W.-H. Ip

Some dynamical aspects of the accretion of Uranus and Neptune: The exchange of orbital angular momentum with planetesimals

Abstract The final stage of the accretion of Uranus and Neptune is numerically investigated. The four Jovian planets are considered with Jupiter and Saturn assumed to have reached their present sizes, whereas Uranus and Neptune are taken with initial masses 0.2 of their present ones. Allowance is made for the orbital variation of the Jovian planets due to the exchange of angular momentum with interacting bodies (“planetesimals”). Two possible effects that may have contributed to the accretion of Uranus and Neptune are incorporated in our model: (1) an enlarged cross section for accretion of incoming planetesimals due to the presence of extended gaseous envelopes and/or circumplanetary swarms of bodies; and (2) intermediate protoplanets in mid-range orbits between the Jovian planets. Significant radial displacements are found for Uranus and Neptune during their accretion and scattering of planetesimals. The orbital angular momentum budgets of Neptune, Uranus, and Saturn turn out to be positive; i.e., they on average gain orbital angular momentum in their interactions with planetesimals and hence they are displaced outwardly. Instead, Jupiter as the main ejector of bodies loses orbital angular momentum so it moves sunward. The gravitational stirring of planetesimals caused by the introduction of intermediate protoplanets has the effect that additional solid matter is injected into the accretion zones of Uranus and Neptune. For moderate enlargements of the radius of the accretion cross section (2–4 times), the accretion time scale of Uranus and Neptune are found to be a few 10 8 years and the initial amount of solid material required to form them of a few times their present masses. Given the crucial role played by the size of the accretion cross section, questions as to when Uranus and Neptune acquired their gaseous envelopes, when the envelopes collapsed onto the solid cores, and how massive they were are essential in defining the efficiency and time scale of accretion of the two outer Jovian planets.

On a hot oxygen corona of Mars

Abstract Analogous to the case of Venus, electron dissociative recombination of the ionospheric O 2 + ions can be an important source of suprathermal atomic oxygen in the exosphere of Mars. Because of the weaker surface gravitational attraction on Mars as compared to that on Venus, a hot oxygen corona so formed could be denser than the corresponding corona on Venus at altitudes >2000 km in spite of the lower ionospheric content of Mars. Modification to the solar wind interaction via ionization pickup of the exospheric oxygen ions may be detectable by ion mass spectrometer experiment on a Mars orbiter mission. If an extended oxygen corona exists, collisional interaction with the Martian satellite, Phobos, would lead to the formation of an oxygen gas torus of average number density of only 〈 n 〉 ≈ 1−2 cm −3 along the orbit of Phobos. In comparison, intrinsic gas emission from Phobos, if total gas production rate is ≈10 23 H 2 O molecules sec −1 , would contribute to a gas torus with 〈 n 〉 ≈ 10 3 oxygen atoms cm −3 exceeding the ambient value of 100–200 cm −3 as estimated for the hot oxygen corona.

Dynamical evolution of a cometary swarm in the outer planetary region

The dynamical evolution of bodies under the gravitational influence of the accreting proto-Uranus and proto-Neptune is investigated. The main aim of this study is to analyze the interrelations between the accretion of Uranus and Neptune with other processes of cosmological importance as, for example, the formation of a cometary reservoir from bodies placed into near-parabolic orbits by planetary perturbations and the scattering of bodies to the region of the terrestrial planets. Starting with a mass ratio (initial mass/present mass) of 0.1, Uranus and Neptune acquire masses close to their present ones in a time scale of 108 years. Neptune is found to be the most important contributor of comets to the cometary reservoir. The time scale of bodies scattered by Neptune to reach near-parabolic orbits (semimajor axes a > 104 AU)is about 109 years. The contribution of Uranus was partially inhibited because a large part of the residual bodies of its accretion zone fell under the strong gravitational influence of Jupiter and Saturn. A significant fraction of the bodies dispersed by Uranus and Neptune reached the region of the terrestrial planets in a time scale of some 108 years.

