On the importance of dust in cometary nuclei

The icy conglomerate model introduced by Whipple more than 40 years ago has been widely accepted in cometary science because it is able to describe numerous cometary phenomena. In this model comets are described as a conglomerate of ices and dust where the ices represent the major component. However, some recent observations seem to favour dust rich comets. The purpose of this paper is to summarize the observational facts supporting the dominance of refractories in comets and to discuss the consequences of a dust dominated nucleus for cometary physics.     

On the importance of dust in cometary nuclei

The icy conglomerate model introduced by Whipple more than 40 years ago has been widely accepted in cometary science because it is able to describe numerous cometary phenomena. In this model comets are described as a conglomerate of ices and dust where the ices represent the major component. However, some recent observations seem to favour dust rich comets. The purpose of this paper is to summarize the observational facts supporting the dominance of refractories in comets and to discuss the consequences of a dust dominated nucleus for cometary physics.     

On the formation of cometary nuclei in dense globules

Evolution of cometary orbits by planetary perturbations, weakly hyperbolic original orbits of comets calculated by Marsdenet al. (1978) are taken to indicate the interstellar origin of comets, and the possible formation of cometary nuclei in interstellar globules is discussed. The process is sedimentation of dust grains. It is shown that if a globule is at 40 K, its lifetime is sufficiently long to allow the sedimentation.     

Thermal stresses in cometary nuclei

Assuming cometary nuclei composed of weakly attached cometesimals, thermal stresses due to the temperature differences between the surface and the core are calculated. Both homogeneous icy bodies and cometesimals with material inhomogeneities are considered. It is shown that spherical inclusions in water ice cause strong stresses. Even if viscoelastic effects are taken into account the stresses in the superficial regions exceed the strength of water ice and therefore cause cracks to form. The consequences of this for such irregular cometary activity as splitting and outbursts are discussed.     

On the evolution and activity of cometary nuclei

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

Volatiles in the cometary nuclei

The argument for the similarity of the composition of cometary volatiles to that of interstellar molecules has been strengthened by the analysis of CO⁺ and CO ₂ ⁺ emission of the comet West. The strong 6300 Å emission of oxygen atoms can be interpreted in terms of photodissociation of OH by the solar Lyman-alpha radiation, and not as being due to photo-dissociation of CO₂ of speculatively large amount.     

On the rotational breakup of cometary nuclei and centaurs

Here we estimate the regions of stability, fragmentation, and destruction for cometary bodies versus rotational breakup in the radius-rotational period plane. By testing different plausible physical models of the cometary nucleus equation of state, we show that the plane is divided into 3 segments: the allowed, damaged, and forbidden regions. We then compare the location of well-observed comets with respect to the separation lines. The range of constituent material parameters from the literature for cometary nuclei are used to show that all the observed comets lie in the allowed region, except for Comet C/1995 O1 (Hale-Bopp), which resides in the damaged region (where the body is fractured and only held together gravitationally). We speculate that the extremely high activity demonstrated by Comet Hale-Bopp during the 1997 apparition may have been due to its highly fractured state. Comet Hyakutake, observed to emit fragments at perigee in 1996, may be near the boundary of the damaged region. Comet C/1999 S4 (LINEAR) was solidly in the rotationally allowed region, making its disintegration in July 2000 due to centrifugal forces unlikely. In contrast to the comets, the centaurs do not cluster in the allowed region, with the majority falling instead into the rotationally damaged and forbidden regions. The centaurs are only stable against breakup assuming much stronger solid water ice properties, strongly suggesting that on the whole, these bodies have different bulk physical properties than cometary nuclei.     

