A model of the galactic tidal interaction with the oort comet cloud

We consider a model of the in situ Oort cloud which is isotropic with a random distrihution of perihelia directions and angular momenta. The energy distribution adopted has a continuous range of values appropriate for long-period (>200 yr) comets. Only the tidal torque of the Galaxy is included as a perturbation of comet orbits and it is approximated to be that due to a quasi-steady state distribution of matter with disk-like symmetry. The time evolution of all orbital elements can be analytically obtained for this case. In particular, the change in the perihelion distance per orbit and its dependence on other orbital elements is readily found. We further make the assumption that a comet whose perihelion distance was beyond 15 AU during its last passage through the Solar System would have orbit parameters that are essentially unchanged by planetary perturbations. Conversely, if the prior passage was inside 15 AU we assume that planetary perturbations would have removed the comet from the in situ energy distribution accessible by the galactic tide. Comets which had their perihelia changed from beyond 15 AU to within 5 AU in a single orbit are taken to be observable. We are able to track the evolution of 10⁶ comets as they are made observable by the galactic tidal touque. Detailed results are obtained for the predicted distribution of new (0 < 1/ < 10^–4 AU^–1) comets. Further, correlations between orbital elements can be studied. We present predictions of observed distributions and compare them with the random in situ results as well as with the actual observed distributions of class I comets. The predictions are in reasonable agreement with actual observations and, in many cases, are significantly different from random when perihelia directions are separated into galactic northern and southern hemispheres. However the well-known asymmetry in the north-south populations of perihelia remains to be explained. Such an asymmetry is consistent with the dominance of tidal torques today if a major stochastic event produced it in the past since tidal torques are unable to cause the migration of perihelia across the latitude barriers ±26°.6 in the disk model.     

Long-period comet flux in the planetary region: Dynamical evolution from the Oort cloud

This study analyzes the evolution of 2 × 10⁵ orbits with initial parameters corresponding to the orbits of comets of the Oort cloud under the action of planetary, galactic, and stellar perturbations over 2 × 10⁹ years. The dynamical evolution of comets of the outer (orbital semimajor axes a > 10⁴ AU) and inner (5 × 10³ < a (AU) < 10⁴) parts of the comet cloud is analyzed separately. The estimates of the flux of “new” and long-period comets for all perihelion distances q in the planetary region are reported. The flux of comets with a > 10⁴ AU in the interval 15 AU < q < 31 AU is several times higher than the flux of comets in the region q < 15 AU. We point out the increased concentration of the perihelia of orbits of comets from the outer cloud, which have passed several times through the planetary system, in the Saturn-Uranus region. The maxima in the distribution of the perihelia of the orbits of comets of the inner Oort cloud are located in the Uranus-Neptune region. “New” comets moving in orbits with a < 2 × 10⁴ AU and arriving at the outside of the planetary system (q > 25 AU) subsequently have a greater number of returns to the region q < 35 AU. The perihelia of the orbits of these comets gradually drift toward the interior of the Solar System and accumulate beyond the orbit of Saturn. The distribution of the perihelia of long-period comets beyond the orbit of Saturn exhibits a peak. We discuss the problem of replenishing the outer Oort cloud by comets from the inner part and their subsequent dynamical evolution. The annual rate of passages of comets of the inner cloud, which replenish the outer cloud, in the region q < 1 AU in orbits with a > 10⁴ AU (～ 5.0 × 10^?14 yr^?1) is one order of magnitude lower than the rate of passage of comets from the outer Oort cloud (～ 9.1 × 10^?13 yr^?1).     

The effect of the Galaxy on cometary orbits

The effect of galactic perturbations on long-period cometary orbits is re-examined using a more realistic galactic model. Numerical and analytical calculations confirm the general result of an earlier paper which demonstrated that the Galaxy can perturb comets into and out of the Oort cloud. New equations are developed to describe the perturbed orbits.     

