The formation of the Galilean satellites of Jupiter (Io, Europa, Ganymede, and Callisto) was investigated by Canup & Ward (2002, 2006, 2009) and Mosqueira & Estrada (2003a,b), considering a circumplanetary disk composed by gas, embryos, and satellitesimals. The formation of satellitesimals is possible only under special conditions (Shibaike et al., 2017), presenting an open point in their models. Recent papers as Shibaike et al. (2019) and Batygin & Morbidelli (2020) worked around the satellitesimals formation problem by including the growth by pebble accretion. Other challenging points of the system are the laplacian resonance 4:2:1 between the satellites Io, Europa, and Ganymede and the non-triangular distribution of masses. In this work, we analyze the dynamical evolution and growth by pebble accretion of a family of embryos immersed in the gas disc proposed by Canup & Ward (2002).
The numerical simulations were performed in the Mercury package (Chambers, 1999) including the effects of the type I migration (Paardekooper et al., 2010), eccentricity and inclination damping (Cresswell & Nelson, 2008), gas drag (Adachi et al. 1976) and the pebble accretion (Ormel & Liu, 2018). The dynamical system is composed of Jupiter, the gas disc proposed by Canup & Ward (2002), and 50 embryos. We set the disk decay timescale as τ=1.0 Myears and performed a set of simulations with a pebbles-to-gas ratio of ζ=700, 1000, 2000, and 3000.
We found that the simulations with ζ=2000 gave rise to 4 satellites involved in an 8:4:2:1 MMR chain (the semi-major axes of the three inner ones are similar to the Galileans), the first, second, and last satellite with masses similar to Io, Europa, and Callisto and ice fractions coherent with the real system.
However, these systems also share a Ganymede analog less massive than the real one and satellites in high excited orbits (e ~ 0.1). These results showed that we need to invoke post-gas-dissipation effects as the tidal effect to reduce the eccentricities of the satellites and migrates Callisto outward for its actual position.