Secular instability of Saturn's rings.

Details Secular instability of Saturn's rings. Secular instability of Saturn's rings.

Jul 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996a%26a...311.1033g&link_type=abstract

Astronomy and Astrophysics, v.311, p.1033-1042

Astronomy and Astrophysics

Astrophysics

9

Planets And Satellites: General, Saturn, Instabilities, Celestial Mechanics, Stellar Dynamics

Scientific paper

Kinetic theory with the Boltzmann and Poisson's equations is used to determine the stability and oscillations of the two-dimensional collisional system of identical particles of Saturn's rings. The effects of physical collisions between particles are taken into account by using in the Bolztmann kinetic equation a phenomenological Bhatnagar-Gross-Krook collisional integral (Bhatnagar et al. 1954). This model collisional integral was modified following Shu & Stewart (1985) to allow collisions to be inelastic. The dynamics of a system with rare collisions is considered, that is, {OMEGA}^2^>>ν_c_^2^, with {OMEGA} being the orbital angular frequency and ν_c_ the collision frequency. It is shown that in a Jeans-stable system the simultaneous action of self-gravity and collisions leads to a secular dissipative type instability. It is also shown that generally the growth rate of this aperiodic instability is small, Im ω_*_~ν_c_. However, in the marginally Jeans-stable gravitationally parts of the disk, the growth rate is a maximum, and may become a large, Im ω_*_=~(ν_cOMEGA^2^)^1/3^>>ν_c_. In such parts of the Saturn's system the instability will develop on the time scale only of several revolutions even at moderately low values of the local optical depth, τ=~ν_c_/{OMEGA}~0.1. The radial wavelength of the most unstable oscillations is of the order λ=~2πρ, where ρ=~c/{OMEGA} is the epicyclic radius and c is the mean dispersion of random velocities of particles. The secular instability may be suggested as the cause of much of the irregular, narrow ~2πρ~100m structure in low optical depth regions of Saturn's rings. Cassini spacecraft high-resolution images may resolve such hyperfine structure in the C ring, the inner B ring and the A ring.

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