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.     

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.     

Long-term evolution of Oort Cloud comets: methods and comparisons

Two long-term simulation methods for cometary orbits, a Monte Carlo method and a direct integration method, are compared with each other. The comparison is done in seven inclination and perihelion distance intervals, and shows differences in dynamical lifetime and capture probabilities for the following main reasons. We use a finite energy step approximation in the Monte Carlo method and the method considers only close approaches with the planets. The differences can be taken into account statistically and it is possible to calculate the correction factors for the capture probability and dynamical lifetime in the Monte Carlo method. Both corrections depend on the inclination and on the value of the minimum energy step. The capture probabilities of the short-period comets originating in the Oort Cloud are calculated by the corrected Monte Carlo method and compared with published results.     

Algorithms for Stellar Perturbation Computations on Oort Cloud Comets

We investigate different approximate methods of computing the perturbations on the orbits of Oort cloud comets caused by passing stars, by checking them against an accurate numerical integration using Everhart’s RA15 code. The scenario under study is the one relevant for long-term simulations of the cloud’s response to a predefined set of stellar passages. Our sample of stellar encounters simulates those experienced by the Solar System currently, but extrapolated over a time of 10¹⁰ years. We measure the errors of perihelion distance perturbations for high-eccentricity orbits introduced by several estimators – including the classical impulse approximation and Dybczyński’s (1994, Celest. Mech. Dynam. Astron. 58, 1330–1338) method – and we study how they depend on the encounter parameters (approach distance and relative velocity). We introduce a sequential variant of Dybczyński’s approach, cutting the encounter into several steps whereby the heliocentric motion of the comet is taken into account. For the scenario at hand this is found to offer an efficient means to obtain accurate results for practically any domain of the parameter space.     

Origin of short period comets

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

Impact cratering and the Oort Cloud

We calculate the expected flux profile of comets into the planetary system from the Oort Cloud arising from Galactic tides and encounters with molecular clouds. We find that both periodic and sporadic bombardment episodes, with amplitudes an order of magnitude above background, occur on characteristic time-scales ∼25–35 Myr. Bombardment episodes occurring preferentially during spiral arm crossings may be responsible both for mass extinctions of life and the transfer of viable microorganisms from the bombarded Earth into the disturbing nebulae. Good agreement is found between the theoretical expectations and the age distribution of large, well-dated terrestrial impact craters of the past 250 Myr. A weak periodicity of ∼36 Myr in the cratering record is consistent with the Sun's recent passage through the Galactic plane, and implies a central plane density  ∼0.15 M_⊙ pc⁻³  . This leaves little room for a significant dark matter component in the disc.     

The scattered disk population as a source of Oort cloud comets: evaluation of its current and past role in populating the Oort cloud

We have integrated the orbits of the 76 scattered disk objects (SDOs), discovered through the end of 2002, plus 399 clones for 5 Gyr to study their dynamical evolution and the probability of falling in one of the following end states: reaching Jupiter's influence zone, hyperbolic ejection, or transfer to the Oort cloud. We find that nearly 50% of the SDOs are transferred to the Oort cloud (i.e., they reach heliocentric distances greater than 20,000 AU in a barycentric elliptical orbit), from which about 60% have their perihelia beyond Neptune's orbit (31 AU<q<36 AU) at the moment of reaching the Oort cloud. This shows that Neptune acts as a dynamical barrier, scattering most of the bodies to near-parabolic orbits before they can approach or cross Neptune's orbit in non-resonant orbits (that may allow their transfer to the planetary region as Centaurs via close encounters with Neptune). Consequently, Neptune's dynamical barrier greatly favors insertion in the Oort cloud at the expense of the other end states mentioned above. We found that the current rate of SDOs with radii R>1 km incorporated into the Oort cloud is about 5 yr⁻¹, which might be a non-negligible fraction of comet losses from the Oort cloud (probably around or even above 10%). Therefore, we conclude that the Oort cloud may have experienced and may be even experiencing a significant renovation of its population, and that the trans-neptunian belt—via the scattered disk—may be the main feeding source.     

Directional Distribution of Observable Comets Induced by A Star Passage Through the Oort Cloud

We simulated the passage of a star through the Oort cometary cloud andanalyzed the resulting sample of observable long period comets, noting strong asymmetries in the directional distribution of the perihelion points of thosecomets. We discuss the results previously published byWeissman (1996) for the same case. An explanation is suggestedwhy the isotropic output can be obtained only for a very peculiar case. The``cometary shower' density variation with time is also presented and thetime-dependence of the directional distribution is discussed.     

