A practical tool for simulating the presence of gas comae in thermophysical modeling of cometary nuclei

A longstanding problem in thermophysical modeling of cometary nuclei has been to accurately formulate the boundary conditions at the nucleus/coma interface. A correct treatment of the problem, where the Knudsen layer gas just above the cometary surface (which is not in thermodynamic equilibrium) is modeled in parallel with the nucleus, is extremely time-consuming and has so far been avoided. Instead, simplifying assumptions regarding the coma properties are used, e.g., the surface gas density is assumed equal to zero or set to the local saturation value, and the coma backflux is neglected or given some realistic but approximate value. The resulting inaccuracy regarding the exchange of mass, energy, and momentum between the nucleus and the coma, may introduce significant errors in the calculated nucleus temperature profiles, gas production rates, and momentum transfer efficiencies. In this paper, we present a practical, accurate, and time-efficient tool which makes it possible to consider the nucleus and the innermost coma of a comet (the former assumed to consist of a porous mixture of crystalline water ice and dust) as a coupled, physically consistent system. The tool consists of interpolation tables for the surface gas density and pressure, the recondensing coma backflux, and the cooling energy flux due to diffusely scattered coma molecules. The tables cover a wide range of surface temperatures and sub-surface temperature profiles, and can be used to improve the boundary conditions used in thermophysical models. The interpolation tables have been obtained by calculating the transmission distribution functions of gas emerging from sublimating porous ice/dust mixtures with various temperature profiles, which then are used as source functions in a Direct Simulation Monte Carlo model of inelastic intermolecular collisions in the Knudsen layer.     

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.     

Processing of cometary grains at the nucleus surface

Cometary material inevitably undergoes chemical changes before and on leaving the nucleus. In seeking to explain comets as the origin of many IDPs (interplanetary dust particles), an understanding of potential surface chemistry is vital. Grains are formed and transformed at the nucleus surface; much of the cometary volatiles may arise from the organic material. In cometary near-surface permafrost, one expects cryogenic chemistry with crystal growth and isotope. This could be the hydrous environment where IDPs form. Seasonal and geographic variations imply a range of environmental conditions and surface evolution. Interplanetary dust impacts and electrostatic forces also have roles in generating cometary dust. The absence of predicted cometary dust ‘envelopes’ is compatible with the wide range of particle structures and compositions. Study of IDPs would distinguish between this model and alternatives that see comets as aggregates of core-mantle grains built in interstellar clouds.     

Influence of the magnetic field on the density distribution of solar wind protons and cometary ions in the shock layer ahead of cometary ionospheres

The “mass loading” of the solar wind by cometary ions produced by the photoionization of neutral molecules outflowing from the cometary nucleus plays a major role in the interaction of the solar wind with cometary atmospheres. In particular, this process leads to a decrease in the solar wind velocity with a transition from supersonic velocities to subsonic ones through the bow shock. The so-called single-fluid approximation, in which the interacting plasma flows are considered as a single fluid, is commonly used in modeling such an interaction. However, it is occasionally necessary to know the distribution of parameters for the components of the interacting plasma flows. For example, when the flow of the cometary dust component in the interplanetary magnetic field is considered, the dust particle charge, which depends significantly on the composition of the surrounding plasma, needs to be known. In this paper, within the framework of a three-dimensional magnetohydrodynamic model of the solar wind flow around cometary ionospheres, we have managed to separately obtain the density distributions of solar wind protons and cometary ions between the bow shock and the cometary ionopause (in the shock layer). The influence of the interplanetary magnetic field on the position of the point of intersection between the densities with the formation of a region near the ionopause where the proton density is essentially negligible compared to the density of cometary ions is investigated. Such a region was experimentally detected by the Vega-2 spacecraft when investigating Comet Halley in March 1986. The results of the model considered below are compared with some experimental data obtained by the Giotto spacecraft under the conditions of flow around Comets Halley and Grigg–Skjellerup in 1986 and 1992, respectively. Unfortunately, our results of calculations on Comet Churyumov–Gerasimenko are only predictive in character, because the trajectory of the Rosetta spacecraft, which manoeuvred near its surface for several months, is complex.     

The destruction of the cometary nucleus – The case of 73P/Schwassmann-Wachmann

The paper presents an analysis of the actual brightness change of comet 73P/Schwassmann-Wachmann, which took place in 1995. The consequence of a cometary outburst is the destruction of a fragment of its surface. This causes the emission of comet material from both the surface and from exposed subsurface layers. Therefore, the calculations take into account the scattering cross-sections that come from ice and dust particles. It was assumed that the dust particles are silicates which are characterized by high irregularity of their structure. This assumption is a consequence of the analysis of the results provided by the Rosetta mission to the comet 67P/Churyumov-Gerasimenko. The main factor determining the amplitude of a cometary outburst is the mass ejected as well as the loss of ice that holds the individual nucleus structures together. Consequently, this phenomenon can significantly contribute to the destruction and even decay of the cometary nucleus.     

