• Institution: Bibliotheks- und Infosystem der Universitaet
  • science, front matter, science features
  • Sign up for PNAS eTOC alerts

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

  1. Jürgen Schmidtf,1
  1. Edited by Neta A. Bahcall, Princeton University, Princeton, NJ, and approved June 12, 2015 (received for review February 26, 2015)

Significance

Although it is well accepted that the particle size distribution in Saturn’s rings is not primordial, it remains unclear whether the observed distribution is unique or universal, that is, whether it is determined by the history of the rings and details of the particle interaction or whether the distribution is generic for all planetary rings. We show that a power-law size distribution with large-size cutoff, as observed in Saturn’s rings, is universal for systems where a balance between aggregation and disruptive collisions is steadily sustained. Hence, the same size distribution is expected for any ring system where collisions play a role, like the Uranian rings, the recently discovered rings of Chariklo and Chiron, and possibly rings around extrasolar objects.

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, rq with q3, 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 2.75q3.5. 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.

Footnotes

  • Author contributions: N.B. designed research; N.B., P.L.K., A.B., H.H., V.S., and J.S. performed research; N.B., P.L.K., A.B., H.H., V.S., and J.S. contributed new reagents/analytic tools; N.B., P.L.K., A.B., V.S., and J.S. analyzed data; and N.B., P.L.K., F.S., and J.S. wrote the paper.

  • The authors declare no conflict of interest.

  • This article is a PNAS Direct Submission.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1503957112/-/DCSupplemental.