The statistical effects of galactic tides on the Oort cloud

This report is a comment on two papers by Matese and Whitman (1989, 1992). We discuss here the applicability of uniform probability densities for the orbital parameters of the Oort cloud comets.     

Formulae for the statistical interrelationships between several orbital parameters of particles in the Oort Cloud and other orbiting aggregates

Assuming the motion of particles in an orbiting aggregate (e.g., the Oort Cloud is unperturbed Keplerian, the mean joint density of distance and speed depends only upon the densities of eccentricity and semi-major axis length. We derive a formula for the mean joint density of distance and speed in terms of these densities. Also provided are formulae which, given an observed mean joint density of distance and speed, permit the computation of the corresponding semi-major axis length and eccentricity densities. The results of this paper permit one to derive the structure of an orbiting aggregate given a minimum of information.Box 58421 Houston, Texas 77058     

Periodic variation of Oort Cloud flux and cometary impacts on the Earth and Jupiter

Time variation in impact probability is studied by assuming that the periodic flux of the Oort Cloud comets within 15 au arises from the motion of the Sun with respect to the Galactic mid-plane. The periodic flux clearly shows up in the impact rate of the captured Oort Cloud cometary population, with a phase shift caused by the orbital evolution. Depending on the assumed flux of comets and the size distribution of comets, the impact rate of the Oort Cloud comets of 1 km in diameter or greater is from 5 to 700 impacts Myr⁻¹ on the Earth and from 0.5 to 70 impacts per 1000 yr on Jupiter. The relative fractions of impacts are 0.09, 0.11, 0.26 and 0.54 for long-period comets, Halley type comets, Jupiter family comets and near-Earth objects, respectively. For Jupiter, the corresponding fractions in the first three categories are 0.18, 0.31 and 0.51. If we consider physical fading of comet activity that is compatible with the observations, then the impact rates of active comets are two orders of magnitude smaller than the total impact rates by all kinds of comets and cometary asteroids of size 1 km or greater.     

The activities of comets related to their aging and origin

Two indices have been developed for the purpose of comparing the natures of various classes of comets. The first is the Activity Index (AI), measuring the inherent magnitude increase in brightness from great solar distances to maximum near perihelion. The second, or Volatility Index (VI), measures the variation in magnitude near perihelion. Tentative determinations of these two indices are derived from observations by Max Beyer over more than 30 years for long-period (L-P) and short-period (S-P) comets near perihelion and from other homogeneous sources. AI determinations are made for 32 long-period (L-P) comets and for 14 short-period (S-P). The range of values of AI is of the order of 3 to 10 magnitudes with a median about 6. An expected strong correlation with perihelion distance q, is found to vary as q ^–2.3. Residuals from a least-square solution (AI) are used for comparing comets of different orbital classes, the standard deviation of a single value of AI is only ±1^m.1 for L-P comets and ±1^m.2 for S-P comets.Among the L-P comets, 19 of period P larger than 10⁴ years yield AI = 0^m.27 ± 0^m.25 compared to 0^m.39 ± 0^m.26 for 13 of period between 10² years and 10⁴ years. This denies any fading with aging among the L-P comets. Also no systematic change with period occurs for the VI index, leading to the same conclusions. Weak correlations are found with the Gas/Dust ratio of comets. No correlations are found between the two indices, nor of either index with near-perihelion magnitudes or orbital inclination.The various data are consistent with a uniform origin for all types of comets, the nuclei being homogeneous on the large scale but quite diverse on a small scale (the order of a fraction of kilometer in extent). Small comets thus may sublimate away entirely, leaving no solid core, while huge comets may develop a less volatile core by radioactive heating and possibly become inactive like asteroids after many S-P revolutions about the Sun. When relatively new, huge comets may be quite active at great solar distances because of volatiles from the core that have refrozen in the outer layers.     

