Development of a comet as it pursues its orbit

The properties of cometary dust-swarms in almost parabolic long-period orbits are examined. In general their self-gravitation is stronger than the solar disruptive influence for all except the relatively small part of the orbit within planetary distances during which the sun dominates by so great a factor that the individual particles of the swarm pursue independent orbits apart from the possibility of collisions between them. At aphelion the internal relative speeds of particles are only a few centimetres per second, but at and near perihelion they may rise to the order of a kilometre per second. For purely dynamical reasons the extent of the swarm in directions perpendicular to the orbital motion will strongly diminish as perihelion is approached and correspondingly increase thereafter, while the dimension along the orbit will change in direct proportion to the orbital velocity. Every particle must cross through the median orbital plane near perihelion, and collisions between a proportion of the particles will occur at speeds capable of fragmenting them into myriads of smaller dustparticles, also heating them at and near the colliding elements of their surfaces. Increase of reflected sunlight will result and also release of material in gaseous form by solar plus collisional heating. Sufficiently finely divided dust particles will be driven out of the comet by radiation-pressure to form a dust-tail, while suitable gaseous compounds if present will be driven out to give a gas-tail. For Sungrazing comets, complete gasification must occur at and near perihelion, and very considerable extension along the orbit. Such comets would recondense to small solid particles on receding again from the Sun. The effect of passage of the solar system through interstellar gas-clouds is shown to be capable of substantially affecting the angular momentum of a comet about the Sun, thus accounting for the existence of comets with high values of perihelion-distance. This same process would enable cometary particles to adsorb interstellar gases at their surfaces and regenerate their gas-content. The mass-loss by a comet at each return strongly indicates, that comets cannot have originated at the same time as the planets, a result further supported by the rapid expulsion of entire comets through purely dynamical action of the planets. That the quiescent structure of comets consists of a vast widely spaced swarm of minute dust-particles receives circumstantial support from the highly varied and peculiar properties long since recorded for numerous comets. These properties exhibit such erratic diversity as to make clear that only a theory involving considerable range of essential parameters can be capable of accounting for them adequately.     

The magnitude distribution, perihelion distribution and flux of long-period comets

The mass distribution and perihelion distribution of long-period comets are re-assessed. The mass distribution index is found to be 1.598±0.016 , indicating that the distribution is somewhat steeper than was obtained by previous analyses of an amalgam of all the available historical data. The number of long-period comets that have orbital perihelion distances, q , that fall in a specific q to q +d q range is found to be independent of q . It is also noted that the flux of long-period comets to the inner Solar system has remained constant throughout recorded history.
The number of long-period comets, , per 1-au interval of perihelion distance, per year, brighter than H , entering the inner Solar system is found to be given by log₁₀ =−2.607+0.359 H . It is therefore estimated that, for example, about 0.5, 30 and 2000 long-period comets with absolute magnitudes brighter than 0, 5 and 10 respectively pass the Sun on orbits with perihelion distances less than 2.0 au, every century.     

Young Meteor Swarms Near the Sun: I. Statistical Correlation of Meteors with Families of Short-Perihelion Comets

We examine the hypothesis about the formation of meteor streams near the Sun. Families of short-perihelion orbit comets, many of which pass just a few radii from the solar surface at perihelion and have high dust production efficiencies, are assumed to be candidates for the parent bodies of these meteor streams. Our statistical analysis of orbital and kinematic parameters for short-perihelion meteoric particles recorded at the Earth and comets from the Kreutz family and the Marsden, Kracht, and Meyer groups led us to certain conclusions regarding the proposed hypothesis. We found a correlation between the ecliptic longitude of perihelion for comet and meteor orbits and the perihelion distance. This correlation may be suggestive of either a genetic connection between the objects of these two classes or the result of an as yet unknown mechanism that equally acts on short-perihelion comet and meteor orbits. A reliable conclusion about this genetic connection can be reached for the meteors that belong to the Arietids stream and the Marsden comet group.     

