Navier-Stokes and direct Monte Carlo simulations of the circumnuclear coma II. Homogeneous, aspherical sources

The dayside near-nucleus comae formed by solar-driven sublimation from two different aspherical nuclei made of an homogeneous mixture of ice and dust are computed by (1) solving Navier-Stokes equations and (2) direct Monte Carlo simulations, for different nucleus sizes, heliocentric distances, and dust-to-ice mixing ratios. Excellent agreement between the two methods is found down to surprisingly low production rates; it is found that the limit of validity of the first method is not simply related to the coma rarefaction: a new dimensionless number is tentatively offered to characterize this limit. The present solutions show that the weak shocks always present in the fluid coma persist practically down to truly free-molecular conditions, excluding the observational discovery of a structureless coma. They also show that rarefied flow in the near-nucleus coma can have a quite complicated structure, in particular inside topographic depressions. As an example, coma recondensation on the sunlit flanks of a cavity was found to be possible. We compute, for the first time, a true collisionless coma and show that structures are still present in it but are confined to the immediate vicinity of the surface. Finally, we describe in detail the kinetic conditions in a rarefied water coma, i.e., the velocity distribution asymmetry and the rotational-translational nonequilibrium. The significance of the results for future missions to comets is outlined.     

Navier-Stokes and direct Monte-Carlo simulations of the circumnuclear gas coma: III. Spherical, inhomogeneous sources

We pursue our program of comparative simulations of the cometary gas coma by the two most advanced techniques available: (1) numerical solution of Navier-Stokes equations coupled to the Boltzman equation in the surface boundary layer, and (2) direct Monte-Carlo simulation. Here, we consider two different spherical but compositionally inhomogeneous nuclei, at three very different levels of gas production. The results show the same excellent agreement between the two methods in a domain adjacent to the surface as found precedingly, practically down to free-molecular conditions. A wealth of coma density patterns with non-intuitive structure is obtained. Some of these structures appear even under free-molecular effusion from the surface. The physical origin of all structures is discussed, and their evolution with changing gas production is studied. The computed comae are compared to those computed by various authors precedingly. Intercomparison of the present results demonstrates that differing inhomogeneity patterns may lead to similar structures in the gas coma. Comparison between these structures and those created by homogeneous, aspherical surfaces shows that it is not possible to guess from empirical rules which one of the two processes is responsible for the creation of a given structure. The implications for the interpretation of future high resolution images, or of future in situ mass spectrometric samplings of the near-nucleus gas coma are discussed.     

The striae in the dust tails of great comets — a comparison to various theories

We reanalyse positions and motion of the striae in the dust tails of the bright comets Mrkos 1957 V and West 1976 VI. Two theories are compared to the data: the high speed particle ejection theory of NOTNI (1964) and the two-step kinematical sequence proposed by SEKANINA and FARRELL (1980) in their particle fragmentation theory. The final decision is in favour of the two step sequence, though the real situation may be a mixtum compositum of both. The parent clouds (first step) are found to have low lateral velocity dispersion and higher than expected acceleration. The question how these clouds originate remains unsolved. It is suggested that they comprise particles which left the coma into a tailward region of high magnetic field and plasma density. Another possibility, additionally accounting for the sometimes apparent duplicity, is an origin out of an optically thick coma at angles orthogonal to the radius vector.     

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)].     

IRCS/Subaru observations of water in the inner coma of Comet 73P-B/Schwassmann-Wachmann 3: Spatially resolved rotational temperatures and ortho-para ratios

Comet 73P-B/Schwassmann-Wachmann 3 was observed with IRCS/Subaru at geocentric distance of 0.074 AU on UT 10 May 2006. Multiple H₂O emission lines were detected in non-resonant fluorescence near 2.9 μm. No significant variation in total H₂O production rate was found during the (3 h) duration of our observations. H₂O rotational temperatures and ortho-to-para abundance ratios were measured for several positions in the coma. The temperatures extracted from two different time intervals show very similar spatial distributions. For both, the rotational temperature decreased from ∼110 to ∼90 K as the projected distance from the nucleus increased from ∼5 to ∼30 km. We see no evidence for OPR change in the coma. The H₂O ortho-para ratio is consistent with the statistical equilibrium value (3.0) for all spatially resolved measurements. This implies a nuclear spin temperature higher than ∼45 K.     

