An Analytical Theory for the Growth from Planetesimals to Planets by Polydisperse Pebble Accretion
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Wladimir Lyra↗
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Outgassing Composition of the Murchison Meteorite: Implications for Volatile Depletion of Planetesimals and Interior-atmosphere Connections for Terrestrial Exoplanets
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Maggie A. Thompson↗
RW Aur A: SpeX Spectral Evidence for Differentiated Planetesimal Formation, Migration, and Destruction in an ∼3 Myr Old Excited CTTS System
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C. M. Lisse↗
Detailed Calculations of the Efficiency of Planetesimal Accretion in the Core-accretion Model
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Morris Podolak↗
Detailed Calculations of the Efficiency of Planetesimal Accretion in the Core-accretion Model. II. The Effect of Saturn
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Nader Haghighipour↗
Formation Of the Giant Planets By Concurrent Accretion Of Solids And Gas
New numerical simulations of the formation of the giant planets are presented, in which for the first time both the gas and planetesimal accretion rates are calculated in a self-consistent, interactive fashion. The simulations combine three elements: 1) three-body accretion cross-sections of solids onto an isolated planetary embryo, 2) a stellar evolution code for the planet's gaseous envelope, and 3) a planetesimal dissolution code within the envelope, used to evaluate the planet's effective capture radius and the energy deposition profile of accreted material. Major assumptions include: The planet is embedded in a disk of gas and small planetesimals with locally uniform initial surface mass density, and planetesimals are not allowed to migrate into or out of the planet's feeding zone. All simulations are characterized by three major phases. During the first phase, the planet's mass consists primarily of solid material. The planetesimal accretion rate, which dominates that of gas, rapidly increases owing to runaway accretion, then decreases as the planet's feeding zone is depleted. During the second phase, both solid and gas accretion rates are small and nearly independent of time. The third phase, marked by runaway gas accretion, starts when the solid and gas masses are about equal. It is engendered by a strong positive feedback on the gas accretion rates, driven by the rapid contraction of the gaseous envelope and the rapid expansion of the outer boundary, which depends on the planet's total mass. The overall evolutionary time scale is generally determined by the length of the second phase. The actual rates at which the giant planets accreted small planetesimals is probably intermediate between the constant rates assumed in most previous studies and the highly variable rates that we have used. Within the context, of the adopted model of planetesimal accretion, the joint constraints of the time scale for dissipation of the solar nebula and the current high-Z masses of the giant planets lead to estimates of the initial surface density (sigma(sub init)) of planetesimals in the outer region of the solar nebula. The results show sigma(sub init) approx. = 10 g/sq cm near Jupiter's orbit and that sigma(sub init) proportional to alpha(sup -2), where alpha is the distance from the Sun. These values are a factor of 3 - 4 times as high as that of the "minimum mass" solar nebula at Jupiter's distance and a factor of 2 - 3 times as high it Saturn's distance. Our estimates for the formation time of Jupiter and Saturn are 1 - 10 million years while those for Uranus fall in the range of 2 - 16 million years. These estimates follow from the properties of our Solar System and do not necessarily apply to giant planets in other planetary systems.
Pollack, James B.↗
Orbital Resonances in the Solar Nebula: Strengths and Weaknesses
A planetesimal moving in the Solar Nebula experiences an aerodynamic drag which causes its orbit to circularize and shrink. However, resonant perturbations from a protoplanet interior to the planetesimal's orbit can counteract both the orbital decay and the damping of the eccentricity: the planetesimal can be captured into an orbital resonance and its eccentricity pumped up to a modestly high equilibrium value. Thus, orbital resonances constitute (partial) barriers to the delivery of planetesimals into the feeding zone of the protoplanet. We have established the characteristics of the phenomenon of resonance capture by gas drag in the circular restricted three-body approximation. We have determined the strengths of the equilibrium resonant orbits with respect to impulsive velocity perturbations. We conclude that planetesimals captured in orbital resonances are quite vulnerable to being dislocated from these orbits by mutual planetesimal interactions, but that the resonances are effective in slowing down the rate of orbital decay of planetesimals. Only very small bodies, less than or equal to 100 m, are able to reach a approx. 1 Earth mass protoplanet without being slowed down by resonances.
