On the existence of small comets and their interactions with planets

Arguments are presented for a substantial, unexplored population of comets with radii less than 1 km. Known examples confirm this population and extrapolation of any plausible size-distribution function indicates large numbers. However, their accurate numbers, orbital characteristics, and physical properties are unknown. Thus, even though the small comets may be the most frequent cometary bodies impacting the planets, a quantitative evaluation is not currently possible. We advocate an optimized, dedicated search program to characterize this population.Laboratory for Atmospheric and Space Physics, University of Colorado at BoulderLaboratory for Atmospheric and Space Physics, University of Colorado at BoulderLaboratory for Atmospheric and Space Physics, University of Colorado at Boulder     

On the existence of small comets and their interactions with planets

Arguments are presented for a substantial, unexplored population of comets with radii less than 1 km. Known examples confirm this population and extrapolation of any plausible size-distribution function indicates large numbers. However, their accurate numbers, orbital characteristics, and physical properties are unknown. Thus, even though the small comets may be the most frequent cometary bodies impacting the planets, a quantitative evaluation is not currently possible. We advocate an optimized, dedicated search program to characterize this population.     

H2O + ions in comets: models and observations

An improved magnetohydrodynamic (MHD) model with chemistry is presented. The analysis of the source and sink terms for H₂O ⁺ shows that for small comets up to 11% of water molecules are finally ionized. For large comets (such as Halley) this fraction decreases to less than 3%. From the MHD scaling laws a similarity law for the individual ion densities is deduced which takes into account that the mother molecules are depleted by dissociation. This is applied to H₂O ⁺ ions. Radial density profiles from model calculations, observations by Giotto near comet Halley, and ground based observations of three comets confirm this scaling law for H₂O ⁺ ions. From the similarity law for the density a scaling law for the column density is derived which is more convenient to apply for ground based observations. From these scaling laws methods are derived which allow the determination of the water production rate from the ground based images of the H₂O ⁺ ions. Finally, the two dimensional images of model column densities are compared with observations.     

Radiogenic heating of comets by 26Al and implications for their time of formation

The effect of radiogenic heating on the thermal evolution of spherical icy bodies with radii 1 km < R < 100 km was investigated. The radioisotopes considered were 26Al, 40K, 232Th, 235U, and 238U. Except for the 26Al abundance, which was varied, the other initial abundances were kept fixed, at values derived from those of chondritic meteorites and corresponding to a gas-to-dust ratio of 1. The initial models were homogeneous and isothermal (To = 10 K) amorphous ice spheres, in a circular orbit at 10(4) AU from the Sun. The main object of this study was to examine the conditions under which the transition temperature from amorphous into cubic ice (Ta = 137 K) would be reached. It was shown that the influence of the short-lived radionuclide 26Al dominates the effect of other radioactive species for bodies of radii up to approximately 50 km. Consequently, if we require comets to retain their ice in amorphous form, as suggested by observations, an upper limit of approximately 4 x 10(-9) is obtained for the initial 26Al abundance in comets, a factor of 100 lower than that of the inclusions in the Allende meteorite. A lower limit for the formation time of comets may thus be derived. The possibility of a coexistence of molten cometary cores and extended amorphous ice mantles is ruled out. Larger icy spheres (R > 100 km) reached Ta even in the absence of 26Al, due to the decay of the other radionuclides. As a result, a crystalline core formed whose relative size depended on the composition assumed. Thus the outermost icy satellites in the solar system, which might have been formed of ice in the amorphous state, have probably undergone crystallization and may have exhibited eruptive activity when the gas trapped in the amorphous ice was released (e.g., Miranda).     