A Determination of The Nuclear Size of Comet Hale–Bopp (C/1995 O1)

The signal of the nucleus was digitally extracted from six images of the innermost coma of this comet, obtained with the Hubble Space Telescope’s Wide-Field Planetary Camera 2 in the planetary mode between October 23, 1995 and October 17, 1996. Two different anisotropic, power-type laws were used to filter out the contribution from the dust coma: one peaking at the center of the elliptical surface brightness distribution (law A), the other peaking at its focus (law B). The nuclear R magnitudes in the Cousins system, reduced to a zero phase angle and to 1 AU from Earth and the Sun with a phase coefficient of 0.035 mag/deg and an inverse square distance power law, are found to average 9.46 ± 0.07 and 9.48 ± 0.18 when law A and law B are applied, respectively. These results become 9.49 ± 0.07 and 9.51 ± 0.17, when the nucleus signal on the October 1995 image is assumed to consist of a sum of the contributions from two unresolved nuclear components. In either scenario, no systematic variations are apparent in the nuclear brightness with time, which suggests the absence of any significant contamination of the extracted nuclear signal by the coma. Assuming a geometric albedo of 4 percent, the corresponding effective nuclear diameter amounts to 71 ± 4 km (formal error). This result substantially exceeds the size estimates published by Weaver et al., which are based only on the October 1995 observation and which were obtained with the help of a different reduction method. Runs in which a power-type law fitting the contribution from the coma was assumed to hold all the way to a small fraction of a pixel from the nucleus led to distinctly inferior solutions and yielded spurious values ll70 km for the nuclear diameter. This revised version was published online in July 2006 with corrections to the Cover Date.     

Coma Morphology of Three Non-periodic Comets

The coma morphology and short-term evolution was investigated of three non-periodic comets in retrograde orbits, C/2001 Q4 (NEAT), C/2002 T7 (LINEAR), and C/2003 K4 (LINEAR). All three comets display distinct coma features, which were very different from one comet to the next and remained rather constant in shape during the observational period. A single, broad feature perpendicular to the sun-tail direction dominated the coma of C/2003 K4 in all used filters (B,V,R,I), whereas the coma of Comet C/2002 T7 exhibited different features in blue and red filters. C/2001 Q4 showed rather complex coma morphology with clear short-term variability in coma brightness. Therefore, these non-periodic comets neither show a featureless coma nor any similarities of the features detected. The overall distribution of coma material was investigated from the shape of radial coma profiles averaged around the comet nucleus. For C/2001 Q4 and C/2002 T7, the slopes fitted to the linear part of these profiles are flatter in the blue than in the red, which can be explained by the presence of coma gas. For C/2003 K4 no such difference is indicated in the May observations (r = 2.3 AU), while in July (r = 1.7 AU) the profiles in the B-filter are flatter than in V, R, and I, hence gas contamination was relevant at least in the B filter. The R and I filter images were used to determine approximate Afρ values of each comet as a function of time.     