Vaporization of comet nuclei: Light curves and life times

We have examined the effects of vaporization from the nucleus of a comet and show that a latitude dependence of vaporization can, in some cases, explain asymmetries in cometary light curves. We also find that a non-uniform distribution of solar radiation over a comet can considerably shorten the vaporization lifetime compared to the results normally obtained by assuming that the nuclear surface is isothermal.Independent of any latitude effects, comets with CO₂-dominated nuclei and with perihelion distances less than 0.5 AU have vaporization lifetimes less than or comparable to their dynamical ejection times. This may explain the observed deficit of comets with small perihelion distances. Similarly comets with CO₂-dominated nuclei and perihelia near Jupiter's orbit have vaporization lifetimes that are shorter than the time for capture into short-period orbits. We suggest, therefore, that at least some new comets are composed in large part of CO₂, while only H₂O-dominated comets, with lower vaporization rates, can survive to be captured into short-period orbits.     

Observations of the long-lasting activity of the distant Comets 29P Schwassmann-Wachmann 1, C/2003 WT42 (LINEAR) and C/2002 VQ94 (LINEAR)

We investigated three comets, which are active at large heliocentric distances, using observations obtained at the 6-m BTA telescope (SAO RAS, Russia) in the photometric mode of the focal reducer SCORPIO. The three comets, 29P/Schwassmann-Wachmann 1, C/2003 WT42 (LINEAR), and C/2002 VQ94 (LINEAR), were observed after their perihelion passages at heliocentric distances between 5.5 and 7.08 AU. The dust production rates in terms of Afρ was measured for these comets. Using the retrieved values, an average dust production rate was derived under different model assumptions. A tentative calculation of the total mass loss of the comet nucleus within a certain observation period was executed. We calculated the corresponding thickness of the depleted uppermost layer where high-volatile ices completely sublimated. The results obtained in our study strongly support the idea that the observed activity of Comet SW1 requires a permanent demolition of the upper surface layers.     

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.     

Secular light curve of Comet 28P/Neujmin 1 and of spacecraft target Comets 1P/Halley, 9P/Tempel 1, 19P/Borrelly, 21P/Giacobinni-Zinner, 26P/Grigg-Skjellerup, 67P/Churyumov-Gerasimenko, and 81P/Wild 2

We present the secular light curves of eight comets listed in the title. Two plots per comet are needed to study these objects: a reduced magnitude (to Δ=1 AU = geocentric distance) vs time, and a reduced magnitude vs LogR (R=heliocentric distance). A total of over 16 new parameters, are measured from both plots, and give an unprecedented amount of information to characterize these objects: the onset of sublimation (RON), the offset of sublimation (ROFF), the time lag at perihelion (LAG), the absolute magnitude (m(1,1)), the maximum magnitude at perihelion (mMAX(1,LAG)), the nuclear magnitudes (VN), the amplitude of the secular light curve (ASEC), plus several others, and the photometric functions needed to describe the envelope. The most significant findings of this investigation are: (a) The envelope of the observations is the best representation of the secular light curve. (b) The H10 photometric system is unable to explain the curves and a new set of photometric rules and functions is used. (c) Only four comets exhibit power laws in their secular light curves, and only partially: 1P, 19P, 21P, and 81P. All others have to be described by more complex functions. Of the four, three exhibit a break of the power law, requiring two laws pre-perihelion and one post-perihelion. The reason for this behavior is not understood. (d) We predict the existence of a photometric anomaly in the secular light curve of 67P/Churyumov-Gerasimenko, evidenced by a region of diminished activity from −119 to −6 days before perihelion, that might be interpreted as a topographic effect or the turn off of an active region. (e) We define a photometric parameter (P-AGE) that attempts to measure the relative age of a comet through the activity exhibited in the secular light curve. 81P/Wild 2 (a comet that has recently entered the inner Solar System) is confirmed as a young object, while 28P/Neujmin 1 is confirmed as a very old comet. (f) Arranging the comets by P-AGE also classifies them by shape. A preliminary classification is achieved. (g) The old controversy of what is a nuclear magnitude is clearly resolved.     