Malhotra, Renu↗
Orbital Resonances in the Solar Nebula: Strengths and Weaknesses
A planetesimal moving in the Solar Nebula experiences an aero- dynamic drag which causes its orbit to circularize and shrink. However, resonant perturbations from a protoplanet interior to the planetesimal's orbit ran counteract both the orbital decay and the damping of the eccentricity: the planetesimal can be captured into an orbital resonance and its eccentricity pumped up to a modestly high equilibrium value. Thus, orbital resonances constitute (partial) barriers to the delivery of planetesimals into the feeding zone of the protoplanet. We have established the characteristics of the phenomenon of resonance capture by gas drag in the circular restricted three-body approximation. We have determined the strengths of the equilibrium resonant orbits with respect to impulsive velocity perturbations. We conclude that planetesimals captured in orbital resonances are quite vulnerable to being dislocated from these orbits by mutual planetesimal interactions, but that the resonances are effective in slowing down the rate of orbital decay of planetesimals. Only very small bodies, less or approx. equal to 100 m, are able to reach a approx. 1 mass of the earth protoplanet without being slowed down by resonances.
Malhotra, Renu↗
Formation and Migration of Trans-Neptunian Objects
We consider that trans-Neptunian objects (TNOs) with diameter d greater than 100 kilometers moving now in not very eccentric orbits could be formed directly by the compression of large rarefied dust condensations (with a greater than 30 AU), but not by the accretion of smaller solid planetesimals. Probably, some planetesimals with d approximately 100- 1000 kilometers in the feeding zone of the giant planets and even large main-belt asteroids also could be formed directly by such compression. Some smaller objects (TNOs, planetesimals, asteroids) could be debris of larger objects, and other such objects could be formed directly by compression of condensations. A small portion of planetesimals from the feeding zone of the giant planets that entered into the trans-Neptunian region could left in eccentrical orbits beyond Neptune and became so called "scattered objects". Our computer runs in which gravitational interactions of bodies were taken into account with the use of the spheres method, showed that the embryos of Uranus and Neptune could increase their semimajor axes from less than 10 AU to their present values, moving permanently in orbits with small eccentricities, due to gravitational interactions with the migrating planetesimals. Later on, Thommes et al. considered a similar model using direct numerical integration. The total amount of water delivered to the Earth during the formation of the giant, planets was about the mass of water in the Earth oceans. The end of such bombardment could be caused mainly by the planetesimals that became scattered objects. For the present mass of the trans-Neptunian belt, the collisional lifetime of 1-kilometer TNO is about the age of the Solar system, but only a small portion (less than 1%) of 100-km TNOs could be destroyed during this age. The probability of destruction of a typical TNO (with 30 less than a,less than 50 AU) by scattered objects can be of the same order of magnitude as that by typical TNOs. TNOs could be even more often destroyed during planet formation than during last 4 Gyr. The analysis of the results of the orbital evolution of Jupiter-crossing objects (JCOs) and TNOs showed that, in principle, the trans-Neptunian belt can provide up to 100% of Earth-crossing objects, but, of course, some of them came from the main asteroid belt. Most of the collisions of former JCOs with the Earth were from orbits with aphelia inside Jupiter's orbit and belonged to a small portion of objects which moved in such orbits for a long time. About 1 of 300 JCOs collided with the Sun. The ratio of the total mass of icy planetesimals that migrated from the feeding zone of the giant planets and collided with the planet to the mass of this planet was greater (by a factor of 3 in our runs) for Mars than that for Earth and Venus.
Ipatov, S. I.↗
Why Isn't the Earth Completely Covered in Water?