On the origin of cometary nuclei in the presolar nebula

If we assume that the cometary nuclei originated by the gravitational instability of a dust layer, which formed in the equatorial plane of the outer parts of the presolar nebula (PSN) during a period of approximate equilibrium between gravity, centrifugal force, and the pressure gradient, a simple relation is derived between the PSN's temperature and the upper limit to the mass of the planetesimals. It contains, besides the density of the cometary nuclei _p , only the fraction (by mass) of the condensable elements in the PSN, which became part of the dust particle disc, which, on the basis of available observational evidence on the solid particles in interplanetary and interstellar space and of theoretical considerations on the relationship between them and on the sedimentation process, is found to be of the order of ~10%; this estimate will require still further justification. Assuming a temperature in the range 15–20 K, an equatorial diameter of the PSN of 0.1 pc and _p few 0.1 g/cm³, upper limits for the planetesimal's mass of 10¹⁸g and for their radius of 10 km are obtained (on the basis of conservation of circulation, of mass and of angular momentum in the differentially rotating disc), in fair agreement with observation. With the dispersion of those parts of the PSN — of an assumed original mass of 2–3M —, which did not become part of the Sun or the planets, by the young Sun's activity, the planetesimals must have lost a large part of their gravitational binding energy and their orbits must have become so large (semimajor axis several 10⁴ A.U. or more, if not negative), that stellar perturbations produced the distribution in configurational and in velocity space now observed.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978.The earlier work done since about 1950 in the U.S.S.R. is described in Safronov (1972).     

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.     

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.     

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.     

A new model for cometary nuclei

A new model for the nucleus of comets is presented, hypothesizing formation at large heliocentric distances from many independent solid bodies. It is shown that such a configuration would collapse to a single assemblage if it is to survive into the inner solar system. Prior to collapse, the bodies would be subject to coating by interstellar gas and particles, which would form the material lost into the coma at subsequent inner solar system perihelia. Quantitative estimates place an upper limit to the body sizes of 2.3m and a lower limit of the number as 3 × 101° with sizes of a few tenths of a micron and numbers of about 10³³ most probable. The major structural and evolutionary features of such comet nuclei are consistent with the Whipple icy-conglomerate model.     

Temperature profiles and thermal stresses in cometary nuclei

Assuming a spherical nucleus of water ice with an isothermal surface, temperature profiles are computed for several heliocentric distances of Halley's comet. Sublimation of ice and the temperature dependence of the material properties are taken into account. The resulting strongly nonlinear heat diffusion problem is solved numerically. With some simplifications an analytical solution is derived. The heat conduction causes a “thermal hysteresis” of the surface temperature and a slow increase of the inner temperature. The complete thermal equilibrium is reached, however, only after 100 or more revolutions in the inner solar system. The calculated temperature profiles are used to estimate the thermal stresses in the nucleus. It is shown that thermal stresses can give a plausible explanation for cometary outbursts and splits.     

Heat content and evolution of cometary nuclei

In continuation of an earlier study of the influence of phase transitions on the thermal behavior of cometary nuclei, the heat flux into nuclei at various distances from the Sun before and after perihelion has been investigated for the isothermal case and for the fixed subsolar point. It turns out that this heat flux may be a large fraction of the incident solar heat input, so that the surface temperature and the associated rate of evaporation are lower than usually calculated. The effect is strongly dependent on the porosity of the nucleus. The surface temperature of the nucleus reaches a maximum after perihelion, as does the size of the coma, in agreement with several observations. The denser surface layers made either of ice or of dust may break away. An ideal, initially homogeneous and spherical nucleus cannot remain isothermal so that it must gradually develop considerable surface nonuniformities through localized phase changes, evaporation, and break-away. An explanation of the splitting of comets as far as 9 AU from the Sun is suggested in terms of heating of a CO₂-rich inclusion in a nucleus.     

On the modification of structure of cometary nuclei by the transport of super-volatiles

Earlier, a study has been made of the transport mechanism of volatile molecules such as N₂ and CO through cometary nuclei as they are heated by radioactive elements. Coupled equations of heat and gas transport in the presence of gas sublimation and recondensation, as well as a heat source, were numerically solved. And it was shown that supervolatiles such as N₂ and CO are transported through the pores of the nucleus, and consequently the volatile molecules become more abundant near the surface than deep inside the nucleus. Here, the process is investigated for a wider range of paramaters such as porosity and nuclear radius. It is shown that provided the central temperature attains the sublimation point of the super-volatiles, they are transported toward the surface regardless of the values of the parameters.     

Radioactive heating and layered structure of cometary nuclei

Following the work of Whipple and Stefanik, radioactive heating by uranium, thorium and pottasium of a cometary nucleus is discussed. The assumed composition is that of interstellar medium. If thermal diffusivity is 10^–4 cm²s^–1, the central temperature of a nucleus with radius 10 km can be above 50 K, while if the thermal diffusivity is 5 × 10^–3, the central temperature can be only 25 K or so. Volatile gases such as N₂ and CO will flow toward the outer part of the nucleus and are lost in their first several approaches to the sun. This mechanism appears capable of explaining the depletion of N₂ and CO relative to the interstellar abundance. It is argued that unfamiliar activity of comet Bowell could be explained by sublimation mainly of N₂ and CO.     

