Origin of short period comets

Reasons for interest in the origin of short-period comets and the difficulties of computing their long-term dynamcal evolution are reviewed. The relative advantages of a source region in an extended inner core of the Oort cloud or a compact comet belt just beyond the planetary system are finely balanced, and it is premature to consider the problem solved. A complication is that some comets belonging to the Jupiter family may be part of a time-dependent system, possibly the remains of a giant comet such as Chiron which could have been part of the system 104 yr ago. The origin of short-period comets plays a pivotal role in many areas of solar system science: planet formation, the source of water (possibly life) on the terrestrial planets, the cratering record on the terrestrial planets and satellites of the outer planets, and the environmental impact posed by massive bodies and their decay products in the Earth's near-space environment.     

Protosolar nebula and composition of comets

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

Giant planet formation

The accumulation of giant planets involves processes typical for terrestrial planet formation as well as gasdynamic processes that were previously known only in stars. The condensible element cores of the gas-giants grow by solid body accretion while envelope formation is governed by stellar-like equilibria and the dynamic departures thereof. Two hypotheses for forming Uranus/Neptune-type planets — at sufficiently large heliocentric distances while allowing accretion of massive gaseous envelopes, i.e. Jupiter-type planets at intermediate distances — have been worked out in detailed numerical calculations: (1) Hydrostatic gas-accretion models with time-dependent solid body accretion-rates show a slow-down of core-accretion at the appropriate masses of Uranus and Neptune. As a consequence, gas-accretion also stagnates and a window is opened for removing the solar nebula during a time of roughly constant envelope mass. (2) Gasdynamic calculations of envelope accretion for constant planetesimal accretion-rates show a dynamic transition to new envelope equilibria at the so called critical mass. For a wide range of solar nebula conditions the new envelopes have respective masses similar to those of Uranus and Neptune and are more tightly bound to the cores. The transitions occur under lower density conditions typical for the outer parts of the solar nebula, whereas for higher densities, i.e. closer to the Sun, gasdynamic envelope accretion sets in and is able to proceed to Jupiter-masses.     

A note on the total mass of comets in the solar system

The assumption that the very low albedo determined for Halley's comet is typical of all short period comets, taken together with the assumption that the average sizes of long and short period comets are approximately equal, leads to an increase in the total mass of comets in the solar system by almost two orders of magnitude. If gravitational ejection from the Uranus - Neptune zone during the later phases of planet formation is indeed responsible for the classical Oort cloud between 10⁴–10¹⁵ AU, then the mass of comets in this transplanetary region during cosmogonie times has to exceed the combined masses of Uranus and Neptune by over an order of magnitude. Furthermore, if the recent arguments for as many as 10¹⁴ comets in an inner Oort cloud between ~40– 10⁴AU are valid, then the total mass of comets in the solar system approaches 2% of a solar mass.     

Contraction of the solar nebula

The concept of Roche limit is applied to the Laplacian theory of the origin of the solar system to study the contraction of a spherical gas cloud (solar nebula). In the process of contraction of the solar nebula, it is assumed that the phenomenon of supersonic turbulent convection described by Prentice (1978) is operative and brings about the halt at various stages of contraction. It is found that the radius of the contracting solar nebula follows Titius-Bode law R _p = Ra^p, where R is the radius of the present Sun and a = 1.442. We call a the Roche's constant. The consequences of the relation are also discussed. The aim, here, is an attempt to explain, on the basis of the concept of Roche limit, the distribution of planets in the solar system and try to understand the physics underlying it.     

The provenance and evolution of comets

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

Satellites of minor planets: A new frontier for celestial mechanics

Most minor planets have satellites. This observation is predicted to have a major impact on the theory of minor planets, comets, and meteors.Presented at the Symposium Star Catalogues, Positional Astronomy and Celestial Mechanics, held in honor of Paul Herget at the U.S. Naval Observatory, Washington, November 30, 1978.     

