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Brilliantov et al. (PNAS, 2015) propose a model for the size distribution~R^-3 for small particles with radius R and ~exp(-(R/Rc)^3) for largeparticles, where Rc=5.5 m. In 1989 Longaretti found analytically ~R^-3 forsmall particles and R^-6 for large ones (2). The law R^-6 also describesmoonlets with size ~ 0.1-1 km. Cut-off law from Brilliantov et al. model doesnot describe moonlets and requires new mechanism for the origin of ~ 1 km sizebodies. This model does not take into account the key effects ofself-gravitation of large particles and differential rotation of the rings.Longaretti used a more accurate model of destruction of particles: "A relativeincrease of the erosion/destruction rate of the large particles must takeplace, because these particles have relative velocities of collision largerthan the dispersion velocity, due to the differential Keplerian motion". Thenew model does not explain the difference between the rings and the satellitesand the authors suggest that their calculations are applicable to the rings ofthe Chariklo and Chiron. In fact, the Chariklo rings are not examples ofplanetary rings, but proto-satellite disks. Simplified physical model that doesnot describe moonlets and the outer boundary of the rings makes the new modelnot a step forward but a step backwards in comparison with the papers of 20-30years old.

Size distribution of particles in Saturn's rings, missed moonlets and misinterpretation of Chariklo rings