On the variations in the insolation at Mercury resulting from oscillations of the orbital eccentricity

This paper describes variations in the insolation on Mercury resulting from fluctuations of the orbital eccentricity (0.11≤e≤0.24) of the planet. Equations for the instantaneous and the daily insolation are briefly discussed and several numerical examples are given illustrating the sensitivity of the solar radiation to changes ine. Special attention is paid to the behavior of the solar radiation distribution curves near sunrise and sunset which at the warm pole of Mercury (longitudes ±90°) occur as the planet goes through perihelion. It has been found that for eccentricities larger than about 0.194 there exists two permanent thermal bulges on opposite sides of the Mercurian surface that alternately point to the Sun at every perihelion passage. The critical value ofe past which the Sun shortly sets after perihelion is near 0.213.     

Long-term effects of the Galactic tide on cometary dynamics

We introduce a model for integrating the effects of Galactic tides on Oort cloud comets, which involves two procedures, according to the values of the osculating semi-major axis a and eccentricity e. Ten simulations of the dynamics of 10⁶ comets over 5 Gyr are performed using this model. We thus investigate the long-term effects of the Galactic tide with and without a radial component, the effects of the local density of the Galactic disk, and those of the Oort constants. Most of the results may be understood in terms of the integrability or non-integrability of the system. For an integrable system, which occurs for moderate semi-major axes with or without radial component, the dynamics is explained by periodic variation of the cometary perihelion, inducing the depletion of the outer region of the Oort cloud, a constant flux from the inner region after 500 Myr, and the quick formation of a reservoir of comets with argument of perihelion near 26.6°. When the system is non-integrable, the efficiency of the tide in reducing the cometary perihelion distance is enhanced both by replenishing the Oort cloud domain from which comets are sent toward the planetary system, and by reducing the minimal value that the perihelion distance may reach. No effects of varying the Oort constants were observed, showing that the flat rotation curve is a satisfactory approximation in Oort cloud dynamics.     

An idealized short-period comet model: Surface insolation,H2O flux,dust flux,and mantle evolution

A model of cometary activity is developed which integrates the feedback processes involving heat, gas, and dust transport, and dust mantle development. The model includes the effects of latitude, rotation, and spin axis orientation. Results are obtained for various grain size distributions, dust-to-ice ratios, and spin axis orientations. Attention is focused on the development, change of structure and distribution of dust mantles and their mutual interaction with ice surface temperature and gas and dust production. In this model the dust mantle controls the mechanism of gas transport not onlu by its effect on the temperature but, more importantly, by its own dynamic stability. Results suggest that an initially homogeneous short-period comet with a “cosmic” dust-to-water ice ratio, typical orbit, rotation rate, and grain size distribution would develop at most only a thin (<1 mm) cyclic mantle at all points on the nucleus. Such a fully developed temporary mantle would exist throughout the diurnal cycle only beyond ～4AU. Thus, cyclic behavior would be expected for such an idealized comet, at least for most of its lifetime. Long-term irreversible mantle development on comets with typical rotation rates was not found except regionally on Encke and also on objects with perihelia ?1.5 AU. Even in these cases, free silicate exists, after a few cycles, only as relatively rare large grains and agglomerates with radii ～1 cm scattered over exposed ice. Full mantle development would require hundreds to thousands of cycles. In the case of an initially homogeneous comet Encke, this slow incipient mantle development is shown to be the direct result of its peculiar axial orientation. High obliquity appears required for long-term mantle development for typical rotation rates and perihelia ?1.5 AU. Heat conduction into the nucleus for an incompletely mantled or bald comet has been found to be very important in maintaining relatively higher ice surface temperatures, and hence fluxes, during those portions of the diurnal and orbital cycles which would otherwise be cooler. It is also shown to be at least one cause of post perihelion brightness asymmetries, especially in lower obliquity comets. Maximum heliocentric distances at which 1-μm dust, sand, pebbles, cobbles, and boulders can be permanently ejected from the subsolar point by H₂O (CO₂) are (in AU): 6.9 (16.8), 5.2 (11.5), 1.8 (3.0), 0.21 (0.34) and 0.07 (0.11), respectively. A detailed anatomy of temperature, gas and dust fluxes vs latitude and longitude for a homogeneous rotating comet with fixed axis is given for comparison with future observations. Most H₂O flux histories deduced from brightness data are found to be in reasonable agreement with the model, allowing for uncertainty in radius and albedo. A clear exception is Encke. It is shown that the large discrepancy between Encke's observed and model predicted fluxes, based on radar cross section, can be used to evaluate the extent of exposed ice (<10%). The model is then used to place an active area so as to explain a reported sharp drop in flux on approach to the Sun at 0.78 AU. An active area or areas, <10% of the comet's surface, centered near 65°N latitude appears indicated. Although cyclic mantles are generally indicated for the set of parameters we used, our results show that a global mantle only 1 to 3 cm thick (depending on the orbit) consisting of a full range of grain sizes can cause irresversible evolution to a noncometary body. We investigated the long-term evolution of such a postulated initially thinly mantled cometary object. It was found that after the first few passes and until the end of its dynamic lifetime the object averaged <3 × 10^?12 g cm^?1 sec^?1 H₂O flux. Therefore, if cometary objects evolve into Apollo asteroids, ice should always be accessible within 10 m of the surface despite numerous close perihelion passages. The possible impact of factors not included in the model, such as initial inhomogeneities, coma scattering of radiation, and global redistribution of ejected silicate around the nucleus, are discussed.     

