Modeling the Comet Nucleus Interior

Numerical simulation of the structure and evolution of a comet nucleus is reviewed both from the mathematical and from the physical point of view. Various mathematical procedures and approximations are discussed, and different attempts to model the physical characteristics of cometary material, such as thermal conductivity, or permeability to gas flow, are described. The evolution and activity of comets is shown to depend on different classes of parameters: Defining parameters, such as size and orbit, structural parameters, such as porosity and composition, and initial parameters, such as temperature and live radio isotope content. The latter are related to the formation of comets. Despite the large number of parameters, general conclusions, or common features, appear to emerge from the numerous model calculations — for different comets — performed to date. Thus, the stratified structure of comet nuclei, volatile depletion, and the role of crystallization of ice in cometary outbursts are discussed. Finally, an evolution model applied to comet C/1995 O1 Hale-Bopp — using different assumptions — is described and analysed in the light of observations.     

Radio observations of Jupiter-family comets

Radio observations from decimetric to submillimetric wavelengths are now a basic tool for the investigation of comets. Spectroscopic observations allow us: (i) to monitor the gas production rate of the comets, by directly observing the water molecule, or by observing secondary products (e.g., the OH radical) or minor species (e.g., HCN); (ii) to investigate the chemical composition of comets; (iii) to probe the physical conditions of cometary atmospheres: kinetic temperature and expansion velocity. Continuum observations probe large-size dust particles and (for the largest objects) cometary nuclei.Comets are classified from their orbital characteristics into two separate classes: (i) nearly isotropic, mainly long-period comets and (ii) ecliptic, short-period comets, the so-called Jupiter-family comets (JFCs). These two classes apparently come from two different reservoirs, respectively, the Oort cloud and the trans-Neptunian scattered disc. Due to their different history and—possibly—their different origin, they may have different chemical and physical properties that are worth being investigated.The present article reviews the contribution of radio observations to our knowledge of the JFCs. The difficulty of such a study is the commonly low gas and dust productions of these comets. Long-period, nearly isotropic comets from the Oort cloud are better known from Earth-based observations. On the other hand, JFCs are more easily accessed by space missions. However, unique opportunities to observe JFCs are offered when these objects come by chance close to the Earth (like 73P/Schwassmann-Wachmann 3 in 2006), or when they exhibit unexpected outbursts (as did 17P/Holmes in 2007).About a dozen JFCs were successfully observed by radio techniques up to now. Four to ten molecules were detected in five of them. No obvious evidence for different properties between JFCs and other families of comets is found, as far as radio observations are concerned.     

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)     

Atlas of secular light curves of comets

In this work we have compiled 37,692 observations of 27 periodic and non-periodic comets to create the secular light curves (SLCs), using two plots per comet. The data have been reduced homogeneously. Our overriding goal is to learn the properties of the ensemble of comets. More than 30 parameters are listed, of which over ∼20 are new and measured from the plots. We define two ages for a comet using activity as a proxy, the photometric age P-AGE, and the time-age, T-AGE. It is shown that these parameters are robust, implying that the input data can have significant errors but P-AGE and T-AGE come out with small errors. This is due to their mathematical definition. It is shown that P-AGE classifies comets by shape of their light curve. The value of this Atlas is twofold: The SLCs not only show what we know, but also show what we do not know, thus pointing the way to meaningful observations. Besides their scientific value, these plots are useful for planning observations. The SLCs have not been modeled, and there is no cometary light curve standard model as there is for some variable stars (i.e. eclipsing binaries). Comets are classified by age and size. In this way it is found that 29P/Schwassmann-Wachmann 1 is a baby goliath comet, while C/1983 J1 Sugano-Saigusa-Fujikawa is a middle age dwarf. There are new classes of comets based on their photometric properties. The secular light curves presented in this Atlas exhibit complexity beyond current understanding.     

