Orbits of short period comets captured from the Oort cloud

Oort cloud comets occasionally obtain orbits which take them through the planetary region. The perturbations by the planets are likely to change the orbit of the comet. We model this process by using a Monte Carlo method and cross sections for orbital changes, i.e. changes in energy, inclination and perihelion distance, in a single planet-comet encounter. The influence of all major planets is considered. We study the distributions of orbital parameters of observable comets, i.e. those which have perihelion distance smaller than a given value. We find that enough comets are captured from the Oort cloud in order to explain the present populations of short period comets. The median value of cos i for the Jupiter family is 0.985 while it is 0.27 for the Halley types. The results may explain the orbital features of short period comets, assuming that the active lifetime of a comet is not much greater than 400 orbital revolutions.     

Orbits of short period comets captured from the Oort cloud

Oort cloud comets occasionally obtain orbits which take them through the planetary region. The perturbations by the planets are likely to change the orbit of the comet. We model this process by using a Monte Carlo method and cross sections for orbital changes, i.e. changes in energy, inclination and perihelion distance, in a single planet-comet encounter. The influence of all major planets is considered. We study the distributions of orbital parameters of observable comets, i.e. those which have perihelion distance smaller than a given value. We find that enough comets are captured from the Oort cloud in order to explain the present populations of short period comets. The median value of cos i for the Jupiter family is 0.985 while it is 0.27 for the Halley types. The results may explain the orbital features of short period comets, assuming that the active lifetime of a comet is not much greater than 400 orbital revolutions.     

Origin of oort cloud comets in the interstellar space

Comets must form a major part of the interstellar medium. The solar system provides a flux of comets into the interstellar space and there is no reason to suspect that many other stars and their surrounding cometary systems would not make a similar contribution. Occasionally interstellar comets must pass through the inner solar system, but Whipple (1975) considers it unlikely that such a comet is among the known cases of apparently hyperbolic comets. Even so the upper limit for the density of unobserved interstellar comets is relatively high.In addition, we must consider the possibility that comets are a genuine component of interstellar medium, and that the Oort Cloud is merely a captured part of it (McCrea, 1975). Here we review various dynamical possibilities of two-way exchange of comet populations between the Solar System and the interstellar medium. We describe ways in which a traditional Oort Cloud (Oort, 1950) could be captured from the interstellar medium. However, we note that the so called Kuiper belt (Kuiper, 1951) of comets cannot arise through this process. Therefore we have to ask how necessary the concept of the yet unobserved Kuiper belt is for the theory of short period comets.There has been considerable debate about the question whether short period comets can be understood as a captured population of the Oort Cloud of comets or whether an additional source has to be postulated. The problem is made difficult by the long integration times of comet orbits through the age of the Solar System. It would be better to have an accurate treatment of comet-planet encounters in a statistical sense, in the form of cross sections, and to carry out Monte Carlo studies. Here we describe the plan of action and initial results of the work to derive cross sections by carrying out large numbers of comet — planet encounters and by deriving approximate analytic expressions for them. Initially comets follow parabolic orbits of arbitrary inclination and perihelion distance; cross sections are derived for obtaining orbits of given energy and inclination after the encounter. The results are used in subsequent work to make evolutionary models of the comet population.     

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.     

Long-term evolution of Oort Cloud comets: capture of comets

We test different possibilities for the origin of short-period comets captured from the Oort Cloud. We use an efficient Monte Carlo simulation method that takes into account non-gravitational forces, Galactic perturbations, observational selection effects, physical evolution and tidal splittings of comets. We confirm previous results and conclude that the Jupiter family comets cannot originate in the spherically distributed Oort Cloud, since there is no physically possible model of how these comets can be captured from the Oort Cloud flux and produce the observed inclination and Tisserand constant distributions. The extended model of the Oort Cloud predicted by the planetesimal theory consisting of a non-randomly distributed inner core and a classical Oort Cloud also cannot explain the observed distributions of Jupiter family comets. The number of comets captured from the outer region of the Solar system are too high compared with the observations if the inclination distribution of Jupiter family comets is matched with the observed distribution. It is very likely that the Halley-type comets are captured mainly from the classical Oort Cloud, since the distributions in inclination and Tisserand value can be fitted to the observed distributions with very high confidence. Also the expected number of comets is in agreement with the observations when physical evolution of the comets is included. However, the solution is not unique, and other more complicated models can also explain the observed properties of Halley-type comets. The existence of Jupiter family comets can be explained only if they are captured from the extended disc of comets with semimajor axes of the comets   a <5000 au  . The original flattened distribution of comets is conserved as the cometary orbits evolve from the outer Solar system era to the observed region.     