Searches for transplutonian planets using long-period comets

We discuss the dynamical connection of long-period and nearly parabolic comets with hypothetical transplutonian planets. The statistics includes 792 comets with periods P > 200 years. The orbital plane of the parent planet can be determined from the observed distribution of the perihelia and poles of cometary orbits. The radius of a planetary orbit can be calculated using the Radzievsky-Tisseran criterion. We calculated the minimum distance of each of the 792 orbits to 11 hypothetical planetary orbits. Testing for the kinematic connection of comets with transplutonian planets yielded a negative result. The presence of the nodes of cometary orbits in the transplutonian region is shown to be the result of a geometric effect. We found a high concentration of the nodes and perihelia of cometary orbits in the zone of the terrestrial planets.     

Comet formation in molecular clouds

The observed properties of the long-period comet system, and its periodic disturbance by galactic forces manifesting as terrestrial impact episodes, may be indicative of a comet capture/escape cycle as the Solar System orbits the Galaxy. A mean number density of comets in molecular clouds of ～10^?1±1 AU^?3 is implied. This is sufficient to deplete metals from the gaseous component of the interstellar medium, as observed, but leads to the problem of how stars are formed nevertheless with solar metal abundances. Formation of comets prior to stars in dense systems of near-zero energy may be indicated, and isotope signatures in cometary particles may be diagnostic of conditions in young spiral arm material.     

Dynamical capture and physical decay of short-period comets

The brightness evolution of short-period comets is discussed in connection with their physical lifetimes. It is shown that changes in the fraction of the free-subliming area of the nuclear surface may be more important than mass decrease in determining brightness variations. The decrease in the activity of short-period comets caused by the buildup of a dust mantle may be interrupted—and partially reversed—by dust blowoffs that leave exposed areas of fresh ices. Short-period comets may thus be subject to random brightness fluctuations that make quite uncertain any derivation of their physical lifetime based on comparisons of their absolute brightness at different apparitions. As an alternate procedure, the numerical integration of the whole sample of short-period comet orbits carried out by A. Carusi, L.Kresák, E. Perozzi and G. B. Valsecchi (1984, Long-Term Evolution of Short-Period Comets. Istituto Astrofisica Spaziale Internal Report 12, Rome) is used to draw conclusions about the transfer rate of their perihelia from Jupiter's region to the region of the terrestrial planets (heliocentric distances<1.5 AU). It is found that about one short-period comet per century reaches the region of the terrestrial planets. From this result and under the assumption of a steady-state comet population, an average lifetime of the order of 6 × 10³ years (～10³ revolutions) is derived for a typical kilometer-sized short-period comet of perihelion distance q ～ 1 AU. Such a rather long comet lifetime, as compared to some previous derivations, is consistent with the survival of some periodic comets on small-q orbits of long dynamical time scales.     

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.     

A former asteroidal planet as the origin of comets

The idea of a missing planet between Mars and Jupiter has been with us since the formulation of the Titius-Bode law. The discovery of the asteroid belt in that location led to speculation about a planetary breakup event. Both ideas remained conjectures until Ovenden's finding in 1972, from which it could be derived that the mass of the missing planet was about 90 Earth masses and that its breakup was astronomically recent. Apparently much of that mass was blown out of the solar system during the disruption of the planet. Because of the action of planetary perturbations, only two types of orbits of surviving fragments could remain at present-asteroid orbits and once-around very-long-period elliptical orbits. Objects in the latter type of orbit are known to exist-the very-long-period comets. A large number of these are on elliptical trajectories with periods of revolution of 5 million years; yet they are known to have made no more than one revolution in an orbit passing close to the Sun. By direct calculation it is possible to predict the distribution of the orbital elements of objects moving on long-period ellipses which might have originated in a breakup event in the asteroid belt 5 million years ago. The comet orbits have the predicted distribution in every case where a measure is possible. Some of the distribution anomalies, such as a bias in the directions of perihelion passage, are statistically strong and would be difficult to explain in any other uncontrived way. In addition, a relative deficiency of orbits with perihelia less than 1 AU indicates that the comets must have had small perihelion distances since their origin, rather than that they have been perturbed into small perihelion orbits from a distant “cloud” of comets by means of stellar encounters. The comet orbital data lead to the conclusion that all comets originated in a breakup event in the asteroid belt (5.5±0.6) × 10⁶ years ago. Asteroid and meteoritic evidence can now be interpreted in a way which not only is supportive but also provides fresh insights into understanding their physical, chemical, and dynamical properties. Particularily noteworthy are the young cosmic-ray exposure ages of meteorites, evidence of a previous high-temperature/pressure environment and of chemical differentiation of the parent body, and compositional similarities among comets, asteroids, and meteorites. Certain “explosion signatures” in asteroid orbital element distributions are likewise indicative. Tektites may also have originated in the same event; but if so, there are important implications regarding the absolute accuracy of certain geological dating methods. Little is known about possible planetary breakup mechanisms of the requisite type, though some speculations are offered. In any case, the asteroid belt is an existing fact; and the arguments presented here that a large planet did disintegrate 5 million years ago must be judged on their merits, even in the absence of a suitable theory of planetary explosions.     

