Hamiltonian Formulation and Perturbations for Dust Motion Around Cometary Nuclei

In this paper we analyze the dynamical behavior of large dust grains in the vicinity of a cometary nucleus. To this end we consider the gravitational field of the irregularly shaped body, as well as its electric and magnetic fields. Without considering the effect of gas friction and solar radiation, we find that there exist grains which are static relative to the cometary nucleus; the positions of these grains are the stable equilibria. There also exist grains in the stable periodic orbits close to the cometary nucleus. The grains in the stable equilibria or the stable periodic orbits won’t escape or impact on the surface of the cometary nucleus. The results are applicable for large charge dusts with small area-mass ratio which are near the cometary nucleus and far from the Solar. It is found that the resonant periodic orbit can be stable, and there exist stable non-resonant periodic orbits, stable resonant periodic orbits and unstable resonant periodic orbits in the potential field of cometary nuclei. The comet gravity force, solar gravity force, electric force, magnetic force, solar radiation pressure, as well as the gas drag force are all considered to analyze the order of magnitude of these forces acting on the grains with different parameters. Let the distance of the dust grain relative to the mass centre of the cometary nucleus, the charge and the mass of the dust grain vary, respectively, fix other parameters, we calculated the strengths of different forces. The motion of the dust grain depends on the area-mass ratio, the charge, and the distance relative to the comet’s mass center. For a large dust grain (> 1 mm) close to the cometary nucleus which has a small value of area-mass ratio, the comet gravity is the largest force acting on the dust grain. For a small dust grain (< 1 mm) close to the cometary nucleus with large value of area-mass ratio, both the solar radiation pressure and the comet gravity are two major forces. If the a small dust grain which is close to the cometary nucleus have the large value of charge, the magnetic force, the solar radiation pressure, and the electric force are all major forces. When the large dust grain is far away from the cometary nucleus, the solar gravity and solar radiation pressure are both major forces.     

Large Dust Grains Around Cometary Nuclei

Large amounts of particles ejected from the nucleus surface are present in the vicinity of the cometary nuclei when comets are near the Sun (at heliocentric distances ≤2 AU). The largest dust grains ejected may constitute a hazard for spatial vehicles. We tried to obtain the bounded orbits of those particles and to investigate their stability along several orbital periods. The model includes the solar and the cometary gravitational forces and the solar radiation pressure force. The nucleus is assumed to be spherical. The dust grains are also assumed to be spherical, and radially ejected. We include the effects of centrifugal forces owing to the comet rotation. An expression for the most heavy particles that can be lifted is proposed. Using the usual values adopted for the case of Halley’s comet, the largest grains that can be lifted have a diameter about 5 cm, and the term due to the rotation is negligible. However, that term increases the obtained value for the maximum diameter of the lifted grain in a significant amount when the rotation period is of the order of a few hours.     

The dust trail of Comet 67P/Churyumov-Gerasimenko

We report the detection of Comet 67P/Churyumov-Gerasimenko's dust trail and nucleus in 24 μm Spitzer Space Telescope images taken February 2004. The dust trail is not found in optical Palomar images taken June 2003. Both the optical and infrared images show a distinct neck-line tail structure, offset from the projected orbit of the comet. We compare our observations to simulated images using a Monte Carlo approach and a dynamical model for comet dust. We estimate the trail to be at least one orbit old (6.6 years) and consist of particles of size ?100 μm. The neck-line is composed of similar sized particles, but younger in age. Together, our observations and simulations suggest grains 100 μm and larger in size dominate the total mass ejected from the comet. The radiometric effective radius of the nucleus is 1.87±0.08 km, derived from the Spitzer observation. The Rosetta spacecraft is expected to arrive at and orbit this comet in 2014. Assuming the trail is comprised solely of 1 mm radius grains, we compute a low probability (∼¹⁰⁻³) of a trail grain impacting with Rosetta during approach and orbit insertion.     

