Orbital evolution of long-period comets I. Trivariate Monte Carlo simulation

The mean orbital evolution of long-period comets for 16 representative initial orbits to short-period comets is calculated by a Monte Carlo method. First, trivariate perturbation distributions of barycentric Kepler energy, total angular momentum, and its z component in single encounters of comets with Jupiter are obtained numerically. Their characteristics are examined in detail and the distributions are found to be simple, symmetric, and easy to handle. Second, utilizing these distributions, we have done trivariate Monte Carlo simulations of the orbital evolution of long-period comets, with special emphasis on high-inclination orbits. About half of the 16 initial orbits are traced up to 5000 returns. For each of these orbits, the mean values of semimajor axis, perihelion distance, and inclination; their standard deviations, survival, and capture rates; as well as time scales of orbital evolution are calculated as functions of return number. Survival rates of the initial orbits with high inclination (～90°) and small perihelion distance (～1–2 AU) have been found to be only two or three times smaller than those of the main-source orbits of short-period comets established quantitatively by Everhart. The time scales of orbitsl evolution of the former, however, are nearly 10 times longer than the latter. There is a general trend that, for smaller perihelion distance, the survival efficiency becomes higher. The results of this paper should be considered a basis for a succeeding paper (Paper II) in which the physical lifetime of comets will be determined, and a comparison with the orbital data will be done.     

Searching for the source of short-period comet nuclei: The direction of the spatial migration of comets

An attempt is made to determine the spatial location of the main source of short-period comet nuclei. Numerical calculations for the orbital evolution of Jupiter family comets, medium-period comets, and Centaurs are used to show that the orbits of small solar system bodies tend to evolve in the direction of increasing semimajor axes. This relates to bodies that can experience encounters with planets and whose orbital evolution is shaped by gravitational perturbations. It is concluded that there is good reason to search for the main source of the nuclei of Jupiter family comets at distances of 6 AU or less from the sun.     

Numerical simulations of comet nuclei: II. The effect of the dust mantle

The insulating effect of an evolving dust mantle is examined. The role of this mantle in determining the surface temperature of the ice core is studied as a function of the mass fraction of the dust in the ice-dust mixture and the thermal conductivity of the nucleus. Using the so-called “looselattice” model of D.A. Mendis and G.D. Brin (1977, Moon17, 359–372) (which was also extended to include cracks and pores in the mantle), it was found that both high dust to ice ratios and high core conductivities inhibit mantle blowoff. Indeed, it is often possible to build an essentially permanent dust mantle around an ice nucleus, so that the nucleus will take on an asteroidal appearance.     

Numerical simulation of cometary nuclei: III. Internal temperatures of cometary nuclei

A one-dimensional heat-diffusion model was used to calculate internal temperatures in cometary nuclei composed of either crystalline or amorphous ice, and for a range of orbits. It was found that the final central temperature, T_c, was a complex function of the comet's orbital semimajor axis, a, and eccentricity, e, as well as the functional form of the thermal conductivity. For cometary nuclei with identical thermal properties, T_c was found to decrease with eccentricity for a short-period orbit with a = 3 AU. For an intermediate-period orbit with a = 20 AU, T_c initially increased with eccentricity but then declined at large values of e for a crystalline ice nucleus, while for amorphous ice T_c increased monotonically. In addition, it was found that for conductivities of similar magnitude, crystalline ice (for which the conductivity varies inversely proportional to temperature) reached the final central temperature twice as fast as amorphouslike ice (for which the conductivity is proportional to temperature). T_c also depended on the magnitude of the conductivity. A four- to fivefold decrease in the conductivity resulted in a 3–4°K decrease in T_c at large eccentricities, while at small eccentricities T_c was only weakly dependent on the conductivity. Finally, the numerical results are compared to the analytical solutions of J. Klinger (1981, Icarus 47, 320–324) and C. P. McKay, S. W. Squyres, and R. T. Reynolds (1986, Icarus, 66, 625–629), and a numerical correction factor is derived for the McKay et al. expression for the central temperature.     