Thermal modeling of cometary nuclei

A new model of the sublimation of volatile ices from a cometary nucleus has been developed which includes the effects of diurnal heating and cooling, rotation period and pole orientation, and thermal properties of the ice and subsurface layers. The model also includes the contribution from coma opacity, scattering, and thermal emission, where the properties of the coma are derived from the integrated rate of volatile production by the nucleus. The model is applied to the specific case of the 1986 apparition of Halley's comet. It is found that the generation of a cometary dust coma actually increases the total energy reaching the Halley nucleus. This results because of the significantly greater geometrical cross section of the coma as compared with the bare nucleus, and because the coma provides an essentially isotropic source of multiply scattered sunlight and thermal emission over the entire nucleus surface. For Halley, the calculated coma opacity is approximately 0.2 at 1 AU from the Sun, and 1.2 at perihelion (0.587 AU). At 1 AU this has little effect on dayside temperatures (maximum ≈200°K) but raises nightside temperatures (minimum ≈150°K) by about 40°K. At perihelion the higher opacity results in a nearly isothermal nucleus with only small diurnal and latitudinal temperature variations. The general surface temperature is 205°K with a maximum of 209°K at local noon on the equator. Some possible consequences of the results with respect to the generation of nongravitational forces, observed volatile production rates for comets, and cometary lifetimes against sublimation are discussed.     

Negative ion chemistry in the coma of comet 1P/Halley

Negative ions (anions) were identified in the coma of comet 1P/Halley during in situ Electron Electrostatic Analyzer measurements performed by the Giotto spacecraft in 1986. These anions were detected with masses in the range 7–110 amu, but with insufficient mass resolution to permit unambiguous identification. We present details of a new chemical‐hydrodynamic model for the coma of comet Halley that includes—for the first time—atomic and molecular anions, in addition to a comprehensive hydrocarbon chemistry. Anion number densities are calculated as a function of radius in the coma, and compared with the Giotto results. Important anion production mechanisms are found to include radiative electron attachment, polar photodissociation, dissociative electron attachment, and proton transfer. The polyyne anions C₄H^? and C₆H^? are found to be likely candidates to explain the Giotto anion mass spectrum in the range 49–73 amu. The CN^? anion probably makes a significant contribution to the mass spectrum at 26 amu. Larger carbon‐chain anions such as C₈H^? can explain the peak near 100 amu provided there is a source of large carbon‐chain‐bearing molecules from the cometary nucleus.     

Photometric investigations of distant comets C/2002 VQ94 (LINEAR) and 29P/Schwassmann-Wachmann-1

We present an analysis of the results of photometric investigations of two distant comets, C/2002 VQ94 (LINEAR) and 29P/Schwassmann-Wachmann-1, obtained with the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences. The comets under study demonstrate sufficient activity out of the zone of water ice sublimation (at heliocentric distances longer than 5 AU). In the spectra of the investigated comets, we found the CO⁺ and N₂⁺ emission. The presence of this emission may say that the comets were formed in the outer parts of the Solar System, in a protoplanetary cloud at a temperature ≤25 K. We found that the photometric maximum of the ionosphere (in the CO⁺ filter) of the comet C/2002 VQ94 (LINEAR) is shifted relative to the photometric center of the dust coma by 1.4″ (7.44 × 10³ km) in the direction deflected by 63° from the direction to the Sun. Using special filters to process the images, we picked out active structures (jets) in the dust coma of the 29P/Schwassmann-Wachmann-1 comet.     

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?     

Visible and Infrared Images of C/1999 S4 (LINEAR) during the Disruption of Its Nucleus

An analysis of the behavior of the dust coma of the Comet C/1999 S4 (LINEAR) from visible and infrared images acquired shortly before and after the disruption of the comet's nucleus is presented. During the predisruption phase, the overall dust production increased by a factor of 11 in two steps; an initial outburst occurred between July 18 and 19 and a second stronger one occurred between July 20 and 21. Postdisruption images obtained on July 26 and 27 suggest that most of the dust was released in the huge outburst produced during the disruption of the nucleus a few days before. The color of the dust coma did not show any measurable day-to-day variation and was also very uniform throughout the coma. The latter is an indication of the homogeneity of the dust component of the nucleus.     