On the time evolution of the cometary influx in the region of the terrestrial planets

Abstract It has been argued that Uranus and Neptune could reach their present sizes only at the expense of an initial amount of mass in their accretion zones far exceeding their current masses [e.g., V.S. Safronov, Evolution of the Protoplanetary Cloud and Formation of the Earth and the Planets (translated from Russian (1972) by the Israel Program for Scientific Translation, Jerusalem), 1969, and in The Motion, Evolution of Orbits, and Origin of Comets ( G. A. Chebotarev, E. I. Kazimirchak-Polonskaya, and B. G. Marsden, Eds.), pp. 329–334, IAU Symposium No. 45, 1972 ]. From a numerical analysis, it is determined that such a scenario would have led to a heavy bombardment of the inner planetary region by cometary bodies as well as the formation of a cometary reservoir (the so-called “Oort cloud”) at very large heliocentric distances. The cometary influx event can be characterized by the arrival of two different populations of stray bodies. At the beginning, the stray population is made up of “outer planetary region” comets, transferred ffrom the Uranus-Neptune region to the region of the terrestrial planets by gravitational perturbations of the Jovian planets. These comets are characterized for having low-inclination orbits and, once they reach the region of the terrestrial planets, for being mainly under the gravitational influence of Jupiter. Later, “Oort-cloud” comets, driven into the inner planetary region by stellar perturbations, become the dominant component among the incoming comets. The crossover from a outer planetary region comets-dominated regime to a Oort cloud comets-dominated one is found to occur at t ∼1.5–2AE. Besides the Oort cloud population, a residual population of mass about 10 −5 times the initial mass is found to remain in the outer planetary region at present. Most of the survivors move on orbits with perihelia in the Uranus-Neptune region and aphelia beyond Neptunes orbit, reaching heliocentric distances up to hundreds or even thousands AU. We thus propose two possible cometary sources: (1) A cometary reservoir—the “Oort cloud”—of rather spherical structure with a concentration of aphelion points at several times 10 4 AU. Members of the cloud are subjected to the perturbing influence of passing stars. (2) A rather flat system of cometary bodies—the “cometary belt” — subjected to planetary perturbations but where stellar perturbations have a negligible role due to the larger binding energies of belt comets. Despite their long dynamical time scales, they will be finally ejected or scattered to the region of the terrestrial planets. In the latter case, such belt objects will appear as short-period comets. Therefore, a belt of residual bodies in the outer fringes of the planetary region may be a likely source of the observed family of short-period comets.

Dynamics of electrons and heavy ions in Mercury's magnetosphere

Abstract Several basic magnetospheric processes at Mercury have been investigated with simple models. These include the adiabatic acceleration and convection of equatorially mirroring charged particles, the current sheet acceleration effect, and the acceleration of Na+ and other exospheric ions by the magnetospheric electric and magnetic fields near the planetary surface. The current steady-state treatment of the magnetospheric drift and convection processes suggests that the region of the inner magnetosphere as explored by the Mariner 10 spacecraft during its encounter with Mercury should be largely devoid of energetic (>100 keV) electrons in equatorial mirroring motion. As for ion motion, the large gyroradii of the heavy ions permit surface reimpact as well as loss via intercepting the magnetopause. Because of the kinetic energy gained in the gyromotion, the first effect could lead to sputtering processes and hence generation of secondary ions and neutrals. The second effect could account for the loss of about 50% of Mercurys exospheric ions.

Exchange of condensed matter among the outer and terrestrial protoplanets and the effect on surface impact and atmospheric accretion

Abstract One current picture of the accretion process of Uranus and Neptune invokes extensive gravitational scattering of the icy planetesimals by the photoplanets as they grew to significant masses. This phase should last a few 100 million years during which the planetary scattering effect could lead to implantation of comets in the Oort cloud. The injection of the scattered planetesimals into the inner Solar System also leads to a gain of volatile materials by the terrestrial planets. The potential H 2 O input to primordial Earth, for instance, could be on the order of 10 25 – 10 26 g even though a large part of it might have been subsequently lost via atmospheric escape process. This early planetesimal impact event was followed by a much more gradual process, i.e., the return of the icy cometary cores from the distant Oort cloud via stellar perturbations. The total amount of volatile material as accreted by the terrestrial planets was quite small as compared with the earlier episode accompanied by the formation of Uranus and Neptune. As an example, the Earth would have recieved about 6 × 10 20 g of cometary material in total over the last 4 billion years if the cometary nucleus density is as high as 0.5 g cm −3 . Within the context of H 2 O inventory (the terrestrial ocean mass is 1.3 × 10 24 g) the cometary influx should have minor effects. On the other hand, because of the paucity of H 2 O content in the atmospheres of Mars and Venus, cometary impact could produce strong time variation in their water contents. As for Titan, its nitrogen atmosphere could be derived from cometary impact only if the early phase of comet bombardment was very intense. A comparison of the adopted comet flux model with the crater count statistics indicates a certain discrepancy (a factor of 10–50) in the estimated comet impact rates. Possible sources of errors could come from the size distribution of the long-period comets, their average density, albedo, and other factors. A more complete survey of the population of subkilometer comets in the outer Solar System by Space Telescope and other instruments will be critical importance in clarifying the interrelation among the original mass of the Oort cloud, the volatile accruement by the terrestrial planets, and the impact crater production rates on planetary and satellite surfaces.

