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