A probability of encounter with interstellar comets and the likelihood of their existence

A theory of the probability of encounter of the Sun with an interstellar comet at a distance comparable to the Earth-Sun distance is formulated, and a general expression is derived establishing the relationship among the influx rate of interstellar comets, the perihelion distance, the space density of the comets, the Maxwellian distribution of comet velocities in the interstellar cloud, and the cloud's systematic velocity relative to the Sun. The fact that no comet with a strongly hyperbolic orbit has so far been observed is used to determine an upper limit of 6 × 10^?4 solar masses per cubic parsec (4 × 10^?26 gcm^?3) for the space density of interstellar comets. The theoretical distribution of semimajor axes of interstellar comets is derived to show that a strong hyperbolic excess must be present in the orbits of a majority of interstellar comets regardless of the dynamical characteristics of the comet cloud, except when the cloud is moving along with the Sun and the distribution of individual velocities has a very low dispersion. This case, however, implies a possibility of capture by the Sun and thus becomes a problem of an Oort-type cloud.     

Planet X and the origins of the shower and steady state flux of short-period comets

In the planet X model periodic comet showers are associated with passages of the planet's perihelion and aphelion points through a primordial disk of comets believed to lie beyond the orbit of Neptune. A strong feature of this model is that the required orbital elements and mass of planet X are consistent with independently predicted values based on the residuals in the motions of Uranus and Neptune. Here we present a more extensive analysis of the model taking into account the fact that only those comets scattered directly into the zones of influence of Saturn and Jupiter can contribute to a shower whose duration is consistent with observation (≲ 15 myr). These requirements impose a minimum planetary inclination of ≈25°, which in turn restricts the semimajor axis to be ≲100 AU. A fraction of the comets scattered directly into the zones of influence of Uranus and Neptune will evolve on time scales of ∼10⁸ years into the steady state flux of short-period comets. We find that the absolute numbers of shower and steady state are comparable and compatible with the known terrestrial cratering rate, assuming the existence of long-lived extinct comet cores. Canonical planet X model parameters, deduced in part from the scattering dynamics analysis, are: semimajor axis ≈80 AU, eccentricity ≈0.3, inclination ≈45°, and mass ≈5m_⊕. An analysis is given which suggests that planet X, in its present orbit, can create the requisite density gradient of comets near perihelion and aphelion during the lifetime of the Solar System. The required inclination of planet X's orbit (≳25°) may explain the failure of previous surveys to discover the planet as its present latitude is not likely to be near the ecliptic. It it exists, the best immediate hope of finding planet X is the ongoing IRAS search in the 100-μm band and the full sky optical survey by Shoemaker and Shoemaker. Independent of the question of periodic comet showers, the existence of planet X and the comet disk can readily explain the origin of the steady state flux of short-period comets over a wide range of parameters.     

