The structure of cometary ionospheres 2. CO-rich comets

The structure of the ionosphere of a CO-rich comet is computed using two different models. The first one, the photochemical model, assumes that the dissociation and ionization of cometary neutrals and ions are due to photoionization and photodissociation by solar uv radiation together with dissociative recombinations and ion-neutral reactions. The second one, the internal source model, also incorporates the ionization and dissociation effects of an electric current dischanging through the inner coma. The generation of this current has been discussed in earlier papers. It is concluded that the internal source model can explain qualitatively the basic morphology of the ionospheres of CO-rich comets such as Humason (1962, VIII) and Morehouse (1908, III), whereas the photochemical model cannot. The main aim of this paper is not so much to provide accurate numerical estimates as to draw attention to a process which may very well dominate the structures of cometary ionospheres.     

H2O + ions in comets: models and observations

An improved magnetohydrodynamic (MHD) model with chemistry is presented. The analysis of the source and sink terms for H₂O ⁺ shows that for small comets up to 11% of water molecules are finally ionized. For large comets (such as Halley) this fraction decreases to less than 3%. From the MHD scaling laws a similarity law for the individual ion densities is deduced which takes into account that the mother molecules are depleted by dissociation. This is applied to H₂O ⁺ ions. Radial density profiles from model calculations, observations by Giotto near comet Halley, and ground based observations of three comets confirm this scaling law for H₂O ⁺ ions. From the similarity law for the density a scaling law for the column density is derived which is more convenient to apply for ground based observations. From these scaling laws methods are derived which allow the determination of the water production rate from the ground based images of the H₂O ⁺ ions. Finally, the two dimensional images of model column densities are compared with observations.     

From the Oort cloud to observable short-period comets – I. The initial stage of cometary capture

We investigate the first stage of the dynamical evolution of Oort cloud comets entering the planetary region for the first time. To this purpose, we integrate numerically the motions of a large number of fictitious comets pertaining to two samples, both with perihelion distances up to 5.7 au and random inclinations; the first sample is composed of comets whose orbits have at least one node close to 5.2 au, while the second is not subject to this constraint. We examine the orbits when the comets come to aphelion after their first perihelion passage within the planetary region, and find that there is a clear statistical dependence of the energy perturbations on the Tisserand parameter. There appear to be two main processes, of comparable importance, governing the shortening of semimajor axes to values of less than 1000 au, i.e. planetary close encounters, especially with Jupiter, and indirect perturbations due to the shifting of the motion from barycentric to heliocentric and back; the former process mostly affects comets crossing the ecliptic at about 5.2 au, or on low-inclination orbits, while the latter mostly affects comets of small perihelion distance. This last result may help to understand the relative paucity of Halley-type comets with perihelion distances larger than about 1.5 au.     

Fan-shaped coma,orientation of rotation axis,and surface structure of a cometary nucleus I. Test of a model on four comets

Conspicuous anisotropy in the outgassing from comets, especially from short-period ones, appears to be the factor responsible for a frequent occurrence of a fan-shaped coma, extending in the general direction of the Sun. It is proposed that the pattern of deviations from the sunward direction contains information on the orientation of the spin axis and on the time lag in the sublimation process, which in turn provides insight into the nature of the nuclear surface. A simple model of a spherical rotating nucleus is formulated and a trial-and-error technique devised to determine the axis-orientation constants and a lage angle, a meaasure of the time lag in units of the rotation period. The results of application of this method to periodic comets Encke, Tempel 2, Borrelly, and Schwassmann-Wachmann 3 are presented. It is shown that the sense of rotation determined in this fashion is consistent with the results established for three of the four comets from the transverse component of the nongravitational force affecting their orbital motions. It is found that in general the time lag is strongly time dependent and that lag angles approaching 90° are rather common near perihelion, suggesting a complex surface structure that involves an insulting crust of dust of variable thickness and strength. These results are compared with the observed lightcurves of the four comets and with the calculated distributions of integrated insolation at the nuclear surface as functions of the cometocentric latitude and time. Noticed is a tendency of the comets to turn their spin axes to the Sun near perihelion and to replace, on the outbound leg of orbit, the established fan-orientation pattern by a “late”-tail pattern indicative of old, slowly accelerated particles. It is suggested that the motion of P/Schwassmann-Wachmann 3, which is due for a favorable return in 1979, was affected by a secular deceleration in 1930.     

The destruction of cometary grains and changes in the luminosity of comets

One explanation of the sudden changes in the brightness of comets is proposed based on the author's earlier suggestions involving the fragmentation of cometary grains. Within the inner coma, a core‐mantle model of the structure of grains is assumed. The proposed mechanism is a combination of electrostatic stress and thermodynamical fragmentation of the cometary grains water‐ice mantle. It has been shown that the vapour pressure of volatile inclusions placed in the waterice mantle of grains can increase sufficiently to cause their fragmentation. It takes place before grains can completely sublime into the vacuum away. Numerical calculations have been carried out for a large range of values of probable physical characteristics of cometary material. The proposed approach yields increases in cometary brightness consistent with observations of typical cometary outbursts. It is concluded that this approach can provide an explanation of the sudden change in activity of comets for a wide range of heliocentric distances (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The structure of cometary atmospheres

The temperature distributions in cometary atmospheres at various heliocentric distances for comets of Bennett and Encke types have been calculated by taking into account heating due to the absorption of solar ultraviolet radiation, cooling by H₂O far infrared emission, and various dynamical processes (expansion, advection, and thermal conduction). The agreement of the results with the observations is in general satisfactory. The conversion of CH₄ and NH₃ to CO and N₂ through thermochemical reaction with H₂O is concluded to be impossible, since the temperature is too low at a heliocentric distance 1.5 AU where CO⁺ ions begin to be observable.     