Maximum non-gravitational acceleration due to out-gassing cometary nuclei

Maximum possible acceleration due to out-gassing from cometary nuclei is calculated for H₂O and CO(N₂) molecules. It is found that the maximum excess velocity at great distance is 0.18 km s^–1 so that excess velocities less than this value are compatible with the non-gravitational acceleration due to non-symmetric out-gassing. On the other hand, Comet 1975q and comet 1955V have excess velocities 0.81 and 0.80 km s^–1 respectively. These comets may be regarded as the candidates for possible interstellar comets.     

Space missions to small bodies: asteroids and cometary nuclei

The knowledge of the physical and dynamical properties, distribution, formation, and evolution of small bodies is fundamental to understand how planet formation occurred and, even more importantly, if and how these objects have played a role in the apparition of life on Earth. In the last century, asteroids began to no longer appear as starlike points of light in our telescopes, but to be resolved worlds with distinctly measurable sizes, shapes, and surface morphologies. Only in the last 25 years, the exploration of small bodies by spacecraft has begun and revealed objects widely diverse in formation region, evolution and properties (e.g. shape, albedo density, gravity, regolith size distribution, and porosity). In this paper we will provide a chronological analysis of comet nuclei and asteroids as revealed by space missions. The real breakthrough began with the ESA Giotto mission in 1986 to the comet Halley, while the latest JAXA Hayabusa mission was devoted to hover above the small asteroid Itokawa with a touch-and-go for a sample return of asteroidal regolith. Comet and asteroid science stands at the threshold of a new exceptional era, with many new missions to be devoted to these widely diverse and still poorly known small bodies.     

Thermal state and gas production rate of rotating cometary nuclei

We formulate a completely three-dimensional nonstationary model of the thermal state and gas production rate of rotating spherical cometary nuclei moving in circular and elliptical orbits around the Sun. We perform a thermophysical analysis of the problem and formulate a system of similarity criteria. The possible thermal regimes of cometary nuclei are analyzed in the space of suggested similarity criteria. Only one criterion dependent on the nucleus spin period is shown to play a dominant role for rotating nuclei at a given heliocentric distance. This simplifies greatly a parametric study of the gas production rate of real cometary nuclei under conditions of uncertainty in their parameters. Based on the developed model, we numerically investigate the thermal state and gas production rate of rotating nuclei. The results of our calculations are in complete agreement with those of the similarity analysis for the problem. We perform a comparative analysis of the currently used simplified thermal models for cometary nuclei and determine the range of their applicability.     

Processes affecting the composition and structure of silicate grains in cometary nuclei

Nucleation is a non-equilibrium process: the products of this process are seldom the most thermodynamically stable condensates but are instead those which form fastest. It should therefore not be surprising that grains formed in a circumstellar outflow will undergo some degree of metamorphism if they are annealed or are exposed to a chemically active reagent. Metamorphism of refractory particles continues in the interstellar medium (ISM) where the driving forces are sputtering by cosmic ray particles, annealing by high energy photons and grain destruction in supernova generated shocks. Studies of the depletion of the elements from the gas phase of the interstellar medium tell us that if grain destruction occurs with high efficiency in the ISM, then there must be some mechanism by which grains can be formed in the ISM. Various workers have shown that refractory mantles could form on refractory cores by radiation processing of organic ices. A similar process may operate to produce refractory inorganic mantles on grain cores which survived the supernova shocks. Most grains in a cloud which collapses to form a star will be destroyed; many of the surviving grains will be severely processed. Grains in the outermost regions of the nebula may survive relatively unchanged by thermal processing or hydration. It is these grains which we hope to find in comets. However, only those grains encased in ice at low temperature can be considered pristine since a considerable degree of hydrous alteration might occur in a cometary regolith if the comet enters the inner solar system. Some discussion of the physical, chemical and isotopic properties of a refractory grain at each stage of its life cycle will be attempted based on the limited laboratory data available to date. Suggestions will be made concerning types of experimental data which are needed in order to better understand the processing history of cosmic dust.