Modeling a cometary nucleus

Considerations are summarized concerning the physical properties of and plasma phenomena around a cometary nucleus aiming at a new model of the nucleus and its interaction with the solar wind.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Physical-mechanical properties of a cometary nucleus

Physical-mechanical properties of cometary nuclei matter are described in detail. As compared to other Solar System bodies, cometary nuclei are characterized by low strength properties. The ultimate tensile strength of cometary matter and cometary nuclei on the whole is about 2 kPa. An analysis performed based on a rheological model of a self-gravitating triaxial solid body showed that cometary nuclei less than 50–60 km (this actually being all known comets) are characterized by a constant ultimate tensile strength which is determined only by the matter composition and structure. The effective ultimate tensile strength for bodies larger than 50–60 km is determined by the body mass and figure parameters and increases according to the quadratic law depending on the body dimensions and mass. Such an increase of the effective strength can explain the absence or deficit of cometary nuclei more than 60 km in size, since it can significantly affect the parameters of the parent body destruction and the formation of a secondary population. The dependence of the mechanism and character of destruction on the parameters of the figure for Kuiper objects more than 50–60 km is size can yield a deficit of the population of the bodies whose figure parameters are a/c > 1.75 with respect to the bodies with a/c < 1.75 figure parameters.     

Organic component of cometary ice

Investigations of the luminescence of frozen hydrocarbon particles of icy cometary halo have been made. The process of luminescence of icy particles in shortwavelength solar radiation field is considered. The comparative analysis of observed and laboratory data leads of 72 luminescent emission lines in the spectrum of 153P/Ikeya-Zhang comet. Several aspects of the problem are discussed.     

Theoretical aspects and interpretation of thermal measurements concerning the subsurface investigation of a cometary nucleus

Part of the lander payload for the comet rendezvous mission Rosetta is the thermal probe multi-purpose sensors for surface and subsurface science (MUPUS). In this paper, we discuss the relationship of the expected MUPUS data to structural and textural parameters of the near-surface layers of the cometary nucleus. Such properties could be crucial parameters concerning the formation and evolution of the nucleus. Thus, we calculate the thermal conductivity of a porous material in terms of microstructural parameters, using a geometrical model with a solid matrix, a surrounding pore space and a distinct contact area between different particles. We include the possibility that a significant amount of heat may be transported by pore filling vapour in addition to heat conducted via the matrix. Furthermore, we consider that the heat is transmitted through only a fraction of the grains and these are organized into a chain-like structure. These chains—and not the single grains—should be regarded as the basic unit of structure. Applying our model to measured thermal conductivities of porous water ice, we interpret the material in terms of microparameters and estimate the effective size of the contact area and the effective pore radius. The results are in good agreement with our knowledge of the prepared samples. Contrary, we can also show that popular models used in cometary research do not fit with laboratory data at all.     

Monte Carlo modelling of cometary dynamics

Monte Carlo simulations can either be viewed as a numerical method for solving evolutionary equations or as a way for statistically modelling the outcome of chaotic dynamical systems. Thus they are well suited for treating many aspects of cometary dynamics. We present a critical review of past applications of Monte Carlo simulations for both long- and short-period comets indicating the strength and weaknesses of the methods with suggestions for future applications.     

A model of the macro-features of the surface layer of a cometary nucleus

The macro-features of the surface layer of a 'fresh' cometary nucleus are modelled by assuming that the dust and the snow particles of which it consists both have a mass distribution index of 1.65, and that the dust/gas mass ratio is 0.45. Conclusions are drawn as to how this model helps us to understand the cometary sublimation process and the cometary surface layer. The latter most probably consists of weak, low-density, friable, slightly dusty snow. Its ability effectively to support even the small weight of, say, the Rosetta landing probe is in considerable doubt.     

