Debris disks: seeing dust, thinking of planetesimals and planets

Debris disks are optically thin, almost gas-free dusty disks observed arounda significant fraction of main-sequence stars older than about 10 Myr. Since the circumstellar dust is short-lived, the very existence of these disks is considered as evi-dence that dust-producing planetesimals are still present in mature systems, in whichplanets have formed – or failed to form – a long time ago. It is inferred that theseplanetesimals orbit their host stars at asteroid to Kuiper-belt distances and continuallysupply ...     

Delivery of icy planetesimals to inner planets in the Proxima Centauri planetary system

The estimates of the delivery of icy planetesimals from the feeding zone of Proxima Centauri c (with mass equal to 7m_E, m_E is the mass of the Earth) to inner planets b and d were made. They included the studies of the total mass of planetesimals in the feeding zone of planet c and the probabilities of collisions of such planetesimals with inner planets. This total mass could be about 10–15m_E. It was estimated based on studies of the ratio of the mass of planetesimals ejected into hyperbolic orbits to the mass of planetesimals collided with forming planet c. At integration of the motion of planetesimals, the gravitational influence of planets c and b and the star was taken into account. In most series of calculations, planetesimals collided with planets were excluded from integrations. Based on estimates of the mass of planetesimals ejected into hyperbolic orbits, it was concluded that during the growth of the mass of planet c the semi-major axis of its orbit could decrease by at least a factor of 1.5. Depending on possible gravitational scattering due to mutual encounters of planetesimals, the total mass of material delivered by planetesimals from the feeding zone of planet c to planet b was estimated to be between 0.002m_E and 0.015m_E. Probably, the amount of water delivered to Proxima Centauri b exceeded the mass of water in Earth's oceans. The amount of material delivered to planet d could be a little less than that delivered to planet b.     

Editorial

A simulation of collisional and gravitational interaction in the early solar system generates planets ～500 km in diameter from an initial swarm of kilometer-sized planetesimals, such as might have resulted from gravitational instabilities in the solar nebula. The model treats collisions according to experimental and theoretical impact results (such as rebound, cratering, and catastrophic fragmentation) for a variety of materials whose parameters span plausible values for early solid objects. Ad hoc sticking mechanisms are avoided. The small planets form in ～10⁴ yr, during which time most of the mass of the system continues to reside in particles near the original size. The relative random velocities remain of the order of a kilometer-sized body's escape velocity, with random velocities of the largest objects somewhat depressed because of damping by the bulk of the material. The simulation is terminated when the largest objects' random motion is of smaller dimension than their collision cross sections, so that the “particle-in-a-box” statistical methods of the model break down. The few 500-km planets, in a swarm still dominated by kilometer-scale planetesimals, may act as “seeds” for the subsequent, gradual, accretional growth into full-sized planets.     

Core instability models of giant planet accretion – II. Forming planetary systems

We develop a simple model for computing planetary formation based on the core instability model for the gas accretion and the oligarchic growth regime for the accretion of the solid core. In this model several planets can form simultaneously in the disc, a fact that has important implications especially for the changes in the dynamic of the planetesimals and the growth of the cores since we consider the collision between them as a source of potential growth. The type I and type II migration of the embryos and the migration of the planetesimals due to the interaction with the disc of gas are also taken into account. With this model we consider different initial conditions to generate a variety of planetary systems and analyse them statistically. We explore the effects of using different type I migration rates on the final number of planets formed per planetary system such as on the distribution of masses and semimajor axis of extrasolar planets, where we also analyse the implications of considering different gas accretion rates. A particularly interesting result is the generation of a larger population of habitable planets when the gas accretion rate and type I migration are slower.     

