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H. Daisaka, H. Tanaka, S. Ida (Tokyo Institute of Tech.)
We have investigated the structure and transport process in a dense planetary ring such as Saturn's main rings by performing local N-body simulations including both self-gravitational interactions and inelastic collisions between ring particles. In such a system, Salo~(1995) demonstrated the formation of wake structure with 100 meter size, which may exist within the observed, axisymmetric ringlets with the width ~10km in the Saturn's ring. The presence of such wakes significantly affects the transport process such as angular momentum in the ring system, which may govern the formation mechanism of the axisymmetric ringlets.
From our numerical results, we evaluate the viscosity (angular momentum transfer rate) in the system where wakes strongly develop. We separately calculate the gravitational viscosity due to torque caused by the wake structure, the translational(local) viscosity, and the collisional viscosity.
The phenomena of wakes alter the transport properties studied in the ring without wakes (e.g., Goldreich & Tremaine, 1978; Araki & Tremaine, 1986; Wisdom & Tremaine, 1988). In the case where wake formation does not arise, our results is consistent with such previous studies. When the wakes strongly develop, the gravitational viscosity and the translational viscosity due to collective motion of the particles caused by wakes are dominant, whereas the collisional viscosity and the local viscosity due to random motion are less significant in the ring's viscosity. The total viscosity is considerably larger than that in the non-self-gravity case. For Saturnian B-ring parameters, the enhancement factor is as large as 10. In such a case, the gravitational viscosity is always nearly equal to the local viscosity due to the collective motion, and the total viscosity is given by ~q 10 G2 \Sigma2/\Omega3. where G is the gravitational constant, \Sigma is the surface density of a ring, and \Omega is Keplerian frequency. Such results can be interpreted easily by considering the physical properties of the wakes (typical scale of wakes and coherent motion of particles in the wakes).
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