Mass Transfer in the Near-Surface Layer of a Cometary Nucleus: A Gas-Kinetic Approach

A self-consistent model of the kinetically nonequilibrium near-surface layer of a cometary nucleus is developed on the basis of the gas-kinetic approach. The weight method of direct statistical simulation is used to model numerically the two-dimensional gas outflow from an ice sample subjected to radiative heating. The effective coefficient of water ice sublimation is estimated. Mass transfer in a porous ice and mineral (scattering) nonisothermal medium is investigated by the method of test particles, and the effective gas release is evaluated taking into account the proper rotation of the cometary nucleus for various model parameters. In these calculations, allowance is made for the kinetic character of the flow and volume sublimation and condensation of the volatile constituents of the material of the cometary nucleus.     

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.     

Infrared heating of Comet Halleys atmosphere

The warm circumnuclear dust in the inner cometary coma reradiates in the IR in the wavelength range of the ground state rotational band of the dominant atmospheric molecule, H₂O. However, the interaction of this radiation with H₂O has hitherto not been taken into account in cometary atmospheric models. Here we have extended our earlier two-phase, multifluid model of the dusty atmosphere by including this effect. Although this IR radiation initially pumps the rotational levels of H₂O, frequent intermolecular collisions in the inner coma transfer this energy from rotational modes to translational modes. As a result the temperature in the innermost coma no longer decreases to about 10 K, as predicted by the earlier models, but reaches a minimum of only about 120 K.     

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.     

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.     

The neutral atmospheres of comets

In this paper we have endeavored to critically evaluate our present understanding of cometary atmospheres. Following a brief introduction of the significance of the study of cometary atmospheres (Section 1), the relevant photometric and spectroscopic observations are summarized in Section 2.The interaction with the solar radiation, with regard to both the excitation of the observed species as well as the dissociation of stable molecules evaporating from the nucleus, is considered in Sections 3 and 4. The gas phase chemistry likely to take place in the dense inner coma is next considered in Section 5.The exospheric and hydrodynamic models of the expanding cometary atmosphere are considered in detail in Section 6, and both their limitations as well as possible improvements are discussed.The observed chemical composition of the neutral atmosphere and the inferred chemical composition of the volatile component of the nucleus, together with possible variations between different classes of comets is next considered in Section 7, and their possible cosmogonic significance is discussed.In conclusion, some of the important directions in which future research should progress, in order to provide more complete and secure knowledge of cometary atmospheres, are stressed (Section 8).Astrophysics and Space Science Review Paper.     

Challenging a Paradigm: Do We Need Active and Inactive Areas to Account for Near-Nuclear Jet Activity?

We briefly describe an advanced 3D gas dynamical model developed for the simulation of theenvironment of active cometary nuclei. The model canhandle realistic nucleus shapes and alternative physical models for the gas and dust production mechanism.The inner gas coma structure is computed by solving self-consistently(a) near to the surface the Boltzman Equation(b) outside of it, Euler or Navier-Stokes equations.The dust distribution is computed from multifluid ``zero-temperature' Euler equations,extrapolated with the help of a Keplerian fountain model.The evolution of the coma during the nucleus orbital and spin motion,is computed as a succession of quasi-steady solutions. Earlier versions of the model using simple,``paedagogic' nuclei have demonstrated that the surface orographyand the surface inhomogeneity contribute similarly to structuring the near-nucleusgas and dust coma,casting a shadow on the automatic attribution of such structures to ``active areas'.The model was recently applied to comet P/Halley, for whichthe nucleus shape is available. In the companion paper of this volume,we show that most near-nucleus dust structuresobserved during the 1986 Halley flybys are reproduced, assuming that the nucleus is strictly homogeneous. Here, we investigate the effect of shape perturbations and homogeneityperturbations. We show that the near nucleus gas coma structure is robust vis-a-vissuch effects. In particular, a random distribution of active and inactive areaswould not affect considerably this structure, suggesting that such areas,even if present, could not be easily identified on images of the coma.     