Vaporization in comets; Outbursts from comet Schwassmann-Wachmann 1

We propose that the outbursts frequently observed from Comet P/Schwassmann-Wachmann 1 do not require storage of energy as suggested by many authors. We present revised estimates to show that the total mass and kinetic energy in a typical outburst are lower than previously estimated and we show that this mass is comparable to the mass of gas vaporized as inferred from recent observations of CO⁺ in this comet. We propose simple equilibrium vaporization of CO₂ or CO which is suddenly exposed on a nucleus which is otherwise composed primarily of H₂O. Calculations of the variation of vaporization with rotational phase under these conditions indicate that quantitatively the mechanism can produce outbursts of the size observed.     

The enigma of comet nuclei

Results of space missions to in-situ study comets and the derived current challenges to better understand the properties of comet nuclei are discussed and summarized shortly, particularly in view of the origin of comets in the protoplanetary disk. The main conclusion is that we are far away from a complete understanding of comets. This frontier is yet wide open. Critical items are described and new aspects have been introduced.     

Gas release in comet nuclei

The evolution of a comet nucleus is investigated, taking into account the crystallization process by which the gas trapped in the ice is released to flow through the porous ice matrix. The equations of conservation of the energy and of the masses of ice and gas are solved throughout the nucleus, to obtain the evolution of the temperature, gas pressure and density profiles. A spherical nucleus composed of cold, porous amorphous ice, with 10% of CO trapped in it, serves as initial model. Several values of density (porosity) and pore size are considered. For each combination of parameters the model is evolved for 20-30 revolutions in comet P/Halley's orbit. Two aspects of the release of gas upon crystallization are analyzed and discussed: (a) the resulting continuous outward flux with high peaks at the time of crystallization, which is a cyclic process in the low-density models and sporadic in the high-density ones; (b) the internal pressures obtained down to depths of a few tens to approximately 200 m (depending on parameters), that are found to exceed the compressional strength of cometary ice. As a result, both cracking and explosions of the overlying ice layer and ejection of gas and ice/dust grains are expected to follow crystallization. They should appear as outbursts or sudden brightening of the comet. The model of 0.2 g cm-3 density is found to reproduce quite well many of the light-curve and activity characteristics of comet P/Halley.     

That's the way the comet crumbles: Splitting Jupiter-family comets

Our current understanding of split, Jupiter-family comets is reviewed. The focus is on what recent studies of comets have told us about the nature of the splitting phenomenon. The goal is to not repeat the information given in recent reviews of split comets, but to build upon it. In particular, we discuss comets that have suffered splitting or fragmentation events in the past few years. These include comets (a) 57P/du Toit-Neujmin-Delporte, observed with a long train of fragments in 2002; (b) 73P/Schwassmann-Wachmann 3, which split in 1995 and was extensively studied during its relatively close passage to Earth in 2006, during which dozens of fragments were discovered and studied; and (c) 174P/Echeclus, a Centaur and potentially future JFC, which split in late 2005 and was the first such Centaur observed to do so. We also discuss recent observations by SOHO of split comets that are likely of short-period. The Spitzer Space Telescope has observed many JFCs and provided us with unprecedented detailed views of cometary debris trails, which may be thought of as a middle ground between “normal” ejection of micron-sized dust grains and the cleaving off of meter-to-kilometer sized fragments. We will also discuss potential breakthroughs in studying splitting JFCs that may come from future surveys.     

A possible comet and asteroid link in the formation of comets

The origin of comets is reassessed in the light of IRAS discoveries of particles in the asteroid belt and much cooler “cirrus” clouds at large heliocentric distances. The component of the asteroid particles with ratios of radiation pressure to gravitational forces near one-half will be forced into highly eccentric orbits, with heliocentric distances in the outer Solar System region of the hypothesized Oort Cloud. While slowly passing near their aphelia these particles could acquire a mantle of interstellar frost. It is proposed that larger asteroidal bodies gravitationally perturbed to similar distances would serve as centers for gravitational collation so that upon their return to the inner Solar System they will have a structure satisfying the observational requirements of Whipple's dirty snowball model. This model of origin would explain the established connections to meteor streams and fireballs, the possible connection to carbonaceous chondrites, and can be tested in several ways. The model would lead to the conclusion that comets are a renewable resource and eliminates the need for the 10¹⁰-fold multiplication between the number of observed and hypothesized comets necessary for the Oort Cloud model.     