Models of P/Wirtanen nucleus: active regions versus non-active regions

From the current understanding we know that comet nuclei have heterogeneous compositions and complex structures. It is believed that cometary activity is the result of a combination of physical processes in the nucleus, like sublimation and recondensation of volatile ices, dust grains release, phase transition of water ice, depletion of the most volatile components in the outer layers and interior differentiation.The evolution of the comet depends on the sublimation of ices and the release of different gases and dust grains: the formation of a dust crust, the surface erosion and the development of the coma are related to the gas fluxes escaping from the nucleus. New observations, laboratory experiments and numerical simulations suggest that the gas and dust emissions are locally generated, in the so-called active regions. This localized activity is probably superimposed to the global nucleus activity. The differences between active and inactive regions can be attributed to differences in texture and refractory material content of the different areas.In this paper we present the results of numerical models of cometary nucleus evolution, developed in order to understand which are the processes leading to the formation of active and non-active regions on the cometary surface. The used numerical code solves the equations of heat transport and gas diffusion within a porous nucleus composed of different ices—such as water (the dominant constituent), CO₂, CO- and of dust grains embedded in the ice matrix.By varying the set of physical parameters describing the initial properties of comet P/Wirtanen, the different behaviour of the icy and dusty areas can be followed.Comet P/Wirtanen is the target of the international ROSETTA mission, the cornerstone ESA mission to a cometary nucleus. The successful design of ROSETTA requires some knowledge of comet status and activity: surface temperatures, amount of active and inactive surface areas, gas production rate and dust flux.     

Dust tail of the active distant Comet C/2003 WT42 (LINEAR) studied with photometric and spectroscopic observations

We present the study of dust environment of dynamically new Comet C/2003 WT42 (LINEAR) based on spectroscopic and photometric observations. The comet was observed before and after the perihelion passage at heliocentric distances from 5.2 to 9.5 AU. Although the comet moved beyond the zone where water ice sublimation could be significant, its bright coma and extended dust tail evidenced the high level of physical activity. Afρ values exceeded 3000 cm likely reaching its maximum before the perihelion passage. At the same time, the spectrum of the comet did not reveal molecular emission features above the reflected continuum. Reddening of the continuum derived from the cometary spectrum is nonlinear along the dispersion with the steeper slop in the blue region. The pair of the blue and red continuum images was analyzed to estimate a color of the comet. The mean normalized reflectivity gradient derived from the innermost part of the cometary coma equals to 8% per 1000 Å that is typical for Oort cloud objects. However, the color map shows that the reddening of the cometary dust varies over the coma increasing to 15% per 1000 Å along the tail axis. The photometric images were fitted with a Monte Carlo model to construct the theoretical brightness distribution of the cometary coma and tail and to investigate the development of the cometary activity along the orbit. As the dust particles of distant comets are expected to be icy, we propose here the model, which describes the tail formation taking into account sublimation of grains along their orbits. The chemical composition and structure of these particles are assumed to correspond with Greenberg’s interstellar dust model of comet dust. All images were fitted with the close values of the model parameters. According to the results of the modeling, the physical activity of the comet is mainly determined by two active areas with outflows into the wide cones. The obliquity of the rotation axis of the nucleus equals to 20° relative to the comet’s orbital plane. The grains occupying the coma and tail are rather large amounting to 1 mm in size, with the exponential size distribution of a^−4.5. The outflow velocities of the dust particles vary from a few centimeters to tens of meters per second depending on their sizes. Our observations and the model findings evidence that the activity of the nucleus decreased sharply to a low-level phase at the end of April–beginning of May 2007. About 190 days later, in the first half of November 2007 the nucleus stopped any activity, however, the remnant tail did not disappear for more than 1.5 years at least.     