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.     

Opportunities for the stratospheric collection of dust from short‐period comets

Abstract— We have identified four comets which have produced low‐velocity Earth‐crossing dust streams within the past century: 7P/Pons‐Winnecke, 26P/Grigg‐Skjellerup, 73P/Schwassmann‐Wachmann 3, and 103P/Hartley 2. These comets have had the rare characteristics of low eccentricity, low inclination orbits with nodes very close to 1 AU. Dust from these comets is directly injected into Earth‐crossing orbits by radiation pressure, unlike the great majority of interplanetary dust particles collected in the stratosphere which spend millennia in space prior to Earth‐encounter. Complete dust streams from these comets form within a few decades, and appreciable amounts of dust are accreted by the Earth each year regardless of the positions of the parent comets. Dust from these comets could be collected in the stratosphere and identified by its short space exposure age, as indicated by low abundances of implanted solar‐wind noble gases and/or lack of solar flare tracks. Dust from Grigg‐Skjellerup probably has the highest concentration at Earth orbit. We estimate that the proportion of dust from this comet will reach at least several percent of the background interplanetary dust flux in the >40 μm size range during April 23–24 of 2003.     

Atlas of secular light curves of comets

In this work we have compiled 37,692 observations of 27 periodic and non-periodic comets to create the secular light curves (SLCs), using two plots per comet. The data have been reduced homogeneously. Our overriding goal is to learn the properties of the ensemble of comets. More than 30 parameters are listed, of which over ∼20 are new and measured from the plots. We define two ages for a comet using activity as a proxy, the photometric age P-AGE, and the time-age, T-AGE. It is shown that these parameters are robust, implying that the input data can have significant errors but P-AGE and T-AGE come out with small errors. This is due to their mathematical definition. It is shown that P-AGE classifies comets by shape of their light curve. The value of this Atlas is twofold: The SLCs not only show what we know, but also show what we do not know, thus pointing the way to meaningful observations. Besides their scientific value, these plots are useful for planning observations. The SLCs have not been modeled, and there is no cometary light curve standard model as there is for some variable stars (i.e. eclipsing binaries). Comets are classified by age and size. In this way it is found that 29P/Schwassmann-Wachmann 1 is a baby goliath comet, while C/1983 J1 Sugano-Saigusa-Fujikawa is a middle age dwarf. There are new classes of comets based on their photometric properties. The secular light curves presented in this Atlas exhibit complexity beyond current understanding.     

The composition of dust in Jupiter-family comets inferred from infrared spectroscopy

We review the composition of Jupiter-family comet (JFC) dust as inferred from infrared spectroscopy. We find that JFCs have silicate emission features with fluxes roughly 20-25% over the dust continuum (emission strength 1.20-1.25), similar to the weakest silicate features in Oort Cloud (OC) comets. We discuss the grain properties that alter the silicate emission feature (composition, size, and structure/shape), and emphasize that thermal emission from the comet nucleus can have significant influence on the derived silicate emission strength. Recent evidence suggests that grain porosity is the is different between JFCs and OC comets, but more observations and models of silicates in JFCs are needed to determine if a consistent set of grain parameters can explain their weak silicate emission features. Models of 8 m telescope and Spitzer Space Telescope observations have shown that JFCs have crystalline silicates with abundances similar to or less than those found in OC comets, although the crystalline silicate mineralogy of comets 9P/Tempel and C/1995 O1 (Hale-Bopp) differ from each other in Mg and Fe content. The heterogeneity of comet nuclei can also be assessed with mid-infrared spectroscopy, and we review the evidence for heterogeneous dust properties in the nucleus of comet 9P/Tempel. Models of dust formation, mixing in the solar nebula, and comet formation must be able to explain the observed range of Mg and Fe content and the heterogeneity of comet 9P/Tempel, although more work is needed in order to understand to what extent do comets 9P/Tempel and Hale-Bopp represent comets as a whole.     