Finite difference time domain simulation of radar wave propagation through comet nuclei dielectric models

Abstract— The 90 MHz radar‐wave experiment, Comet Nucleus Sounding Experiment by Radiowave Transmission (CONSERT), on board the Rosetta mission (ESA, 2004) is expected to probe the nucleus of the comet 67P/Churyumov‐Gerasimenko (67P/C‐G) to reveal information on its physical properties, chemical composition, and internal structure. This investigation assesses the potential to recognize lithological structure in the comet nucleus with a radar experiment such as CONSERT. Radar simulations at 90 MHz were performed with a finite difference time domain (FDTD) method. The amplitude and losses of the transmitted and reflected electric field components of an incident radar pulse were evaluated as a function of time. Seven different dielectric models of sections of a hypothetical comet nucleus were used, representative of existing theories of comet nuclei. Values of dielectric constant assigned to these models are based on mixing laws for a porous mixture of ice and meteoritic dust, employing laboratory measured values of relative permittivity for mainly chondritic meteorites. Our results confirm that structural differences such as layers or inclusions are discernable from transmitted and reflected radar signals at 90 MHz, the central frequency of the CONSERT instrument. Such simulations help to constrain the ambiguities that might exist in future radar data associated with the nature of the comet nuclei, whether conglomerate or layered in nature.     

On the visibility of nuclei of dusty comets

The problem of visibility of a cometary nucleus discussed in general terms for single scattering by dust grains. The ratio of radiatio scattered in the dust column above the surface and that reflected from the nucleus determines the visibility of features on the nuclear surface. A contrast parameter characterizing the ration of radiation foming from the nuclear surface and that of the nuclear vicinity describes the visibility of the full nucleus against the dust fore- and background. These quantities and the intensity distribution of scattered solar radiation across the nucleus and its vicinity are calculated for the case of comet Halley at a heliocentric distance of 0.9 AU after perihelion (Giotto encounter). The scattering calculations are based on an isotropic dust distribution derived from hydrodynamics gas-dust interactions resulting in a steep densiity increase right above the surface. For Newburn's nominal model of comet Halley, an optical depth of about 0.5 impairs the visibility of the nucleus somewhat.     

Vaporization in comets: The icy grain halo of comet west

The variation with heliocentric distance of the production rates of various species in Comet West (1975n=1976 VI) is explained with a cometary model consisting of a CO₂-dominated nucleus plus a halo of icy grains of H₂O or clathrate hydrate. We conclude that the parents of CN and C₃ are released primarily from the nucleus but that the parent of C₂ is released primarily from the halo of icy grains.     

Laboratory simulation of the physical processes occurring on and near the surfaces of comet nuclei

Abstract— Laboratory comet simulation experiments are discussed in the context of theoretical models and recent ground-based and spacecraft observations, especially the Giotto observations of P/Halley. The set-up of various comet simulation experiments is reviewed. A number of small-scale experiments have been performed in many laboratories since the early 1960s. However, the largest and most ambitious series of experiments were the comet simulation experiments known as KOSI (German = Kometen Simulation). These experiments were prompted by the appearance of Comet P/Halley in 1986 and in planning for the European Space Agency's Rossetta mission that was originally scheduled to return samples. They were performed between 1987 and 1993 using the German Space Agency's (DLR) space hardware testing facilities in Cologne. As with attempts to reproduce any natural phenomenon in the laboratory, there are deficiencies in such experiments while there are major new insights to be gained. Simulation experiments have enabled the development of methods for making comet analogues and for exploring the properties of such materials in detail. These experiments have provided new insights into the morphology and physical behavior of aggregates formed from silicate grains likely to exist in comets. Formation of a dust mantle on the surfaces and a system of ice layers below the mantle caused by chemical differentiation have been identified after the insolation of the artificial comet. The mechanisms for heat transfer between the comet's surface and its interior, the associated gas diffusion from the interior of the surface, and compositional, structural, and isotopic changes that occur near the surface have been described by modeling 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 have also been explored.     

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.     