Modelling the circumnuclear coma of comets: objectives,methods and recent results

We investigate whether the modelling of the immediate vicinity of an active nucleus—currently unobservable—can, as the modelling of the outer, observable coma, be based on unrealistic simple assumptions such as those of nucleus and dust grains sphericity. We point out the inconsistency of models based on such assumptions, which, to manage compatibility with the observations, have to introduce additional assumptions that conflict with the previous ones, such as the existence of active areas of the nucleus. We argue that, while the outer coma models being phenomenological in nature, can perhaps tolerate such inconsistencies, the circumnuclear coma models must be predictive, having to obviate the lack of observational data, and therefore must exclude implausible and ad hoc assumptions, and advocate only well-understood physical processes and duly validated modelling methods. We describe the first steps of development of a predictive circumnuclear coma model, and present a set of results obtained with parameters fitted to comet P/Wirtanen, the target of the Rosetta mission, but of a quite general significance. Considering, first an inhomogeneous spherical nucleus with spherical dust grains, and then an aspherical homogeneous nucleus with spherical dust grains, we show that, in both cases (1) the surface temperature and initial gas parameters differ considerably from the Hertz–Knudsen values; (2) the near-surface gas and dust flows are not in general vertical, (3) the gas and dust density do not always monotonically decrease outwards, (4) the gas and dust velocity vary strongly from point to point, (5) shock structures are formed, which result in the formation of pseudo-jets of dust grains originating from various points of the surface. No simple method to distinguish between dust structures created by the surface inhomogeneity and by the surface orography is found. We show, for the first time, the deformation of the near-nucleus dust coma during a full rotation of an homogeneous, aspherical nucleus. We also show that identical active regions located at different points of an inhomogeneous spherical nucleus produce very different dust distributions, suggesting that the dust distribution is also strongly deformed during the rotation of such a nucleus. Finally, we consider, for the first time, a spherical homogeneous nucleus emitting aspherical dust grains. We show that, in such a case, the terminal grain velocity depends upon the shape, initial position, and even possibly upon the initial orientation of the grain at the surface, so that there cannot exist a precise relation between terminal velocity and dust grain mass. We conclude that, far from giving an approximate or average representation of the circumnuclear coma, the classical modelling approach yields in this region predictions that are in total conflict with the real behaviour of the gas and dust. As a most dramatic consequence, the use of this classical approach may have obscured completely the significance of the few direct and of the many indirect informations acquired hitherto on the nucleus activity.     

Clusters and packets of grains in comet Halley and the fragmentation of dust

Clusters and packets of dust grains, detected by the VEGA spacecrafts in the coma of comet Halley, are interpreted either as due to microjets arising directly from the nucleus or as due to fragmentation processes of larger conglomerates. After a summary of the characteristics of the particle swarms observed and of the conclusion from their interpretation as microjets, some aspects from the fragmentation scenario of this phenomenon are outlined. From the spatial widths and the total number of grains in a particle swarm the mass of the parent conglomerate can be estimated. For the clusters and packets parent bodies of about 1 to several 100 g can be expected. Their travel time in the coma after release from the nucleus range from 10 to about 100 days before the spacecraft encounters. Finally, possible fragmentation processes are discussed and some comments for further investigations, both in theory and for in-situ data, are given.     

On the visibility of nuclei of dusty comets

The problem of visibility of a cometary nucleus discussed in general terms for single scattering by dust grains. The ratio of radiatio scattered in the dust column above the surface and that reflected from the nucleus determines the visibility of features on the nuclear surface. A contrast parameter characterizing the ration of radiation foming from the nuclear surface and that of the nuclear vicinity describes the visibility of the full nucleus against the dust fore- and background. These quantities and the intensity distribution of scattered solar radiation across the nucleus and its vicinity are calculated for the case of comet Halley at a heliocentric distance of 0.9 AU after perihelion (Giotto encounter). The scattering calculations are based on an isotropic dust distribution derived from hydrodynamics gas-dust interactions resulting in a steep densiity increase right above the surface. For Newburn's nominal model of comet Halley, an optical depth of about 0.5 impairs the visibility of the nucleus somewhat.     