Dynamics and Origin of Comets: New Problems Appeared after the <Emphasis Type="Italic">Rosetta</Emphasis> Space Mission

The data obtained in the recent Rosetta space mission to comet 67P/Churyumov–Gerasimenko have had a profound impact on the understanding of the nature of comets. In addition to revising the notions on the physical properties and structure of comets, this addresses dynamical aspects of the formation of the observed cometary populations (short- and long-period comets, Centaurs, trans-Neptunian objects, and Oort-cloud objects). In the review, we discuss new problems that have appeared in the theory of dynamical evolution and origin of comets due to the Rosetta mission.     

Near-Earth object velocity distributions and consequences for the Chicxulub impactor

An Öpik-based geometric algorithm is used to compute impact probabilities and velocity distributions for various near-Earth object (NEO) populations. The resulting crater size distributions for the Earth and Moon are calculated by combining these distributions with assumed NEO size distributions and a selection of crater scaling laws. This crater probability distribution indicates that the largest craters on both the Earth and the Moon are dominated by comets. However, from a calculation of the fractional probabilities of iridium deposition, and the velocity distributions at impact of each NEO population, the only realistic possibilities for the Chicxulub impactor are a short-period comet (possibly inactive) or a near-Earth asteroid. For these classes of object, sufficiently large impacts have mean intervals of 100 and 300 Myr respectively, slightly favouring the cometary hypothesis.     

Plasma environment of Jupiter family comets

As any comet nears the Sun, gas sublimes from the nucleus taking dust with it. Jupiter family comets are no exception. The neutral gas becomes ionized, and the interaction of a comet with the solar wind starts with ion pickup. This key process is also important in other solar system contexts wherever neutral particles become ionized and injected into a flowing plasma such as at Mars, Venus, Io, Titan and interstellar neutrals in the solar wind. At comets, ion pickup removes momentum and energy from the solar wind and puts it into cometary particles, which are then thermalised via plasma waves. Here we review what comets have shown us about how this process operates, and briefly look at how this can be applied in other contexts. We review the processes of pitch angle and energy scattering of the pickup ions, and the boundaries and regions in the comet-solar wind interaction. We use in-situ measurements from the four comets visited to date by spacecraft carrying plasma instrumentation: 21P/Giacobini-Zinner, 1P/Halley, 26P/Grigg-Skjellerup and 19P/Borrelly, to illustrate the process in action. While, of these, comet Halley is not a Jupiter class comet, it has told us the most about cometary plasma environments. The other comets, which are from the Jupiter family, give an interesting comparison as they have lower gas production rates and less-developed interactions. We examine the prospects for Rosetta at comet Churyumov-Gerasimenko, another Jupiter family comet where a wide range of gas production rates will be studied.     