Numerical simulation of high-velocity impact ejecta following falls of comets and asteroids onto the Moon

High-velocity comet and asteroid impacts onto the Moon are considered and the material masses ejected after such impacts at velocities above the second-cosmic velocity for the Moon (2.4 km/s) are calculated. Although the results depend on a projectile type and the velocity and angle of an impact, it has been demonstrated that, on average, the lunar mass decreases with time. The Moon has lost about 5 × 10¹⁸ kg, that is, about one-hundredth of a percent of its mass, over the last 3.8–3.9 billion years. The ejection of lunar meteorites and lunar dust, rich in ³He, is considered as well. The results of the study are compared to the results of earlier computations and data on lunar meteorites.     

Probing the internal structure of the nuclei of comets

There is no direct evidence about the internal structure of cometary nuclei, which are mostly hidden by their gas and dust comae, and have not yet been orbited by any spacecraft. Their densities are low, typically of about 400 kg m⁻³ for 9P/Tempel 1 (that was impacted by the Deep Impact probe) and 67P/Churyumov-Gerasimenko (that is the target of the Rosetta mission). Such low densities are in favour of a high macro-porosity, or a high micro-porosity, or both. Observations of disruption or splitting of nuclei indeed suggest that some huge sub-nuclei or some meter-sized fragments could be the building blocks of comets. Analysis, from in-situ measurements and from remote light scattering observations, of the structure of the dust particles, which significantly consist of fluffy aggregates of submicron-sized grains, could be in favour of a fractal structure. However, the presence of huge icy grains in the innermost coma, and of flat layers on the surface of 9P/Tempel 1, are clues to the complexity of these objects, which have suffered drastic erosion phenomena on their elongated orbits. It is expected that the Rosetta mission will provide a fair understanding of the structure of the deep interior of the nucleus of 67P/Churyumov-Gerasimenko, thanks to the on-board CONSERT experiment.     

Numerical simulation of high-velocity ejecta following comet and asteroid impacts: Preliminary results

The influence of different projectile and target characteristics on the mass and velocity of high-velocity (>1 km/s) ejecta from impact craters is investigated numerically. The problem of how the computation accuracy affects the resulting ejection velocity distribution is considered.     

The structure of dust tails of comets II. The tail and dust content of comet Arend-Roland

The modified distribution function of dust particles, f(γ), which can be determined from tail brightness profiles on the basis of mechanical theory, is discussed with special regard to its reliability and accuracy. Physical significance of f(γ) is also discussed in terms of dust model parameters, and it is shown that f(γ), if treated carefully, will serve as an effective tool in studying cometary dust. Four isophotes of Comet Arend-Roland, 1957 III, in the orange-red light (λλ 0.53–0.68 micron) obtained by Ceplecha (1958), are analysed by the numerical method described in Paper I (KIMURA and LIU 1975) with some improvements and higher approximations. The distribution f(γ) thus obtained shows a bimodal character with peaks at γ = 0.10 and 0.010 with a relative height ratio of 1 to 0.6. Dust emission rate, which is assumed to follow the inverse square law of heliocentric distance, is estimated to give P_dC_sca = (1.3±0.5) × 10⁹ cm²/sec, where P_d is the rate of particle emission at 1 a.u. and the C_sca is a mean effective cross section of particles for light scattering including the phase effect (the scattering angles of present interest range from about 80 to 100 degrees).     

Numerically improved thermochemical evolution models of comet nuclei

An improved unidimensional model of the heat transport and gas diffusion within a porous cometary nucleus is presented, in which the time-dependent gas diffusion equation is coupled with the heat diffusion equation to describe the energy transport due to sublimation and recondensation of volatiles, but is solved independently using a different discrete time step. Also, the erosion of interfaces within the nucleus, due to the sublimation of ices and the removal of dust, is now treated by means of a continuous adaptation of the discrete grid to the interfaces positions, removing numerical stability problems associated with the variation of structure and composition of the discrete layers. The results of this model are then compared with those of another unidimensional model which does not make use of the above-mentioned numerical methods, both computed for the same set of physical parameters describing comet P/Wirtanen, and the effects of the different modelling assumptions on the results are discussed. A new bidimensional model of the heat transport within a porous comet nucleus is presented, and its results are compared with those obtained from the above-mentioned unidimensional model (modified to include the same physics of the bidimensional model). The ability of bidimensional models to better describe the effects of variations in the local physical conditions on the comet activity is then discussed.