Earth-orbit-approaching comets and their theoretical meteor radiants

Sixteen comets produce recognizable meteor showers that are found in A. F. Cook's (1973, In Evolutionary and Physical Properties of Meteoroids (C. L. Hemenway, P. M. Millman, and A. F. Cook, Eds.), pp. 183–191, U.S. Govt. Printing Office, Washington, D.C.), working list of meteor streams. Of these, five are long period, including one in a parabolic and one in a hyperbolic orbit. The largest Earth-comet orbit miss distance is 0.20 AU for P/Encke and the Northern and Southern Taurids. Using this is an upper limit for meteor showers from comets, all comets which approach the Earth's orbit to within 0.20 AU were extracted from the Catalogue of Cometary Orbits (B. G. Marsden, 1979. 3rd ed., Central Bureau of Astronomical Telegrams, IAU SAO, Cambridge, Mass.). A compilation of such comets is presented by date minimum approach, along with the distance of closest approach and the theoretical geocentric radiants and velocities of possible associated meteor showers. Both pre- and postpperihelion encounters with the Earth's orbit are considered. There are 240 entries for 178 long-period comets, and 36 for 28 short-period comets. It is noted that all short-period comets that have approached the Earth's orbit to within 0.08 AU have produced meteors, except P/Lexell, P/Finlay, P/Denning-Fujikawa, and P/Grigg-Skjellerup. Attention is called to the favorable observing conditions for detecting meteors from P/Grigg-Skjellerup in April 1982, and for the possibility of another great Draconid storm from P/Giacobini-Zinner in October 1985. A comparison is made between observed sporadic meteor rates and the distribution of theoretical radiants throughout the year, from which it is concluded that the currently known comets can account for sporadic meteors. A criterion is developed to test whether or not an observed meteor shower can be associated with a given theoretical radiant. Based on known examples, a qualitative model for comet/meteor relationships is also presented.     

The formation of comets in wind-driven shells around protostars

It is shown that the dense, turbulent, decelerating shells produced by protostellar flows around young stars are a probable site for rapid grain growth by coalescing collisions. The growth of grains occurs in a thin dust layer at the leading edge of the gas shell until a critical grain size on the order of 1−10 μm is reached. Grains larger than this decouple from the turbulence and eventually reach sizes of ≈100 μm. These large grains form a thin dust shell with low-velocity dispersion, in which ultimately local gravitational instability takes place. This causes the accumulation of comet-sized aggregations of dust, assuming that the dust velocity dispersion is on the order of 10⁻² m sec⁻¹. It is proposed that the mechanism could lead to a high space density of comets in molecular clouds. The efficient formation of “giant” grains, and even comet nuclei, in the regions around young stars has important implications both for cometary astronomy and for understanding the dynamical and chemical evolution of molecular clouds and the interstellar medium.     

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.     

On the possibility of H2-near-infrared detection in comets with large gas production

Comets with large gas production offer a unique chance to observe a H₂-flux of about 10⁵ photon cm^–2 s^–1 sr^–1 (1 Rayleigh) at wavelengths 8497.4 Å, 8560.2 Å and 8747.9 Å-i.e., where photon counting methods are still applicable. In the following it will be shown that population of the vibrational levels, giving rise to these quadrupole overtone transitions, is dominated by photodissociation of methane, and that the emission even of quadrupole lines is not attenuated by collisional quenching. Wavelength scanning by ±1 Å is shown to be enough to discriminate between cometary and atmospheric emissions by phase-sensitive subtraction techniques. Solid angle of <10^–7 sr has to be used, whence follows that a large ground-based telescope combined with a tilting Fabry-Perotfilter is best suited for detection of the near-infrared H₂-emissions at reasonable counting rates and sufficient rejection of the atmospheric background.Since H₂ is supposed to be formed mainly by the photolysis of CH₄, the optimum time for detection will be during approach to perihelion when, because of its high vapor pressure, methane will vaporize from the cometary nucleus. Variation of the source strength of both CH₄ and its photolysis product H₂ with time are particularly valuable indicators for the structure of the nucleus, its thermal history and conditions of formation. A high-resolution tilting filter photometer, which allows phase-sensitive background subtraction was used for the first time for near-infrared observations on the dust coma of Comet Kohoutek (Barbieriet al., 1974). The same technique was successfully used for the determination of an upper limit for CH₄ production at 3.3 by airborne observations on the same comet (Cosmoviciet al., 1974).     