Ring torque of Saturn from interplanetary meteoroid impact

Reevaluation of the interplanetary meteoroid mass flux at 10 AU obtains a value of M≈6×104g sec−1 for the meteoroid mass loading rate to the rings of Saturn. This meteoroid impact flux suggests that a large change to the configuration of the ring system could occur in a relatively short time (≲109years). This new element thus should be taken into consideration in discussion of the dynamical evolution of the rings.

Time-dependent injection of Oort Cloud comets into earth-crossing orbits

The effect of close stellar encounters in modulating the influx rate of Oort cloud comets is investigated. In particular, it is shown that comet showers intense enough to be reflected in crater statistics can be produced at intervals of 80 million years or so, provided we are dealing with an Oort cloud consisting of a heavy core of comets. In this case, there is found a strong predominance of incoming comets from the sky zone where the perturbing star makes its closest approach. We have also performed numerical simulations of the time evolution of comet showers or bursts. From this numerical study, a long tail of residual shower comets is found to follow the major event with an intensity (as compared with the intensity of the shower as its peak) of ∼10−2 after 20—30 million years. Our results thus suggest that residual shower comets may be clustered mainly on certain sky areas and observable at practically any time given the lasting effects of a shower. This might explain some of the observed clustering of aphelion points of long-period comets.

Collisional interactions of ring particles: The ballistic transport process☆

Abstract As the erosion rate of the Saturnian rings resulting from meteoroid bombardment can be quite significant in the evolutionary history of the ring system, a simple model is constructed to study the relevant dynamics of ballistic transport of the impact ejecta. The combined process of collision with the ring plane particles, with the impact probability related to the optical depth and inelastic rebound from the ring plane until the random motion of the particle is effectively damped, is traced by using the Monte Carlo method. The numerical results indicate that the final distribution of the ejecta depends very much on the initial ejection velocity. For high-velocity fragments, their distribution tends to follow the optical depth variation of the rings. But for low-velocity fragments, pronounced edge effect with ejected particles accumulated at the boundaries of optical depth discontinuities could result. Therefore, in a global scale, the large increase of optical depth near the inner edge of the B ring, for example, as well as the depletion of micrometer-sized particles in the B ring and the Cassini division may be interpreted by the mechanism of ballistic transport. The edge effect found in the calculations might also be closely related to the formation of sharp edges and double peaks in a number of narrow ringlets. (The simultaneous operation of ballistic transport diffusion and gravitational resonant effects of satellites remains to be investigated.)

Dynamical processes of macro-accretion of Uranus and Neptune: a first look

Abstract The process of macro-accretion of Uranus and Neptune is studied using a program which simulates the random effect of gravitational scattering and accretionfor a system of Earth-sized objects. While the exclusion of a population of small planetesimals and the suppression of erosion and fragmentation at hypervelocity impact tend to bias the present result toward the formation and buildup of Earth- to Uranus-size objects, the numerical results are instructive in approximating the time scale (a few times 108 years) of stochastic collisions and hence of the large tilting of the protoplanets; we find that (i) it is probable that the insertion of a small number of Earth-sized objects in the trans-Neptunian region acts as the driver of inward orbital diffusion for a cometary belt located outside the orbit of Neptune and (ii) it is possible that a few large planetesimals were scattered into orbits crossing the asteroid belt and hence gravitationally stirred the orbits of the main-belt asteroids. The dynamical process of macro-accretion of the outer planets thus could have a very extensive effect on the general structure and evolution of the Solar System.