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All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Shock vaporization and the accretion of the icy satellites of Jupiter and Saturn

The role of impact vaporization acting during the formation of the Jovian and Saturnian satellites is examined in an attempt to explain the observed density in terms of composition of these rock and ice objects. A hypothesis is examined which states that the smaller satellites of Saturn having mean densities in the 1.1 to 1.4 Mg/cu m range represent primordial accreted planetesimal condensates formed in the proto-Jovian and Saturnian accretionary planetary discs. These densities are in the range expected for water-ice/silicate mixtures constrained in the solar values of O/Si and O/Mg atomic ratios. It is demonstrated that if the large satellites accreted from the same group of planetesimals which formed the small Saturnian satellites impact vaporization of water upon accretion in a porous regolith, at low H2O partial pressure, can account for the increase in mean planetesimal density from 1.6 Mg/cu m (43% H2O + 57% silicate) to a mean planetary density of 1.9 Mg/cu m for Ganymedean-sized water silicate objects. If impact volatilization of initially porous planetesimals is assumed, it can be demonstrated starting with planetesimals composed of 54% H2O and 40% silicate partial devolatilization upon accretion will yield a Ganymede-sized planet, having a radius of 2600 km and a density of 1.85 kg/cu m, similar to that of Ganymede, Callisto, and Titan.

Ahrens, T. J.↗
NASA NTRS1991

Accretion rates of protoplanets 2: Gaussian distribution of planestesimal velocities

The growth rate of a protoplanet embedded in a uniform surface density disk of planetesimals having a triaxial Gaussian velocity distribution was calculated. The longitudes of the aspses and nodes of the planetesimals are uniformly distributed, and the protoplanet is on a circular orbit. The accretion rate in the two body approximation is enhanced by a factor of approximately 3, compared to the case where all planetesimals have eccentricity and inclination equal to the root mean square (RMS) values of those variables in the Gaussian distribution disk. Numerical three body integrations show comparable enhancements, except when the RMS initial planetesimal eccentricities are extremely small. This enhancement in accretion rate should be incorporated by all models, analytical or numerical, which assume a single random velocity for all planetesimals, in lieu of a Gaussian distribution.

Greenzweig, Yuval↗
NASA NTRS1993

Planetary accretion in circumstellar disks

The formation of terrestrial planets and the cores of Jovian planets is reviewed in the framework of the planetesimal hypothesis, wherein planets are assumed to grow via the pairwise accumulation of small solid bodies. Emphasis is placed on the dynamics of solid body accretion from kilometer size planetesimals to terrestrial type planets. This stage of planetary growth is least dependent on the characteristics of the evolutionary state of the central star. It is concluded that the evolution of the planetesimal size distribution is determined by the gravitationally enhanced collision cross-section, which favors collisions between planetesimals with smaller velocities. Runaway growth of the largest planetesimal in each accretion zone appears to be a likely outcome. The subsequent accumulation of the resulting protoplanets leads to a large degree of radial mixing in the terrestrial planet region, and giant impacts are probable.