Gas‐melt interactions and their bearing on chondrule formation

Abstract— Interactions between nebular gas and molten silicates or oxides could have played a major role in the formation and differentiation of the first solids formed in the solar system. In order to simulate such interactions, we set up a new experimental device in which isothermal condensation experiments have been conducted. Partially molten chondrule‐like samples have been exposed to high SiO(g) partial pressures, for intervals between 80 and 300 s and at temperatures ranging from 1600 to 1750 K. Results show that silica entering from the gas phase could be responsible for several textural and mineralogical features observed in natural chondrules. For instance, these experiments reproduce not only the mineralogical zonation of porphyritic olivine‐pyroxene chondrules with the peripheral location of pyroxenes, but also olivine resorption textures and the common poikilitical enclosure of olivines in pyroxenes. In the light of these similarities, we advocate that gas‐melt interactions through condensation are viable mechanisms for chondrule formation and hence may place severe constraints on the history of these primitive objects. In the nebula, high SiO(_g) partial pressures could have been established by the volatilization of regions with high dust/gas ratio. A possible scenario for this stochastic thermal activity is the intense activity of the protosun in its young stellar object phase.     

The activities of comets related to their aging and origin

Two indices have been developed for the purpose of comparing the natures of various classes of comets. The first is the Activity Index (AI), measuring the inherent magnitude increase in brightness from great solar distances to maximum near perihelion. The second, or Volatility Index (VI), measures the variation in magnitude near perihelion. Tentative determinations of these two indices are derived from observations by Max Beyer over more than 30 years for long-period (L-P) and short-period (S-P) comets near perihelion and from other homogeneous sources. AI determinations are made for 32 long-period (L-P) comets and for 14 short-period (S-P). The range of values of AI is of the order of 3 to 10 magnitudes with a median about 6. An expected strong correlation with perihelion distance q, is found to vary as q ^–2.3. Residuals from a least-square solution (AI) are used for comparing comets of different orbital classes, the standard deviation of a single value of AI is only ±1^m.1 for L-P comets and ±1^m.2 for S-P comets.Among the L-P comets, 19 of period P larger than 10⁴ years yield AI = 0^m.27 ± 0^m.25 compared to 0^m.39 ± 0^m.26 for 13 of period between 10² years and 10⁴ years. This denies any fading with aging among the L-P comets. Also no systematic change with period occurs for the VI index, leading to the same conclusions. Weak correlations are found with the Gas/Dust ratio of comets. No correlations are found between the two indices, nor of either index with near-perihelion magnitudes or orbital inclination.The various data are consistent with a uniform origin for all types of comets, the nuclei being homogeneous on the large scale but quite diverse on a small scale (the order of a fraction of kilometer in extent). Small comets thus may sublimate away entirely, leaving no solid core, while huge comets may develop a less volatile core by radioactive heating and possibly become inactive like asteroids after many S-P revolutions about the Sun. When relatively new, huge comets may be quite active at great solar distances because of volatiles from the core that have refrozen in the outer layers.     

H2O maser pumping: The effect of quasi-resonance energy transfer in collisions between H2 and H2O molecules

The effect of quasi-resonance energy transfer in collisions between H₂ and H₂O molecules in H₂O maser sources is investigated. New data on the state-to-state rate coefficients for collisional transitions for H₂O and H₂ molecules are used in the calculations. The results of ortho-H₂O level population inversion calculations for the 22.2-, 380-, 439-, and 621-GHz transitions are presented. The ortho-H₂O level population inversion is shown to depend significantly on the population distribution of the para-H₂ J = 0 and 2 rotational levels. The possibility of quasi-resonance energy transfer in collisions between H₂ molecules at highly excited rotational-vibrational levels and H₂O molecules is considered. The quasi-resonance energy transfer effect can play a significant role in pumping H₂O masers in the central regions of active galactic nuclei and in star-forming regions.     