Characteristics and Frequency of Weak Stellar Impulses of the Oort Cloud

We have developed a model of the response of the outer Oort cloud of comets to simultaneous tidal perturbations of the adiabatic galactic force and a stellar impulse. The six-dimensional phase space of near-parabolic comet orbital elements has been subdivided into cells. A mapping of the evolution of these elements from beyond the loss cylinder boundary into the inner planetary region over the course of a single orbit is possible. This is done by treating each perturbation separately, and in combination, during a time interval of 5 Myr. We then obtain the time dependence of a wide range of observable comet flux characteristics, which provides a fingerprint of the dynamics. These include the flux distributions of energy, perihelion distance, major axis orientation, and angular momentum orientation. Correlations between these variables are also determined. We show that substantive errors occur if one superposes the separately obtained flux results of the galactic tide and the stellar impulse rather than superposing the tidal and impulsive perturbations in a single analysis. Detailed illustrations are given for an example case where the stellar mass and relative velocity have the ratio M∗/V_rel=0.043 M⊙/km s⁻¹ and the solar impact parameter is 45,000 AU. This case has features similar to the impending Gliese 710 impulse with the impact parameter selected to be close to the low end of the predicted range. We find that the peak in the observable comet flux exceeds that due to the galactic tide alone by ≈41%. We also present results for the time dependence of the flux enhancements and for the mean encounter frequency of weak stellar impulse events as functions of M∗/V_rel and solar impact parameter.     

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.     

Embedded star clusters and the formation of the Oort Cloud

Observations suggest most stars originate in clusters embedded in giant molecular clouds [Lada, C.J., Lada, E.A., 2003. Annu. Rev. Astron. Astrophys. 41, 57-115]. Our Solar System likely spent 1-5 Myrs in such regions just after it formed. Thus the Oort Cloud (OC) possibly retains evidence of the Sun's early dynamical history and of the stellar and tidal influence of the cluster. Indeed, the newly found objects (90377) Sedna and 2000 CR₁₀₅ may have been put on their present orbits by such processes [Morbidelli, A., Levison, H.F., 2004. Astron. J. 128, 2564-2576]. Results are presented here of numerical simulations of the orbital evolution of comets subject to the influence of the Sun, Jupiter and Saturn (with their current masses on orbits appropriate to the period before the Late Heavy Bombardment (LHB) [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461]), passing stars and tidal force associated with the gas and stars of an embedded star cluster. The cluster was taken to be a Plummer model with 200-400 stars, with a range of initial central densities. The Sun's orbit was integrated in the cluster potential together with Jupiter and Saturn and the test particles. Stellar encounters were incorporated by directly integrating the effects of stars passing within a sphere centred on the Sun of radius equal to the Plummer radius for low-density clusters and half a Plummer radius for high-density clusters. The gravitational influence of the gas was modeled using the tidal force of the cluster potential. For a given solar orbit, the mean density, 〈ρ〉, was computed by orbit-averaging the density of material encountered. This parameter proved to be a good measure for predicting the properties of the OC. On average 2-18% of our initial sample of comets end up in the OC after 1-3 Myr. A comet is defined to be part of the OC if it is bound and has q>35 AU. Our models show that the median distance of an object in the OC scales approximately as 〈ρ〉^−1/2 when . Our models easily produce objects on orbits like that of (90377) Sedna [Brown, M.E., Trujillo, C., Rabinowitz, D., 2004. Astrophys. J. 617, 645-649] within ∼1 Myr in cases where the mean density is or higher; one needs mean densities of order to create objects like 2000 CR₁₀₅ by this mechanism, which are reasonable (see, e.g., Guthermuth, R.A., Megeath, S.T., Pipher, J.L., Williams, J.P., Allen, L.E., Myers, P.C., Raines, S.N., 2005. Astrophys. J. 632, 397-420). Thus the latter object may also be part of the OC. Close stellar passages can stir the primordial Kuiper Belt to sufficiently high eccentricities (e?0.05; Kenyon, S.J., Bromley, B.C., 2002. Astron. J. 123, 1757-1775) that collisions become destructive. From the simulations performed it is determined that there is a 50% or better chance to stir the primordial Kuiper Belt to eccentricities e?0.05 at 50 AU when . The orbit of the new object 2003 UB₃₁₃ [Brown, M.E., Trujillo, C.A., Rabinowitz, D.L., 2005. Astrophys. J. 635, L97-L100] is only reproduced for mean cluster densities of the order of , but in the simulations it could not come to be on its current orbit by this mechanism without disrupting the formation of bodies in the primordial Kuiper Belt down to 20 AU. It is therefore improbable that the latter object is created by this mechanism.