Formation of a single large moon around a gas giant: Saturn-Titan system

Circumplanetary disks are regarded as birthplaces of large moons. While Jupiter has four large satellites known as Galilean moons, Titan is the only large moon around Saturn. N-body simulations using a simple power-low disk suggest a system tend to have multiple moons or loses all the moons due to inward migration. Thus, forming a single satellite system in a disk is known to be difficult. 
 The orbits of moons are continuously affected by the interaction with the disk, and the direction and speed of the migration depend on the disk structures, i.e., surface density and temperature. Therefore, the final configuration of the moon system is determined during the dissipation of the disk. We studied the orbital evolution of moons in various circumplanetary disks to find a way of configuring a single-large-moon system. 
 We model dissipating circumplanetary disks with taking the effect of opacity into account when we calculate the temperature structure. Because of this, our disk has multiple slopes, and thus, the migration speed of a moon varies with the orbital location. Then, we calculate the orbital evolution of Titan-mass moons in the final evolution stage of the disks. We performed N-body simulations with initially many satellites to see whether single-moon systems can form at the end. 
 We found that the radial slope of the temperature structure characterized by the dust/ice opacity produces a patch of orbits where the Titan-mass moons resist inward migration with a certain range of the viscosity. We call such a patch as “safety zone.” The safety zone assists moons initially located in the outer orbits to remain in the disk, while those in the inner orbits migrate toward the planet. When the satellite formation is not very efficient in the outer radii of circumplanetary disks, the system can end up with a single large moon at a distant from the planet while the inner orbits are cleared out. Smaller moons may stay in the inner orbits as their migration speed is slower compared to the Titan-mass ones. We demonstrated the formation of systems with single large moon around gas giants for the first time.