Julio A. Fernández

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.

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.

Evolution of comet orbits under the perturbing influence of the giant planets and nearby stars

The orbital evolution of 500 hypothetical comets during 109 years is studied numerically. It is assumed that the birthplace of such comets was the region of Uranus and Neptune from where they were deflected into very elongated orbits by perturbations of these planets. Then, we adopted the following initial orbital elements: perihelion distances between 20 and 30 AU, inclinations to the ecliptic plane smaller than 20°, and semimajor axes from 5 × 103 to 5 × 104 AU. Gravitational perturbations by the four giant planets and by hypothetical stars passing at distances from the Sun smaller than 5 × 105 AU are considered. During the simulation, somewhat more than 50% of the comets were lost from the solar system due to planetary or stellar perturbations. The survivors were removed from the planetary region and left as members of what is generally known as the cometary cloud. At the end of the studied period, the semimajor axes of the surviving comets tend to be concentrated in the interval 2 × 104 < a < 3 × 104 AU. The orbital planes of the comets with initial a ≧ 3 × 104 AU acquired a complete randomization while the others still maintain a slight predominance of direct orbits. In addition, comet orbits with final a < 6 × 104AU preserve high eccentricities with an average value greater than 0.8 Most “new” comets from the sample entering the region interior to Jupiters orbit had already registered earlier passages through the planetary region. By scaling up the rate of paritions of hypothetical new comets with the observed one, the number of members of the cometary cloud is estimated to be about 7 × 1010 and the conclusion is drawn that Uranus and Neptune had to remove a number of comets ten times greater.

Cometary masses derived from non-gravitational forces

We compute masses and densities for ten periodic comets with known sizes: 1P/Halley, 2P/Encke, 6P/d’Arrest, 9P/Tempel 1, 10P/Tempel 2, 19P/Borrelly, 22P/Kopff, 46P/Wirtanen, 67P/Churyumov-Gerasimenko and 81P/Wild 2. The method follows the one developed by Rickman and colleagues (Rickman 1986, 1989; Rickman et al. 1987), which is based on the gas production curve and on the change in the orbital period due to the non-gravitational force. The gas production curve is inferred from the visual lightcurve. We found that the computed masses cover more than three orders of magnitude: ≃ (0.3 - 400) × 10 12 kg. The computed densities are in all cases very low ( < 0.8 g cm 3 ), with an average value of 0.4 g cm 3 , in agreement with previous results and models of the cometary nucleus depicting it as a very porous object. The computed comet densities turn out to be the lowest among the different populations of solar system minor bodies, in particular as compared to those of near-Earth asteroids (NEAs). We conclude that the model applied in this work, in spite of its simplicity (as compared to more sophisticated thermophysical models applied to very few comets), is useful for a statistical approach to the mean density of the cometary nuclei. However, we cannot assess from this simple model if there is a real dispersion among the bulk densities of comets that could tell us about differences in physical structure (porosity) and/or chemical composition.

Mass removed by the outer planets in the early solar system

Abstract The changes in the heliocentric energies of particles due to close encounters with the outer planets are analyzed. Two stages in the evolution of the planets are proposed. The first phase was characterized by the rapid growth of the protoplanets. During this stage the collisions prevailed over the ejection of particles in close encounters. The second phase was characterized by the “spreading” of the residual solid matter toward the inner and outer regions of the solar system. For the outer planets the probabilities that a particle is ejected out of the solar system or achieves a near-parabolic orbit, after a close encounter, are calculated. The particles in near-parabolic orbits might have originated the cometary cloud that presumably surrounds the solar system. It is found that the ratio between these particles and the total number of ejected particles increases with the planet-Sun distance. It is estimated that the solid material from the region of the outer planets ejected from the solar system ranged from tens to hundreds of terrestrial masses. It is also suggested that Neptune, and perhaps Uranus, could have supplied an important fraction of the total mass of the cometary cloud.

Numerical simulations of the accretion of Uranus and Neptune

Abstract The accretion process of the outer planets was one of the most collective phenomena during the formation of the solar system. From the region of the terrestrial planets up to its outermost boundary, the Oort cloud, the solar system has been strongly influenced by this process ( Fernandez and Gallardo, 1996 ). Much progress has been done in our understanding of the formation of the outer planets and scattering of the residual mass from the early theoretical research of Safronov, 1972 . Nevertheless, there are several aspects not yet understood that deserve further study.

The role of collisions with interplanetary particles in the physical evolution of comets

Effects of collisions with interplanetary particles are investigated. To this purpose, collision probabilities for comets with different orbital elements are computed. It is found that collisions may have a non-negligible effect on the physical evolution of comets. In this connection, it is shown that under certain conditions collisional lifetimes may be shorter than dynamical or vaporization lifetimes. In particular, collisional lifetimes are on average shorter for comets in retrograde orbits than those for direct ones. It is further suggested that catastrophic collisions may contribute to prevent long-period comets in retrograde orbits from reaching short-period orbits by orbital diffusion. Collisions may also produce irregularities of the nucleus brightness by leaving exposed regions of fresh volatile material and may in this way lead to a ‘rejuvenation’ of old dusty short-period comets. Catastrophic collision probabilities are too low to account for the observed comet splittings, so other trigger mechanisms should be at work. However, it is shown that collisional mini-bursts (increases in brightness of one magnitude or so) caused by decimeter-sized bodies may occur rather frequently on short-period comets when they pass through the asteroid belt. The burst observed in comet Tempel-2 at ∼3 AU in December, 1978 could be an example of such collisional mini-bursts. The systematic observation of periodic comets when they pass through the asteroid belt could give valuable information about the spatial density of decimeter and meter-sized bodies. In particular, collisional effects for comet Halley, for which a continuous surveillance is planned, are evaluated.

On the Existence of a Distant Solar Companion and its Possible Effects on the Oort Cloud and the Observed Comet Population

We analyze the possible existence and detection of a distant massive solar companion. Such an object?if it exists?should be very faint in the visible, so its direct detection might depend on current or future infrared sky surveys, like WISE. Alternatively, its presence could be uncovered through its perturbing effects on nearby objects such as, for instance, Oort Cloud comets (OCCs). We then estimate how putative solar companions of different masses and semimajor axes can perturb nearby OCCs causing an enhancement of the comet flux along the companions path. We find that a companion of 5 Jupiter masses (MJ ) can produce a signature detectable with the current record of observed new comets, provided that the Oort Cloud contains a dense inner core of comets and that the distance of the perturber is smaller than ~2 ? 104 AU. A 1 MJ perturber can produce a signature detectable in the current record only if its distance were smaller than ~(2-3) ? 103 AU. The sample of discovered new comets is found to be two orders of magnitude too small to show a signature caused by a Neptune-mass companion at any distance above ~103 AU to a significant level. We also estimate that the Oort Cloud will withstand the steady perturbing effects by a massive solar companion over the solar system age, with only a minor erosion, unless the companion had a mass a few MJ , and were at a distance a few 103 AU.

The Scattered Disk Population and the Oort Cloud

The trans-Neptunian belt has been subject to a strong depletion that has reduced its primordial population by a factor of one hundred over the solar systems age. One by-product of such a depletion process is the existence of a scattered disk population in transit from the belt to other places, such as the Jupiter zone, the Oort cloud or interstellar space. We have integrated the orbits of the scattered disk objects (SDOs) so far discovered by 2500 Myr to study their dynamical time scales and the probability of falling in each of the end states mentioned above, paying special attention to their contribution to the Oort cloud. We found that their dynamical half-time is close to 2.5 Gyr and that about one third of the SDOs end up in the Oort cloud.