Insolation of a cometary crater at the stage of dust-jet formation

An important cause of the activation and development of active processes on the surface of a cometary nucleus is direct solar radiation illuminating a part of the surface that is not shielded by dust. The intensity of solar radiation near the surface of a cometary nucleus depends on the thickness of the dust cloud above the active area. If the size of the dust cloud noticeably changes, the intensity considerably depends on time. In the present paper, we consider the nonlinear equation of radiative transfer in a dust cloud growing towards the incident wave front with a constant velocity. The change in the intensity of direct solar radiation along the dust jet originating from the active surface area of a cometary nucleus has been found. For the sake of comparison, the linear equation of radiative transfer was solved in the framework of this task. It turns out that the linear approach to the solution of the considered problem suggests a noticeable loss in the amount of direct radiation participating in the dust-jet formation. This loss is comparable with the intensity of solar radiation incident to the active area of a cometary nucleus after scattering in the cometary atmosphere.     

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.     

Gas flow and dust acceleration in a cometary Knudsen layer

An analytical model of the innermost gas–dust coma region is proposed. The kinetic Knudsen layer adjacent to the surface of the cometary nucleus, where the initially non-equilibrium velocity distribution function of gas molecules relaxes to Maxwell equilibrium distribution function and, as a result, the macro-characteristics of gas and dust flows vary several-fold, is considered. The gas phase model is based on the equations for mass, momentum and energy flux conservation, and is a natural development of the Anisimov, 1968 and Cercignani, 1981 approaches. The analytical relations between the characteristics of the gas flow on the boundaries of the non-equilibrium layer and the characteristics of the returning gas flow adsorbed by the surface are determined. These values form a consistent basis both for hydrodynamic models of the inner coma and for jet force models. Three particular models are presented: (1) sublimation of a polyatomic one-component gas; (2) sublimation of a two-component polyatomic gas mixture, in both cases from a plane surface; and (3) sublimation of water ice through a porous dust mantle. We conclude that the characteristics of the gas flow emerging from the Knudsen layer over a porous dust mantle is not very sensitive to the structure of the mantle.We also treat the expansion of dust into the coma, concentrating on the interaction between a non-equilibrium gas flow and a test particle. The dynamics of a grain of idealized shape is explored by using several simplifying assumptions for the variation of the drag force. The velocity of a particle at the exterior boundary of the Knudsen layer is thus estimated. Examining various model behaviours of the drag force inside the Knudsen layer, we show that the dust velocity is not sensitive to these variations.     

Processing of cometary grains at the nucleus surface

Cometary material inevitably undergoes chemical changes before and on leaving the nucleus. In seeking to explain comets as the origin of many IDPs (interplanetary dust particles), an understanding of potential surface chemistry is vital. Grains are formed and transformed at the nucleus surface; much of the cometary volatiles may arise from the organic material. In cometary near-surface permafrost, one expects cryogenic chemistry with crystal growth and isotope. This could be the hydrous environment where IDPs form. Seasonal and geographic variations imply a range of environmental conditions and surface evolution. Interplanetary dust impacts and electrostatic forces also have roles in generating cometary dust. The absence of predicted cometary dust envelopes is compatible with the wide range of particle structures and compositions. Study of IDPs would distinguish between this model and alternatives that see comets as aggregates of core-mantle grains built in interstellar clouds.     

A kinetic model of gas flow in a porous cometary mantle

A numerical study of gas flow through a porous cometary mantle is presented. A kinetic model based on the well-known Test Particle Monte Carlo Method for the solution of rarefied gas dynamics problems is proposed. The physical model consists of two spatial plane regions: the condensed ice phase and a porous dust mantle. The structure of the porous dust layer is described as a bundle of cylindrical inclined channels not crossing each other. A vertical temperature gradient may exist across the dust mantle. The aim is to investigate how the characteristics of molecular flow depend on the capillary length, inclination angle, and temperature gradient. Examples illustrating a significant deviation of some results from equilibrium values are shown. In particular, the gas velocity distribution at both ends of the pore is strongly non-Maxwellian if there is an important temperature contrast across the pore. The emergent gas flow rate is found to vary with the pore length/radius ratio in excellent agreement with Clausing's empirical formula. The degree of collimation of the flow is quantitatively studied as a function of the length/radius ratio, and consequences for the jet force of outgassing through a dust mantle or, indeed, a rough surface are estimated.     

