Beyond solar metallicity: How enhanced solid content in disks re-shape low-mass planet torques

TL;DR

This paper investigates how enhanced disk metallicity ($b5=0.03$ and $0.1$) reshapes the torques on a $1 M_igoplus$ planet by treating solids as a pressureless fluid fully coupled to gas via drag. Using global 2D hydrodynamic simulations with back-reaction, the authors show solid torques scale nearly linearly with $b5$, but gas torques can change by $50$--$100 ext{ extpercent}$ and even reverse sign for $ ext{St}\u2264 1$ at high metallicity due to feedback-driven gas perturbations in the co-orbital region, amplified by accretion. Accurate total torques are recovered only for $ ext{St}$, with linear metallicity rescalings failing for $ ext{St}$; thus, metallicity cannot be treated via simple rescalings in metal-rich disks. Overall, the results establish metallicity as a crucial parameter for early planetary architecture and demonstrate that fully coupled solid–gas dynamics are essential for predicting migration tracks of low-mass planets.

Abstract

The migration of low-mass planets is tightly controlled by the torques exerted by both gas and solids in their natal disks. While canonical models assume a solar solid-to-gas mass ratio (epsilon=0.01) and neglect the back-reaction of solid component of the disk, recent work suggests that enhanced metallicity can radically alter these torques. We quantify how elevated metallicities (epsilon=0.03 and epsilon=0.1) modify the gas and solid torques, test widely used linear scaling prescriptions, and identify the regimes where solid back-reaction becomes decisive. We performed global, 2D hydrodynamic simulations that treat solid material as a pressureless fluid fully coupled to the gas through drag and include the reciprocal back-reaction force. The planet was maintained on a fixed circular orbit, thus we computed static torques. The Stokes number was varied from 0.01 to 10, three surface-density slopes (p=0.5, 1.0, and 1.5) and three accretion efficiencies (eta=0, 10, and 100%) were explored. Torques, obtained by rescaling canonical epsilon=0.01 results, were compared with direct simulations. Solid torques scale linearly with epsilon, but gas torques deviate by 50-100% and can even reverse sign for St<=1 in epsilon=0.1 disks. These are due to strong, feedback-driven, asymmetric gas perturbations in the co-orbital region, amplified by rapid planetary accretion. 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.

Figures (7)

• Figure 1: Normalized torques felt by an$1~M_\oplus$ planet with metallicities of $\epsilon=0.01,~0.03,$ and $0.1$. Three accretion efficiencies were modeled: $\eta= 0,~0.1,$ and 1. The columns from left to right show three sets of models that assume different slopes for the initial disk density profile:$p = 0.5, 1.0,$ and 1.5. Symbols represent the different Stokes numbers, $\mathrm{St}=0.01,~0.1,~1,~2,~3,~4,~5,$ and 10. For the elevated metallicities, two models are shown: predicted (left) and numerical simulations (right). The shaded regions of positive (red), weakened negative (blue), and strengthened negative (green) torques darken with the metallicity. The normalization factor is the absolute value of the appropriate non-back-reacting gas torque. Panels A1, A2, and A3: Solid torques in the back-reacting models normalized by the absolute value of the solid torque non-back-reacting models with $\epsilon=0.01$. Panels B1, B2, and B3: Gas torques in the back-reacting models normalized by the absolute value of the gas torque in the non-back-reacting models with $\epsilon=0.01$. Panels C1, C2, and C3: Total torques in the back-reacting models normalized by the absolute value of the gas torque in the non-back-reacting models with $\epsilon=0.01$.
• Figure 2: Gas density distribution at the end of the simulation normalized with respect to the initial distribution around an Earth-mass planet for $\mathrm{St}=0.01$ in a high-metallicity disk with $\epsilon=0.1$. The three different initial disk density profiles with steepness values of $p = 0.5, 1.0,$ and 1.5, and the three different accretion efficiencies with values of $\eta=0\%, 10\%,$ and $100\%,$ are shown. The circles represent the planetary Hill sphere. The orbital motion of the planet is indicated.
• Figure 3: Final gas density distribution normalized by that in the canonical-metallicity model in the vicinity of an Earth-mass planet, assuming a solid species with $\mathrm{St} = 0.01$ in a disk with a metallicity of $0.03$ (top) and $0.1$ (bottom) and a density profile of $p = 0.5$.
• Figure 4: Difference in the azimuthally averaged radial gas torque profiles for species with $\mathrm{St} = 0.01$ in disks of varying metallicities. The different accretion efficiencies $\eta=0\%, 10\%$, and $100\%$ are shown in black, blue, and red, respectively.
• Figure 5: Gas density distribution at the end of the simulation normalized with respect to the initial distribution around an Earth-mass planet for $\mathrm{St}=1$ in disk assuming metallicities of $\epsilon=0.01,~0.03,$ and $0.1$ and $p=0.5$. The three different accretion efficiencies, $\eta=0\%, 10\%,$ and $100\%,$ are shown. The circles represent the planetary Hill sphere. The orbital motion of the planet is indicated.