VISCOUS OVERSTABILITIES IN DENSE NARROW PLANETARY RINGS

We present a study of viscous overstabilities that can arise in a narr ow ring whose particles are tightly packed, so that the pressure tense r exhibits a behavior different than that in a more dilute ring. The m ain objective of this work is to investigate the role of viscous overs tabilities in the excitation of(azimuthal) eccentric modes in narrow r ings. The problem is studied through an analytical study of a 2-stream line model and supported by a 10-streamline numerical simulation. Ther e are two possible regimes of instabilities, one in which the mean ecc entricity of the ring (i.e., of its azimuthal mode) decreases to a sma ll but finite and nearly constant value, while internal modes of libra tion reach comparable amplitudes (''small eccentricity regime''), and the other one in which the mean eccentricity of the ring increases to a much larger asymptotic value (''large eccentricity regime'') while i nternal librations are strongly reduced, but not fully damped. This is to be contrasted with the behavior of viscously stable rings, in whic h both the librations and the mean eccentricity are fully damped, if o ne neglects the role of the shepherd satellites. Whether one or the ot her of these regimes is obtained depends on the initial conditions, bu t the final state in each regime is controlled by the viscous and self -gravitational evolution and not by these initial conditions. In both regimes, there is no rotating frame in which the ring looks stationary , in opposition to the assumption made in data analyses and in previou s theoretical modeling. The large eccentricity regime is generically a ble to produce rings with stabilized mean eccentricities and mean ecce ntricity gradients quite similar to those of the eccentric rings of Ur anus; however, this regime cannot be reached from an initially circula r state, so that if viscous overstabilities alone are to account for t he eccentricity of narrow rings, then the ring material must have been in eccentric motion at the time of formation. The residual librations in the large eccentricity regime may explain the problems of the stan dard self-gravity model for the rigid precession for the epsilon ring, but this appears much more difficult to accomplish for the alpha and beta rings; these residual librations may account for some of the kine matic residuals of the uranian rings, and may also relate to the absen ce of width-longitude relation in the smaller eccentric rings. (C) 199 5 Academic Press, Inc.