The viscosity in an optically thick planetary ring
Abstract
We have investigated the viscosity (angular momentum transfer rate) in an optically thick planetary ring through local N-body simulations including both gravitational interactions and inelastic collisions between ring particles. As Salo(1995) and Daisaka and Ida (1999) showed, in an optically thick planetary ring, wake structure with 100 meter size is formed by self-gravity and collisional damping. The wake structure is non-axisymmetric and it significantly enhances angular momentum transfer rate (viscosity) in the ring. We separately calculate the gravitational viscosity due to torque caused by the wake structure, the translational(local) viscosity, and the collisional viscosity from the results of our N-body simulations. The viscosity is evaluated analytically and numerically in the ring system without the self-gravity, where wake structure does not develop (e.g., Goldreich & Tremaine 1978, Araki & Tremaine 1986, Wisdom & Tremaine 1988). The results of our N-body simulations are as follows: The viscosity is consistent with that in the previous studies when optical depth (τ ) is smaller than unity and wake structure is weak. em If τ exceeds unity, the gravitational viscosity and the local viscosity due to collective motion of the particles caused by the wake structure overwhelm the collisional viscosity and the local viscosity due to random motion. The total viscosity is considerably larger than that in the non-self-gravity case. For Saturnian B-ring parameter, the enhancement factor is as large as 10. em In the case with τ > 1, the gravitational viscosity is always nearly equal to the local viscosity due to the collective motion, and the total viscosity is given by = 10 G2 Σ 2/Ω ^3 where Σ is the surface density of the ring and Ω is Keplerian frequency. More global ring dynamics should be reconsidered by the viscosity we found.
- Publication:
-
AAS/Division of Dynamical Astronomy Meeting
- Pub Date:
- May 2000
- Bibcode:
- 2000DDA....31.0805D