Lissauer, Jack J.↗
NASA NTRS1993

Heliocentric zoning of the asteroid belt by aluminum-26 heating

Variations in petrology among meteorites attest to a strong heating event early in solar system history, but the heat source has remained unresolved. Aluminum-26 has been considered the most likely high-energy, short-lived radionuclide (half-life 0.72 million years) since the discovery of its decay product - excess Mg-26 - in Allende CAI's. Furthermore, observation of relict Mg-26 in an achondritic clast and in feldspars within ordinary chondrites (3,4) provided strong evidence for live Al-26 in meteorite parent bodies and not just in refractory nebular condensates. The inferred amount of Al-26 is consistent with constraints on the thermal evolution of both ordinary and carbonaceous chondrite parent objects up to a few hundred kilometers in diameter. Meteorites can constrain the early thermal evolution of their parent body locations, provided that a link can be established between asteroid spectrophotometric signature and meteorite class. Asteroid compositions are heliocentrically distributed: objects thought to have experienced high metamorphic or even melting temperatures are located closer to the sun, whereas apparently unaltered or mildly heated asteroids are located farther away. Heliocentric zoning could be the result of Al-26 heating if the initial amount of the radionuclide incorporated into planetesimals was controlled by accretion time, which in turn varies with semimajor axis. Analytic expressions for planetary accretion may be integrated to given the time, tau, required for a planetesimal to grow to a specified radius: tau varies as a(sup n), where n = 1.5 to 3 depending on the assumptions about variations in the surface density of the planetesimal swarm. Numerical simulations of planetesimal accretion at fixed semimajor axis demonstrate that variations in accretion time among small planetesimals can be strongly nonlinear depending on the initial conditions and model assumptions. The general relationship with semimajor axis remains valid because it depends only on the initial orbit properties and distribution of the planesimal swarm. In order to demonstrate the basic dependence of thermal evolution on semimajor axis, we parameterized accretion time across the asteroid belt according to tau varies as a(sup n) and calculated the subsequent thermal history. Objects at a specified semimajor axis were assumed to have the same accretion time, regardless of size. We set the initial Al-26/Al-27 ratio = 6 x 10(exp -5) and treated n and tau(sub 0) at a(sub 0) = 3 AU as adjustable parameters. The thermal model included temperature-dependent properties of ice and rock (CM chondrite analog) and the thermodynamic effects of phase transitions.

Grimm, R. E.↗
NASA NTRS2000

Production of Star-Grazing and Star-Impacting Planetestimals via Orbital Migration of Extrasolar Planets

During the orbital migration of a giant extrasolar planet via ejection of planetesimals (as studied by Murray et al. in 1998), inner mean-motion resonances can be strong enough to cause planetesimals to graze or impact the star. We integrate numerically the motions of particles which pass through the 3:1 or 4:1 mean-motion resonances of a migrating Jupiter-mass planet. We find that many particles can be trapped in the 3:1 or 4:1 resonances and pumped to high enough eccentricities that they impact the star. This implies that for a planet migrating a substantial fraction of its semimajor axis, a fraction of its mass in planetesimals could impact the star. This process may be capable of enriching the metallicity of the star at a time when the star is no longer fully convective. Upon close approaches to the star, the surfaces of these planetesimals will be sublimated. Orbital migration should cause continuing production of evaporating bodies, suggesting that this process should be detectable with searches for transient absorption lines in young stars. The remainder of the particles will not impact the star but can be ejected subsequently by the planet as it migrates further inward. This allows the planet to migrate a substantial fraction of its initial semimajor axis by ejecting planetesimals.

Quillen, A. C.↗
NASA NTRS1977

Why is a minor planet minor

A hypothesis based on the accretion model of planet formation is proposed which can explain why minor planets could not grow into full-sized planets. Temperature and impact-velocity conditions for bouncing, accumulation, and fragmentation of planetesimals are evaluated for silicate and iron planetesimals at the heliocentric distances of Mercury, Venus, earth, Mars, and the asteroid belt. The results indicate that the low-temperature environment of the asteroids very likely hampered their growth into ironlike planetesimals, which in turn inhibited the accumulation of silicate planetesimals. It is concluded that the brittleness of iron at temperatures below 200 to 250 K is the primary reason why minor planets are 'minor' and could not grow to full size.

Matsui, T.↗
NASA NTRS1985

Orbital resonances in the solar nebula - Implications for planetary accretion

The influence of gas drag and gravitational perturbations by a planetary embryo on the orbit of a planetesimal in the solar nebula was examined. Non-Keplerian rotation of the gas causes secular decay of the orbit. If the planetesimal's orbit is exterior to the perturber's, resonant perturbations oppose this drag and can cause it to be trapped in a stable orbit at a commensurability of order j/(j + 1), where j is an integer. Numerical and analytical demonstrations show that resonant trapping occurs for wide ranges of perturbing mass, planetesimal size, and j. Induced eccentricities are large, causing overlap of orbits for bodies in different resonances with j greater than 2. Collisions between planetesimals in different resonances, or between resonant and nonresonant bodies, result in their disruption. Fragments smaller than a critical size can pass through resonances under the influence of drag and be accreted by the embryo. This effect speeds accretion and tends to prevent dynamical isolation of planetary embryos, making gas-rich scenarios for planetary formation more plausible.