Rotation of the nucleus of comet p/Arend-Rigaux

Time-resolved charge-coupled device photometry of Comet p/Arend-Rigaux shows a cyclic variation in cometary brightness consistent with the periods T₁ = 574 ± 5 min (9.58 ± 0.08 hr) and T₂ = 407 ± 5 min (6.78 ± 0.08 hr). The variation has a 30% range and is confined to the inner coma. The relative photometric stability of the outer coma indicates that the variations in the inner coma are associated with the nucleus and probably result from its rotation at, or at a multiple of, one of the above periods.     

The photochemistry and dynamics of a dusty cometary atmosphere

A self-consistent solution of the dynamical and thermal structure of an H₂O-dominated, two-phase, dusty-gas cometary atmosphere has been obtained by solving the simultaneous set of differential equations representing conservation of number density, momentum and energy together with the transfer of solar radiation in the streams responsible for the major photolytic processes and the heating of the nucleus. The validity of the model is restricted to the collision-dominated region where all the gas species are assumed to attain a common velocity and common temperature. Two models are considered for the transfer of solar radiation through the circum-nuclear dust halo. In the first only the direct extinction by the dust is considered. In the second, the finding of some recent models, that the diffuse radiation field due to multiple scattering by the dust halo more or less compensates for radiation removed by direct absorption when the optical depth is near unity, is approximated by neglecting the attenuation of the radiation by the dust altogether.As has been shown earlier, the presence of dust results in a transonic solution, and it is obtained by a two-step iterative procedure which makes use of the asymptotic behaviour of the radiation fields sufficiently far from the nucleus and a regularity condition at the sonic point.The calculations were performed for a medium sized comet (R _n =2.5 km) having a dust to gas production rate ratio of unity, at a heliocentric distance of 1 AU. The dust grains were assumed to be of the same radius (1), of low density (1g cm^–3) and be strongly absorbing (having the optical properties of magnetite).The main effect of the dust on the cometary atmosphere is dynamic. While the dust-gas coupling persists to about 20R _n , the strong throat effect of the dust friction on the gas causes the latter to go supersonic quite rapidly. Consequently the sub-sonic region around the nucleus is very thin, varying between 45 and 85m in the two models considered. On the other hand, while this highly absorbing dust has a temperature substantially above that of the gas in the inner coma, heat exchange between them does not significantly change the temperature profile of the gas. This is because of the predominance of the expansion cooling, and even more importantly, the IR-cooling by H₂O, in the inner coma. Consequently, the gas temperature goes through a strong inversion, as in the dust-free case, achieving a temperature as low as about 6K within about 50km of the nucleus, before increasing to about 700K atr=10⁴km, due to the high efficiency of photolytic heating over the cooling process in the outer coma. The Mach number achieves a maximum value of about 10 at the distance of the temperature minimum, thereafter steadily decreasing to a value of about 2.5 atr10⁴km.It is shown that while the dust attenuation has a strong effect on the production rate of H₂O, it also has an interesting effect on the electron density profile. It increases the electron density in the inner coma over the unattenuated case, while at the same time, decreasing it in the outer coma. In conclusion, the limitations of the present model and the necessity to extend it using a multi-fluid approach are discussed.     

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.     

Millimeter-wave experiments for cometary space missions

Predicted brightness temperatures for a variety of cometary nucleus models, consisting of homogeneous layers comprised of mixtures of water ice and refractory grains, are presented as functions of wavelength. These illustrative spectra are computed using simple radiative transfer techniques adapted from modeling of terrestrial ice and snow fields. The computed millimeter-wave spectra are sensitive to the values of physically significant nucleus parameters such as crust thickness, the subsurface temperature gradient, and the boundary temperature of the sublimating surface. It appears that millimeter-wave sensing from an interplanetary spacecraft is an effective means for distinguishing between alternate models of the nucleus and for inferring the rough physical state of substrata; modern theories on the nature of the nucleus indicate that sublimation from the substrata provides the gas phase cometary volatiles that are actually observed from ground-based and Earth-orbiting instruments. Antenna beam dilution is a major obstacle for ground-based molecular spectral line radio observations (e.g., water and ammonia) of comets but a modest millimeter-wave radiometer system in the near vicinity of the comet would not be subject to this problem. Such a system can make definitivebservations of several candidate parent molecules in the gas phase and should contribute to the understanding of the physics of the inner coma.     