Effects of Planetary Migration on Natural Satellites of the Outer Planets

Numerous studies in the past few years have analyzed possible effects of planetary migration on the small bodies of the Solar System (mainly asteroids and KBOs), with the double aim of explaining certain dynamical structures in these systems, as well as placing limits on the magnitude of the radial migration of the planets. Here we undertake a similar aim, only this time concentrating on the dynamical stability of planetary satellites in a migration scenario. However, different from previous works, the strongest perturbations on satellite systems are not due to the secular variation of the semimajor axes of the planets, but from the planetesimals themselves. These perturbations result from close approaches between the planetesimals and satellites.We present results of several numerical simulations of the dynamical evolution of real and fictitious satellite systems around the outer planets, under the effects of multiple passages of a population of planetesimals representing the large-body component of a residual rocky disk. Assuming that this component dominated the total mass of the disk, our results show that the present systems of satellites of Uranus and Neptune do not seem to be compatible with a planetary migration larger than even one quarter that suggested by previous studies, unless these bodies were originated during the late stage of evaporation of the planetesimal disk. For larger variations of the semimajor axes of the planets, most of the satellites would either be ejected from the system or suffer mutual collisions due to excitation in their eccentricities. For the systems of Jupiter and Saturn, these perturbations are not so severe, and even large migrations do not introduce large instabilities.Nevertheless, even a small number of 1000-km planetesimals in the region may introduce significant excitation in the eccentricities and inclinations of satellites. Adequate values of this component may help explain the present dynamical distribution of distant satellites, including the highly peculiar orbit of Nereid.     

Planet formation: Compositional mixing and lunar compositional anomalies

Significant fractions of each planet's late-accreted mass originated not at its own distance from the Sun, but from a neighboring planet's orbit, according to results that follow from calculations by Wetherill (1975). “Late-accreted” refers to a loosely defined period after planets acquired most of their present mass. In an idealized model, Mercury, Venus, Earth, and Mars received 47, 45, 37, and 52% of their late-accreted mass from planetesimals formed closer to other planets. Resulting compositional anomalies in outer parts of early planets could be significant; atmospheric tests of Lewis's predicted S deficiency on Venus may be inconclusive.The Moon's orbit around Earth puts it in a special category: sorting occurs between Moon-impacting and Earth-impacting material according to approach velocity. In the above model, the moon receives 60% of its late-accreted mass from planetesimals formed near Venus' orbit. Distant planetesimals could be perturbed into the Earth-Moon system and cause major changes in the Moon's composition with only minor effect on Earth. The entire lunar bulk composition anomaly could be explained by plausible reservoirs of distant low-density material.     

High-resolution simulations of the final assembly of Earth-like planets I. Terrestrial accretion and dynamics

The final stage in the formation of terrestrial planets consists of the accumulation of ∼1000-km “planetary embryos” and a swarm of billions of 1-10 km “planetesimals.” During this process, water-rich material is accreted by the terrestrial planets via impacts of water-rich bodies from beyond roughly 2.5 AU. We present results from five high-resolution dynamical simulations. These start from 1000-2000 embryos and planetesimals, roughly 5-10 times more particles than in previous simulations. Each simulation formed 2-4 terrestrial planets with masses between 0.4 and 2.6 Earth masses. The eccentricities of most planets were ∼0.05, lower than in previous simulations, but still higher than for Venus, Earth and Mars. Each planet accreted at least the Earth's current water budget. We demonstrate several new aspects of the accretion process: (1) The feeding zones of terrestrial planets change in time, widening and moving outward. Even in the presence of Jupiter, water-rich material from beyond 2.5 AU is not accreted for several millions of years. (2) Even in the absence of secular resonances, the asteroid belt is cleared of >99% of its original mass by self-scattering of bodies into resonances with Jupiter. (3) If planetary embryos form relatively slowly, then the formation of embryos in the asteroid belt may have been stunted by the presence of Jupiter. (4) Self-interacting planetesimals feel dynamical friction from other small bodies, which has important effects on the eccentricity evolution and outcome of a simulation.     

Simulations of the Dynamics of the Debris Disks in the Systems Kepler-16, Kepler-34, and Kepler-35

We investigate the long-term dynamics of planetesimals in debris disks in models with the parameters of the binary star systems Kepler-16, Kepler-34, and Kepler-35 with planets. Our calculations show that the formation of a stable ring coorbital with the planet is possible for Kepler-16 and Kepler-35. In Kepler-34 significant orbital eccentricities of the binary system and the planet can prevent the formation of such a structure. The detection of circumbinary ring-like structures in observations of binary star systems can be evidence for the existence of planets retaining coorbital rings of dust and planetesimals.     

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

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 10⁸ 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.     

The formation of iron,stone, and mixed planetesimals in the early solar system

The interaction of dust grains with each other in a finite-temperature solar nebula are examined, taking into account the important fact that such grains would carry net steady-state charges like those of grains in interstellar clouds. This charge is given by the well-known Spitzer relation. It provides a screening mechanism that operates during accretion and results in bodies of differing compositions depending on the local temperature in the nebula. In a typical nebula, it is found that planetesimals of 0.1–10²-cm size form in a time of order 10⁶–10⁷ years. These planetesimals are of iron and stone and mixed composition in the inner solar system, but of mixed composition only in the outer solar system. The predictions of this type of charged-dust accretion can be compared to known data on meteorites and the composition of the planets.     