Weidenschilling, S. J.↗
NASA NTRS1987

Accumulation of the planets

In modeling the accumulation of planetesimals into planets, it is appropriate to distinguish between two stages: an early stage, during which approximately 10 km diameter planetesimals accumulate locally to form bodies approximate 10 to the 25th g in mass; and a later stage in which the approximately 10 to the 25th g planetesimals accumulate into the final planets. In the terrestrial planet region, an initial planetesimal swarm corresponding to the critical mass of dust layer gravitational instabilities is considered. In order to better understand the accumulation history of Mercury-sized bodies, 19 Monte-Carlo simulations of terrestrial planet growth were calculated. A Monte Carlo technique was used to investigate the orbital evolution of asteroidal collision debris produced interior to 2.6 AU. It was found that there are two regions primarily responsible for production of Earth-crossing meteoritic material and Apollo objects. The same techniques were extended to include the origin of Earth-approaching asteroidal bodies. It is found that these same two resonant mechanisms predict a steady-state number of Apollo-Amor about 1/2 that estimated based on astronomical observations.

Wetherill, G. W.↗
NASA NTRS1991

Accretion and evolution of solar system bodies

We use a combination of analytical and numerical methods to study dynamical processes involved in the formation of planets and smaller bodies in the solar system. Our goal was to identify and understand critical processes and to link them in a numerical model of planetesimal accretion. We study effects of these processes by applying them in the context of the standard model of solar system formation, which involves accretion of the terrestrial planets and cores of the giant planet from small planetesimals. The principal focus of our research effort is the numerical simulation of accretion of a swarm of planetesimals into bodies of planetary size. Our computer code uses a Monte Carlo method to determine collisional interactions within the swarm. These interactions are not determined simply by a relative velocity, but rather by explicit distributions of keplerian orbital elements. The planetesimal swarm is divided into a number of zones in semimajor axis, which are allowed to interact. The present version of our code has the capability of following detailed distributions of size, eccentricity, and inclination in each zone.

Weidenschilling, S. J.↗
NASA NTRS1992

Tidal disruption of viscous bodies

Tidal disruptions are investigated in viscous-fluid planetesimals whose radius is small relative to the distance of closest (parabolic-orbit) approach to a planet. The planetesimal surface is in these conditions always ellipsoidal, facilitating treatment by coupled ODEs which are solvable with high accuracy. While the disrupted planetesimals evolve into needlelike ellipsoids, their density does not decrease. The validity of viscous fluid treatment holds for solid (ice or rock) planetesimals in cases where tidal stresses are greater than material strength, but integrity is maintained by self-gravity.

Sridhar, S.↗
NASA NTRS1991

What heated the parent meteorite planets?

The plausibility of the two most wide discussed mechanisms, decay of short-lived Al-26 and solar wind induction heating, for heating the small planetesimals in which the meteorites formed are examined and shown to have significant problems. The main problem for the Al-26 decay mechanism is the fact that eucritic lavas, melted by the mysterious heating mechanism in some early planetesimal, did not contain enough Al-26 to decay to radiogenic Mg-26 when they erupted to their planetesimal surface and cooled. It is necessary to postulate that the lavas lingered underground while their Al-26 decayed away. The solar wind induction heat concept has the problem that astrophysical evidence has made is seem increasingly unlikely that an intense solar wind flux blew past planetesimals in the early solar system. Instead, it was probably collimated in the direction of the sun's poles by the persistence of the solar nebula during the T Tauri epoch.

Wood, John A.↗
NASA NTRS1992

On the origin of the prograde rotation of the planets

A series of analytic and numerical calculations of the systematic component of angular momentum accretion is described. Wide ranges of planetesimal eccentricities and planetary radii are considered. Numerical simulations using a Rayleigh distribution of eH values show that very little prograde rotation is produced in a disk with a realistically broad range of planetesimal eccentricities. It is hypothesized that the observed spin rates may result from nonuniformities in the disk of planetesimals, specifically, a partial gap in planetesimal semimajor axes around that of the planet. This would yield an overabundance of impactors from the edges of the planet's accretion zone. Bodies from this region produce strongly prograde rotation at most values of eH.