Optical properties of the carbon dust grains in the envelopes around asymptotic giant branch stars

We have investigated the optical properties of the carbon dust grains in the envelopes around carbon-rich asymptotic giant branch stars, paying close attention to the infrared observations of the stars and the laboratory-measured optical data of the candidate dust grain materials. We have compared the radiative transfer model results with the observed spectral energy distributions of the stars including IRAS Point Source Catalog and IRAS Low Resolution Spectrograph data. We have deduced an opacity function of amorphous carbon dust grains from model fitting with infrared carbon stars. From the opacity function, we have derived the optical constants of the AMC grains. The optical constants satisfy the Kramers–Kronig relation and produce the opacity function that fits the observations of infrared carbon stars better than previous works in the wide wavelength range 1–1000 μm. We have used simple mixtures of the AMC and silicon carbide grains for modelling. We have compared the contributions that AMC and SiC grains make to the opacity for the cases of simple mixtures of them and spherical core–mantle type grains consisting of a SiC core and an AMC mantle .     

The composition of dust in Jupiter-family comets inferred from infrared spectroscopy

We review the composition of Jupiter-family comet (JFC) dust as inferred from infrared spectroscopy. We find that JFCs have silicate emission features with fluxes roughly 20-25% over the dust continuum (emission strength 1.20-1.25), similar to the weakest silicate features in Oort Cloud (OC) comets. We discuss the grain properties that alter the silicate emission feature (composition, size, and structure/shape), and emphasize that thermal emission from the comet nucleus can have significant influence on the derived silicate emission strength. Recent evidence suggests that grain porosity is the is different between JFCs and OC comets, but more observations and models of silicates in JFCs are needed to determine if a consistent set of grain parameters can explain their weak silicate emission features. Models of 8 m telescope and Spitzer Space Telescope observations have shown that JFCs have crystalline silicates with abundances similar to or less than those found in OC comets, although the crystalline silicate mineralogy of comets 9P/Tempel and C/1995 O1 (Hale-Bopp) differ from each other in Mg and Fe content. The heterogeneity of comet nuclei can also be assessed with mid-infrared spectroscopy, and we review the evidence for heterogeneous dust properties in the nucleus of comet 9P/Tempel. Models of dust formation, mixing in the solar nebula, and comet formation must be able to explain the observed range of Mg and Fe content and the heterogeneity of comet 9P/Tempel, although more work is needed in order to understand to what extent do comets 9P/Tempel and Hale-Bopp represent comets as a whole.     

Constraints on the nucleus and dust properties from mid-infrared imaging of comet Hyakutake

We use Mie scattering theory to determine the expected thermal emission from dust grains in cometary comae and apply these results to mid-infrared images of comet Hyakutake (C/1996 B2) obtained preperihelion in 1996 March. Calculations were performed for dust grains in the size range from 0.1 to 10 micrometers for two different compositions: amorphous olivine (a silicate glass) and an organic residue mixture. The resulting emission efficiencies are complicated functions of wavelength and particle size and are significantly different for the two materials in question. The Hyakutake data set consists of three nights of high-resolution imaging (100-150 km pixel-1 at the comet) of the inner coma at 8.7, 11.7, 12.5, and 19.7 micrometers. Attempts to fit the observed colors (ratios of fluxes at different wavelengths) using a single grain composition failed. However, fits to the data were achieved for all three nights using a mixture of approximately 1 micrometer olivine grains and approximately 7 micrometers organic grains. The resulting olivine mass fraction was between 8% and 16% of the total dust mass-loss rate. We also estimate the radius of the nucleus to be r = 2.1 +/- 0.4 km.     

