Dynamical Evolution of the Debris Disk after a Satellite Catastrophic Disruption around Saturn
The hypothesis of a recent origin of Saturn's rings and its mid-sized moons is actively debated. It was suggested that a proto-Rhea and a proto-Dione might have collided recently, giving birth to the modern system of mid-sized moons. It is also suggested that the rapid viscous spreading of the debris may have implanted mass inside Saturn's Roche limit, giving birth to the modern Saturn's ring system. However, this scenario has been only investigated in very simplified way for the moment. This paper investigates it in detail to assess its plausibility by using $N$-body simulations and analytical arguments. When the debris disk is dominated by its largest remnant, $N$-body simulations show that the system quickly re-accrete into a single satellite without significant spreading. On the other hand, if the disk is composed of small particles, analytical arguments suggest that the disk experiences dynamical evolutions in three steps. The disk starts significantly excited after the impact and collisional damping dominates over the viscous spreading. After the system flattens, the system can become gravitationally unstable when particles are smaller than $\sim$ 100 m. However, the particles grow faster than spreading. Then, the system becomes gravitationally stable again and accretion continues at a slower pace, but spreading is inhibited. Therefore, the debris is expected to re-accrete into several large bodies. In conclusion, our results show that such a scenario may not form the today's ring system. In contrast, our results suggest that today's mid-sized moons are likely re-accreted from such a catastrophic event.