A&A 400, 375-383 (2003)
On the stability of Saturn's rings to gravity disturbancesE. Griv1, M. Gedalin1 and C. Yuan2
Department of Physics, Ben-Gurion University of the Negev,
PO Box 653, Beer-Sheva 84105, Israel
Academia Sinica Institute of Astronomy and Astrophysics
(ASIAA), PO Box 23-141, Taipei, Taiwan
(Received 7 August 2002 / Accepted 20 December 2002)
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.
planets and satellites: individual: Saturn --
Offprint request: E. Griv, firstname.lastname@example.org
© ESO 2003