A Monte Carlo investigation of Jovian perturbations on short-period comet orbits

We present statistical distributions of Jovian perturbations on short-period comet orbits resulting from accurate numerical integrations. Our sample of 60, 000 cometary orbits with low inclinations and random orientations is characterized by perihelia between 0 and 7 AU and aphelia between 4 and 13 AU. The perturbations considered are those experienced because of Jupiter's gravitation per orbital revolution by the comets. Regularization and accurate step-length control in the numerical integration gives statistical results appreciably different from those computed by Rickman and Vaghi (1978). Their use of a crude method of integration led to erroneous results for close encounters. Strong asymmetries of the $\text{δ(}\text{1}\text{a}\text{)}$ distributions, in particular for the extreme tails, are observed for perihelion- or aphelion-tangent orbits. These orbits are also shown to experience the strongest energy perturbations on the average. Some results concerning the perturbations of Tisserand parameters are indicated. The perturbation distributions for the angular elements are described and discussed. The role of the minimum distance from Jupiter as an indicator of perturbations is investigated.     

On the actual existence of the periodic and long-period comet families of Uranus

Aphelion distances of the known periodic comets in the range 12–26 AU are analyzed. The aphelia of 12 of the 38 known comets are found to be concentrated at 19.23–20.91 AU, i.e., near the heliocentric distance of Uranus, which seems unlikely to be a coincidence. It is shown by testing that there is also a significant redundancy of distant nodes of the periodic comets’ orbits in the region of motion of Uranus. This is confirmed by the analysis of the MOIDs in the comet-Uranus system. The values of the Tisserand constant for some of the comets exhibit less dispersion relative to Uranus than to Saturn, Jupiter, and the Earth. We selected 20 long-period comets with distant nodes near the region of motion of Uranus. It is shown that, given a uniform spatial distribution, there must be 12 such nodes. Considering the distant nodes and the MOIDs, the planet is likely to have a dynamical connection with the selected group of comets. The distant nodes and perihelia of both periodic and long-period comets are found to be redundant in the directions 76° and 256°, which is qualitatively consistent with the hypothesis of eruptive origin of comets.     

Time-dependent injection of Oort cloud comets into Earth-crossing orbits

The effect of close stellar encounters in modulating the influx rate of Oort cloud comets is investigated. In particular, it is shown that comet showers intense enough to be reflected in crater statistics can be produced at intervals of 80 million years or so, provided we are dealing with an Oort cloud consisting of a heavy core of comets. In this case, there is found a strong predominance of incoming comets from the sky zone where the perturbing star makes its closest approach. We have also performed numerical simulations of the time evolution of comet showers or bursts. From this numerical study, a long tail of residual shower comets is found to follow the major event with an intensity (as compared with the intensity of the shower as its peak) of ∼10⁻² after 20—30 million years. Our results thus suggest that residual shower comets may be clustered mainly on certain sky areas and observable at practically any time given the lasting effects of a shower. This might explain some of the observed clustering of aphelion points of long-period comets.     

Oort Cloud Comet Perihelion Asymmetries: Galactic Tide, Shower or Observational Bias?