Gaseous drag and planetary formation by accretion

We have made numerical experiments of the collisional and gravitational interaction of a planetesimal swarm in the early Solar System. In particular we study the dynamical evolution of an initial population of kilometer-size planetesimals subject to collisions (accretion, rebound, cratering, and catastrophic fragmentation). This study is based on a Monte-Carlo statistical method and provides the mass and velocity distributions of the planetesimal swarm as a function of time as well as their distribution in heliocentric distance. Several experiments have been performed and three of them are presented here. They simulate the accretional growth of numerous planetesimals in the absence (or presence) of gaseous drag, with (or without) one larger embryo among them, and with (or without) a size gradient. The results show that (i) for a population of planetesimals submitted to a negative gradient in size as the heliocentric distance increases, the outer planetesimals spiral toward the Sun faster than inner ones, leading after some time to an accumulation of bodies inside the cloud which allows the formation of an embryo; (ii) the growth of one embryo among a population of planetesimals is accelerated by the presence of gas and is warranted as long as its feeding zone is fed by the inward flow of planetesimals due to gas drag. These results offer some complementary new insights in the understanding of the accretional formation of 4–5 terrestrial planets instead of the numerous Moon-size planets generally found in numerical experiments.     

Fractionation of noble gases by thermal escape from accreting planetesimals

A model for the selective loss of noble gases by thermal escape of the gases from planetesimals as they grow to form the terrestrial planets has been developed. The initial elemental and isotopic abundance ratios are assumed to be solar. Competition between gravitational binding and escape determines the degree of fractionation that occurs. Two classes of planetesimals can be formed on a time scale consistent with modern models of accretion. One class is depleted in neon and, in some cases, partly in ³⁶Ar. The other class is neon rich. Subject to the validity of some assumptions regarding loss of planetary atmospheres following collisions between very large embryo planets and a strong radial dependence in the rate of accumulation of neon-rich planetesimals, the mechanism can account for all known properties of the noble gas volatiles on the terrestrial planets except one. This is the ³⁶Ar/³⁸Ar ratios for Earth and Mars which are predicted to be much lower than observed. This failure is probably fatal for the hypothesis.     

Late stage of accumulation and chemical composition of the terrestrial planets

The model in which the differences of chemical composition of the terrestrial planets are determined by special conditions at the later stage accumulation is discussed. Impact heating would rapidly lead to differentiation of Mercury's interiors. Subsequent high-velocity collisions of Mercury with planetesimals of a comparable size would erode away much of the silicate crust and mantle; such silicates would be accumulated by Venus and fall into the Sun. This model is in agreement with the current models of the terrestrial planets internal constitution.     

Capture of planetesimals by the giant planets

We investigate the possibility of gravitational capture of planetesimals as temporary or permanent satellites of Uranus and Neptune during the process of planetary growth. The capture mechanism is based in the enhancement of the Hill's sphere of action not only due to the mass acquired by the planet, but also by the variation of the planet-Sun distance as a consequence of the scattering of planetesimals by the planets of the outer solar system. Our calculations indicate that satellite capture was very important, specially during the first stages of the accretion process, contributing in a significant way to the planetary growth.     

Accretion rates of planetesimals by protoplanets embedded in nebular gas

When protoplanets growing by accretion of planetesimals have atmospheres, small planetesimals approaching the protoplanets lose their energy by gas drag from the atmospheres, which leads them to be captured within the Hill sphere of the protoplanets. As a result, growth rates of the protoplanets are enhanced. In order to study the effect of an atmosphere on planetary growth rates, we performed numerical integration of orbits of planetesimals for a wide range of orbital elements and obtained the effective accretion rates of planetesimals onto planets that have atmospheres. Numerical results are obtained as a function of planetesimals’ eccentricity, inclination, planet’s radius, and non-dimensional gas-drag parameters which can be expressed by several physical quantities such as the radius of planetesimals and the mass of the protoplanet. Assuming that the radial distribution of the gas density near the surface can be approximated by a power-law, we performed analytic calculation for the loss of planetesimals’ kinetic energy due to gas drag, and confirmed agreement with numerical results. We confirmed that the above approximation of the power-law density distribution is reasonable for accretion rate of protoplanets with 1-10 Earth masses, unless the size of planetesimals is too small. We also calculated the accretion rates of planetesimals averaged over a Rayleigh distribution of eccentricities and inclinations, and derived a semi-analytical formula of accretion rates, which reproduces the numerical results very well. Using the obtained expression of the accretion rate, we examined the growth of protoplanets in nebular gas. We found that the effect of atmospheric gas drag can enhance the growth rate significantly, depending on the size of planetesimals.     