Kary, D. M.↗
NASA NTRS1993

On the origin of planetary spins

We examine the rate of accretion of mass and spin angular momentum by a spherical solid body ('planet') immersed in a differentially rotating disk of particles ('planetesimals'). If the planet travels on a circular orbit, the accretion process is described by two dimensionless parameters r and s, which measure the ratio of the planet's radius to its Hill radius and the ratio of the rms radial velocity of the planetesimals to the shear across the Hill radius, respectively. Using a combination of analytic arguments and numerical simulations, we derive the mass and angular momentum accretion rates and their scaling with r and s. By introducing an additional parameter, the effective mass of the planetesimals relative to the planet, we can derive the obliquities and spins arising from the stochastic nature of the accretion process. Our results are consistent with those of previous calculations by Lissauer and Kary (1991) wherever there is overlap in parameter space. In particular, we conclude that ordered accretion from a uniform or slowly varying disk of small bodies cannot result in rotation as rapid as that of earth or Mars for any value of the disk velocity dispersion s. The spin rates of these planets are most naturally explained as arising from one or a few 'giant' impacts by planetesimals.

Dones, Luke↗
NASA NTRS1993

I-Xe structure of ILAFEGH 009 and shallowater: Evidence for early formation and rapid cooling of impact-derived enstatite meteorites

Enstatite meteorites have proven to be ideal samples for past studies of the I-Xe system. This work focuses on two enstatite meteorites that were formed by impact processes. Ilafegh 009 is a clast-free impact melt rock from the EL chondrite parent body. The Shallowater aubrite likely formed when a fully molten planetesimal collided with a solid planetesimal, mixing fragments of the solid planetesimal into the enstatite mantle of the molten planetesimal. A complex three-stage cooling history resulted from this mixing and later break-up and reassembly of the parent body. The present study indicates that the I-Xe structure of these two meteorites resulted from in situ decay of live I-129 and that both experienced xenon closure of the iodine host phase at approximately the same time. I-Xe cooling rates are consistent with the cooling rates derived from mineralogic and petrologic studies of these objects. The similarities in ages suggest that the region of the nebula in which enstatite parent bodies formed must have experienced an intense early bombardment.

Kehm, K.↗
NASA NTRS1993

Particle-Gas Dynamics in the Midplane of a Protoplanetary Nebula

In this paper, we study the stage of planetary formation during which the particulate material is still dispersed as centimeter-to-meter sized primordial aggregates. During this stage, particles are able to settle toward the midplane into a layer of mass density comparable to or much greater than that of the gas. Nonlinear, coupled interactions between the particles and the nebula gas become significant and ultimately determine the vertical profiles of the particle density and the mean velocities of the particles and the nearby gas. This is the environment in which the earliest planetesimals probably form. Our numerical models rely on the Reynolds averaged Navier-Stokes equations for the gas and particles and are fully viscous and turbulent (and, for the particles. compressible). Our turbulence modeling uses a Prandtl local shear parametrization, validated by laboratory experiments. We have developed a new model for particle diffusion involving the profile of the nebula gas turbulence and the particle Schmidt number, which is a function of particle size and density. We model a cool, quiescent nebula at 1 AU (280 K) and 10 AU (90 K) and a higher temperature stage (1000 K) at 1 AU. Our main results include: (a) rapid accretion of planetesimals by gravitationally unstable fragmentation on an orbital time scale (the 'Goldreich-Ward instability') is unlikely to occur until objects have already accreted by some other process to the mass of the largest known meteorite samples, if at all; (b) from 'seeds' as small as 10 m, growth of 10- to 100-km planetesimals can proceed rapidly by drift-augmented accretion in the particle-rich midplane with orbital decay of about 1% for the growing planetesimals; (c) outward transport of vapor and small entrained chips can account for significant radial compositional and mineralogical mixing in primitive meteorite parent bodies. Other implications may be drawn concerning particle random collisional velocities and the time scales of midplane turbulence.

