Beyond solar metallicity

How enhanced solid content in disks reshapes low-mass planet torques

¹ HUN-REN CSFK Konkoly Observatory, MTA Centre of Excellence, Konkoly Thege M. út 15-17, Budapest 1121 Hungary
² ELTE Eötvös Loránd University, Institute of Physics and Astronomy, Department of Astronomy, 1117 Budapest, Pázmány Péter sétány 1/A Hungary

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 2 August 2025
Accepted: 27 January 2026

Abstract

Context. The migration of low-mass planets (M_p ≤ 10 M_⊕) is tightly controlled by the torques exerted by both the gas and solids in their natal disks. While canonical models assume a solar solid-to-gas mass ratio (ε ≃ 0.01) and neglect the back-reaction of the solid component of the disk, recent work suggests that enhanced metallicity can radically alter these torques.

Aims. We quantify how elevated metallicities (ε = 0.03 and ε = 0.1) modify the gas and solid torques acting on an Earth-mass planet, test widely used linear scaling prescriptions, and identify the regimes where solid back-reaction becomes decisive.

Methods. We performed global, two-dimensional hydrodynamic simulations that (i) treat solid material as a pressureless fluid fully coupled to the gas through drag and (ii) include the reciprocal back-reaction force. The low-mass planet was maintained on a fixed circular orbit, and thus we computed static torques. The Stokes number was varied from 0.01 to 10, and three surface-density slopes (p = 0.5, 1.0, and 1.5) and three accretion efficiencies (η = 0, 10, and 100%) were explored. Predicted torques, obtained by rescaling canonical ε = 0.01 results, were compared with direct simulations.

Results. Solid torques scale nearly linearly with ε, but gas torques deviate by 50–100% and can even reverse sign for St ≤ 1 in ε = 0.1 disks. These discrepancies arise from strong, feedback-driven, asymmetric gas perturbations in the co-orbital region, which are amplified by rapid planetary accretion. Accurate total torques are recovered only for St ≥ 3, independent of ε or η; for St ≤ 2 the linear prescription systematically overestimates the magnitude, sometimes predicting the wrong sign.

Conclusions. Solid back-reaction in high-metallicity environments can dominate the migration torque budget of low-mass planets. Simple metallicity rescalings are therefore unreliable for St ≤ 2, implying that precise migration tracks - particularly in metal-rich disks - require simulations that fully couple solid and gas dynamics. These results highlight metallicity as a key parameter in shaping the early orbital architecture of planetary systems.