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Planetary rings
(2002)
We develop a model of stochastic radiation pressure for rotating non-spherical particles and apply the model to circumplanetary dynamics of dust grains. The stochastic properties of the radiation pressure are related to the ensemble-averaged characteristics of the rotating particles, which are given in terms of the rotational time-correlation function of a grain. We investigate the model analytically and show that an ensemble of particle trajectories demonstrates a diffusion-like behaviour. The analytical results are compared with numerical simulations, performed for the motion of the dusty ejecta from Deimos in orbit around Mars. We find that the theoretical predictions are in a good agreement with the simulation results. The agreement however deteriorates at later time, when the impact of non-linear terms, neglected in the analytic approach, becomes significant. Our results indicate that the stochastic modulation of the radiation pressure can play an important role in the circumplanetary dynamics of dust and may in case of some dusty systems noticeably alter an optical depth. (c) 2006 Elsevier Ltd. All rights reserved.
Charged dust grains in circumplanetary environments experience, beyond various deterministic forces, also stochastic perturbations caused, by fluctuations of the magnetic field, the charge of the grains, by chaotic rotation of aspherical grains, etc. Here we investigate the dynamics of a dust population in a circular orbit around a planet which is perturbed by a stochastic planetary magnetic field B', modeled by an isotropically Gaussian white noise. The resulting perturbation equations give rise to a modified diffusion of the inclinations i and eccentricities e. The diffusion coefficient is found to be D proportional to w^2 O /n^2 , where the gyrofrequency, the Kepler frequency, and the synodic frequency are denoted by w , O, and n, respectively. This behavior has been checked against numerical simulations. We have chosen dust grains (1 m in radius) ejected from Jupiter's satellite Europa in circular equatorial orbits around Jupiter and integrated numerically their trajectories over their typical lifetimes (100 years). The particles were exposed to a Gaussian fluctuating magnetic field B' with the same statistical properties as in the analytical treatment. These simulations have confirmed the analytical results. The theoretical studies showed the statistical properties of B' to be of decisive importance. To estimate them, we analyzed the magnetic field data obtained by the Galileo spacecraft magnetometer at Jupiter and found almost Gaussian fluctuations of about 5% of the mean field and exponentially decaying correlations. This results in a diffusion of orbital inclinations and eccentricities of the dust grains of about ten percent over the lifetime of the particles. For smaller dusty motes or for close-in particles (e.g., in Jovian gossamer rings) stochastics might well dominate the dynamics.
The recent radar detection by Baggaley (2000) of a collimated stream of interstellar meteoroids postulated to be sourced at beta Pictoris, a nearby star with a prominent dust disk. presents a challenge to theoreticians. Two mechanisms of possible dust ejection from beta Pic have been proposed: ejection of dust by radiation pressure from comets in eccentric orbits and by gravity of a hypothetical planet in the disk. Here we re-examine observational data and reconsider theoretical scenarios, substantiating them with detailed modeling to test whether they can explain quantitatively and simultaneously the masses, speeds, and fluxes. Our analysis of the stream geometry and kinematics confirms that beta Pic is the most likely source of the stream and suggests that an intensive dust ejection phase took place similar to0.7 Myr ago. Our dynamical simulations show that high ejection speeds retrieved from the observations can be explained by both planetary ejection and radiation pressure mechanisms, providing, however, several important constraints. In the planetary ejection scenario, only a "hot Jupiter"-type planet with a semimajor axis of less than 1 AU can be responsible for the stream, and only if the disk was dynamically "heated" by a more distant massive planet. The radiation pressure scenario also requires the presence of a relatively massive planet at several AU or more, that had heated the cometesimal disk before the ejection occurred. Finally, the dust flux measured at Earth can be brought into reasonable agreement with both scenarios, provided that beta Pic's protoplanetary disk recently passed through an intensive short-lasting (similar to0.1 Myr) clearance stage by nascent giant planets, similar to what took place in the early solar system