We investigate the distribution of Oort cloud comet perihelia. The data considered includes comets having orbital elements of the two highest quality classes with original energies designated as new or young. Perihelion directions are determined in galactic, ecliptic and geocentric equatorial coordinates. Asymmetries are detected in the scatter and are studied statistically for evidence of adiabatic galactic tidal dynamics, an impulse-induced shower and observational bias. The only bias detected is the well-known deficiency of observations with perihelion distances q > 2.5 AU. There is no significant evidence of a seasonal dependence. Nor is there a substantive hemispherical bias in either ecliptic or equatorial coordinates. There is evidence for a weak stellar shower previously detected by Biermann which accounts for ≈ 10% of the total observations. Both the q bias and the Biermann star track serve to weaken the evidence for a galactic tidal imprint. Nevertheless, statistically significant asymmetries in galactic latitude and longitude of perihelia remain. A latitude asymmetry is produced by a dominant tidal component perpendicular to the galactic disk. The longitude signal implies that ≈ 20% of new comets need an additional dynamical mechanism. Known disk non-uniformities and an hypothetical bound perturber are discussed as potential explanations. We conclude that the detected dynamical signature of the galactic tide is real and is not an artifact of observational bias, impulsive showers or poor data. This revised version was published online in July 2006 with corrections to the Cover Date.     

The role of collisions with interplanetary particles in the physical evolution of comets

Effects of collisions with interplanetary particles are investigated. To this purpose, collision probabilities for comets with different orbital elements are computed. It is found that collisions may have a non-negligible effect on the physical evolution of comets. In this connection, it is shown that under certain conditions collisional lifetimes may be shorter than dynamical or vaporization lifetimes. In particular, collisional lifetimes are on average shorter for comets in retrograde orbits than those for direct ones. It is further suggested that catastrophic collisions may contribute to prevent long-period comets in retrograde orbits from reaching short-period orbits by orbital diffusion. Collisions may also produce irregularities of the nucleus brightness by leaving exposed regions of fresh volatile material and may in this way lead to a rejuvenation of old dusty short-period comets. Catastrophic collision probabilities are too low to account for the observed comet splittings, so other trigger mechanisms should be at work. However, it is shown that collisional mini-bursts (increases in brightness of one magnitude or so) caused by decimeter-sized bodies may occur rather frequently on short-period comets when they pass through the asteroid belt. The burst observed in comet Tempel-2 at 3 AU in December, 1978 could be an example of such collisional mini-bursts. The systematic observation of periodic comets when they pass through the asteroid belt could give valuable information about the spatial density of decimeter and meter-sized bodies. In particular, collisional effects for comet Halley, for which a continuous surveillance is planned, are evaluated.     

Capture of comets from the Oort cloud into Halley-type and Jupiter-family orbits

This paper analyzes the capture of comets into Halley-type and Jupiter-family orbits from the nearparabolic flux of the Oort cloud. Two types of capture into Halley-type orbits are found. The first type is the evolution of near-parabolic orbits into short-period orbits (with heliocentric orbital periods P < 200 years) as a result of close encounters with giant planets. This process is followed by a very slow drift of cometary orbits into the inner part of the Solar System. Only those comets may pass from short-period orbits into Halley-type and Jupiter-family orbits, which move in orbits with perihelion distances q < 13 au. In the second type of capture, the perihelion distances of cometary orbits become rather small (< 1.5 au) during the first stage of dynamic evolution under the action of perturbations from the Galaxy, and then their semimajor axes decrease as a result of diffusion. The capture takes place, on average, in 500 revolutions of the comet about the Sun, whereas in the first case, the comet is captured, on average, after 12500 revolutions. The region of initial orbital perihelion distances q > 4 au is found to be at least as important a source of Halley-type comets as the region of perihelion distances q < 4 au. More than half of the Halley-type comets are captured from the nearly parabolic flux with q > 4 au. The analysis of the dynamic evolution of objects moving in short-period orbits shows that the distribution of Centaurs orbits agrees well with the observed distribution corrected for observational selection effects. Hence, the hypothesis associating the origin of Centaurs with the Edgeworth-Kuiper belt and the trans-Neptunian region exclusively should be rejected.     