On the relationship of long-period comets to known and unknown planets

Statistical aspects of the question of the dynamical relationship of long-period comets to giant planets (Saturn, Uranus, Neptune), dwarf planets (Pluto, 2003 EL₆₁, 2003 UB₃₁₃), and five hypothetical planets are investigated. Data for 859 and 888 comets (2005, 2006) with periods P > 200 years are used in the statistics. No comets of the Kreutz, Marsden, Kracht, and Meyer groups are considered. The minimum interorbital distances of comets from the listed planetary bodies are mainly analyzed. Effects testifying to the kinematical relationship of some of the comets to planets have been established by testing the cometary data relative to 67 planes. The distribution of the perihelia of long-period comets is also discussed.     

On the process of accretion in the formation of the planets and comets

The physically reasonable assumption that the seed bodies which initiated the accretion of the individual asteroids, planets, and comets (subsequently these objects are collectively called planetoids) formed by stochastic processes requires a radius distribution function which is unique except for two scaling parameters: the total number of planetoids and their most probable radius. The former depends on the ease of formation of the seed bodies while the second is uniquely determined by the average pre-encounter velocity, V, of the accretable material relative to an individual planetoid. This theoretical radius function can be fit to the initial asteroid radius distribution which Anders (1965) derived from the present-day distribution by allowing for fragmentation collisions among the asteroids since their formation. Normalizing the theoretical function to this empirical distribution reveals that there were about 10² precollision asteroids and that V = (2?4) × 10^?2 km/sec which was presumably the turbulent velocity in the Solar Nebula. Knowing V we can determine the scale height of the dust in the Solar Nebula and consequently its space density. The density of accretable material determines the rate of accretion of the planetoids. From this we find, for example, that the Earth formed in about 8 × 10⁶ yr and it attained a maximum temperature through accretion of about 3 × 10³°K. From the total mass of the terrestrial planets and the theoretical radius function we find that about 2 × 10³ planetoids formed in the vicinity of the terrestrial planets. Except for the asteroids the smaller planetoids have since been accreted by the terrestrial planets. About 15% of the present mass of the terrestrial planets was accumulated by the secondary accretion of these smaller primary planetoids. There are far fewer primary planetoids than craters on the Moon or Mars. The craters were likely produced by the collisional breakup of a few primary planetoids with masses between one-tenth and one lunar mass. This deduction comes from comparing the collision cross sections of the planetoids in this mass range to that of the terrestrial planets. This comparison shows that two to three collisions leading to the breakup of four to six objects likely occurred among these objects before their accretion by the terrestrial planets. The number of these fragments is quite adequate to explain the lunar and Martin craters. Furthermore the mass spectrum of such fragments is a power-law distribution which results in a power-law distribution of crater radii of just the type observed on the Moon and Mars. Applying the same analysis to the planetoids which formed in the vicinity of the giant planets reveals that it is unlikely that any fragmentation collisions took place among them before they were accreted by these planets due to the integrated collision cross section of the giant planets being about three orders of magnitude greater than that of the terrestrial planets. We can thus anticipate a marked scarcity of impact craters on the satellites of these outer planets. This prediction can be tested by future space probes. Our knowledge of the radius function of the comets is consistent with their being primary planetoids. The primary difference between the radius function of the planetoids which formed in the inner part of the solar system and that of the comets results from the fact that the seed bodies which grew into the comets formed far more easily than those which grew into the asteroids and the terrestrial planets. Thus in the outer part of the Solar Nebula the principal solid material (water and ammonia snow) accreted into a huge (～10¹²⁺) number of relatively small objects (comets) while in the inner part of the nebula the solid material (hard-to-stick refractory substances) accumulated into only a few (～10³) large objects (asteroids and terrestrial planets). Uranus and Neptune presumably formed by the secondary accretion of the comets.     

