Patrick G. Whitman

The galactic disk tidal field and the nonrandom distribution of observed Oort cloud comets

Abstract We consider the interaction of the galaxy with the Oort cloud of comets. If the perturbation is limited to the secularly averaged first-order disk tidal term, analytic solutions for the time evolution of orbital elements are possible. In turn, Monte Carlo techniques then become a practical means of estimating the distributions of orbital elements for those comets which become observable. We demonstrate that the detected nonrandomness in the distribution in galactic latitudes of perihelia is a real phenomenon caused by the tidal perturbation and is not the result of observational selection effects. Results on the refilling of the liss cylinder are also presented.

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/α < 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.

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.

Near-Earth populations of bodies coming from the Oort cloud and their impacts with planets

When Oort cloud comets enter the planetary region their orbital evolution is dominated by encounters with the planets. Some of them become short period comets and enter the terrestrial planetary region to form a potential source of cratering. We have computed the orbital evolution of comets by encounters with the seven major planets. We find 0.5–2 impacts/Myr on the Earth, somewhat lower than the observed rate of about 2.8 impacts per Myr causing craters ≥ 20 km in diameter. Thus as far as numbers go, it is quite possible that dead comets are a major, even if not the dominant source of cratering on the Earth. We have also tested how well the expected variations in the Oort cloud comet flux show up in the rate of impacts. We find that the periodicity is reflected also in the cratering rate, though with a time delay and with added noise.

Velocity streaming of IRAS main-sequence disk stars and the episodic enhancement of particulate disks by interstellar clouds

We have discovered evidence of velocity streaming in a set of nearby main-sequence A-type IRAS disk stars. This conservatively chosen set of the five most significant particulate-disk stars consists of β Pic, α Lyr, α Psa, β Leo, and ζ Lep. Monte Carlo simulations were used to compare the velocity dispersion of this set to the dispersions of sets chosen at random from the remaining 17 main-sequence A stars listed in the Gliese catalog (<22 pc). It was found that dispersion velocities less than those of the particulate-disk star set occurred by chance in only 2% of the cases. Small dispersion velocities are normally indicative of streaming clusters or young field stars. However, the velocity dispersion of the set of particulate-disk stars is inconsistent with either interpretation

Why we study the geological record for evidence of the solar oscillation about the galactic midplane

The Solar System oscillates about the plane defined by the disk of matter in our Galaxy. This oscillatory motion gives rise to a substantial modulation in the tidally induced flux of Oort cloud comets. An observational determination of the quasi-periodicity of this motion carries with it significant information about the population, distributions, dynamics and origins of short-period and long-period comets. An additional incentive for emphasizing such a study is the information about dark disk matter that a period can yield. If dark disk matter is completely negligible, the amplitude of the solar motion will be sufficiently large that the peak-to-trough flux ratio will be ≈ 2.5 and the plane-crossing period will exceed 40 Myr. Dark disk matter comparable in mass to bright disk matter and distributed in any manner is inconsistent with K-dwarf distributions and can be rejected as a working hypothesis. But if a modest fraction of the disk matter is dark and distributed like the interstellar medium, as is consistent with limits deduced from K-giant and K-dwarf velocity distributions, the peak-to-trough flux ratio can increase to a factor of 4 even though the solar z amplitude is decreased. In that case the period can be as little as 30 Myr and the implied Oort population is smaller by a factor of 3. We should carefully reconsider the geological record as a potential discriminator of these options.

Generalized Lagrangian orbital elements for central force problems

We consider the definitions and resulting equations of motion for the Lagrangian orbital elements associated with conventional osculating orbit theory for central forces. The analysis indicates that the definitions themselves lead to difficulties which are most apparent in the circular limit. An alternate set of defining relations is presented which eliminates the problems associated with osculating elements. The remaining equation of motion based on these new definitions is reduced to quadratures. This solution completely expresses the orbits for central force problems with no restriction on the eccentricity. Both bounded and open orbits are considered. A generalized Laplace-Runge-Lenz vector is developed and a number of example solutions are presented.