Activity of comets: Gas transport in the near-surface porous layers of a cometary nucleus

The gas transport through non-volatile random porous media is investigated numerically. We extend our previous research of the transport of molecules inside the uppermost layer of a cometary surface ( [Skorov and Rickman, 1995] and [Skorov et al., 2001]). We assess the validity of the simplified capillary model and its assumptions to simulate the gas flux trough the porous dust mantle as it has been applied in cometary physics. A microphysical computational model for molecular transport in random porous media formed by packed spheres is presented. The main transport characteristics such as the mean free path distribution and the permeability are calculated for a wide range of model parameters and compared with those obtained by more idealized models. The focus in this comparison is on limitations inherent in the capillary model. Finally a practical way is suggested to adjust the algebraic Clausing formula taking into consideration the nonlinear dependence of permeability on layer porosity. The retrieved dependence allows us to accurately calculate the permeability of layers whose thickness and porosity vary in the range of values expected for the near-surface regions of a cometary nucleus.     

On the Formation of Planetesimals: Radial Contraction of the Dust Layer Interacting with the Protoplanetary Disk Gas

Radial contraction of the dust layer in the midplane of a gas–dust protoplanetary disk that consists of large dust aggregates is modeled. Sizes of aggregates vary from centimeters to meters assuming the monodispersion of the layer. The highly nonlinear continuity equation for the solid phase of the dust layer is solved numerically. The purpose of the study is to identify the conditions under which the solid matter is accumulated in the layer, which contributes to the formation of planetesimals as a result of gravitational instability of the dust phase of the layer. We consider the collective interaction of the layer with the surrounding gas of the protoplanetary disk: shear stresses act on the gas in the dust layer that has a higher orbital velocity than the gas outside the layer, this leads to a loss of angular momentum and a radial drift of the layer. The stress magnitude is determined by the turbulent viscosity, which is represented as the sum of the α-viscosity associated with global turbulence in the disk and the viscosity associated with turbulence that is localized in a thin equatorial region comprising the dust layer and is caused by the Kelvin–Helmholtz instability. The evaporation of water ice and the continuity of the mass flux of the nonvolatile component on the ice line is also taken into account. It is shown that the accumulation of solid matter on either side of the ice line and in other regions of the disk is determined primarily by the ratio of the radii of dust aggregates on either side of the ice line. If after the ice evaporation the sizes (or density) of dust aggregates decrease by an order of magnitude or more, the density of the solid phase of the layer’s matter in the annular zone adjacent to the ice line from the inside increases sharply. If, however, the sizes of the aggregates on the inner side of the ice line are only a few times smaller than behind the ice line, then in the same zone there is a deficit of mass at the place of the modern asteroid belt. We have obtained constraints on the parameters at which the layer compaction is possible: the global turbulence viscosity parameter (α < 10^?5), the initial radial distribution of the surface density of the dust layer, and the distribution of the gas surface density in the disk. Restrictions on the surface density depend on the size of dust aggregates. It is shown that the timescale of radial contraction of a dust layer consisting of meter-sized bodies is two orders of magnitude and that of decimeter ones, an order of magnitude greater than the timescale of the radial drift of individual particles if there is no dust layer.     

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.     

Connection between micrometeorites and Wild 2 particles: From Antarctic snow to cometary ices

Abstract— We discuss the relationship between large cosmic dust that represents the main source of extraterrestrial matter presently accreted by the Earth and samples from comet 81P/Wild 2 returned by the Stardust mission in January 2006. Prior examinations of the Stardust samples have shown that Wild 2 cometary dust particles contain a large diversity of components, formed at various heliocentric distances. These analyses suggest large‐scale radial mixing mechanism(s) in the early solar nebula and the existence of a continuum between primitive asteroidal and cometary matter. The recent collection of CONCORDIA Antarctic micrometeorites recovered from ultra‐clean snow close to Dome C provides the most unbiased collection of large cosmic dust available for analyses in the laboratory. Many similarities can be found between Antarctic micrometeorites and Wild 2 samples, in terms of chemical, mineralogical, and isotopic compositions, and in the structure and composition of their carbonaceous matter. Cosmic dust in the form of CONCORDIA Antarctic micrometeorites and primitive IDPs are preferred samples to study the asteroid‐comet continuum.     

