Representing the formation process is regarded difficult for satellite systems around gas giants that have only one large moon, such as Titan around Saturn. Relatively large moons are thought to form in gaseous circumplanetary disks and the orbits of them are affected by the interaction between the disk gas. Thus, the final configuration of the system is determined along the dissipation of the disk. According to N-body simulations in the literature, a system tend to have multiple moons or loses all the moons if a simple power-low disk is assumed.
We study the orbital evolution of moons to find a way of configuring a single-large-moon system. Because the direction and speed of the orbital migration depend on the properties of circumplanetary disks, we model dissipating circumplanetary disks with considering the effect of temperature structures. We calculate the orbital evolution of satellites with the mass of Titan in the final evolution stage of various circumplanetary disks. We also perform N-body simulations with initially many satellites to see whether single-moon systems can form at the end.
We find that the radial slope of the temperature structure characterized by the dust opacity produces a patch of orbits where the Titan-mass satellites stop inward migration and even migrate outwards in a certain range of the viscosity. The patch assists satellites initially located in the outer orbits to remain in the disk, while others in the inner orbits are lost into the planet. We demonstrated, for the first time, the formation of systems with only one large moon around gas giants. Our results suggest satellite formation was not very efficient in the outer radii of circumplanetary disks.