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 liquid phases in cometary nuclei

In this paper we review the relevant literature and investigate conditions likely to lead to melting of H₂O ice, methanol (CH₃OH) ice, ethane (C₂H₆) ice and other volatile ices in cometary nuclei. On the basis of a heat balance model which takes account of volatiles loss, we predict the formation of occasional aqueous and hydrocarbon liquid phases in subsurface regions at heliocentric distances, r_h of 1–3 AU, and 5–12 AU, respectively. Low triple-point temperatures and low vapour pressures of C₂H₆, C₃H₈, and some higher-order alkanes and alkenes, favour liquid phase formation in cometary bodies at high r_h. Microporosity and the formation of a stabilization crust occluding the escape of volatiles facilitate liquid-phase formation. Characteristics of the near-surface which favour subsurface melting include; low effective surface emissivity (at low r_h), high amorphous carbon content, average pore sizes of ～10 μm or less, presence of solutes (e.g. CH₃OH), mixtures of C₂–C₆ hydrocarbons (for melting at high r_h), diurnal thermal cycling, and slow rotation rate. Applying the principles of soil mechanics, capillary forces are shown to initiate pre-melting phenomena and subsequent melting, which is expected to impart considerable strength of ～10⁴ Pa in partially saturated layers, reducing porosity and permeability, enhancing thermal conductivity and heat transfer. Diurnal thermal cycling is expected to have a marked effect on the composition and distribution of H₂O ice in the near-surface leading to frost heave-type phenomena even where little if any true melting occurs. Where melting does take place, capillary suction in the wetted zone has the potential to enhance heat transfer via capillary wetting in a low-gravity environment, and to modify surface topography creating relatively smooth flat-bottomed features, which have a tendency to be located within small depressions. An important aspect of the “wetted layer” model is the prediction that diurnal melt–freeze cycles alter the mixing ratio vs. depth of solutes present, or of other miscible components, largely through a process of fractional crystallization, but also potentially involving frost heave. Wetted layers are potentially durable and can involve significant mass transport of volatile materials in the near-surface, increasing in extent over many rotations of the nucleus prior to and just after perihelion passage, and causing stratification and trapping of the lowest-melting mixtures at depths of several metres. A possible mechanism for cometary outbursts is proposed involving a heat pulse reaching the liquid phase in the deepest wetted zone, leading to supersaturation and triggering the sudden release under pressure of dissolved gases, in particular CO₂, CO, CH₄ or N₂, contained beneath a consolidated near-surface layer. This study indicates that liquid water can persist for long periods of time in the near-surface of some intermediate-sized bodies (10²–10³ km radius) within protoplanetary discs.     

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.     

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.     

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).     

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.     

Temperature of cometary dust

The variation of the dust temperature with heliocentric distance for a comet is calculated using the optical constants of an astronomically important silicate.     

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.     

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.     

Light scattering in cometary dust comae

Detailed single and multiple scattering calculations were carried out for a spherically symmetric cometary atmosphere irradiated by a plane parallel source. Using simplifying assumptions in the single scattering approximation, analytical expressions were derived for the total flux impinging the cometary nucleus, which was shown to be a decreasing function of the coma opacity. Moreover, while highly anisotropic phase functions resulted in more light reaching the nucleus than was the case for isotropic phase functions, the net energy flux at the nucleus surface was still found to be smaller in the presence of a coma than in the no coma case. This increased flux due to the anisotropic phase functions was attributed mostly to the effect of directional scattering in the forward Sun-comet axis. The isotropic multiply scattered flux at the surface was found tobe an increasing function of the opacity, , for 2.5. At larger values of , the maximum in the downward directed scattered flux was still seen to increase, but occurred at a height of several radii above the nucleus, resulting in a reduction at the surface. On the other hand, the total flux at the surface was again shown to be a decreasing function of and always less than in the no coma case. Finally, on comparing the multiply scattered flux with that obtained in the plane parallel approximation, it was quite apparent that except in the vicinity of the Sun-comet axis, the plane parallel geometry tends to underestimate the degree of scattering.NRC Resident Research Associate.     

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.     

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.     

Experimental aqueous alteration of cometary dust

Abstract– Recent spacecraft missions to comets have reopened a long‐standing debate about the histories and origins of cometary materials. Comets contain mixtures of anhydrous minerals and ices seemingly unaffected by planetary processes, yet there are indications of a hydrated silicate component. We have performed aqueous alteration experiments on anhydrous interplanetary dust particles (IDPs) that likely derived from comets. Hydrated silicates rapidly formed from submicrometer amorphous silicates within the IDPs at room temperature in mildly alkaline solution. Hydrated silicates may thus form in the near‐surface regions of comets if liquid water is ever present. Our findings provide insight into origins of cometary IDPs containing both anhydrous and hydrated minerals and help reconcile the seemingly inconsistent observations of hydrated silicates from the Stardust and Deep Impact missions.     

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.     

Composition of cometary dust from polarization spectra

The wavelength dependence of the polarization (“polarization spectra”) of cometary dust is discussed. It is shown that, in the case of large phase angles, the wavelength dependence of the polarization is mainly controlled by the complex refractive index of the particle material, whereas the spectral dependence of the intensity is also sensitive to the size of the particles. This suggests that observations of “polarization spectra” may determine the composition of cometary dust. An attempt is made to find the composition of the cometary dust material by comparing the observed polarimetric data with laboratory measurements of complex refractive indices of possible cometary constituents. Silicates, graphite, metals, organics, water ice and their mixtures are considered. It is shown that astronomical silicate must be the most abundant constituent of cometary dust in the range of heliocentric distances from 0.8 to 1.8 AU, whereas the volume fraction of pure graphite or pure metals is less then 1%. A substance similar to that of F-type asteroids may be present in comets. There is evidence for an organic material that is being destroyed between heliocentric distances of 0.8–1.8 AU.     

Physical properties of cometary and interplanetary dust

In the absence of numerous in situ studies, physical properties of cosmic dust may be derived from observations of their light scattering and thermal properties, through numerical simulations making use of realistic assumptions. Estimations about cometary and interplanetary dust composition, structure, size, as well as about their light scattering and thermal properties, are first summarized. We then present and discuss the numerical simulations we have performed with different types of particles: core-mantle submicron-sized elongated grains (having contributed to the formation of cometary dust), fractal aggregates of such grains (found in cometary comae and in the interplanetary dust cloud), and fractal aggregates of large dust grains (found in cometary dust trails).A very satisfactory fit to the numerous polarimetric observations of comet Hale-Bopp is obtained for a mixture with about 33–60% of organics in mass, with a power law size distribution with an index of (−3) and a radius of 20 μm for the upper cut-off. For the less-constrained polarimetric observations of interplanetary dust near 1 AU, a fit is obtained for a mixture with about 40% of organics in mass, with a similar size distribution and a radius of about 50 μm for the upper cut-off. The ensemble of results obtained for the interplanetary dust strongly suggest that its light scattering and thermal properties stem from the presence of compact and fluffy particles, with compositions ranging from silicates to more absorbing materials, whose contribution decreases with decreasing distance to the Sun.     

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.     

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.