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.     

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.     

Star passages through the Oort cloud

Stars passing through the Oort cloud eject comets to interstellar space and initiate showers of comets into the planetary region. Monte Carlo simulations of such passages are performed on a representative distribution of cometary orbits. Ejected comets generally lie along a narrow tunnel drilled by the star through the cloud. However, shower comets come from the entire cloud, and do not give a strong signature of the star's passage, except in the inverse semimajor axis distribution for the shower comets. The planetary system is likely not experiencing a cometary shower at this time.     

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.     

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.     

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.     

Impulse approximation improved

Improved formulas of impulse approximation method for stellar perturbations are derived. The method proposed involves a deflection of the stellar path. It is also applicable to an arbitrary time interval. A comparison of the classical vs improved method is presented both in qualitative discussion and numerical results for Oort cloud cometary orbits.     

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.     

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.     

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     

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.     

Comparison between Different Models of Galactic Tidal Effects on Cometary Orbits

Different models of the action of the galactic tide are compared. Each model is a substitute for direct numerical integrations allowing a drastic decrease of the computation time. The models are built using two different techniques, (i) averaging of the fast variable (the mean anomaly) over one cometary period and (ii) fixing the comet in its aphelion direction. Moreover, we consider two different formalisms (Lagrangian and Hamiltonian) and also two different sets of variables. As expected, we find that the model results are independent of the formalism and the set of variables considered, and are highly accurate, whereas mathematical technique leads to poor results. In order to further reduce the computation time, mappings are built from the development of the solution of the models. We show that for these mappings, the set of variables giving the most accurate results is strongly dependent on the cometary eccentricity, e, and semimajor axis, a.     

Structure and Dynamics of the Centaur Population: Constraints on the Origin of Short-Period Comets

The origin of Jupiter-family comets is linked to the intermediate stage of evolution through the Centaur region. Thus the structure of the Centaur population provides important constraints on sources of short-period comets. We show that our model of the Oort cloud evolution gives results which are consistent with the orbital distribution of observed Centaurs. In particular, it explains the existence of the large population of Centaurs with semimajor axes greater than 60 AU. The main source for these objects is the inner Oort cloud. Both Jupiter-family and Halley-type comets are produced by Centaurs originating from the Oort cloud. The injection rate for Jupiter-family comets coming from the inner Oort cloud is, at least, not less than that for a model based on the observed sample of high-eccentricity trans-Neptunian objects.     

Long-term effects of the Galactic tide on cometary dynamics

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

On stellar encounters and their effect on cometary orbits in the Oort cloud

We systematically investigate the encounters between the Sun and neighbouring stars and their effects on cometary orbits in the Oort cloud, including the intrinsic one with the star Gl 710 (HIP 89 825), with some implications to stellar and cometary dynamics. Our approach is principally based on the combination of a Keplerian‐rectilinear model of stellar passages and the Hipparcos Catalogue (ESA 1997). Beyond the parameters of encounter, we pay particular attention to the observational errors in parallaxes and stellar velocities, and their propagation in time. Moreover, as a special case of this problem, we consider the collision probability of a star passing very closely to the Sun, taking also into account the mutual gravitational attraction between the stars. In the part dealing with the influence of stellar encounters on the orbital elements of Oort cloud comets, we derive new simple formulae calculating the changes in the cometary orbital elements, expressed as functions of the Jeans impulse formula. These expressions are then applied to calculate numerical values of the element changes caused by close encounters of neighbouring stars with some model comets in the Oort cloud. Moreover, the general condition for an ejection of comets from the cloud effected by a single encounter is derived and discussed.     

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.     

New orbits for comets C/1843 J1 (Mauvais) and C/1853 W1 (van Arsdale)

New orbits for comet C/1843 J1 (Mauvais) and comet C/1853 W1 (van Arsdale) are calculated. Both orbits are hyperbolic, with e = 1.001145 and semi‐major axis a = –1412.18 AU for Mauvais and e = 1.000700 and a = –2919.24 AU for van Arsdale. Integrating the orbits backwards indicate that both comets were born in the far Oort cloud. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)