An N-body population synthesis framework for the formation of moons around Jupiter-like planets

The moons of giant planets are believed to form in situ in Circumplanetary Discs (CPDs). Here we present an N-body population synthesis framework for satellite formation around a Jupiter-like planet, in which the dust-to-gas ratio, the accretion rate of solids from the Protoplanetary Disc, the number, and the initial positions of protosatellites were randomly chosen from realistic distributions. The disc properties were from 3D radiative simulations sampled in 1D and 2D grids and evolved semi-analytically with time. The N-body satellitesimals accreted mass from the dust component of the disc, interacted gravitationally with each other, experienced close-encounters, both scattering and colliding. With this improved modeling, we found that about $15\%$ of the resulting population is more massive than the Galilean one, and only $8.5\%$ were in resonances. The moons reach Europa's mass most frequently in $10^5$ years. In $10\%$ of the cases, moons are engulfed by the planet, and $1\%$ of the satellite-systems lose at least 1 Earth-mass into the planet, contributing to the giant planet's envelope's heavy element content. In $1\%$ of cases, we found eccentricities and inclinations of moons above 0.1. We examined the differences in outcome between the 1D and 2D disc models and used machine learning (Randomized Dependence Coefficient together with t-SNE) to compare our population with the Galilean system. Detecting our population around known transiting Jupiter-like planets via transits and TTVs would be challenging, but $14\%$ of the moons could be with an instrumental transit sensitivity of $10^{-5}$.