Callisto's Nonresonant Orbit as an Outcome of Circum-Jovian Disk Substructure

TL;DR

The study addresses why Callisto avoids the Laplace resonance by proposing a pressure bump in the circum-Jovian disk that acts as a migration trap. Using N-body simulations with self-consistent satellite-disk interactions, it shows Io, Europa, and Ganymede are sequentially captured at the bump and then migrate across it in lockstep, while Callisto remains trapped interior to the bump. This yields a 4:2:1 Laplace resonance among Io, Europa, and Ganymede with Callisto nonresonant, without requiring Callisto to accrete late. The bump parameter space contains a Goldilocks zone (Δh/w ≈ 0.45–0.6) within which the architecture emerges; outside this range, the system trends toward alternative resonances or instability. The results relieve timing constraints on Callisto’s accretion and link the scenario to ice-line and disk-substructure physics, with implications for Callisto’s interior structure that future missions like JUICE will probe.

Abstract

The Galilean moons of Io, Europa, and Ganymede exhibit a 4:2:1 commensurability in their mean motions, a configuration known as the Laplace resonance. The prevailing view for the origin of this three-body resonance involves the convergent migration of the moons, resulting from gas-driven torques in the circum-Jovian disk wherein they accreted. To account for Callisto's exclusion from the resonant chain, a late and/or slow accretion of the fourth and outermost Galilean moon is typically invoked, stalling its migration. Here, we consider an alternative scenario in which Callisto's nonresonant orbit is a consequence of disk substructure. Using a suite of N-body simulations that self-consistently account for satellite-disk interactions, we show that a pressure bump can function as a migration trap, isolating Callisto and alleviating constraints on its timing of accretion. Our simulations position the bump interior to the birthplaces of all four moons. In exploring the impact of bump structure on simulation outcomes, we find that it cannot be too sharp nor flat to yield the observed orbital architecture. In particular, a "Goldilocks" zone is mapped in parameter space, corresponding to a well-defined range in bump aspect ratio. Within this range, Io, Europa, and Ganymede are sequentially trapped at the bump, and ushered across it through resonant lockstep migration with their neighboring, exterior moon. The implications of our work are discussed in the context of uncertainties regarding Callisto's interior structure, arising from the possibility of non-hydrostatic contributions to its shape and gravity field, unresolved by the Galileo spacecraft.

Figures (8)

• Figure 1: Schematic of the circum-Jovian decretion disk. Gas and dust from the circumsolar accretion disk are subsumed into the Jovian disk from approximately one hydrostatic scale height via meridional flows, and move outward beyond the magnetospheric truncation radius. Decretion $\dot{M}$ is driven by turbulence manifesting as a macroscopic viscosity, and parametrized by the Shakura-Sunyaev $\alpha$ parameter. The four Galilean moons are envisioned to form beyond the ice-line and pressure bump, and undergo Type-I migration inwards. The bump serves as a migration trap, preventing Callisto from convergent migration into resonance with Io, Europa, and Ganymede.
• Figure 2: Simulation results for $R_{stop} = 0.03 R_{Hill} > R_T = 5 R_J$ and $r_0 = 0.18 R_{Hill}$, assuming fiducial $R_{\alpha} = 2.5$ and $w=1.25 h_0$. Panels indicate the (a) semi-major axes and (b) eccentricities of the moons, (c) their outer-inner period ratios, and (d) resonant arguments between Io, Europa, and Ganymede. Key resonant captures are denoted by vertical lines. See Section 4.1 for discussion.
• Figure 3: Final simulation outcomes from exploration of $R_{\alpha}-w$ parameter space. Three main regimes are discerned: (i; red) for thin and tall disks to the top left, the bump is too "stiff" a trap, ultimately leading to a dynamical instability; (ii; yellow) for short and wide disks to the bottom right, the bump fails to trap the moons, leading to the formation of a 6:3:2:1 resonant chain; (iii; green) between (i) and (ii) lies a "goldilocks" zone wherein the bump can both function as a trap, and allow the moons to be "pushed" across it by migration in lockstep following resonant capture. This zone corresponds roughly to bump aspect ratios $\Delta h$ between 0.45 and 0.6. Along its former boundary are simulations wherein alternatives to the resonant chain in (ii) are realized (light green: 8:4:2:1; and white: e.g., 12:6:3:2). The green star corresponds to the fiducial case discussed in Section 4.1. See Section 4.2 for discussion.
• Figure 4: Figure 4. Simulation results for $R_{stop} = R_T = 5R_J$ and $r_0$ just beyond (i.e., 1.25 times) the ice-line ($r_0\sim 0.04 R_{Hill}$), with $R_{\alpha} = 2$ and $w = h_0$. Panels indicate the (a) semi-major axes of the moons and (b) their outer-inner period ratios. Key resonant captures are denoted by vertical lines. See Section 4.3 for discussion.
• Figure 5: ; S1. Simulation results for $R_{stop}= 0.03 R_{Hill}$ and $r_0 = 0.18 R_{Hill}$ , with $R_{\alpha} = 2.5$ and $w = 2h_0$. Panels indicate the (a) semi-major axes of the moons and (b) their outer-inner period ratios. Key resonant captures are denoted by vertical lines. Here, the bump is too "flat" (i.e., short/wide; $\Delta h/w \lesssim 0.45$) to function as a migration trap. As such, all four moons individually make it past the bump, establishing a 6:3:2:1 resonance interior to it. See Section 4.2 for discussion, and Fig. 3 for all $R_{\alpha}-w$ pairs explored that correspond to this final outcome.