Radio Line Observations Of Molecular And Isotopic Species In Comet C/1995 O1 (Hale-Bopp)

We present here a review of the radio observations of the remarkable comet Hale-Bopp C/1995 O1 in which most major radio astronomical facilities have been involved. These observations started in August 1995, soon after the discovery of the comet (it was then at ∼7 AU from the sun), and well before its perihelion on April 1st, 1997; they are still going on, hopefully up to end of 1998. Extended cartographies have been obtained using multibeam receivers and on-the-fly techniques. High spatial resolution (a few ″) has been achieved with interferometers. Submillimetric observations are playing an increasing role, and high resolution (R ∼ 10⁶−10⁷) spectroscopy of cometary lines is now performed from decimetric to submillimetric wavelengths. The number of species observed at radio wavelengths now reaches ∼28,when it was ∼14 for comet C/1996 B2 Hyakutake. Most of these species are parent molecules. However, ions have been observed for the first time at radio wavelengths, and their velocities measured. Several isotopic species (involving D,¹³C,³⁴S,¹⁵N) have been sought, allowing isotopic enrichment determinations. The abundances of cometary molecules present many similarities and some differences with the abundances of interstellar molecules in regions where grain mantles are believed to be evaporated to the gas phase (hot cores, bipolar flows). They will be discussed for their implications on the origin of cometary ices and of comets themselves. This revised version was published online in July 2006 with corrections to the Cover Date.     

Present and Future Cometary Science with the IRAM Plateau de Bure Interferometer

Interferometric observations are essential to probe the molecular emission in the inner cometary atmospheres and study the outgassing from the nucleus. Mapping the continuum emission can provide information about the dust and/or nucleus properties. We present here a summary of the observations of the dust and gas coma of comet 17P/Holmes and nuclear observations of 8P/Tuttle, both carried out with the IRAM interferometer at Plateau de Bure (PdBI) in 2007–2008. The observations of these two comets demonstrate the ability of the PdBI in terms of cometary science. In the near future, several improvements will be made (new receivers at 0.8 mm, a new wide-band correlator) allowing more frequent and more detailed studies of comets. On the long term, NOEMA, an expansion project, may add up to six antennas to the Plateau de Bure Interferometer, and increase the baseline lengths. Such an instrument would offer a complement to ALMA to track comets of the northern hemisphere with about half the sensitivity of ALMA for continuum studies.     

Collisional Quenching of OH Radio Emission from Comet Hale-Bopp

Observations of comets in the 18-cm OH transitions offer a means to probe gas production, kinematics, and OH excitation in comets. We present initial results of OH observations of comet Hale-Bopp obtained with the NRAO 43 m antenna located in Greenbank, WV. Maps of the emission provide strong constraints on the amount of quenching of the inversion of the OH ground state Λ-doublet in the coma. Analysis of the total radio OH flux and maps of its radial brightness distribution indicate a quenched region on the order of ∼500,000 km during March and April 1997. This large value is generally consistent with previous observations of radio OH quenching in lower production rate comets when the high production rate of comet Hale-Bopp is considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Chemical Diversity of Comets: Synergies Between Space Exploration and Ground-based Radio Observations

A fundamental question in cometary science is whether the different dynamical classes of comets have different chemical compositions, which would reflect different initial conditions. From the ground or Earth orbit, radio and infrared spectroscopic observations of a now significant sample of comets indeed reveal deep differences in the relative abundances of cometary ices. However, no obvious correlation with dynamical classes is found. Further results come, or are expected, from space exploration. Such investigations, by nature limited to a small number of objects, are unfortunately focussed on short-period comets (mainly Jupiter-family). But these in situ studies provide “ground truth” for remote sensing. We discuss the chemical differences in comets from our database of spectroscopic radio observations, which has been recently enriched by several Jupiter-family and Halley-type comets.     

The provenance and evolution of comets

The process of comet formation through the hierarchical aggregation of originally submicron-sized interstellar grains to form micron-sized particles and then larger bodies in the protoplanetary disc, culminating in the formation of planetesimals in the disc extending from Jupiter to beyond Neptune, is briefly reviewed. The ‘planetesimal’ theory for the origin of comets implies the existence of distinct cometary reservoirs, with implications for the immediate provenance of observed comets (both long-period and short-period) and their evolution as a result of planetary perturbations and physical decay, for example splitting and sublimation. The principal mode of cometary decay and collisional interaction with the terrestrial planets is through the formation and evolution of streams of cometary debris and hitherto undiscovered ‘families’ of cometary asteroids. Recent dynamical results, in particular the sungrazing and sun-colliding end-state for short-period comet and asteroid orbits, are briefly discussed.     

