Size distribution of particles in Saturn's rings from aggregation and fragmentation

Nikolai Brilliantov, P. L. Krapivsky, Anna Bodrova, Frank Spahn, Hisao Hayakawa, Vladimir Stadnichuk, Jürgen Schmidt

Research output: Contribution to journalArticlepeer-review

83 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)9536-9541
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number31
Publication statusPublished - 4 Aug 2015
Externally publishedYes


  • Coagulation-fragmentation
  • Kinetic theory
  • Planetary rings


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