Cuzzi, Jeffrey N.↗
NASA NTRS1998

Sources of Terrestrial Volatiles

Atmospheres are found enveloping those planets and satellites best able to hold them. The obvious conclusion is that volatile escape must have played nearly as great a role as volatile supply. A consequence of this view is that volatile supplies were probably much greater than the atmospheres that remain. The likeliest candidates are sources associated with the main events of planetary accretion itself such as volatile-rich planetesimals, or direct gravitational capture of nebular gases. Late asteroidal or cometary volatile-rich veneers are attractive, but they present quantitative difficulties. Comets in particular are inadequate, because the associated mass of stray comets that would have been scattered to the Oort Cloud or beyond is excessive. This difficulty applies to Uranus-Neptune planetesimals as well as to a putative massive early Kuiper Belt. Another potential problem with comets is that the D/H ratio in the three comets for which this has been measured is about twice that of Earth's oceans. Objects falling from a much augmented ancient asteroid belt remain a viable option, but timing is an issue: Can the depopulation of the asteroid belt be delayed long enough that it makes sense to talk of asteroids as a late veneer? Early accretion of asteroids as objects scattered into the maw of infant Earth makes more sense. Another appealing candidate population of volatile-rich objects for the inner solar system would be scattered planetesimals associated with the accretion of Jupiter, for two reasons: (1) Before there was Jupiter, there was no object in the solar system capable of expelling comets efficiently, and (2) the cross section of the inner solar system to stray objects was Greater when there were m many planetesimals.

Zahnle, K. J.↗
NASA NTRS1998

Modelling the Diversity of Outer Planetary Systems: Formation and Evolution - 1

The process of planetary growth is extremely complicated, involving a myriad of physical and chemical processes, many of which are poorly understood. The ultimate configuration that a planetary system attains depends upon the properties of the disk out of which it grew, of the star at the center of the disk and, at least in some cases, of the interstellar environment. However, this dependence is poorly understood. Thus, in an effort to numerically survey the possible diversity of planetary systems, we have constructed synthetic systems of giant planets and integrated their orbits to determine the dynamical lifetimes and thus the viability of these systems. Our construction algorithm begins with 110 -- 180 planetesimals located between 4 and 40 AU from a one solar mass star; most initial planetesimals have masses several tenths that of Earth. We integrate the orbits of these bodies subject to mutual gravitational perturbations and gas drag for $10^6 - 10^7$ years, merging any pair of planetesimals which passed within one-tenth of a Hill Sphere of one another and adding "gas" to embryos larger than 10 Earth masses. Use of such large planetesimal radii provided sufficient damping to prevent the system from excessive dynamical heating. Subsequently, systems were evolved without gas drag, either with the inflated radii or with more realistic radii. Systems took from a few million years to greater than ten billion years to become stable ($10^9$ years without mergers of ejections). Some of the systems produced with the inflated radii closely resemble our Solar System. Encounters in simulations using realistic radii resulted in ejections, typically leaving only a few planets per system, most of which were in highly eccentric orbits. The structure and dynamics of the resulting "stable" systems is discussed in detail in the abstract by Levison et al.

Lissauer, J. J.↗
NASA NTRS2002

Migration of Matter from the Edgeworth-Kuiper and Main Asteroid Belts to the Earth

The main asteroid belt (MAB), the Edgeworth-Kuiper belt (EKB), and comets belong to the main sources of dust in the Solar System. Most of Jupiter-family comets came from the EKB. Comets can be distracted due to close encounters with planets and the Sun, collisions with small bodies, a nd internal forces. We support the Eneev's idea that the largest objects in the ELB and MAB could be formed directly by the compression of rarefied dust condensations of the protoplanetary cloud but not by the accretion of small (for example, 1-km) planetesimals. The total mass of planetesimals that entered the EKB from the feeding zone of the giant planets during their accumulation could exceed tens of Earth's masses. These planetesimals increased eccentricities of 'local' trans-Neptunian objects (TNOs) and swept most of these TNOs. A small portion of such planetesimals could left beyond Neptune's orbit in highly eccentric orbits. The results of previous investigations of migration and collisional evolution of minor bodies were summarized. Mainly our recent results are presented.

Ipatov. S. I.↗