Determination of Non-gravitational Effects in the Motion of Near-Sun Objects 321P, 322P, 323P,and 342P

At the beginning of this century, the SOHO space observatory discovered near-Sun comets with perihelion distances q ≈ 0.05 AU, which remained observable over several close encounters with the Sun. This became one of the surprises in studying the small bodies of the Solar System. Currently, there are objects that have already been observed in four (342P) and five (321P, 322P, and 323P) apparitions. In the present work, the estimates of nongravitational effects are obtained for these objects based on the pair-wise linkage of the apparitions. The calculations show that the observations of these objects are poorly represented if solely the gravitational forces are considered. The magnitude of nongravitational effects in the semimajor axis noticeably changes with time. The motion of all comets is significantly affected by the components of nongravitational forces that are perpendicular to the orbital plane.     

Comet color changes with solar distance

JHK colors of 14 comets are correlated with cometary distance from the Sun. The correlation could be explained by (1) changes in coma particle size as comets approach the Sun, (2) decrease in the ice/dirt ratio in coma grains as comets approach the Sun, and/or (3) phase reddening. Short-term color changes in individual comets at fixed phase angles suggest that phase reddening does not explain all color changes. Short-term changes are consistent with jets injecting fresh (high ice/dirt) nuclear material into parts of the coma. All colorimetric data are consistent with pristine coma material being relatively low-albedo dirty ice grains colored by carbonaceous dirt like that in RD-type asteroids. Ice sublimation near the Sun may leave residual pure RD dirt grains, explaining the observed color changes.     

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.     

Remote comets and related bodies: VJHK colorimetry and surface materials

Spectrophotometric data show that major compositional groups among outer solar system (OSS) surfaces include bright ices and at least two distinct classes of blackish carbonaceous-like materials, called C-type and RD-type. VJHK colorimetry of asteroids, satellites, and laboratory samples shows that these three classes can be distinguished by VJHK colors. We define an “α index” that denotes the position of objects in VJHK color - color diagrams; it empirically increases with albedo and ice/dirt ratio. We use the above data to define color fields that may be useful in interpreting our observations of eight comets (1980–1981). All eight comets have colors generally resembling RD asteroids and are inconsistent with reflection off clean ice surfaces. The observations suggest that these comets' halos contain RD dirt or dirty ice grains colored by RD dirt, supporting J. Gradie and J. Veverka's [Nature283, 840–842 (1980)] prediction of RD, rather than C, material in comets. Remote Comet P/Schwassmann-Wachmann 1 was observed both during outburst and quiescence and had the highest α index of any observed comet. Comet α indices appear to be correlated with solar distance. Further work will be needed to clarify possible coloring effects due to particle size, dispersal, and composition. We suggest a number of physical interpretations based on a single two-component mixing model, which assumes that all OSS planetesimals formed primarily from bright ices and dark carboneceous-like dirt, consistent with condensation theory. We discuss differentiation processes that concentrated one component or the other at the surface. All measured OSS interplanetary bodies have surfaces of dark dirt or dark dirty ice colored by the dirt component. Comets, consistent with the Whipple dirty iceberg model, are such objects close enough to the Sun for volatilization to throw dirty ice grains into the coma. In remote comets, the ice component of the grains remains stable, and we see dirty ice grains; in near comets, the ice component vaporizes, and we see dirt grains. A volatile-depleted dusty regolith on P/Schwassmann-Wachmann 1 and other remote comets could explain their eruptive behavior by means of gas pressure buildup in the porous, weakly bonded dust.     

Cometary brightness variation and nucleus structure

The Bobrovnikoff and Beyer photometric data for more than 100 comets have been analyzed for intrinsic brightness variations,before andafter perihelion, according to ther ^–n law, wherer is solar distance. The Oort and Schmidt classification of comet age has been extended and applied with Marsden's new determinations of inverse semi-major axis, 1/a, original. All classes of comets withP>25 yr show statistically the same value ofn after perihelion. New comets approach perihelion with smaller values ofn and older comets with increasingly larger values (Table II). For comets ofP<25 yr,n is larger and erratic.A physical interpretation involves the quick loss of a frosting of super-volatile materials from new comets; then, for all comets, the development of an insulating crust after perihelion. The crust also includes globs of meteoroidal and icy material. The crust tends to be purged near perihelion but generally to grow in a spotty fashion with cometary age. The orientation of the axes of rotating comets is shown to be an important unknown factor in cometary brightness variations. A speculation is made concerning the axis of rotation for C/Kohoutek, 1973 XII.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May 1978.This research has been supported by Grant No. NSG 7082 from the U.S. National Aeronautics and Space Administration.     