The volatile fraction of the cometary nucleus

In order to prepare a flyby mission to Comet Encke, six different sources of information on the possible chemical composition of the cometary nucleus are compared. These are: the neutral and charged radicals and molecules observed in cometary spectra; the chemical composition of type I carbonaceous chondrites; the meteor spectra; the metallic ions collected in the upper atmosphere and correlated with the meteor shower associated with Comet Encke; and finally the volatile molecules observed in a volatile-rich sample of lunar soil, that were interpreted as a possible cometary impact. Possible molecular abundances for the volatile fraction of Comet Encke are tentatively proposed.     

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 note on the mass-loaded MHD flow of the solar wind towards a cometary nucleus

Dependence of the central velocity gradients on Hubble's type is presented for 78 spiral galaxies with existing rotation curves. Also the dependence of the maximum rotational velocities of 27 galaxies on both Hubble's type and the luminosity is studied. The central velocity gradient is shown to be related with Hubble's type. Maximum rotational velocities of 27 galaxies of our sample depend on Hubble's type such that the mean values of maximum rotational velocity decrease from Sa through Sc. It is also determined that there is a dependence of the maximum rotational velocity on the absolute blue magnitude for each intrinsic Hubble type. For each Hubble type, maximum rotational velocity increases with increasing absolute blue magnitudes.     

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.     

Mechanistic studies on the decomposition of carbon suboxide in a cometary ice analog

A cometary ice analog sample consisting primarily of carbon suboxide ice (C₃O₂) was produced from the irradiation of its precursor, carbon monoxide. This carbon suboxide sample was subjected to irradiation with energetic electrons at 10 K to simulate the interaction of carbon suboxide-rich cometary analog ices with ionizing radiation. The destruction of carbon suboxide as well as the production of the primary degradation products, dicarbon monoxide (C₂O), and carbon monoxide (CO), were monitored quantitatively by infrared spectroscopy in situ; the gas phase was simultaneously sampled via quadrupole mass spectrometry. A kinetic model was produced to help explain the decomposition kinetics of carbon suboxide in cometary ices and to infer the underlying reaction mechanisms.     

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.     

Direct statistical simulation of the near-surface layers of a cometary atmosphere. II: A nonspherical nucleus

The study presents the results of numerical simulations of mass-transfer processes in the near-surface layer of the cometary nucleus and in the inner part of the cometary atmosphere, which is formed under the action of solar radiation. The gas-kinetic model of the inner part of the cometary atmosphere surrounding a spherical nucleus (Skorov et al., 2004) is extended to the case of a nonspherical nucleus with axial symmetry. After high-resolution images of comets 19P/Borrelly and Wild 2 have been obtained by Deep Space 1 and Stardust spacecraft, such an extension seems to be vital and important. The nucleus and the inner part of the coma are closely related to each other because of the permanent exchange of energy and mass; therefore, they are modeled consistently. As in the first part of our study, the boundary conditions at the inner boundary of the simulation domain, which are necessary for gas-kinetic simulations, were determined from the self-consistent model of heat and mass transfer in a porous cometary nucleus that was developed earlier by the authors. The model took into account the volumetric character of the radiation absorption in a porous sublimating medium, the kinetic regime of the transport of sublimation products in the pores, and the backward gas fluxes from the coma due to intermolecular collisions. We considered different models of the nucleus structure that determined the effective gas production. Using the direct simulation Monte Carlo method, we computed the two-dimensional gas flow from a heterogeneous nonspherical cometary nucleus. The simulations were performed using the SMILE software. The parallel computer implementation of the software made it possible to calculate the spatial structure of the gas flow for the entire circumnucleus zone.     

