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. (1-3) and the observation of rapid processes in the ring system (4) indicate that the shape of the particle size distribution is likely not primordial or a direct result of the ring-creating event. Rather, ring particles are believed to be involved in active accretion-destruction dynamics (5-13) and their sizes vary over a few orders of magnitude as a power law (14-17), with a sharp cutoff for large sizes (18-21). Moreover, tidal forces fail to explain the abrupt decay of the size distribution for house-sized particles (22). One wishes to understand the following: (i) Can the interplay between aggregation and fragmentation lead to the observed size distribution? And (ii) is this distribution peculiar for Saturn's rings, or is it universal for planetary rings in general? To answer these questions quantitatively, one needs to elaborate a detailed model of the kinetic processes in which the ring particles are involved. Here we develop a theory that quantitatively explains the observed properties of the particle size distribution and show that these properties are generic for a steady state, when a balance between aggregation and fragmentation holds. Our model is based on the hypothesis that collisions are binary and that they may be classified as aggregative, restitutive, or disruptive (including collisions with erosion); which type of collision is realized depends on the relative speed of colliding particles and their masses. We apply the kinetic theory of granular gases (23, 24) for the multicomponent system of ring particles to quantify the collision rate and the type of collision. Results and DiscussionModel. Ring particles may be treated as aggregates built up of primary grains (9) of a certain size r 1 and mass m 1 . [Observations indicate that particles below a certain radius are absent in dense rings (16).] Denote by m k = km 1 the mass of rin...

Small particles and self-gravity wakes in Saturn's rings from UVIS and VIMS stellar occultations

“…They find that the size distribution parameters vary across the rings but that generally q ∼2.75-3.5 with particle radii ranging between several millimeters and several meters. This range of q is also corroborated by models of particle aggregation and fragmentation in planetary ring systems ( Brilliantov et al 2015 ). While numerical simulations of adhesion and collisional release by Bodrova et al (2012) predict an absence of sub-cm particles throughout the rings except in regions of increased velocity dispersion.…”

ALMA Discovery of Dust Belts around Proxima Centauri

“…By analogy with the rings of Saturn we expect a power-law distribution with an index of −3.5 and a maximum particle size of 5-10 m (Zebker et al 1985;Brilliantov et al 2015), resulting in a total mass of ∼ 10 −5 M ⊕ for such a planetary ring. Theoretical arguments (Charnoz et al 2017) suggest that evolved planetary rings have a mass ∼ 10 −7 times the mass of the planet.…”

Increasing temperature of cooling granular gases

“…Moreover, while the size distribution of aggregates has been analyzed 27,28,33,35 , a constant mean kinetic energy was assumed; a coupling between the evolution of the size distribution and that of the mean kinetic energy of the aggregates has not been investigated. It is however well known that the mean kinetic energy of the system is not constant but decreases with time 30,31,36–38 , which strongly influences the kinetics of ballistic aggregation.…”