Comet 67P/Churyumov-Gerasimenko: Modeling of orientation and structure

The comet 67P/Churyumov-Gerasimenko is the current target of the mission Rosetta, initially planned to investigate comet 46P/Wirtanen. These two comets have similar orbits, except the distance to the Sun at perihelion, but different orbital histories and different masses. Thus, structures of the nuclei can be significantly different. The evolution of comet Wirtanen was simulated by several authors, while comet Churyumov-Gerasimenko became an object of high interest only recently and is not well investigated. In the present work we simulate the evolution of the nucleus, down to tens of meters below the surface, using an extended version of the model previously applied for comet Wirtanen [Kossacki et al., 1999. Comet 46P/Wirtanen: evolution of the subsurface layer. Icarus 142, 202-218.]. The model includes strengthening of the nucleus due to sintering of the ice grains. Simulations are performed for different latitudes, accounting for the evolution of the orbit and for changes of the nucleus orientation, as well as diurnal and seasonal changes of insolation. The calculated loss of water vapor from the comet is integrated over the nucleus surface and is compared with the observational data. We have found, that the sublimation through the dust mantle can be large enough to reproduce the profile of the total water production as a function of time from perihelion. The required dependence of thickness of the dust layer on latitude qualitatively matches present distribution of the absorbed solar flux. The non-gravitational acceleration in the comet motion together with the simulated sublimation flux are used in order to estimate the mass and the bulk density of the nucleus.     

Dynamics of Dust Particles of Different Structure: Application to the Modeling of Dust Motion in the Vicinity of the Nucleus of Comet 67P/Churyumov–Gerasimenko

We consider the estimates of the main forces acting on dust particles near a cometary nucleus. On the basis of these estimates, the motion of dust particles of different structure and mass is analyzed. We consider the following forces: (1) the cometary nucleus gravity, (2) the solar radiation pressure, and (3) the drag on dust particles by a flow of gas produced in the sublimation of cometary ice. These forces are important for modeling the motion of dust particles relative to the cometary nucleus and may substantially influence the dust transfer over its surface. In the simulations, solid silicate spheres and homogeneous ballistic aggregates are used as model particles. Moreover, we propose a technique to build hierarchic aggregates—a new model of quasi-spherical porous particles. A hierarchic type of aggregates makes it possible to model rather large dust particles, up to a millimeter in size and larger, while no important requirements for computer resources are imposed. We have shown that the properties of such particles differ from those of classical porous ballistic aggregates, which are usually considered in the cometary physics problems, and considering the microscopic structure of particles is of crucial significance for the analysis of the observational data. With the described models, we study the dust dynamics near the nucleus of comet 67P/Churyumov–Gerasimenko at an early stage of the Rosetta probe observations when the comet was approximately at 3.2 AU from the Sun. The interrelations between the main forces acting on dust aggregates at difference distances from the nucleus have been obtained. The dependence of the velocity of dust aggregates on their mass has been found. The numerical modeling results and the data of spaceborne observations with the Grain Impact Analyzer and Dust Accumulator (GIADA) and the Cometary Secondary Ion Mass Analyzer (COSIMA) onboard the Rosetta probe are compared at a quantitative level.     

Observations of the Dust Cloud in Comet Hale-Bopp on 9–11 May 1997

During our monitoring observations of comet Hale-Bopp, we found several sporadic ejections of dust from the nucleus. The most prominent ejection was observed on May 6–9, 1997, in the post-perihelion phase of the apparition. In this paper, we report preliminary analysis of this event, in which the total mass of the dust cloud is estimated to be 1.6 × 10¹¹ g. This revised version was published online in July 2006 with corrections to the Cover Date.     

