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Astron. Astrophys. 346, 1011-1019 (1999)

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1. Introduction

The E ring is the dust complex extending from [FORMULA] to 8 planetary radii in Saturn's equatorial plane. It is composed of grains having a narrow size distribution centered in the interval from 3 to [FORMULA] (Nicholson et al. (1996). The peak of the ring's brightness is located close to the orbit of Enceladus, which strongly suggests that this satellite serves as the source of the E ring dust.

The tiny grains immersed in Saturn's magnetosphere are subject to many perturbations. As long as a grain moves in the ambient plasma, it collects electrostatic charge which rises the Lorentz force in the planetary magnetic field. The interaction with the plasma itself invokes the drag force because of the grain's velocity relative to the bulk of plasma. The solar radiation pressure and the planetary oblateness further complicate the dynamics.

Previous theoretical studies reveal that many features of the E ring can be explained provided the particle dynamics are determined by the combined perturbations due to the radiation pressure, planetary oblateness and the Lorentz force. Horányi et al. (1992) use the sophisticated charging model and predict nearly constant grain's potential throughout the ring's extent. They argue that only micron-sized grains attain orbits with large eccentricities and hence cover the broad range of radial distances. Hamilton & Krivov (1996) develop the analytical theory for the circumplanetary dust dynamics with an application, among others, to Saturn's E ring. Describing the Lorentz force they restrict the theory to the constant charge and find an integral of the planar motion which accounts for the radiation pressure, planetary oblateness, electromagnetism and the solar gravity. For the planar case they consider, this permits them to describe in detail the character of motion in the form of phase portraits.

However, the mechanism of dust charging in space is full of large uncertainties. Several charging models developed by Horányi et al. (1992), Morfill et al. (1993) and Jurac et al. (1995) predict different potentials for the E ring grains. Most potentials do not keep constant when the grain's orbit is eccentric, and the ambient plasma parameters vary periodically. The survival of highly eccentric orbits when the charge varies is crucial for the present model of the E ring. And vice versa if the ring's model is correct, the choice between the charging models can be done on the base of particle dynamics.

Most recently Dikarev & Krivov (1998) added the plasma drag effect to the particle dynamics. Using numerical integrations of the Newtonian equations of the motion, they showed that the growth of the semimajor axis allows the eccentric orbits of the grains to cover the full radial extension of the E ring, at the same time introducing new kinds of the orbital behaviour.

This paper extends the existing models for the circumplanetary dust dynamics in two directions. First, the analytical theory (Hamilton & Krivov (1996) is generalized to account for the variable charge in a reasonable approximation. The consistency of several charging models with the existence of a broad dust complex in view of the particle dynamics is then examined (Sect. 2). Second, the action of the plasma drag is investigated in more detail than in our previous dynamical model (Dikarev & Krivov (1998). In the limit of small eccentricities and zero inclinations, an analytical description of the motion is developed (Sect. 3). Conclusions are made in Sect. 4.

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© European Southern Observatory (ESO) 1999

Online publication: June 17, 1999