title: Size distribution of particles in Saturn's rings from aggregation and fragmentation.
abstract: Saturn's rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative interparticle collisions. For particles in the size range from a few centimeters to a few meters, a power-law distribution of radii, ~r(-q) with q ≈ 3, has been inferred; for larger sizes, the distribution has a steep cutoff. It has been suggested that this size distribution may arise from a balance between aggregation and fragmentation of ring particles, yet neither the power-law dependence nor the upper size cutoff have been established on theoretical grounds. Here we propose a model for the particle size distribution that quantitatively explains the observations. In accordance with data, our model predicts the exponent q to be constrained to the interval 2.75 ≤ q ≤ 3.5. Also an exponential cutoff for larger particle sizes establishes naturally with the cutoff radius being set by the relative frequency of aggregating and disruptive collisions. This cutoff is much smaller than the typical scale of microstructures seen in Saturn's rings.
authors.affiliation: Department of Mathematics, University of Leicester, Leicester, LE1 7RH, United Kingdom;
authors.forename: Nikolai
authors.initials: N
authors.lastname: Brilliantov
authors.affiliation: Department of Physics, Boston University, Boston, MA 02215;
authors.forename: P L
authors.initials: PL
authors.lastname: Krapivsky
authors.affiliation: Faculty of Physics, Moscow State University, Moscow, 119991, Russia; Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany;
authors.forename: Anna
authors.initials: A
authors.lastname: Bodrova
authors.affiliation: Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany;
authors.forename: Frank
authors.initials: F
authors.lastname: Spahn
authors.affiliation: Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan;
authors.forename: Hisao
authors.initials: H
authors.lastname: Hayakawa
authors.affiliation: Faculty of Physics, Moscow State University, Moscow, 119991, Russia;
authors.forename: Vladimir
authors.initials: V
authors.lastname: Stadnichuk
authors.affiliation: Astronomy and Space Physics, University of Oulu, PL 3000, 90014, Oulu, Finland jurgen.a.schmidt@oulu.fi.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Schmidt
keywords: coagulation–fragmentation; kinetic theory; planetary rings