Shape and obliquity effects on the thermal evolution of the Rosetta target 67P/Churyumov-Gerasimenko cometary nucleus

This work is dedicated to the application to 67P/Churyumov-Gerasimenko of a new quasi-3D approach for non-spherically shaped comet nuclei with the aim to interpret the current activity of the comet in terms of initial characteristics and to predict shape and internal stratification evolution of the nucleus. The model is applied to differently shaped nuclei taking into account the characteristics of Comet 67P/Churyumov-Gerasimenko deduced from observations. We focus our attention on the combined effects that shapes and obliquity have on the comet surface and sub-surface evolution. We discuss the results in terms of activity, local dust mantle formation and disruption, erosion of the surface and internal stratigraphy.The results show that differently shaped nuclei can have different internal structures leading to different activity patterns and behaviors. Our calculations have shown that local variations in the dust and gas fluxes can be induced by the nucleus shape. The distribution of “active” areas on Comet 67P/Churyumov-Gerasimenko is different because of different shapes, reflecting the illumination conditions on the surface. These shapes can influence the structure of the inner coma, but the coma far away from the nucleus is only marginally affected by the nucleus shape. However, different comet behaviors can arise from differently shaped comet nuclei, especially in terms of local activity, surface and sub-surface characteristics and properties. The water flux local distribution is the most influenced by the shape as it is directly linked to the illumination. Irregular shapes have large shadowing effects that can result in activity patterns on the comet surface.The effects of different pole directions are discussed to see the relations with the nucleus activity and internal structure. It is shown that the orientation of the rotation axis plays a strong role on the surface evolution of 67P/Churyumov-Gerasimenko, determining seasonal effects on the fluxes. The activity of the comet changes greatly with the nucleus obliquity leading to pre-post-perihelion differences in the activity and seasonal effects. The effects of the dust deposition and crust formation on the cometary activity have also been simulated and are discussed with respect to 67P/Churyumov-Gerasimenko observations. The dust mantling is also strongly obliquity dependent, with different surface distributions of the dust-covered regions according to the different comet pole orientations. Finally, we show that our model can reproduce the fluxes behavior near perihelion in terms of amplitude and asymmetry, and we estimate 20% of the illuminated surface to be active.     

Substances of cometary grains estimated from evaporation and radiation pressure mechanisms

The shape and intensity distribution of tails for several large comets are estimated on the basis of grain properties in the solar radiation field. The following results are obtained: (1) The ratio of the maximum radiation pressure force to the gravitaional force acting on dust grains in cometary tails is found to be less than 2.5. This means that grains such as graphite particles in the size range 0.02–0.2 μm do not exist in them, because such particles would allow forces greater than 2.5 (2) Tail substances supplied near the time of perihelion passage for the Sun-grazing comet Ikeya-Seki (1965 VIII) and Comet Seki-Lines (1962 III) were composed of particular grains which had values of radiation pressure ratio less than 1.0. Therefore, it is concluded that the material was composed of silicate grains only, since iron grains had sublimated and there were no graphite particles.     

Dust coma morphology in the Deep Impact images of Comet 9P/Tempel 1

We present an overview of the dust coma observations of Comet Tempel 1 that were obtained during the approach and encounter phases of the Deep Impact mission. We use these observations to set constraints on the pre-impact activity of the comet and discuss some preliminary results. The temporal and spatial changes that were observed during approach reveal three distinct jets rotating with a 1.7-day periodicity. The brightest jet produces an arcuate feature that expands outward with a projected velocity of about 12 m s⁻¹, suggesting that the ambient dust coma is dominated by millimeter-sized dust grains. As the spatial resolution improves, more jets and fans are revealed. We use stereo pairs of high-resolution images to put some crude constraints on the source locations of some of the brightest features. We also present a number of interesting coma features that were observed, including surface jets detected at the limb of the nucleus when the exposed ice patches are passing over the horizon, and features that appear to be jets emanating from unilluminated sources near the negative pole. We also provide a list of 10 outbursts of various sizes that were observed in the near-continuous monitoring during the approach phase.     