On the nature and origin of comets and their contribution to planets

Observations of comets show that they were formed at extremely low temperatures and probably contain amorphous ices that give off exothermal energy on mild heating. The slow rotation period of 5^d.0 for the large comet P/Schwassmann-Wachmann 1 suggests that it was formed in a gravitationally undisturbed region of space. Many smaller typical comets appear to be rotating rapidly, indicating that encounters among them were frequent during formation. As a consequence, the product of the relaxation time for encounters and the mean space density near the end of comet formation was approximately 2×10² g s cm^–3. A time scale of 10⁶ yr for comet accumulation is suggested. Laboratory studies by Patashnick and Rupprecht support the probably amorphous nature of the ices. The evidence mildly favors Cameron's 1977 theory of the primitive accretion disk.Interstellar grains grown to large sizes in extremely cool clouds might pop on mild heating by supernovae or luminous young stars to increase the local opacity and scattering.Some probable and possible contribution of comets to the solar system are summarized.     

Photodissociation lifetime of 32S2 molecule in comets

Photodissociation lifetime of ³²s₂in comets is calculated by absorption of solar photons into the B^3– state and velocity distributions of sulphur atoms are determined. Absorption of solar photons of wavelength ~ 280 nm leads to a photodissociation lifetime of about 250 s for ³²S₂ molecule in comets when sun-comet distance is 1 AU. Forbidden lines corresponding to ¹D-³P transitions of neutral sulphur atom may be detectable at about 11 306 and 10 821 Å in comets. The production rate of ³²S₂ dimer in comet IRAS-Araki-Alcock 1983d compares well with the production rate of CS, observed in comet Bradfield, when compared at the same heliocentric distance. The chemistry of ³²S₂ dimer formation in the inner coma of a comet is discussed in the framework of some gas phase reactions.Work partially supported by the CNPq, Brasilia, Brasil under contract No. 30.4076/77.     

Chemical effects of H2 formation excitation

The effects of the production on dust grain surfaces of molecular hydrogen in excited states have been investigated. On the assumption that all of the H₂ formed on the surface of grains has a sufficient level of excitation too vercome the energy barriers in the formation reactions for the important OH and CH⁺ radicals, we consider the likely abundances of excited H₂ (H₂ ^*), OH and CH⁺ in various situations. Two different models are employed; the first links the H₂ ^* abundance directly to that of H₂ using a steady-state approximation, whilst the second considers the time-dependence of H₂ ^*. The second model is applied to gas that has been subjected to a strong isothermal shock (specifically, the shock-induced collapse of a diffuse cloud), which results in an extreme (high density, high atomic hydrogen abundance) environment. In general, it is found that the presence of the excited H₂ has only marginal effects on the chemistry of interstellar clouds. However, in the isothermal shock model, the abundances of CH⁺ are significantly enhanced, but only on short timescales, whilst the effects on the OH abundances are smaller, but last longer. We conclude that other than in such exceptional environments there are no obvious chemical signatures of the formation of H₂ ^*. This revised version was published online in July 2006 with corrections to the Cover Date.     

End-states of short-period comets and their role in maintaining the zodiacal dust cloud

Physical lifetimes and end-states of short-period comets are analysed in connection with the problem of the maintainance of the zodiacal dust cloud. In particular, the problem of the comet-asteroid relationship is addressed. Recent studies of the physical properties of Apollo-Amor asteroids and short-period comets (e.g., Hartmann et al., 1987) show significant differences between them, suggesting that they are distinct classes of objects. A few percent of the active SP comets might become asteroidal-like bodies in comet-type orbits due to the buildup of dust mantles. The remainder probably disintegrate as they consume their volatile content so their debris can only be observed as fireballs when they meet the Earth. Unobservable faint SP comets — i.e., comets so small (m 10¹⁴ g) that quickly disintegrate before being detected, might be a complementary source of dust material. They might be completely sublimated even at rather large heliocentric distances (r - 3 AU). Yet the released dust grains can reach the vicinity of the Sun by Poynting-Robertson drag. The mass associated with unobservable SP comets with perihelion distances q 3 AU might be comparable to that computed for the sample of observed SP co-mets with q 1.5 AU. It is concluded that SP comets (from the large to the unobservable small ones) may supply an average of several tons/sec of meteoric matter to the zodiacal dust cloud.