Planets

Saturn's Rings

The ring structure of Saturn is an example of a common phenomena in astrophysics: the disk. We see disk structures on all scales, ranging from the rings surrounding the giant planets of our own Solar System and the accretion disks around neutron stars and black holes up to the disks that form the most visible part of spiral galaxies.

The rings of Saturn have the distinction of being the thinnest disks known to astronomers; the ratio of their thickness to their radius is approximately 10^-6. Measured in number of revolutions, these rings are also the oldest known disks; over their lifetime they have completed 10¹² rotations around Saturn. They exhibit a surprising complexity, with a broad structure that breaks down into ringlets on every observable level.

Observed Ring Structure

The rings of Saturn are very broad, with an inner radius of 69,000 km and an outer radius of 213,000 km (from 1.14 to 3.53 times Saturn's equatorial radius), and they are thin, with a thickness as small as 100m. The rings are subdivided into seven smaller rings, labeled A through G in the order of their discovery. They are inclined to Saturn's orbital plane by 26.7. While most of the rings are circular, eccentric rings are seen; the F ring is an eccentric.

The rings are actually numerous small pieces of ice mixed with a small amount of rocky material. It is the rocky material that gives the rings its color, and the variation of the color shows that the ring composition varies with radius. The rings are predominately vacuum; only about 3% of the volume of the rings is occupied by matter. The pieces of ice in the rings range in size from a centimeter to ten meters. The particle size a is distributed as a^-q, where the index q is between 2.8 and 3.4. Most of the mass in the ring is in meter-sized particles. The total mass of the rings is about 510^-8 the mass of Saturn, which is 310²²g.

The striking features of the rings is that they are subdivided on all scales into ringlets. Many of the more prominent divisions in the rings are caused by resonant interactions with the moons of Saturn. The most prominent division, the Cassini Division, is located at the 2:1 resonance with the moon Mimas, so an object within the Cassini Division will make two revolutions of Saturn for every one revolution that Mimas makes.

Spiral waves of two type?density waves and bending waves?propagate through the rings. The density waves are similar to sound waves in that the density within a rings increases and decreases as the waves pass through. The bending waves are deflections of the rings out of the ring plane. The spiral waves are caused by the resonant interaction of Saturn's moons with the rings. The strongest interactions are for the lowest-order resonances (1:2, 2:3, 3:4, 4:5, 5:6, 3:5, and 6:7). As examples, the moon Janus induces an oscillation in the outer edge of the A ring, and the moom Mimas induces an oscillation in the outer edge of the B ring.

One of the more recent discoveries was that the rings can develop spokes that persist for several hours. This behavior is not well understood; it is thought that the interaction of charged dust in the rings with Saturn's magnetosphere produces this effect.

Astrophysics of Rings

Saturn's rings are a Keplerian disk, meaning that they differentially rotate around Saturn with a period equal to the period of rotation of a satellite in a circular orbit. For a Keplerian disk, the orbital angular velocity is proportional to R^-3/2, where R is the distance from Saturn's center. Individual particles within the ring at a given distance from Saturn deviate slightly from this circular orbit; their orbits are elliptical orbits of very low eccentricity that are slightly out of the plane. This deviation from the Keplerian velocity can be regarded as a thermal component in the motion of particles in the ring, and this thermal component determines the ring thickness.

The differential rotation of the rings is the source of energy that drives much of their complex behavior. The differential energy is converted into the kinetic energy of non-circular orbital motion thorough collisions of particles in elliptical orbits with different angular momenta. The inelastic collisions of particles with the same angular momentum then converts the energy associated with the thermal orbital motion into heat within the particles, which is radiated away as infrared radiation.

Collisions play a central role in the structure seen in the rings, because the process of extracting differential energy does not happen uniformly across the disk. The collision rate is proportional to the square of the density of particles within the disk. This means that energy and angular momentum are redistributed more rapidly at radii of high density than at radii of low density. Over time, the energy in a high-density region will be radiated away, but the angular momentum will be preserved. The effect of this is to cause this region of the disk to collapse away from the surrounding sections of the disk; this occurs because when two adjacent regions of the disk interact, the conservation of angular momentum draws them together. For instance, a ring of mass m₁ and radius R₁ that interacts with a ring of mass m₂ and radius R₂ will merge to produce a ring at the radius R^1/2 = ( m₁ R₁^1/2 + m₂ R₂^1/2)/( m₁ + m₂). One therefore expects a disk of colliding particles to collapse into many ringlets.

The orbits of the particles in the rings are modified by processes other than collisions. The asymmetry of Saturn's gravitational field, which is a consequence of Saturn's rotational flattening and the gravitational fields of the moons orbiting Saturn, causes the elliptical orbits of particles in the ring to precess; this has the effect of uniformly distributing around Saturn the particles with eccentric orbits. The gas of Saturn's magnetosphere exerts a drag on the particles in the rings that causes the particles to loose energy and momentum. The sunlight exerts a drag on the particles through a process called the Poynting-Robertson effect; the sunlight is absorbed by a particle in the disk and is reradiated isotropically. The particle therefore acquires the momentum of the sunlight, which acts to slow the motion of the particle. This effect is most important for small particles.