The distribution of mass in the planetary system and solar nebula

A model solar nebula is constructed by adding the solar complement of light elements to each planet, using recent models of planetary compositions. Uncertainties in this approach are estimated. The computed surface density varies approximately asr ^–3/2. Mercury, Mars and the asteroid belt are anomalously low in mass, but processes exist which would preferentially remove matter from these regions. Planetary masses and compositions are generally consistent with a monotonic density distribution in the primordial solar nebula.     

The peculiar binary system epsilon Aurigae

Over the years, many models have been proposed for the system Aurigae; and in this communication we show that it could be a system where a visible star is eclipsed by a disc of dust and gas orbiting about it and lying in the plane of the orbit. Such a disc must be opaque across its centre but becomes transparent near its edges. It transpires that such a disc could have dimensions consistent with it being a pre-planetary nebula.     

Possibilities of using extreme observations to estimate cometary nucleus sizes

Not considering very rare in situ measurements of cometary nuclei, observations of comets at large heliocentric distances are the only direct source of our knowledge on their sizes. Observations of a cometary nucleus in pure reflected sunlight, at the time when coma is absent, are the way in which the nucleus size can be estimated. Probabilities that extreme observations represent non—active stages of cometary nuclei and also reliability of derived cometary nucleus sizes are investigated. Statistical analysis is based on a sample of 2842 photometric observations of 67 long-period comets observed at large heliocentric distances. For any long-period comet, there is a probability of 2:3 that the sizes derived on the basis of observations at extreme distances are in good agreement with the real nucleus sizes. For new comets in Oort's sense the probability is 3:4 independent of investigated arcs of orbits. For old comets a chance to estimate correct sizes is 1:2 but on the pre-perihelion arc only 1:3. It is also demonstrated that a premature start of activity prior to perihelion or a longer fading after perihelion is more frequent than a short-time isolated activity at large heliocentric distances.     

Some comments on the Oort cloud

The arguments used by Lyttleton to prove the nonexistence of the Oort cloud are reviewed, and it is shown that Oort's hypothesis remains consistent with observation. The 1950 model of the cloud cannot be correct and, by use of the results from a number of more recent papers, an improved model is described and compared with observations. It is emphasized that comparison of the predictions of theory with observations should concentrate on thea-distribution, as the 1/a-distribution masks much of the detailed structure of the theory. An order of magnitude argument is given which shows that 20% of so-called new comets have passed through the planetary system before, and the implications of this to the statistics of near-parabolic comet orbits are briefly investigated.     

Photochemical fractionation of16O in the space medium modeled by resonance excitation of CO by H-Lyman α

Inferences about the formation of primordial matter in our solar system rest on analysis of the earliest preserved materials in meteorites, of the structure of the solar system today, and of matter in evolving stellar systems elsewhere.The isotope distribution in meteorites suggests that molecular excitation processes similar to those observed today in circumstellar regions and dark interstellar clouds were operating in the early solar nebula. Laboratory model experiments together with these observations give evidence on the thermal state of the source medium from which refractory meteoritic dust formed. They indicate that resonance excitation of the broad isotopic bands of molecules such as¹²C¹⁶O, MgO, O₂, AlO, and OH by strong UV line sources such as H-L, MgII, H, and CaII may induce selective reactions resulting in the anomalous isotopic composition of oxygen and possibly other elements in refractory oxide condensates in meteorites.     

Encounter frequency of Halley-like comets with the planets

We present the results of a numerical study on encounter frequencies of fictitious Halley-like comets with the planets in a dynamical model of the solar system, in which we take into account the gravitational forces of the Sun and the planets Venus through Neptune. The change of the orbital elements during a close approach with a planet was carefully monitored with the aid of a thoroughly tested numerical integration method with automatic step size control. We computed the encounter frequencies of the comets' orbits using two different spheres of influence and compared the results. In both cases, it turned out that the encounter frequency of the fictitious Halley-like comets with Jupiter and Saturn is about a factor 10 to 100 higher than for the other planets. Concerning the changes of the semi-major axes and inclinations our results show that an increase and decrease of these elements is equally probable after an encounter.     