The frequency and intensity of comet showers from the Oort cloud

We simulate the Oort comet cloud to study the rate and properties of new comets and the intensity and frequency of comet showers. An ensemble of ∼10⁶ comets is perturbed at random times by a population of main sequence stars and white dwarfs that is described by the Bahcall-Soneira Galaxy model. A cloning procedure allows us to model a large ensemble of comets efficiently, without wasting computer time following a large number of low eccentricity orbits. For comets at semimajor axis a = 20,000 AU, about every 100 myr a star with mass in the range 1M_⊙−2M_⊙ passes within ∼10,000 AU of the Sun and triggers a shower that enhances the flux of new comets by more than a factor of 10. The time-integrated flux is dominated by the showers for comets with semimajor axes less than ∼30,000 AU. For semimajor axes greater than ∼30,000 AU the comet loss rate is roughly constant and strong showers do not occur. In some of our simulations, comets are also perturbed by the Galactic tidal field. The inclusion of tidal effects increases the loss rate of comets with semimajor axes between 10,000 and 20,000 AU by about a factor of 4. Thus the Galactic tide, rather than individual stellar perturbations, is the dominant mechanism which drives the evolution of the Oort cloud.     

The scattered disk as a source of Halley-type comets

We investigate a new dynamical mechanism for producing Halley-type comets from the scattered disk of comets. Levison and Duncan [Levison, H., Duncan, M., 1997. Icarus 127, 13-32] and Duncan and Levison [Duncan, M., Levison, H., 1997. Science 276, 1670-1672] showed that a significant number of objects leave the scattered disk by evolving to semi-major axes greater than 1000 AU. We find that once these objects reach semi-major axes on the order of ¹⁰⁴ AU, a significant fraction immediately have their perihelia driven inward by the galactic tides. Approximately 0.01% of the objects that reach ¹⁰⁴ AU then evolve onto orbits similar to the observed Halley-like comets due to gravitational interactions with the giant planets. The orbital element distribution resulting from this process is statistically consistent with observations. We discuss the implications of this model for the number of objects in the scattered disk in the text. The model predicts a temporal variation in the influx of HTCs with a period of ∼118 Myr. At the peak, the model predicts that there should be roughly 10 times as many HTCs as currently observed (i.e., there should be weak HTC showers). However, the model may inflate the importance of these showers because it does not include the effects of passing stars and giant molecular clouds.     

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.     

Orientation-dependent effects in Oort's theory of comet origin II. Anisotropies in the distribution of long-period comet orbits

The statistical significance of anisotropies in the distribution of orbital orientations among the long-period and nearly parabolic comets is evaluated. It is suggested that these anisotropies are not the result of observational selection effects. A numerical model for the distribution of orbital orientations is constructed, based on Oort's theory of comet origin and the assumption that the observed anisotropies are caused by multiple planetary perturbations over the course of many perihelion passages. The model, which is restricted to comets with peri-helion distances less than 0.3AU, does not predict any significant anisotropies.     

Relationship of comets and planets

We analyze our earlier data on the numerical integration of the equations of motion for 274 short-period comets (with the period P<200 yr) on a time interval of 6000 yr. As many as 54 comets had no close approaches to planets, 13 comets passed through the Saturnian sphere of action, and one comet passed through the Uranian sphere of action. The orbital elements of these 68 comets changed by no more than ±3 percent in a space of 6000 yr. As many as 206 comets passed close to Jupiter. We confirm Everhart’s conclusion that Jupiter can capture long-period comets with q = 4–6 AU and i < 9° into short-period orbits. We show that nearly parabolic comets cross the solar system mainly in the zone of terrestrial planets. No relationship of nearly parabolic comets and terrestrial planets was found for the epoch of the latest apparition of comets. Guliev’s conjecture about two trans-Plutonian planets is based on the illusory excess of cometary nodes at large heliocentric distances. The existence of cometary nodes at the solar system periphery turns out to be a solely geometrical effect.