Modeling of cometary evolution by kinetic theory: Method and first results

Physical evolution of Jupiter family (JF) comets is considered as a simultaneous process of erosion and fading. Dynamical effects are limited to discrete changes of the perihelion distance, that result in changes of the evaporation rate. Assuming that the JF comet population is in a steady state, a distribution function of this population in the two dimensional phase space consisting of radius and active fraction of the nucleus surface is found as the solution of a set of kinetic equations, each one of them for a different perihelion distance. With use of the distribution function some statistical properties of the comet population, like the total number of comets in the considered region of the phase space, the number of objects that evaporate or get dormant per unit time, etc., are obtained. The cumulative distribution function with respect to the absolute brightness is calculated and compared with the observed one as a check on the considered models.     

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.     

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.     

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.     

Are There Many Inactive Jupiter-Family Comets among the Near-Earth Asteroid Population?

We analyze the dynamical evolution of Jupiter-family (JF) comets and near-Earth asteroids (NEAs) with aphelion distances Q>3.5 AU, paying special attention to the problem of mixing of both populations, such that inactive comets may be disguised as NEAs. From numerical integrations for 2×10⁶ years we find that the half lifetime (where the lifetime is defined against hyperbolic ejection or collision with the Sun or the planets) of near-Earth JF comets (perihelion distances q<1.3 AU) is about 1.5×10⁵ years but that they spend only a small fraction of this time (∼ a few 10³ years) with q<1.3 AU. From numerical integrations for 5×10⁶ years we find that the half lifetime of NEAs in “cometary” orbits (defined as those with aphelion distances Q>4.5 AU, i.e., that approach or cross Jupiter's orbit) is 4.2×10⁵ years, i.e., about three times longer than that for near-Earth JF comets. We also analyze the problem of decoupling JF comets from Jupiter to produce Encke-type comets. To this end we simulate the dynamical evolution of the sample of observed JF comets with the inclusion of nongravitational forces. While decoupling occurs very seldom when a purely gravitational motion is considered, the action of nongravitational forces (as strong as or greater than those acting on Encke) can produce a few Enckes. Furthermore, a few JF comets are transferred to low-eccentricity orbits entirely within the main asteroid belt (Q<4 AU and q>2 AU). The population of NEAs in cometary orbits is found to be adequately replenished with NEAs of smaller Q's diffusing outward, from which we can set an upper limit of ∼20% for the putative component of deactivated JF comets needed to maintain such a population in steady state. From this analysis, the upper limit for the average time that a JF comet in near-Earth orbit can spend as a dormant, asteroid-looking body can be estimated to be about 40% of the time spent as an active comet. More likely, JF comets in near-Earth orbits will disintegrate once (or shortly after) they end their active phases.     

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.     

A Model for the Common Origin of Jupiter Family and Halley Type Comets

A numerical simulation of the Oort cloud is used to explain the observed orbital distributions and numbers of Jupiter-family (JF) and Halley-type (HT) short-period (SP) comets. Comets are given initial orbits with perihelion distances between 5 and 36 au, and evolve under planetary, stellar and Galactic perturbations for 4.5 Gyr. This process leads to the formation of an Oort cloud (which we define as the region of semimajor axes a > 1,000 au), and to a flux of cometary bodies from the Oort cloud returning to the planetary region at the present epoch. The results are consistent with the dynamical characteristics of SP comets and other observed cometary populations: the near-parabolic flux, Centaurs, and high-eccentricity trans-Neptunian objects. To achieve this consistency with observations, the model requires that the number of comets versus initial perihelion distance is concentrated towards the outer planetary region. Moreover, the mean physical lifetime of observable comets in the inner planetary region (q < 2.5 au) at the present epoch should be an increasing function of the comets’ initial perihelion distances. Virtually all observed HT comets and nearly half of observed JF comets come from the Oort cloud, and initially (4.5 Gyr ago) from orbits concentrated near the outer planetary region. Comets that have been in the Oort cloud also return to the Centaur (5 < q < 28 au, a < 1,000 au) and near-Neptune high-eccentricity regions. Such objects with perihelia near Neptune are hard to discover, but Centaurs with characteristics predicted by the model (e.g. large semimajor axes, above 60 au, or high inclinations, above 40°) are increasingly being found by observers. The model provides a unified picture for the origin of JF and HT comets. It predicts that the mean physical lifetime of all comets in the region q < 1.5 au is less than ～200 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.     

