Formation of the Galilean Moons

Title: Building the Galilean moons system via pebble accretion and migration: A primordial resonant chain

Authors: Gustavo Madeira, André Izidoro, Silvia M. Giuliatti Winter

First Author’s Institution: Grupo de Dinâmica Orbital & Planetologia, The University of São Paulo State, Guaratinguetá, Brazil

Status: Accepted to MNRAS (open access on arXiv)

In 1610, the Italian polymath Galileo Galilei published Sidereus Nuncius (Sidereal Messenger), within which he observed what appeared to be four stars waving back and forth around Jupiter. The implications of this profound observation – in direct contravention to the theologically correct view at the time – ushered in a new era of astronomy. These four stars are, of course, four moons of Jupiter: Io, Europa, Ganymede and Callisto, and are collectively named in Galileo’s honour. All these moons, with the exception of Callisto, form a chain of orbital resonances. Io, for instance, completes two orbits for every single orbit of Europa (a ratio of 2:1), and four orbits for every single orbit of Ganymede (4:1). Orbital resonances with simple integer ratios are also called mean-motion resonances (MMR). Collectively, the Galilean moons provide ample challenges for studies on the formation of planetary satellites. The authors of today’s paper use N-body simulations to study formation scenarios of the Galilean moons to show that orbital resonant chains are readily produced. They hence propose that the system was a primordial resonant chain, similar to the exoplanets of TRAPPIST-1.

Thunderbolt and Lightning

The general mechanism for the formation of moons around a gas giant is very similar to that of planets forming around a star. Whereas planets form within a gaseous protoplanetary disc (also known as a circumstellar disk or CSD), moons form within a gaseous circumplanetary disc (CPD). The CPD is fed by infall from the CSD, and is also subject to tidal heating from both the parent planet and the parent star. These processes are important when it comes to determining the final composition (e.g. rocky vs. icy content) of the moons that eventually form. Initially the CPD contains tiny satellitesimals (or proto-moons), which grow via two mechanisms; pebble accretion and collisions. As the proto-moon moves through the CPD, it experiences aerodynamic drag with the gas in the disc. This drag disrupts the motion of dust grains, causing some to settle onto the proto-moon via gravitational attraction. Over time this increases the mass of the proto-moon (hence the term pebble accretion). Collisions also occur within the CPD, although the authors explicitly ensured the initial proto-moons are spaced far enough apart so that they are not immediately destroyed.

To the Moons!

The simulation is designed to reproduce as close an analogue to the Galilean moons as possible. Figure 1 shows the initial evolution of one of the simulations, starting with four proto-moons. This simulation sees the innermost pair collide, thus resulting in a final system with only 3 satellites. Curiously, in over 40 simulations starting with 4 satellites, all simulations involved at least one collision, leaving only 3 surviving moons. Thus more than 4 initial satellites are required.

Figure 1: Plots of the semi-major axis (left panel) and mass (right panel) for each of the four proto-moons in the simulation as a function of time. Note the collision between the innermost pair at around 1.2 Myr. The dash-dotted blue line shows the snowline – the region in the disc beyond which water condenses as ice. (Adapted from Fig 2 in the paper)

Figure 2 shows four of the best simulations, with the system in red (shown with the arrow) chosen as the preferred simulation. In all three cases, the simulated moons are locked in an 8:4:2:1 resonant chain (black dotted line). Callisto is a clear outlier in this regard. Another outlier is the Ganymede analogues (third innermost moon), which have much lower masses.

Figure 2: Resulting system configurations of the four best simulations, with the final mass as a function of distance. The black line shows the real Galilean system, the vertical dotted lines show the locations of the 2:1 MMRs, and the pink dashed lines show the simulation mass constraints. The green simulation includes an additional co-orbital satellite. (Adapted from Fig 6 in the paper)

Age of Aquarius

It is one thing to simulate the orbits of a Galilean moon system, but another to correctly replicate their composition. For the Galilean moons, the further out the moon, the more water ice it contains. Io, volcanically active, has very little water content. This stands in stark contrast to Callisto, a moon with up to 55% of its mass as water ice. Figure 3 shows simulated Galilean moon analogues from the three best simulations, but this shown according to their orbital configuration and relative size, coloured according to water ice content. Although in all three simulations the innermost moon has the least water ice, the total content is still significantly overestimated. Only the two outermost moons share similar water ice contents to that of Ganymede and Callisto. The authors suggest that water may escape from the inner moons via hydrodynamic escape, however these effects are not considered in the simulation.

Figure 3: Orbital configurations of three best analogues compared to the Galilean system. Size and colour shade denote radius and water-ice fractions respectively. (Fig 10 in the paper).

Primordial Harmony

These simulations show that orbital resonances, in particular 2:1 MMRs, are readily produced in simulations of Galilean analogues; thus the Galilean moons were resonant to begin with. The authors noted that in every simulation, the outermost moon remained locked in an orbital resonance. They suggest that Callisto, the only Galilean moon not in a 2:1 MMR, may have originally been in an orbital resonance and has since migrated outwards due to tidal interactions, but they suggest that future simulations that explore planet-satellite tidal dissipation are required to know for sure. Similarly, it is unclear whether Io and Europa’s low water content is due to hydrodynamic escape, or if there are other mechanisms at work yet to be accounted for in simulations. Future space missions, such as the Europa Clipper and Jupiter Icy Moons Explorer, will likely shed more light on these mechanisms and ultimately provide tighter constraints for simulations of the Galilean system.

Edited by: Abygail Waggoner
Featured image credit: SpaceEngine

The author wishes to acknowledge the Whadjuk peoples of the Noongar nation, the traditional custodians of the land upon which this post was written, and pays respects to Elders past and present.

About Mitchell Cavanagh

Mitchell is a PhD student in astrophysics at the University of Western Australia. His research is focused on the applications of machine learning to the study of galaxy formation and evolution. Outside of research, he is an avid bookworm and enjoys gaming, languages and code jams.

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