The gas production of Comet 9P/Tempel 1 around the Deep Impact date

The target of the Deep Impact space mission (NASA), Comet 9P/Tempel 1, was observed from two nights before impact to eight nights after impact using the FORS spectrographs at the ESO VLT UT1 and UT2 telescopes. Low resolution optical long-slit spectra were obtained to study the evolution of the gas coma around the Deep Impact event. Following first results of this observing campaign on the CN and dust activity [Rauer, H., Weiler, M., Sterken, C., Jehin, E., Knollenberg, J., Hainaut, O., 2006. Astron. Astrophys. 459, 257-263], this work presents a study of the complete dataset on CN, C₂, C₃, and NH₂ activity of Comet 9P/Tempel 1. An extended impact gas cloud was observed moving radially outwards. No compositional differences between this impact cloud and the undisturbed coma were found as far as the observed radicals are concerned. The gas production rates before and well after impact indicate no change in the cometary activity on an intermediate time scale. Over the observing period, the activity of Comet 9P/Tempel 1 was found to be related to the rotation of the cometary nucleus. The rotational lightcurve for different gaseous species provides indications for compositional differences among different parts of the nucleus surface.     

Coma expansion and photometry of comet Bowell (1980b)

Optical and infrared observations of comet Bowell are presented. The optical observations indicate that the solid grain coma is expanding at only 0.9 ± 0.2 m sec^?1. This is two orders of magnitude slower than the local gas sound speed and may suggest that gas drag is not responsible for stripping the grains from the nucleus. The hypothesis of “electrostatic snap-off” is tentatively advanced to account for the ejection of the grains. Alternatively, the grains may have an unusual size distribution. The extrapolated motion of the grains suggests that the bulk of the coma was formed when the comet was at a heliocentric distance $\text{R ? 10}\text{AU}$. Any water ice in the nucleus would be too cold to give rise to the observed grain coma by equilibrium sublimation at this R. Further evidence against the production of the grain coma by equilibrium sublimation of the nucleus is provided by broadband (J) photometric observations. Almost all of the observed photometric variations of comet Bowell can be ascribed to geometric effects. Simple models indicate that the total grain cross section has been nearly constant since the time of the earliest observations. The present observations, which suggest that water ice sublimation does not control either the optical morphology or the near infrared photometric behavior of comet Bowell, are contrasted with reported high OH production rates. It is concluded that the grain coma may be largely a relic of activity occurring on the nucleus at $\text{R ? 10}\text{AU}$ while the OH may indicate sublimation from the nucleus near perihelion and from coma grains near $\text{R ? 4.6}\text{AU}$.     

The Nucleus of Comet Hale-Bopp (C/1995 O1): Size and Activity

A review of our current understanding of Comet Hale-Bopp’s nuclear size is presented. Currently the best constraints on the effective radiusare derived from late-1996 mid-IR data and near-perihelion radio data.Unfortunately the two regimes give differing answers for the radius. A possible reconciliation of the two datasets is presented that would place the radius at around 30 km. This is a large cometary radius compared to the others that are known, and this motivates a discussion of what makes a large comet different. From several possible large-comet properties, Hale-Bopp’s activity is analyzed, focusing on the production rates, coma jet features, dust optical depth, and relationship with the interplanetary dust environment. The optical depth is particularly important since an optically-thick inner coma could complicate attempted measurements of the “nucleus”.     