The out of ecliptic distribution of interplanetary dust and its relation to other bodies in the solar system

We discuss the out-of-ecliptic component of the interplanetary dust cloud and its relation to the other small bodies in the solar system. The determination of the mass loss of comets, so far is quite uncertain and doesn't allow a finite study of the mass input to the dust cloud. However it is shown, that the dust particles in the inner solar system, i.e. within the earth orbit are most probable produced from a collisional evolution of larger, meteoroid, fragments of cometary origin. A further component of interstellar dust is especially important in the outer solar system and perhaps for the collisional evolution of the small bodies.     

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.     

On the importance of dust in cometary nuclei

The icy conglomerate model introduced by Whipple more than 40 years ago has been widely accepted in cometary science because it is able to describe numerous cometary phenomena. In this model comets are described as a conglomerate of ices and dust where the ices represent the major component. However, some recent observations seem to favour dust rich comets. The purpose of this paper is to summarize the observational facts supporting the dominance of refractories in comets and to discuss the consequences of a dust dominated nucleus for cometary physics.     

Chemical analysis of mineral dust grains by SIMS: Application to a cometary mission

Analysis of a dust sample (e.g. collected during a cometary rendezvous mission) by SIMS (Secondary Ion Mass Spectroscopy) can provide information on elemental abundances (? 100 amu), the molecular composition of grain surfaces, and isotopic ratios of selected elements. This can be accomplished with dust covering as little as 10^?4 of the collector surface area. In order to demonstrate these capabilities a special experimental set-up for substrate preparation, dust collection and SIMS analysis of dust under ultrahigh vacuum conditions was developed. The comparison of elemental abundance ratios for different olivines and pyroxenes measured with the special SIMS equipment with that measured by an electron microprobe indicated an accuracy for SIMS of the elemental abundance measurements of ? 30%. By varying the energy threshold of secondary ions to be mass-analysed from 0 to 50 eV it is possible to identify molecular ions in the spectra and to estimate their abundance with respect to elemental ions on the same mass line. The ratios of molecular to elemental ions vary by a factor of 1–25. The concept for a future cometary rendezvous experiment as well as first results of chemical investigation on mineral dust samples obtained are reported.     

The thermal structure and the location of the snow line in the protosolar nebula: Axisymmetric models with full 3-D radiative transfer

The precise location of the water ice condensation front (‘snow line’) in the protosolar nebula has been a debate for a long time. Its importance stems from the expected substantial jump in the abundance of solids beyond the snow line, which is conducive to planet formation, and from the higher ‘stickiness’ in collisions of ice-coated dust grains, which may help the process of coagulation of dust and the formation of planetesimals. In an optically thin nebula, the location of the snow line is easily calculated to be around 3 AU, subject to brightness variations of the young Sun. However, in its first 5-10 myr, the solar nebula was optically thick, implying a smaller snowline radius due to shielding from direct sunlight, but also a larger radius because of viscous heating. Several models have attempted to treat these opposing effects. However, until recently treatments beyond an approximate 1 + 1D radiative transfer were unfeasible. We revisit the problem with a fully self-consistent 3D treatment in an axisymmetric disk model, including a density-dependent treatment of the dust and ice sublimation. We find that the location of the snow line is very sensitive to the opacities of the dust grains and the mass accretion rate of the disk. We show that previous approximate treatments are quite efficient at determining the location of the snow line if the energy budget is locally dominated by viscous accretion. Using this result we derive an analytic estimate of the location of the snow line that compares very well with results from this and previous studies. Using solar abundances of the elements we compute the abundance of dust and ice and find that the expected jump in solid surface density at the snow line is smaller than previously assumed. We further show that in the inner few AU the refractory species are also partly evaporated, leading to a significantly smaller solid state surface density in the regions where the rocky planets were formed.     

Laboratory simulation of cometary dust collection and analysis

An experiment for the in situ analysis of cometary dust grains during a rendezvous mission to a comet consists of three elements: (1) Substrate preparation, i.e. cleaning of the substrates in order to reduce the background contamination, (2) dust collection and (3) chemical analysis. All three elements have been simulated in a laboratory experiment. Combined heat treatment (up to 200°C) and surface sputtering of the gold substrates by a glow discharge reduced the surface contamination of Na, Al and K by a factor of 1000 and that of all other contaminants below the detection threshold. During the sputtering of the substrates they acquired a surface roughness of ～5 μm, which improved their collection efficiency for dust particles. Dust particles were shot onto those substrates at speeds up to 200 m s^?1.Chemical analysis using secondary ion mass spectroscopy (SIMS) provided information on elemental abundances, the molecular composition and isotopic ratios of selected elements even at a surface dust coverage of 10^?2–10^?4. Both technical details of the new equipment and results of the first investigation on target surface cleaning and SIMS analysis of dust particles will be reported.