Debiased Orbital and Absolute Magnitude Distribution of the Near-Earth Objects

The orbital and absolute magnitude distribution of the near-Earth objects (NEOs) is difficult to compute, partly because only a modest fraction of the entire NEO population has been discovered so far, but also because the known NEOs are biased by complicated observational selection effects. To circumvent these problems, we created a model NEO population which was fit to known NEOs discovered or accidentally rediscovered by Spacewatch. Our method was to numerically integrate thousands of test particles from five source regions that we believe provide most NEOs to the inner Solar System. Four of these source regions are in or adjacent to the main asteroid belt, while the fifth one is associated with the transneptunian disk. The nearly isotropic comets, which include the Halley-type comets and the long-period comets, were not included in our model. Test bodies from our source regions that passed into the NEO region (perihelia q<1.3 AU and aphelia Q≥0.983 AU) were tracked until they were eliminated by striking the Sun or a planet or were ejected out of the inner Solar System. These integrations were used to create five residence time probability distributions in semimajor axis, eccentricity, and inclination space (one for each source). These distributions show where NEOs from a given source are statistically most likely to be located. Combining these five residence time probability distributions with an NEO absolute magnitude distribution computed from previous work and a probability function representing the observational biases associated with the Spacewatch NEO survey, we produced an NEO model population that could be fit to 138 NEOs discovered or accidentally rediscovered by Spacewatch. By testing a range of possible source combinations, a best-fit NEO model was computed which (i) provided the debiased orbital and absolute magnitude distributions for the NEO population and (ii) indicated the relative importance of each NEO source region.Our best-fit model is consistent with 960±120 NEOs having H<18 and a<7.4 AU. Approximately 44% (as of December 2000) have been found so far. The limits on this estimate are conditional, since our model does not include nearly isotropic comets. Nearly isotropic comets are generally restricted to a Tisserand parameter (with respect to Jupiter) of T<2, such that few are believed to have a<7.4 AU. Our computed NEO orbital distribution, which is valid for bodies as faint as H<22, indicates that the Amor, Apollo, and Aten populations contain 32±1%, 62±1%, and 6±1% of the NEO population, respectively. We estimate that the population of objects completely inside Earth's orbit (IEOs) arising from our source regions is 2% the size of the NEO population. This value does not include the putative Vulcanoid population located inside Mercury's orbit. Overall, our model predicts that ∼61% of the NEO population comes from the inner main belt (a<2.5 AU), ∼24% comes from the central main belt (2.5<a<2.8 AU), ∼8% comes from the outer main belt (a>2.8 AU), and ∼6% comes from the Jupiter-family comet region (2<T?3). The steady-state population in each NEO source region, as well as the influx rates needed to replenish each region, were calculated as a by-product of our method. The population of extinct comets in the Jupiter-family comet region was also computed.     

Orbital evolution of long-period comets I. Trivariate Monte Carlo simulation

The mean orbital evolution of long-period comets for 16 representative initial orbits to short-period comets is calculated by a Monte Carlo method. First, trivariate perturbation distributions of barycentric Kepler energy, total angular momentum, and its z component in single encounters of comets with Jupiter are obtained numerically. Their characteristics are examined in detail and the distributions are found to be simple, symmetric, and easy to handle. Second, utilizing these distributions, we have done trivariate Monte Carlo simulations of the orbital evolution of long-period comets, with special emphasis on high-inclination orbits. About half of the 16 initial orbits are traced up to 5000 returns. For each of these orbits, the mean values of semimajor axis, perihelion distance, and inclination; their standard deviations, survival, and capture rates; as well as time scales of orbital evolution are calculated as functions of return number. Survival rates of the initial orbits with high inclination (～90°) and small perihelion distance (～1–2 AU) have been found to be only two or three times smaller than those of the main-source orbits of short-period comets established quantitatively by Everhart. The time scales of orbitsl evolution of the former, however, are nearly 10 times longer than the latter. There is a general trend that, for smaller perihelion distance, the survival efficiency becomes higher. The results of this paper should be considered a basis for a succeeding paper (Paper II) in which the physical lifetime of comets will be determined, and a comparison with the orbital data will be done.     

Capture of comets during the evolution of a star cluster and the origin of the Oort Cloud

It is generally assumed that the Solar System is surrounded by a swarm of comets, the so-called Oort Cloud, which contains approximately 10¹¹ members. The observed comets belong to a small subsection of the Cloud, and they have very elongated orbits. The origin of the Cloud is presently unclear. Here we consider the possibility that the comets were born in a star cluster together with the Sun. We follow the evolution of the star cluster with its embedded swarm of comets and calculate the rate at which stars accumulate stable comet companions. We conclude that if the Oort Cloud of comets was born in this process, then the present day density of comets in interstellar space has to be high, and that comets make a significant contribution to the overall mass density of the Galaxy.     