Coma Structures in Comet 73P/Schwassmann-Wachmann 3, Components B and C,Between January and May 2006

The Jupiter family comet 73P/Schwassmann-Wachmann 3 has been widely observed since 1995 after a nucleus break-up event produced at least five components labeled 73P-A to E. During the 2006 appearance, two of them (B and C) showed very strong coma activity. Our R-filter imaging of 73P-B & C from 21 January to 25 May 2006 revealed the presence of fan-like structures in the comae of both components and evidence for further fragmentation events in component B. As of early April 2006, component C showed two jets emanating from the nucleus, with one continuously visible. Through a simulation of the orbital geometry we infer that the rotation axis of 73P-C has an inclination of 20° to the orbital plane and a longitude of 45° at perihelion. The coma activity of component B was highly variable, displaying signatures of at least 3 fragmentation events. The coma was characterized by the continuous presence of a jet roughly in sunward direction, starting from the beginning of May. The first fragmentation event of component B may have happened between April 16 and April 26, leading to the presence of at least 6 fragments detected in images of May 2. The second one happened on or shortly before May 8, the third one between May 18 and 24. For the rotation axis of 73P-B we infer an inclination of 5°–15° to the orbital plane and a longitude of 20°–30° at perihelion.     

Evolution of cometary perihelion distances in oort cloud: Another statistical approach

The evolution of the perihelion distance distribution in the Oort cloud was studied over the age of the solar system, under the gravitational perturbations of random passing stars, using a statistical approach. These perturbations are accounted for through an empirical relation relating the change in cometary perihelion distance to the closest-approach comet-star distance; this relation is deduced from a previous study [H. Scholl, A. Cazenave, and A. Brahic, Astron. Astrophys.112, 157–166 (1982)]. Two kinds of initial perihelion distances are considered: (a) perihelion distances <2500 AU, associated with an origin of comets as icy planetesimals in the region of the giant planets, and (b) larger perihelion distances (up to 5 × 10⁴ AU), possibly representative of comet formation as satellite fragments in the accretion disk of the primitive solar nebula. Distant star-comet encounters, as well as rare close encounters, are considered. Several quantities are estimated: (i) number of “new” comets entering into the planetary region, (ii) number of comets escaping the Sun sphere of influence or lost by hyperbolic ejection and (iii) percentage of total comet loss over the age of the solar system. From these quantities, the current and original cloud populations are deduced, as well as the corresponding cloud mass, for the two types of formation scenarios.     

From the Oort cloud to observable short-period comets – I. The initial stage of cometary capture

We investigate the first stage of the dynamical evolution of Oort cloud comets entering the planetary region for the first time. To this purpose, we integrate numerically the motions of a large number of fictitious comets pertaining to two samples, both with perihelion distances up to 5.7 au and random inclinations; the first sample is composed of comets whose orbits have at least one node close to 5.2 au, while the second is not subject to this constraint. We examine the orbits when the comets come to aphelion after their first perihelion passage within the planetary region, and find that there is a clear statistical dependence of the energy perturbations on the Tisserand parameter. There appear to be two main processes, of comparable importance, governing the shortening of semimajor axes to values of less than 1000 au, i.e. planetary close encounters, especially with Jupiter, and indirect perturbations due to the shifting of the motion from barycentric to heliocentric and back; the former process mostly affects comets crossing the ecliptic at about 5.2 au, or on low-inclination orbits, while the latter mostly affects comets of small perihelion distance. This last result may help to understand the relative paucity of Halley-type comets with perihelion distances larger than about 1.5 au.