All comets are born equal: infrared emission by dust as a key to comet nucleus composition

The infrared emission of various comets can be matched within the framework that all comets are made of aggregated interstellar dust. This is demonstrated by comparing results on Halley (a periodic comet), Borrelly (a Jupiter family short period comet), Hale-Bopp (a long period comet), and extra-solar comets in the β Pictoris disk. Attempts have been made to generalize the chemical composition of comet nuclei based on the observation of cometary dust and volatiles and the interstellar dust model. Finally, we deduce some of the expected dust and surface properties of comet Wirtanen from the interstellar dust model as applied to other comets.     

The search for a cometary outbursts mechanism: a comparison of various theories

In the paper the potential sources of energy of cometary outbursts have been reviewed. Considerations focus on four probable sources of the outbursts' energy. These are the polymerization of hydrogen cyanide HCN, impacts with the meteoroids, destruction of cometary grains in the field of strong solar wind and the transformation of amorphous water Ice into the crystalline one. The values of released energy and jumps of cometary brightness caused by these mechanisms have been discussed. A modern approach to the problem of the thermodynamical evolution of the comet nucleus which includes amorphous water ice is considered as the starting point in the discussion presented in the paper. The main characteristics of an outburst of a hypothetical comet belonging to the Jupiter family comet are calculated. The obtained results are in a good agreement with the characteristics observed during the real outbursts of comets. The main conclusion of this paper confirms a general presumption that the cometary outbursts can have different causes. However, the hypothesis concerning the amorphous water ice transformation appears to be the most probable one. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sulfur Chemistry at Millimeter Wavelengths in C/Hale-Bopp

The recent availability of bright comets has given us an excellent opportunity to study cometary chemistry. Comet Hale-Bopp (1995 O1)gave us the particularly rare opportunity to study a bright and active comet for almost two years. Our program concentrated on millimeter-wave observations of sulfur-bearing molecules in an effort to understand the total sulfur budget of the comet. Using the National Radio Astronomy Observatory 12-m telescope on Kitt Peak we monitored both the long and short-term variations in H₂S, CS, and OCS, as well as observing H₂CS and SO. This was the first observation of H₂CS in any comet (Figure 1). Additionally, we mapped CS with the BIMA interferometer. Variations in the line profiles and changes in line intensity as large as a factor of two were seen in day to day observations of both H₂S and CS. An example for H₂S is shown in Figure 2. This is the first time we can attempt to study the entire group of sulfur-bearing molecules. Models of the sulfur coma have thus far largely been based on observations of the daughter products CS and atomic sulfur made over the last 18 years using the International Ultraviolet Explorer (IUE) satellite, coupled with radio observations of CS and H₂S in several recent comets. Four new sulfur-bearing species have been observed in comets Hale-Bopp and Hyaku take, three of them parent species. The high resolution maps in CS will also allow spatial information to be included in the sulfur model for the first time. C/Hale-Bopp is the first comet in which so many sulfur species have been observed. Analysis of the abundances of these species in comparison to the total atomic sulfur observed should reveal whether or not we can now account for all of the primary sulfur sources in comets. Perhaps the most interesting question that these observations raised was why C/Hale-Bopp appeared to contain so much more SO and SO₂ (as observed by others) than any other comet. This spurred the discovery that the UV fluorescence models of these species were incorrect (S. J. Kim, this issue). Analysis of the data and modeling of the sulfur budget are still underway. This revised version was published online in July 2006 with corrections to the Cover Date.     