Dynamical evolution of comets and the problem of cometary fading

Possibilities to explain the observed 1/a-distribution are discussed in the light of improved understanding of the dynamical evolution of long-period comets. It appears that the fading problem applies both to single-injection and continuous-injection models. Although uncertainties due to nongravitational effects do not allow detailed results to be drawn from the observed 1/a-distribution at small perihelion distance q, that for q 1.5 AU shows that a constant fading probability cannot explain all the features of the observed distribution. Assuming that comets can reappear following a period of fading, values for the assumed constant fading and renewal probabilities, and the total cometary flux have been estimated for q > 1.5 AU.     

The structure of cometary atmospheres

The distributions of various kinds of molecular ions in the atmospheres of new and old comets made up from dirty ice of the second kind (H₂O ice and hydrate clathrates of CO and N₂) have been computed at various heliocentric distances, by taking into account photoionization, ionmolecular reactions, electron-ion recombinations, and some transport effects. The results have been compared with observations and other computations. It is argued that dirty ice of the second kind model will impose a restriction on the theory of the origin of the solar system.     

Dynamical evolution of comets and the problem of cometary fading

Possibilities to explain the observed 1/a-distribution are discussed in the light of improved understanding of the dynamical evolution of long-period comets. It appears that the ‘fading problem’ applies both to single-injection and continuous-injection models. Although uncertainties due to nongravitational effects do not allow detailed results to be drawn from the observed 1/a-distribution at small perihelion distance q, that for q ? 1.5 AU shows that a constant fading probability cannot explain all the features of the observed distribution. Assuming that comets can reappear following a period of fading, values for the assumed constant fading and renewal probabilities, and the total cometary flux have been estimated for q > 1.5 AU.     

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.     

Thermal destruction of cometary materials – application to activity of comets

Destruction mechanisms connected with thermodynamical behaviour of cometary material are reviewed with a special consideration of their effects on activity of comets. Consequences of thermal stresses which occur in the interior of a comet are discussed with reference to changes in the cometary brightness. Moreover, thermal destruction of grains placed in the head of the comet as well as on the surface of the nucleus is considered. It has been shown that the destruction of the cometary material can lead to an essential increase in the activity of the comet. Calculations have been carried out for a large assumed range of cometary parameters. The obtained simulated changes in the brightness of comets are consistent with the ones observed during the real variations and outbursts of brightness. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Interstellar H2O masers. a tracer of galactic spiral structure?

The large-scale distribution of interstellar H₂O masers is given in this paper. Present results show that H₂O masers can trace galactic spiral structure, and we also briefly discuss how to obtain a more accurate distribution of H₂O masers from future observations.     

Numerical simulation of comet nuclei I. Water-ice comets

A one-dimensional simulation of pure water-ice cometary nuclei is presented, and the effect of the nucleus as a heat reservoir is considered. The phase transition from amorphous to crystalline ice is studied for two cases: (1) where the released latent heat goes entirely into heating adjacent layers and (2) where the released latent heat goes entirely into sublimation. For a Halley-like orbit it was found that for case 1 the phase boundary penetrates about 15 m on the first orbit and does not advance until sublimation brings the surface to some 10 m from the phase boundary. For case 2 the phase boundary penetrates about 1 m below the surface and remains at this depth as the surface sublimates. For an orbit like that of Schwassmann-Wachmann 1 the phase boundary penetrates about 50 m initially for case 1 and about 1 m for case 2. There is no further transformation until the entire comet is heated slowly to near the transition temperature, after which the entire nucleus is converted to crystalline ice. For an Encke-type orbit case 1 gives a nearly continuous transition of the entire nucleus to crystalline ice, while for case 2 the initial penetration is about 8 m and remains at this depth relative to the surface as sublimation decreases the cometary radius. Thus the entire comet is converted to crystalline ice just before it is completely dissipated.     

Large cometary grains – their destruction and changes in the luminosity of comets

The catastrophic thermodynamic destruction of large cometary heterogeneous grains lying on the surface of a comet nucleus is examined. The core–mantle grain-structure model is assumed. Grain fragmentation as an explanation of sudden changes in cometary brightness is proposed. The approach presented to the problem of cometary outbursts is a development of a previous author's paper. The proposed mechanism is based on the idea of thermodynamical destruction of heterogeneous cometary grains. Numerical simulations have been carried out for a wide range of values of physical characteristics of cometary material. The results obtained are consistent with observational data. The main conclusion of this paper is that thermodynamical fragmentation of large grains can explain variations in brightness and also outbursts of comets.     

H2O maser pumping: The effect of quasi-resonance energy transfer in collisions between H2 and H2O molecules

The effect of quasi-resonance energy transfer in collisions between H₂ and H₂O molecules in H₂O maser sources is investigated. New data on the state-to-state rate coefficients for collisional transitions for H₂O and H₂ molecules are used in the calculations. The results of ortho-H₂O level population inversion calculations for the 22.2-, 380-, 439-, and 621-GHz transitions are presented. The ortho-H₂O level population inversion is shown to depend significantly on the population distribution of the para-H₂ J = 0 and 2 rotational levels. The possibility of quasi-resonance energy transfer in collisions between H₂ molecules at highly excited rotational-vibrational levels and H₂O molecules is considered. The quasi-resonance energy transfer effect can play a significant role in pumping H₂O masers in the central regions of active galactic nuclei and in star-forming regions.     

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.