Interaction of planetary nebulae with prenebulae debris

In the present poster we suggest that some of the structures observed in the envelopes of planetary nebulae are caused by the interaction of central star wind and radiation with preplanetary nebula debris: planets, moons, minor objects and ring and ring arcs.Recently considerable amount of planetary material has been reported to exist around solar type stars, this debris could be evaporated during the envelope ejection and alter the chemical abundance and produce some of the envelope inhomogeneities.If there are massive enough rings of material surrounding the progenitor and planets in their vicinity, arc rings could be formed. If the rings are viewed pole on when the envelope is detached from the central star, it will interact with the arc ring material and produce ansae and pedal and garden-hose-shape structures observed in some planetaries.Paper presented at the Conference onPlanetary Systems: Formation, Evolution, and Detection held 7–10 December, 1992 at CalTech, Pasadena, California, U.S.A.     

The influence of spectral resolution on line blending and wavelength positions in the solar UV spectrum

For representative sections of the solar UV spectrum ( 2765 Å– 2790 Å, 2765 Å– 2805 Å) the line density and the accuracy of wavelength positions of absorption features are derived as function of the spectral resolution. In low resolution spectrograms unresolved blends may shift intrinsic wavelength positions of absorption lines by amounts up to a few tenths of the spectral resolution.The results obtained for the solar spectrum are applied to the flux spectrogram of CMi.Guest Investigator in the BUSS Program jointly performed by the Space Research Laboratory, Utrecht, The Netherlands, and the NASA L. B. Johnson Space Center, Houston, U.S.A.     

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.     

Evolutionary tracks of the terrestrial planets

On the basis of the model proposed by Matsui and Abe, we will show that two major factors — distance from the Sun and the efficiency of retention of accretional energy — control the early evolution of the terrestrial planets. A diagram of accretional energy versus the optical depth of a proto-atmosphere provides a means to follow the evolutionary track of surface temperature of the terrestrial planets and an explanation for why the third planet in our solar system is an aqua-planet.     

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.     

Laboratory simulation of cometary erosion by space plasma

A laboratory experiment has been made where a plasma stream collides with targets made of different materials of cosmic interest. The experiment can be viewed as a process simulation of the solar wind particle interaction with solid surfaces in space — e.g., cometary dust. Special interest is given to sputtering of OH and Na.It is also shown that the erosion of solid particles in interplanetary space at large heliocentric distances is most likely dominated by sputtering and by sublimation near the Sun. The heliocentric distance of the limit between the two regions is determined mainly by the material properties of the eroded surface, e.g., heat of sublimation and sputtering yield, a typical distance being 0.5 AU.It is concluded that the observations of Na in comets at large solar distances, in some cases also near the Sun, is most likely to be explained by solar wind sputtering. OH emission in space could be of importance also from dry, water-free, matter by means of molecule sputtering. The observed OH production rates in comets are however too large to be explained in this way and are certainly the results of sublimation and dissociation of H₂O from an icy nucleus.     

The flux ejection dynamo with small diffusivity

A number of examples are worked out to illustrate the consequences of reverse flux ejection from the surface of a convective layer of conducting fluid. Generally the reverse flux ejection has the opposite effect of magnetic buoyancy, tending to bury the fields rather than bringing them through the surface. Even a weak flux ejection effect prevents the excape of magnetic field through the surface. Reverse flux ejection at the surface of an -dynamo profoundly alters the character of the solutions of the dynamo equations. Altogether, flux ejection serves to obscure the interpretation of magnetic observations. The outstanding problem now is to determine under what circumstances there exists cyclonic convection with rotations in excess of ±1/2 in the rising columns of fluid. Negative turbulent diffusion is expected to be a close companion of the flux ejection effect.This work was supported by the National Aeronautics and Space Administration under grant NGL 14-001-001.