Structure and density of cometary nuclei

Abstract— Understanding the nature of the cometary nucleus remains one of the major problems in solar system science. Whipple's (1950) icy conglomerate model has been very successful at explaining a range of cometary phenomena, including the source of cometary activity and the nongravitational orbital motion of the nuclei. However, the internal structure of the nuclei is still largely unknown. We review herein the evidence for cometary nuclei as fluffy aggregates or primordial rubble piles, as first proposed by Donn et al. (1985) and Weissman (1986). These models assume that cometary nuclei are weakly bonded aggregations of smaller, icy‐conglomerate planetesimals, possibly held together only by self‐gravity. Evidence for this model comes from studies of the accretion and subsequent evolution of material in the solar nebula, from observations of disrupted comets, and in particular comet Shoemaker‐Levy 9, from measurements of the ensemble rotational properties of observed cometary nuclei, and from recent spacecraft missions to comets. Although the evidence for rubble pile nuclei is growing, the eventual answer to this question will likely not come until we can place a spacecraft in orbit around a cometary nucleus and study it in detail over many months to years. ESA's Rosetta mission, now en route to comet 67P/Churyumov‐Gerasimenko, will provide that opportunity.     

Simulation Experiments with Cometary Analogous Material

Comet simulation experiments are discussed, in the context of physical models and the results in cometary physics, gathered especially from the GIOTTO space mission to comet P'Halley. The “status of the today knowledge” about comets, the experiments could start from, is briefly reviewed. The setup of the KOSI (German = Kometen Simulation) - experiments and the techniques to produce cometary analogous material, on the basis of that knowledge are described in general, as for the different KOSI experiments. The limitations of the simulation of physical processes at the surface of real comets in an earth-bound laboratory are discussed, and the possibilities to receive common insights in cometary physics are shown. Methods and procedures are described, and the major results reviewed. As with attempting to reproduce any natural phenomenon in the laboratory, there are short-comings to these experiments, but there are possibly major new insights to be gained. Physical laws only have the same consequences under same experimental or environmental conditions. A number of small-scale comet simulation experiments have been performed, since the early 60ties in many laboratories, but the largest and most ambitious series of comet simulation experiments to date were performed between 1987 and 1993 using the German space agency's (DLR) space hardware testing facilities in Cologne. These experiments were triggered by the scientific community after the comet P'Halley's recurrence in 1986 and the many data gathered by the space missions in this year. Simulation experiments have proved valuable in developing methods for making cometary analogues, and for exploring specific properties of such materials in detail. These experiments provided new insights into the morphology and physical behavior of aggregates formed out of silicate- /water-ice -grains likely to exist in comets. The formation of a dust mantle on the surface, and a system of ice layers below the mantle from the different admixed materials, have been detected after the insolation of the artificial comet. The mechanisms for heat transfer between the comet's surface and its interior, compositional, structural, and isotopic changes that occur near the comet's surface, were described by modeling in accordance with the experimental results. The mechanisms of the ejection of dust and ice grains from the surface, and the importance of gas-drag in propelling grains were investigated by close-up video cameras. This revised version was published online in July 2006 with corrections to the Cover Date.     

Protosolar nebula and composition of comets

Comets seem to be composed of matter, which is supposed to have the same molecular composition as protosolar nebula. Although there are no unbiased evidence that cometary nuclei retain the molecular composition inherited from the protosolar cloud, the observed properties of comets indicate that there is at least a resemblance between cometary composition and the material properties of dense interstellar clouds. Therefore the origin of comets could be searched in the cold stages of the protosolar nebula and molecular abundances of grain mantles in this nebula may be similar to those in the cometary dust. It is suggested that comets may contain pristine, virtually unaltered protosolar material and their study might be very relevant way to more information about processes in early stages of the solar nebula. Our knowledge about composition of the cometary nucleus is still relatively scarce, but we can partly deduce it from data obtained either by ground-based spectroscopy or by in situ mass spectrometry from space experiments. Most important were the discovery of fluffy CHON particles composed partly or even completely from compounds containing light elements. No consensus concerning the presence of interstellar pristine matter in comet has been reached from various approaches to determine the relationship between comets and interstellar grains. Most of these studies are based on infrared spectroscopy. Another method is the comparison on the chemical models of the protosolar nebula with the volatile compounds of the cometary nuclei. Both gas-phase and grain-surface chemistry are considered and initial gas-phase atomic abundances are assumed to be protosolar. The cometary matter is certainly not identical with the typical material of dense interstellar cool dense clouds, but it is closer to it than any other type of matter in solar system so far accessible to us. The data from comets combined with models of chemical evolution of matter in environment similar as prevailed the early stage of presolar nebula may at least impose constrains on the condition for comet formation. Here presented study is a preliminary contribution to such studies.     