Possibilities of using extreme observations to estimate cometary nucleus sizes

Not considering very rare in situ measurements of cometary nuclei, observations of comets at large heliocentric distances are the only direct source of our knowledge on their sizes. Observations of a cometary nucleus in pure reflected sunlight, at the time when coma is absent, are the way in which the nucleus size can be estimated. Probabilities that extreme observations represent non—active stages of cometary nuclei and also reliability of derived cometary nucleus sizes are investigated. Statistical analysis is based on a sample of 2842 photometric observations of 67 long-period comets observed at large heliocentric distances. For any long-period comet, there is a probability of 2:3 that the sizes derived on the basis of observations at extreme distances are in good agreement with the real nucleus sizes. For new comets in Oort's sense the probability is 3:4 independent of investigated arcs of orbits. For old comets a chance to estimate correct sizes is 1:2 but on the pre-perihelion arc only 1:3. It is also demonstrated that a premature start of activity prior to perihelion or a longer fading after perihelion is more frequent than a short-time isolated activity at large heliocentric distances.     

Hydrodynamic study of condensation and sublimation of ice particles in cometary atmospheres

Condensation of ice particles in the vicinity of a cometary nucleus as pointed out by Yamamoto and Ashihara (1985, Astron. Astrophys. 152, L17–L20) is fully studied by solving the hydrodynamic equations for ice particles and H₂O gas. Formulation is presented for the hydrodynamics including condensation and sublimation of ice particles, and energy exchange between ice particles and the gas in a dustless comet. It is shown that sublimation of ice particles condensed leads to heating of the ambient gas, resulting in the higher gas temperature than those predicted by the models proposed so far. Compared with the previous calculation carried out under the conditions at the encounter of the spacecraft to Halley's Comet, the present results have revealed that the survival distance of ice particles against sublimation is longer, but that their size, which attains its maximum of 6.4 Å at 51 km from the center of the nucleus, is smaller, resulting in a larger fraction of uncondensed H₂O gas. Discussion is given on the physical conditions under which condensation of ice particles can take place in cometary comae.     

A fully 3-dimensional thermal model of a comet nucleus

A 3-D numerical model of comet nuclei is presented. An implicit numerical scheme was developed for the thermal evolution of a spherical nucleus composed of a mixture of ice and dust. The model was tested against analytical solutions, simplified numerical solutions, and 1-D thermal evolution codes. The 3-D code was applied to comet 67P/Churyumov-Gerasimenko; surface temperature maps and the internal thermal structure was obtained as function of depth, longitude and hour angle. The effect of the spin axis tilt on the surface temperature distribution was studied in detail. It was found that for small tilt angles, relatively low temperatures may prevail on near-pole areas, despite lateral heat conduction. A high-resolution run for a comet model of 67P/Churyumov-Gerasimenko with low tilt angle, allowing for crystallization of amorphous ice, showed that the amorphous/crystalline ice boundary varies significantly with depth as a function of cometary latitude.     

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 evolution and activity of cometary nuclei

The thermal evolution of a spherical cometary nucleus (initial radius of 2.5 km), composed initially of very cold amorphous ice and moving in comet Halley's orbit, is simulated numerically for 280 revolutions. It is found that the phase transition from amorphous to crystalline ice constitutes a major internal heat source. The transition does not occur continuously, but in five distinct rounds, during the following revolutions: 1, 7, 40-41, 110-112, and 248-252. Due to the (slow) heating of the amorphous ice between crystallization rounds, the phase transition front advances into the nucleus to progressively greater depths: 36 m on the first round, and then 91 m, 193 m, 381 m, and 605 m respectively. Each round of crystallization starts when when the boundary between amorphous and crystalline ice is brought to approximately 15 m below the surface, as the nucleus radius decreases due to sublimation. At the time of crystallization, the temperature of the transformed ice rises to 180 K. According to experimental studies of gas-laden amorphous ice, a large fraction of the gas trapped in the ice at low temperatures is released. Whereas some of the released gas may find its way out through cracks in the crystalline ice layer, the rest is expected to accumulate in gas pockets that may eventually explode, forming "volcanic calderas." The gas-laden amorphous ice thus exposed may be a major source of gas and dust jets into the coma, such as those observed on comet Halley by the Giotto spacecraft. The activity of new comets and, possibly, cometary outbursts and splits may also be explained in terms of explosive gas release following the transition from amorphous to crystalline ice.