Cometary nuclear magnitudes from sky survey observations

The determination of the nuclear magnitudes of comets, and with it nuclear size frequency distributions, is strongly complicated by cometary activity. By now, only nuclear size frequency distributions for Jupiter Family comets are available, and they are still subject of uncertainties. For comets of other dynamical classes, nuclear magnitudes are known for only a few comets. The size frequency distributions are thus not well constrained.In this work we study whether nuclear magnitudes of comets can be constrained from sky survey observations as published by the Minor Planet Center. Observations from sky survey programs in which the comet was classified as a point-like source are analyzed in this respect.From the available published observations from 1998 to 2008, we derive nuclear magnitudes, as well as nuclear radii, for 84 comets. Among these are comets of the Jupiter Family, dynamically old and new isotropic comets, Halley-type comets and Centaurs. For Jupiter Family comets and for isotropic comets, the size frequency distributions are presented.Uncertainties of derived nuclear magnitudes arise from photometry and from potentially undetected activity. However, a comparison with objects with well known nuclear parameters shows that, despite substantial observational uncertainties, nuclear magnitudes are constrained to ±0.6 mag, thereby providing first indications for nuclear sizes. This is particularly relevant for isotropic comets with so far ill-constrained size distributions. Exponents of the differential size frequency distributions of for Jupiter Family comets and for isotropic comets are presented. The values derived here form a basis for future, dedicated observational studies which provide higher measurement accuracy.     

Ultraviolet absorption studies of H2O and other species in comet comae with satellite telescope-spectrometers

Ultraviolet absorption by H₂O and other species in the comae of comets could be detected by studying, with satellite telescope-spectrometers, the occultation of hot stars by comets. Such observations could produce the first direct detection of H₂O, the fundamental parent molecule in comet comae, and give measures of molecular level populations. The first instrument suitable for such observations will be the High Resolution Spectrograph on Space Telescope and, therefore, we consider its capabilities. We have used a Haser model to estimate the molecular column densities and to predict equivalent widths for lines of H₂O, OH, CO, and O as functions of time and angular distance from a comet with a high H₂O production rate. We have determined the minimum detectable equivalent widths, and therefore, the maximum angular separation from such a comet at which H₂O, OH, and CO could be studied. A conservative, statistical estimate shows that comets with high water production rates should pass near enough to about 10 to 100 stars suitable for absorption studies of the $\text{C}\text{}\text{X}$ band of H₂O (1240 Å). Estimated equivalent widths for CO, OH, and the resonance lines of C and O indicate that these species may also be detected.     

The effect of non-gravitational forces on the median inclination of short-period comets

The numbered Jupiter family comets (orbital periods   P < 20 yr  ) have a median orbital inclination of about     . In this paper, we integrate the orbits of these comets into the future, under the influence of both typical non-gravitational forces and planetary perturbation, using a Bulirsch–Stoer integrator. In the case where non-gravitational forces were not acting, the median inclination of those comets that remained on   P < 20 yr  orbits increased at the rate of  (1.92 ± 0.12) × 10⁻³ deg yr⁻¹  for the first 3600 yr of the integration. During this time the population of the original family decreases, such that the half-life is about 13 200 ± 800 yr. The introduction of non-gravitational forces slows down the rate of increase in inclination to a value of around  (1.23 ± 0.16) × 10⁻³ deg yr⁻¹  . This rate of increase in inclination was found to be only weakly dependent on the non-gravitational parameters used during the integration. After a few thousand years, the rate of change in inclination decreases, and after 20 000 yr the inclinations of those initial Jupiter family members that still have orbits with   P < 20 yr  become constant at about     , independent of whether non-gravitational forces are acting or not. The presently known Jupiter family of comets is losing members at the rate of one in every 67 yr. To maintain the family in equilibrium, Jupiter has to capture comets at a similar rate, and these captured comets have to be of low inclination to compensate for the pumping up of inclinations by gravitational perturbation.     

Dynamical evolution of the Oort cloud: II. A theoretical approach

We investigate the dynamical evolution of a cloud of comets created by stellar perturbations. We first show the respective advantages of numerical simulations and of studies of more theoretical character. Then we investigate the probability distribution of the velocity changes imparted to comets by passing stars. This distribution is shown to be different from a Maxwellian distribution, mainly because of pronounced tails. The number of fairly large impulses is thus more important than it would be in the case of a Maxwellian distribution. Finally we estimate the probability for a comet to be ejected from the Solar System. About 10% of the cloud population is lost through this mechanism over the age of the Solar System. Taking advantage of the velocity change distribution, we study the random walk of semimajor axes of comets as a function of time. We derive the probability that a comet is lost into interstellar space as a function of its initial semimajor axis.     

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.