Monte-Carlo and multifluid modelling of the circumnuclear dust coma II. Aspherical-homogeneous, and spherical-inhomogeneous nuclei

We use our newly developed Dust Monte-Carlo (DMC) simulation technique [Crifo, J.F., Lukianov, G.A., Rodionov, A.V., Zakharov, V.V., 2005. Icarus 176, 192-219] to study the dynamics of dust grains in the vicinity of some of the benchmark aspherical, homogeneous cometary nuclei and of the benchmark spherical, inhomogeneous nuclei studied by us precedingly. We use the interim unrealistic simplifying assumptions of grain sphericity, negligible nucleus rotation rate, and negligible tidal force, but take accurately into account the nucleus gravitational force, gas coma aerodynamic force, and solar radiation pressure force, and consider the full mass range of ejectable spherical grains. The resulting complicated grain motions are described in detail, as well as the resulting complicated and often counter-intuitive dust coma structure. The results are used to answer several important questions: (1) When computing coma dust distributions, (a) is it acceptable to take into consideration only one or two of the above mentioned forces (as currently done)? (b) to which accuracy must these forces be known, in particular is it acceptable to represent the gravity of an aspherical nucleus by a spherically symmetric gravity? (c) how do the more efficient but less general Dust Multi-Fluid (DMF) computations compare with the DMC results? (2) Are there simple structural relationships between the dust coma of a nucleus at small heliocentric distance rh, and that of the same nucleus at large rh? (3) Are there similarities between the gas coma structures and the associated dust coma structures? (4) Are there dust coma signatures revealing non-ambiguously a spherical nucleus inhomogeneity or an homogeneous nucleus asphericity? (5) What are the implications of the apparently quite general process of grain fall-backs for the evolution of the nucleus surface, and for the survival of a landed probe?     

A comparison of modeled and observed intensity profiles for C2, CN, and the blue continuum for Comet Bradfield (1987s)

Intensity profiles were obtained for the C₂ and CN emission and blue continuum of Comet Bradfield (1987s), from observations obtained over a 10 week period starting shortly before perihelion. Model intensity profiles were produced and then fitted to the observed profiles, and used to put constraints on some of the dust and gas parameters. Most of these parameters, including the gas and dust outflow speeds from the cometary nucleus and the molecular lifetimes, were consistent with expected values. The best fitting models incorporate significant dust particle fragmentation and extended emission of CN from dust, both occurring in the inner coma. In addition, although there may have been enhancement of gas and dust emission on the sunward side of the cometary nucleus, it appears that the tailward side maintained a significant level of activity.     

Chemical and physical properties of gas jets in comets: I. Monte Carlo model of an inner cometary coma

We describe a 3-dimensional, time-dependent Monte Carlo model developed to analyze the chemical and physical nature of a cometary gas coma. Our model includes the necessary physics and chemistry to recreate the conditions applicable to Comet Hale-Bopp when the comet was near 1 AU from the Sun. Two base models were designed and are described here. The first is an isotropic model that emits particles (parents of the observed gases) from the entire nucleus; the second is a jet model that ejects parent particles solely from discrete active areas on the surface of the comet nucleus, resulting in coma jets. The two models are combined to produce the final model, which is compared with observations. The physical processes incorporated in both base models include: (1) isotropic ejection of daughter molecules (the observed gases) in the parent's frame of reference, (2) solar radiation pressure, (3) solar insolation effects, (4) collisions of daughter products with other molecules in the coma, and (5) acceleration of the gas in the coma. The observed daughter molecules are produced when a parent decays, which is represented by either an exponential decay distribution (photodissociation of the parent gas) or a triangular distribution (production from a grain extended source). Application of this model to the analysis the OH, C₂ and CN gas jets observed in the coma of Comet Hale-Bopp is the focus of the accompanying paper [Lederer, S.M., Campins, H., Osip, D.J., 2008. Icarus, in press (this issue)].     