Comet 67P/Churyumov-Gerasimenko: Modeling of orientation and structure

The comet 67P/Churyumov-Gerasimenko is the current target of the mission Rosetta, initially planned to investigate comet 46P/Wirtanen. These two comets have similar orbits, except the distance to the Sun at perihelion, but different orbital histories and different masses. Thus, structures of the nuclei can be significantly different. The evolution of comet Wirtanen was simulated by several authors, while comet Churyumov-Gerasimenko became an object of high interest only recently and is not well investigated. In the present work we simulate the evolution of the nucleus, down to tens of meters below the surface, using an extended version of the model previously applied for comet Wirtanen [Kossacki et al., 1999. Comet 46P/Wirtanen: evolution of the subsurface layer. Icarus 142, 202-218.]. The model includes strengthening of the nucleus due to sintering of the ice grains. Simulations are performed for different latitudes, accounting for the evolution of the orbit and for changes of the nucleus orientation, as well as diurnal and seasonal changes of insolation. The calculated loss of water vapor from the comet is integrated over the nucleus surface and is compared with the observational data. We have found, that the sublimation through the dust mantle can be large enough to reproduce the profile of the total water production as a function of time from perihelion. The required dependence of thickness of the dust layer on latitude qualitatively matches present distribution of the absorbed solar flux. The non-gravitational acceleration in the comet motion together with the simulated sublimation flux are used in order to estimate the mass and the bulk density of the nucleus.     

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.     

Monte Carlo Simulations of Oort Cloud Comets: the Influence of Mantle Blow-off on the Inclination Distribution of Jupiter Family

We have developed an efficient Monte Carlo method by which we can evaluate the evolution of comets. There are many poorly known evolutional parameters, and we have investigated the influence of these parameters on the final populations and the inclination distributions of short-period comets. We compare the observed and calculated inclination distributions of different comet populations and obtain a good fit for the inclinations of the Jupiter family comets by assuming a mantle blow-off and a sudden brightening of the comet when its perihelion distance is lowered in a major jump. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

The absolute magnitude distribution of trans-Neptunian objects

It is shown that the known trans-Neptunian objects (TNOs) have an absolute magnitude distribution index that increases as a function of orbital perihelion distance. In no perihelion range is the TNO index the same as that found for known short-period comets. However, the fact that the median diameters of the known members of these two populations (220 and 2.9 km respectively) differ by a factor of about 75 means that very small TNOs and short-period comets might still be related.     

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.     

Invisible comets on evolutionary track of short-period comets

We systematically surveyed the orbits of short-period (SP) comets that show a large change of perihelion distance (q) between 1–2 AU (visible comets) and 4–5 AU (invisible comets) during 4400 years. The data are taken from Cosmo-DICE (Nakamura and Yoshikawa 1991a), which is a long-term orbital evolution project for SP comets. Recognizing that q is the most critical element for observability of comets, an invisibility factor (f), defined as the ratio of unobservable time span to observable span during 4400 years, is calculated for each of the large-q-change comets. A detection limit for each comet is obtained from the heliocentric distance at discovery and/or the absolute magnitude at recent apparitions. A mean f value for 35 SP comets with 2.9 J (J is the Tisserand's invariant) is found to be 19.8. This implies that for each visible SP comet of this J-range, at every epoch of time, there exist about 20 invisible comets near the capture orbits by Jupiter, under the assumptions of steady-state flux and ergodicity for the SP-comet population.     

Meteoroid Streams Associated to Comets 9P/Tempel 1 and 67P/Churyumov-Gerasimenko

The meteoroid streams associated to short-period comets 9P/Tempel 1 (the target of the Deep Impact mission)^. and 67P/Churyumov-Gerasimenko (the target of the Rosetta mission) are studied. Their structure is overwhelmingly under the control of Jupiter and repeated relatively close encounters cause a reversal of the direction of the spatial distribution of the stream relative to the comet* an initial stream trailing the comet as usually seen eventually collapses, becomes a new stream leading the comet and even splits into several components. Although these two comets do not produce meteor showers on Earth, this above feature shows that meteor storms can occur several years before the perihelion passage of a parent body.     

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.     

Sunskirting comets discovered with the LASCO coronagraphs over the decade 1996–2008

In addition to an unprecedented number of Kreutz sungrazing comets, the LASCO coronagraphs have discovered some 238 unrelated “sunskirting” comets over the 12 years from 1996 to 2008. This new class is organized in several groups, and at least two comets have further been found periodic. This article presents the photometry and the heliocentric light curves of these 238 sunskirting comets. The bulk of them exhibit a continuous increase of the brightness as the comet approaches the Sun, reach a peak before perihelion and then progressively fade with a large variety of brightness gradients. However some of them have peak brightness either at or post-perihelion, whereas a quite large number are approximately flat. Likewise for the sungrazers, we find a color effect prominent between 8 and 40R_⊙ (solar radii) which we interpret as resulting from the emission lines of the Na I doublet (D lines). We finally characterize the different groups of sunskirters on the basis of their cumulative distribution function of the peak brightness and of their fragmentation history.     

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.