Not Just Gas: How Solid-Driven Torques Shaped the Migration of the Galilean Moons

TL;DR

The paper addresses the problem of rapid inward migration of forming Galilean moons in circumplanetary disks. It introduces self-consistent solid dynamics via two-fluid simulations with the code FARGO3D, exploring a range of dust-to-gas ratios $\epsilon$ and Stokes numbers $T_s$ for satellites with masses $M_s$ equal to proto-Moon, Europa, and Ganymede. It finds that solid torques can deviate dramatically from gas-only predictions, producing outward migration at high $T_s$ or high $\epsilon$, or accelerating inward migration in other regimes, with strong differential migration between bodies that can facilitate resonance capture. This solid-driven migration mechanism provides a natural way to mitigate the migration catastrophe and to explain the final architecture and resonant structure of the Galilean system, while highlighting the need to integrate time-evolving solid components into circumplanetary disk models. The results have broad implications for satellite system formation and potentially exomoon formation, emphasizing that detailed solid dynamics are essential for accurate migration histories.

Abstract

Surviving rapid inward orbital migration is a crucial aspect of formation models for the Jupiter's Galilean moons. The primary aim of this study is to investigate the orbital migration of the Galilean moons by incorporating self-consistent solid dynamics in circumjovian disk models. We perform two-fluid simulations using the FARGO3D code on a 2D polar grid. The simulations model a satellite with the mass of a proto-moon, Europa, or Ganymede interacting with a circumjovian disk. The dust component, coupled to the gas via a drag force, is characterized by the dust-to-gas mass ratio ($ε$) and the Stokes number ($T_s$). The effect of solids fundamentally alter the satellites' evolution. We identify a vast parameter space where migration is slowed, halted, robustly reversed -leading to outward migration-, or significantly accelerated inward. The migration rate is dependent on satellite mass, providing a natural source of differential migration. Solid dynamics provides a robust and self-consistent mechanism that fundamentally alters the migration of the Galilean moons, potentially addressing the long-standing migration catastrophe. This mechanism critically affects the survival of satellites and could offer a viable physical process to explain the establishment of resonances through differential migration. These findings establish that solid torques are a critical, non-negligible factor in shaping the final architecture of satellite systems.

Figures (3)

• Figure 1: Normalized time-averaged net torque for all the models considered in this work, as a function of initial dust-to-gas density ratio and Stokes number. From left to right, the mass of the satellite corresponds to $M_s=1.25\times 10^{-5} M_J$, $M_s=2.53\times 10^{-5} M_J$, and $M_s=7.82\times 10^{-5} M_J$, respectively. Blue color indicates a net positive torque (outward orbital migration). The normalization, $\Gamma^0_{\rm gas}$, corresponds to the net torque when $\epsilon=0$. From left to right, $\Gamma^0_{\rm gas} = -3.63 \Gamma_0$, $\Gamma^0_{\rm gas} = -3.33\Gamma_0$ and $\Gamma^0_{\rm gas} = -2.83 \Gamma_0$, with $\Gamma_0 = (M_s/M_J)^2 \Sigma_0 h^{-2} r^4_0 \Omega^2_0$.
• Figure 2: Top row: Dust surface density (color) with superimposed gas (cyan) and dust (white) velocity streamlines. Bottom row: Time evolution of the normalized torques exerted on the embedded moon. The solid black curve shows the net (gas + dust) torque, while the red and green curves correspond to the dust and gas contributions, respectively. The dashed green curve indicates the net gas torque in the corresponding dust-free reference simulation. Simulation corresponds to Proto-Moon with $\epsilon = 0.025$ and $T_s = 0.35$.
• Figure 3: Same as Figure \ref{['fig2']} but for Ganymede with $\epsilon = 0.05$ and $T_s = 0.35$.