the torques felt by low-mass planets. The effect of the back-reaction of solid material is investigated by comparing non-accreting and accreting models.

Methods. We performed locally isothermal, global two-dimensional hydrodynamic simulations of planet-disk interactions using the code GFARGO2. Low-mass planets in the range of 0.1–10 M_⊕ accrete only solid material. The solid component of the disk was treated as a pressureless fluid. Simulations were compared with taking and not taking into account the back-reaction of the solid material on the gas. The solid component was assumed to have a fixed Stokes number in the range of 0.01–10. All models assumed a canonical solid-to-gas mass ratio of 0.01.

Results. The back-reaction of the solid has been shown to have a significant effect on the total torque exerted on a low-mass planet. In general, the inclusion of the back-reaction results in a greater number of models with positive torque values compared to models that neglect the back-reaction. It is clear, therefore, that the simulation of planetary growth and migration via hydrodynamic modeling requires the inclusion of a solid-gas back-reaction. As a result of the back-reaction and accretion, a Mars-sized planetary embryo will experience positive total torques from the disk containing coupled solid components (St ≤ 0.01). Earth-mass planets also experience positive total torques from the disk containing boulder-sized solid components (2 ≤ St ≤ 5). The accretion of weakly coupled solid material tends to increase the positive torques and decrease the negative torques.

Conclusions. Our results suggest that the combined effect of back-reaction and accretion is beneficial to the formation of planetary systems by reducing the likelihood of a young planet being engulfed by the central star.