Note on the structure of comet nuclei

The recent developments in cometary studies suggest rather low mean densities and weak structures for the nuclei. They appear to be accumulations of fairly discrete units loosely bound together, as deduced from the observations of Comet Shoemaker–Levy 9 during its encounter with Jupiter. The compressive strengths deduced from comet splitting by Öpik and Sekanina are extremely low. These values are confirmed by theory developed here, assuming that Comet P/Holmes had a companion that collided with it in 1892. There follows a short discussion that suggests that the mean densities of comets should increase with comet dimensions. The place of origin of short-period comets may relate to these properties.     

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.     

Modeling of meteoroid streams: The velocity of ejection of meteoroids from comets (a review)

An analytical review of the models of ejection of meteoroids from cometary nuclei is presented. Different formulas for the ejection velocity of meteoroids and the corresponding parameters are discussed and compared with the use of comet Halley and the Geminids meteoroid stream as examples. The ejection velocities obtained from observations of the dust trails of comets are discussed, and the values for comets 2P/Encke, 4P/Faye, 17P/Holmes, 22P/Kopff, and 67P/Churyumov-Gerasimenko are compared to the velocities yielded by Whipple’s model. The uncertainty intervals of the results are estimated.     

Observational Constraints On Surface Characteristics Of Comet Nuclei

Direct observations of the nuclear surfaces of comets have been difficult; however a growing number of studies are overcoming observational challenges and yielding new information on cometary surfaces. In this review, we focus on recent determinations of the albedos, reflectances, and thermal inertias of comet nuclei. There is not much diversity in the geometric albedo of the comet nuclei observed so far (a range of 0.025 to 0.06). There is a greater diversity of albedos among the Centaurs, and the sample of properly observed TNOs(2) is still too small. Based on their albedos and Tisser and invariants, Fernández et al. (2001) estimate that about 5% of the near-Earth asteroids have a cometary origin, and place an upper limit of 10%. The agreement between this estimate and two other independent methods provide the strongest constraint to date on the fraction of objects that comets contribute to the population of near-Earth asteroids. There is a diversity of visible colors among comets, extinct comet candidates, Centaurs and TNOs. Comet nuclei are clearly not as red as the reddest Centaurs and TNOs. What Jewitt (2002) calls ultra-red matter seems to be absent from the surfaces of comet nuclei. Rotationally resolved observations of both colors and albedos are needed to disentangle the effects of rotational variability from other intrinsic qualities. New constraints on thermal inertia of comets are consistent with previous independent estimates. The thermal inertia estimates for Centaurs 2060 Chiron and 8405 Asbolus are significantly lower than predicted by thermal models, and also lower than the few upper limits or constraints known for active, ordinary nuclei.     

Dust in cometary comae: Present understanding of the structure and composition of dust particles

In situ probing of a very few cometary comae has shown that dust particles present a low albedo and a low density, and that they consist of both rocky material and refractory organics. Remote observations of solar light scattered by cometary dust provide information on the properties of dust particles in the coma of a larger set of comets. The observations of the linear polarization in the coma indicate that the dust particles are irregular, with a size greater (on the average) than about 1 μm. Besides, they suggest, through numerical and experimental simulations, that both compact grains and fluffy aggregates (with a power law of the size distribution in the −2.6 to −3 range), and both rather transparent silicates and absorbing organics are present in the coma. Recent analysis of the cometary dust samples collected by the Stardust mission provide a unique ground truth and confirm, for comet 81P/Wild 2, the results from remote sensing observations. Future space missions to comets should, in the next decade, lead to a more precise characterization of the structure and composition of cometary dust particles.