Resonance capture and the evolution of the planets

The present nearly resonant orbital periods of the planets are explained in terms of past two-body resonance capture of planetesimals in the solar nebula. Planetary formation then occurs sequentially starting with Jupiter for the outer planets and Venus for the inner planets and propagates outward due to two-body orbital resonances. It might now be possible to reconstruct the evolutionary history of the planets from their nearly commensurable orbital periods and, hence, provide an explanation for the Titius-Bode law.     

Metallicity, debris discs and planets

We investigate the populations of main-sequence stars within 25 pc that have debris discs and/or giant planets detected by Doppler shift. The metallicity distribution of the debris sample is a very close match to that of stars in general, but differs with >99 per cent confidence from the giant planet sample, which favours stars of above average metallicity. This result is not due to differences in age of the two samples. The formation of debris-generating planetesimals at tens of au thus appears independent of the metal fraction of the primordial disc, in contrast to the growth and migration history of giant planets within a few au. The data generally fit a core accumulation model, with outer planetesimals forming eventually even from a disc low in solids, while inner planets require fast core growth for gas to still be present to make an atmosphere.     

Envelope instability in giant planet formation

We compute the growth of isolated gaseous giant planets for several values of the density of the protoplanetary disk, several distances from the central star and two values for the (fixed) radii of accreted planetesimals. Calculations were performed in the frame of the core instability mechanism and the solids accretion rate adopted is that corresponding to the oligarchic growth regime. We find that for massive disks and/or for protoplanets far from the star and/or for large planetesimals, the planetary growth occurs smoothly. However, notably, there are some cases for which we find an envelope instability in which the planet exchanges gas with the surrounding protoplanetary nebula. The timescale of this instability shows that it is associated with the process of planetesimals accretion. The presence of this instability makes it more difficult the formation of gaseous giant planets.     

The origin of the Kuiper Belt high-inclination population

I simulate the orbital evolution of the four major planets and a massive primordial planetesimal disk composed of 10⁴ objects, which perturb the planets but not themselves. As Neptune migrates by energy and angular momentum exchange with the planetesimals, a large number of primordial Neptune-scattered objects are formed. These objects may experience secular, Kozai, and mean motion resonances that induce temporary decrease of their eccentricities. Because planets are migrating, some planetesimals can escape those resonances while in a low-eccentricity incursion, thus avoiding the return path to Neptune close encounter dynamics. In the end, this mechanism produces stable orbits with high inclination and moderate eccentricities. The population so formed together with the objects coming from the classical resonance sweeping process, originates a bimodal distribution for the Kuiper Belt orbits. The inclinations obtained by the simulations can attain values above 30° and their distribution resembles a debiased distribution for the high-inclination population coming from the real classical Kuiper Belt.     

Review of the population of impactors and the impact cratering rate in the inner solar system

Abstract— All terrestrial planets, the Moon, and small bodies of the inner solar system are subjected to impacts on their surface. The best witness of these events is the lunar surface, which kept the memory of the impacts that it underwent during the last 3.8 Gyr. In this paper, we review the recent studies at the origin of a reliable model of the impactor population in the inner solar system, namely the near‐Earth object (NEO) population. Then we briefly expose the scaling laws used to relate a crater diameter to body size. The model of the NEO population and its impact frequency on terrestrial planets is consistent with the crater distribution on the lunar surface when appropriate scaling laws are used. Concerning the early phases of our solar system's history, a scenario has recently been proposed that explains the origin of the Late Heavy Bombardment (LHB) and some other properties of our solar system. In this scenario, the four giant planets had initially circular orbits, were much closer to each other, and were surrounded by a massive disk of planetesimals. Dynamical interactions with this disk destabilized the planetary system after 500–600 Myr. Consequently, a large portion of the planetesimal disk, as well as 95% of the Main Belt asteroids, were sent into the inner solar system, causing the LHB while the planets reached their current orbits. Our knowledge of solar system evolution has thus improved in the last decade despite our still‐poor understanding of the complex cratering process.