On the Relationship of Chemical Abundances in the Nucleus to Those in the Coma

One of the goals of comet research is the determination of the chemical composition of the nucleus because it provides us with the clues about the composition of the nebula in which comet nuclei formed. It is well accepted that photo-chemical reactions must be considered to establish the abundances of mother molecules in the coma as they are released from the comet nucleus or from distributed dust sources in the coma. However, the mixing ratios of mother molecules in the coma changes with heliocentric distance. To obtain the abundances in the nucleus relative to those in the coma, we must turn our attention to the release rates of mother molecules from the nucleus as a function of heliocentric distance. For this purpose, we assume three sources for the coma gas: the surface of the nucleus (releasing mostly water vapor), the dust in the coma (the distributed source of several species released from dust particles), and the interior of the porous nucleus (the source of many species more volatile than water). The species diffusing from the interior of the nucleus are released by heat transported into the interior. Thus, the ratio of volatiles relative to water in the coma is a function of the heliocentric distance and provides important information about the chemical composition and structure of the nucleus. Our goal is to determine the abundance ratios of various mother molecules relative to water from many remote-sensing observations of the coma as a function of heliocentric distance. Comet Hale-Bopp is ideal for this purpose since it has been observed using instruments in many different wavelength regions over large ranges of heliocentric distances. The ratios of release rates of species into the coma are than modeled assuming various chemical compositions of the spinning nucleus as it moves from large heliocentric distance through perihelion. Since the heat flow into the nucleus will be different after perihelion from that before perihelion, we can also expect different gas release rates after perihelion compared to those observed before perihelion. Since not all the data are available yet, we report on progress of these calculations. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Imaging of the Structure and Evolution of the Coma Morphology of Comet Hale–Bopp (C/1995 O1)

Imaging of coma morphology of Comet Hale-Bopp from pre-perihelion through perihelion to post-perihelion is presented. Broad band images from 1996 and late 1997 show nearly radial jets streaking out from the nucleus. During both 1996 and late 1997, the brightest jets are approximately in a northern/northeastern direction. The slight curvature present in these radial jets is consistent with radiation pressure effects. Narrow band images around perihelion show two distinctive pictures of the CN and the continuum coma morphology. Spirals are clearly seen in the CN images but not in the continuum where structure is confined to the sunward side. The CN structure is consistent with continuous outgassing of the source of CN from the nucleus during both day and night. This revised version was published online in July 2006 with corrections to the Cover Date.     

Circular polarization in comets: Observations of Comet C/1999 S4 (LINEAR) and tentative interpretation

Comet C/1999 S4 (LINEAR) was exceptional in many respects. Its nucleus underwent multiple fragmentations culminating in the complete disruption around July 20, 2000. We present circular polarization measurements along the cuts through the coma and nucleus of the comet during three separate observing runs, in June 28-July 2, July 8-9, and July 21-22, 2000. The circular polarization was detected at a rather high level, up to 0.8%. The left-handed as well as right-handed polarization was observed over the coma with the left circularly polarized light systematically observed in the sunward part of the coma. During our observations the phase angle of the comet varied from 61 up to 122°, which allowed us to reveal variations of circular polarization with the phase angle. Correlation between the degree of circular polarization, visual magnitude, water production rate, and linear polarization of Comet C/1999 S4 (LINEAR) during its final fragmentation in July 2000 was found. The mechanisms that may produce circular polarization in comets and specifically in Comet C/1999 S4 (LINEAR) are discussed and some tentative interpretation is presented.     

Hale-Bopp: What Makes a Big Comet Different? Coma Dynamics: Observations and Theory

Comet Hale-Bopp was the largest comet by almost any definition, observed at least since the advent of modern observing techniques. In a more typical comet both the chemical and dynamical influences of collisional processes are limited by the short time a parcel of gas sublimated from the nucleus remains in the dense part of the coma. The resulting large size of the collisional coma in comet Hale-Bopp had important consequences on the dynamics of the coma, which in turn has important consequences on how observations are interpreted with standard models. Measured velocities of typical gas species (mostly the observed radicals) as well as dust were larger than normal comets. Conversely, velocities of super thermal atomic hydrogen were smaller than normal because of the samecollisional processes. Furthermore, as a consequence, dust particles, which are dragged by the outflowing gas, were also accelerated to larger velocities. Such larger velocities are not simply an interesting curiosity in their own right, because nearly all observations of dust and gas are interpreted with models of the coma that depend directly on some measurement or assumption with regard to velocity. In this presentation both observations and theory regarding the dynamical conditions in the coma of comet Hale-Bopp are summarized.