Physical properties of cometary and interplanetary dust

In the absence of numerous in situ studies, physical properties of cosmic dust may be derived from observations of their light scattering and thermal properties, through numerical simulations making use of realistic assumptions. Estimations about cometary and interplanetary dust composition, structure, size, as well as about their light scattering and thermal properties, are first summarized. We then present and discuss the numerical simulations we have performed with different types of particles: core-mantle submicron-sized elongated grains (having contributed to the formation of cometary dust), fractal aggregates of such grains (found in cometary comae and in the interplanetary dust cloud), and fractal aggregates of large dust grains (found in cometary dust trails).A very satisfactory fit to the numerous polarimetric observations of comet Hale-Bopp is obtained for a mixture with about 33–60% of organics in mass, with a power law size distribution with an index of (−3) and a radius of 20 μm for the upper cut-off. For the less-constrained polarimetric observations of interplanetary dust near 1 AU, a fit is obtained for a mixture with about 40% of organics in mass, with a similar size distribution and a radius of about 50 μm for the upper cut-off. The ensemble of results obtained for the interplanetary dust strongly suggest that its light scattering and thermal properties stem from the presence of compact and fluffy particles, with compositions ranging from silicates to more absorbing materials, whose contribution decreases with decreasing distance to the Sun.     

The nature of the orbits of charged dust injected into the Jovian magnetosphere during the tidal break-up of comet Shoemaker-Levy 9

Assuming that the spin and magnetic axis of Jupiter are strictly parallel and that the grain charge remains constant we have derived two integrals of the 3D equations of motion of charged dust grains moving within the co-rotating regions of the Jovian magnetosphere taking into account both planetary gravitation and magnetospheric rotation. We then apply this model to study the fate of fine dust injected into the Jovian magnetosphere as a result of the tidal disruption of comet Shoemaker-Levy 9 during its first encounter with Jupiter in July 1992. This analysis, which uses the integrals of the equation of motion rather than the equation of motion itself as was done by Horanyi (1994), does not allow us to calculate the orbits or the orbital evolution of the grains. But it does allow us to construct the spatial regions to which the grains are confined, at least initially before evolutionary effects take over. We have chosen three points along the path of the disintegrating comet for the injection of dust and used two values for the uncertain floating potential of the dust in the inner Jovian magnetosphere. Grains can have three different fates, depending on their size, their acquired potential and their point of injection. While the smallest grains are quickly lost by collision with the planet at high latitudes independent of the sign of their charge, those in an intermediate but narrow size range, injected near the equatorial plane can be trapped in a region close to it, this being true for both positive and negative grains. While somewhat larger positive grains may be initially ejected outward by the co-rotational electric force, similar negative grains, pulled inward by this force collide with the planet at low latitudes. In all cases the largest grains, which are dominated by planetary gravity, initially escape from the inner magnetosphere by following in the path of the comet.Using a detailed time dependent numerical calculation of the jovicentric orbits of the charged dust debris of the disintegrating comet, that allows for variation in the grain potential, while also allowing for perturbations of the grain orbits due to solar radiation pressure and solar gravity Horanyi (1994) found that grains in the size range (1.5m <a < 2.5m) which initially make large excursions from the planet, will eventually form a ring in the radial range 4.5R _J <r < 6R _J . Our present analytical calculation cannot make such a prediction about the evolutionary fate of the dust debris. It can, however, estimate the size of the grains that are initially confined to regions near the points of injection, before evolutionary effects become important.     

Fully 3-dimensional calculations of dust mantle formation for a model of Comet 67P/Churyumov-Gerasimenko

A fully 3-dimensional implicit numerical model for comet nucleus evolution is presented, emphasizing dust mantle formation. A spherical configuration is considered with an initial composition of amorphous H₂O ice and dust, taking into account a discrete dust-grain size distribution. The model is applied to Comet 67P/Churyumov-Gerasimenko, adopting its orbital elements, rotation period and rotation axis inclination. We find that the dust mantle thickness varies over the surface from 1 cm to about 10 cm (thus lower and higher than the diurnal skin-depth, respectively). The size distribution of ejected grains varies along the orbit and is steeper than the initial one adopted for the nucleus. The crystallization front advances inward in spurts, and its depth varies between 1 and several meters. We test the effect of the thermal conductivity on the surface temperature distribution and depths of the dust mantle and crystallization front.