A multi-fluid model of an H2O-dominated dusty cometary atmosphere

A self-consistent multi-fluid solution of the dynamical and thermal structure of an H₂O-dominated, two-phase dusty-gas cometary atmosphere has been obtained by solving the simultaneous set of differential equations representing conservation of number density, momentum and energy, together with the transfer of solar radiation in streams responsible for the major photolytic processes and the heating of the nucleus. The validity of this model, as in the earlier single-fluid ones, is restricted to the collision-dominated region where all the heavy species (ions and neutrals) are assumed to achieve a common temperature and velocity. However, recognizing that the photo-produced hydrogen is rather inefficient in exchanging energy with the heavier species we treat the hydrogen separately: it is assumed to be composed of a thermalized component (the second fluid) and a pre-thermal component.The present model, which is transonic due to the presence of the dust in the inner coma, causes the heavy species to expand subsonically from the nucleus and to smoothly traverse the sonic point within about 45 m of the nucleus, although the dust-gas coupling persists to about 50 km. While the temperature of the heavy species goes through a strong inversion within about 100 km from the nucleus, due to the effects of IR cooling and expansion, it increases to about 300–400 K in the outermost part of the collision-dominated coma due to UV photolytic heating. These temperatures are smaller by a factor of 2–3 from the predictions of the earlier single-fluid models, which assumed instant thermalization of the photo-produced hydrogen.While the velocities of the heavy species and the thermal hydrogen increase to, respectively, 1.1 km s^–1 and 1.6 km s^–1 in the outer (collisional) coma, the velocity of the pre-thermal component reaches about 15 km s^–1. This latter value is consistent with Ly- observations of a number of comets, which implies a fast (20 km s^–1) hydrogen component in the outer coma. The boundary of the exosphere, where the non-thermal hydrogen dominates, is predicted to be around 1.5×10⁴ km from the nucleus. The calculations are for a comet of radius 2.5 km with a dust/gas ratio of 1, at a heliocentric distance of 1 AU.     

Formation of jets in Comet 19P/Borrelly by subsurface geysers

Observations of the inner coma of Comet 19P/Borrelly with the camera on the Deep Space 1 spacecraft revealed several highly collimated dust jets emanating from the nucleus. The observed jets can be produced by acceleration of evolved gas from a subsurface cavity through a narrow orifice to the surface. As long as the cavity is larger than the orifice, the pressure in the cavity will be greater than the ambient pressure in the coma and the flow from the geyser will be supersonic. The gas flow becomes collimated as the sound speed is approached and dust entrainment in the gas flow creates the observed jets. Outside the cavity, the expanding gas loses its collimated character, but the density drops rapidly decoupling the dust and gas, allowing the dust to continue in a collimated beam. The hypothesis proposed here can explain the jets seen in the inner coma of Comet 1P/Halley as well, and may be a primary mechanism for cometary activity.     

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.     

Sources of cometary radicals and their jets: Gases or grains

The recent discovery of CN and C₂ gas jets in comet Halley has led to basic speculation as to their physical source mechanism. A basic quantitative study of the photosputtering of CHON grains and the spatial evolution of trace gas jets is presented here. Two possible single sources, a parent gas and CHON grains, for both the jet and the background gas, are also investigated. It is shown that a parent trace gas jet will remain focused out to distances as large as 10⁵ km from the nucleus and could provide a source for the observed radical jets. Conversely, photosputtering of small CHON grains by solar UV radiation can provide the source not only for cometary CN and C₂ but also possibly for inner coma C atoms and C⁺ ions. However, constraints on the size and/or morphology of the contributing grains themselves are found. Isotropic speed components comparable to the outflow speed are likely to be added to radicals upon production from either the CHON grain or the parent gas source and will yield a radical jet which becomes more diffuse with increasing distance from the nucleus. However, in neither case will the radical jet completely isotropicize; it will be confined generally to a quadrant as projected on the sky plane. Observational tests which can be made once the large set of in situ and remote observations have been analyzed are suggested to distinguish between the two scenarios.