HydroSyMBA: A 1D Hydrocode Coupled with an N-body Symplectic Integrator

The numerical modeling of coexisting circumplanetary disks/ rings and satellites is particularly challenging because each part of the system requires a very different approach. Disks are generally well represented by a fluid-like dense medium, whose evolution can be calculated by a hydrocode. On the other hand, the orbital evolution of satellites is generally performed using N-body integrators. We have developed a new numerical model that combines a one-dimensional hydrocode with the N-body integrator SyMBA. The disk evolves due to its viscosity, and resonant torques from satellites. The latter is applied to the satellites as an additional "kick" to their accelerations. The integrator also includes the ability to spawn new moonlets at the disk's outer edge if the latter expands beyond a material-dependent Roche limit, as well as the effects of tidal dissipation in the planet and/or the satellite on the satellite orbits. The resulting integrator allows one to accurately model the evolution of an inner circumplanetary disk, and the formation of satellites by accumulation of disk material, all within a single self-consistent framework. Potential applications include the formation of Earth's Moon, the evolution of the inner Saturn system, the Martian and uranian moons, and compact exoplanetary systems.