Astronomy and Astrophysics – Astrophysics
Scientific paper
Mar 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003a%26a...400..375g&link_type=abstract
Astronomy and Astrophysics, v.400, p.375-383 (2003)
Astronomy and Astrophysics
Astrophysics
5
Planets And Satellites: Individual: Saturn, Planets: Rings
Scientific paper
A method for investigating the small-amplitude nonlinear oscillations of low and moderately high optical depth regions of Saturn's main rings is developed through the using of the Boltzmann kinetic equation with a Krook model integral of interparticle collisions and the Poisson equation. A mathematical formalism in the approximation of weak turbulence (a quasi-linearization of the Boltzmann equation) is developed. Conditions under which the quasilinear approximation can be used to describe wave-particle interactions are calculated with reference to the excitation of Jeans-type gravity disturbances (those produced by a spontaneous perturbation and/or a companion system). It is shown that the spontaneous, almost aperiodically growing Jeans-unstable spiral gravity oscillations developing in the disk's plane must influence the distribution of mutually gravitating particles in such a way as to hinder the oscillations excitation, i.e., to increase the spread of random velocities. As a result, finally in the disk there can be established a quasi-stationary distribution so that the Jeans-unstable density waves are completely vanishing. Thus, in the nonlinear regime, the particles can continue developing gravity-unstable density condensations only if some effective mechanism of ``cooling" exists. We suggest that in Saturn's rings the cooling mechanism leading to the long-term density waves activity is actually operating: inelastic (dissipative) collisions reduce the magnitude of the relative velocity of particles.
Gedalin Michael
Griv Evgeny
Yuan Changhe
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