If protoplanets formed from 10 to 20 kilometer diameter planetesimals in a runaway accretion process prior to their oligarchic growth into the terrestrial planets, it is only logical to ask where these planetesimals may have formed in order to assess the initial composition of the Earth. We have used Weidenschilling's model for the formation of comets (1997) to calculate an efficiency factor for the formation of planetesimals from the solar nebula, then used this factor to calculate the feeding zones that contribute to material contained within 10, 15 and 20 kilometer diameter planetesimals at 1 A.U. as a function of nebular mass. We find that for all reasonable nebular masses, these planetesimals contain a minimum of 3% water as ice by mass. The fraction of ice increases as the planetesimals increase in size and as the nebular mass decreases, since both factors increase the feeding zones from which solids in the final planetesimals are drawn. Is there really a problem with the current accretion scenario that makes the Earth too dry, or is it possible that the nascent Earth lost significant quantities of water in the final stages of accretion?
Nuth, Joseph A., III↗
Analysis of Antarctic Ice-Sheet Mass Balance from ICESat Measurements
If protoplanets formed from 10 to 20 kilometer diameter planetesimals in a runaway accretion process prior to their oligarchic growth into the terrestrial planets, it is only logical to ask where these planetesimals may have formed in order to assess the initial composition of the Earth. We have used Weidenschilling's model for the formation of comets (1997) to calculate an efficiency factor for the formation of planetesimals from the solar nebula, then used this factor to calculate the feeding zones that contribute to material contained within 10, 15 and 20 kilometer diameter planetesimals at 1 A.V. as a function of nebular mass. We find that for all reasonable nebular masses, these planetesimals contain a minimum of 3% water as ice by mass. The fraction of ice increases as the planetesimals increase in size and as the nebular mass decreases, since both factors increase the feeding zones from which solids in the final planetesimals are drawn. Is there really a problem with the current accretion scenario that makes the Earth too dry, or is it possible that the nascent Earth lost significant quantities of water in the final stages of accretion?
Zwally, H. Jay↗
Accretion rates of protoplanets
The rate at which planetesimals in a uniform surface density disk collide with, and are (assumed to be) accreted by, a massive protoplanet is calculated. The collision cross-section of a protoplanet is enhanced relative to its geometric cross-section due to its gravitational focusing of planetesimal trajectories. The gravitation enhancement (eccentricities and inclinations) decrease. For large random velocity planetesimals, encounters are sufficiently rapid (less than or approximately = 5 percent of and orbital period) that F(sub g) is well approximated by the two-body particle in a box formula, which neglects the gravitational effect of the Sun. As planetesimal velocities decrease, F(sub g) increases to approximately twice the two-body value, and then rises less rapidly than the two-body value, eventually dropping below it and asymptotically approaching a constant for sufficiently small random velocities. A scaling argument is presented that generalizes the results to protoplanets of arbitrary mass, radius, and orbital semimajor axis. Gravitational scatterings by a protoplanet prevent random velocities of the planetesimals within its accretion zone from becoming to small. When gravitational stirring is included, the maximum plausible value of the gravitation enhancement factor for rock protoplanets 1 Au from the Sun is F(sub g) of approximately 1000. If one protoplanet dominates gravitational scatterings in a given region of a protoplanetary disk, then it was found that the planetesimal inclinations are excited much less rapidly than eccentricities, in contrast to the two-body approximation, in which energy is roughly equipartitioned between eccentric and inclined random motions. The resulting skewed velocity dispersion allows for a more rapid rate of protoplanet growth.
Greenzweig, Yuval↗
Did Earth Eat Its Leftovers? Impact Ejecta as a Component of the Late Veneer
The presence of highly siderophile elements in Earth's mantle indicates that a small percentage of Earth's mass was delivered after the last giant impact in a stage of "late accretion." There is ongoing debate about the nature of late-accreted material and the sizes of late-accreted bodies. Earth appears isotopically most similar to enstatite chondrites and achondrites. It has been suggested that late accretion must have been dominated by enstatite-like bodies that originated in the inner disk, rather than ordinary or carbonaceous chondrites. Here we examine the provenances of "leftover" planetesimals present in the inner disk in the late stages of accretion simulations. Dynamically excited planet formation produces planets and embryos with similar provenances, suggesting that the Moon-forming impactor may have had a stable isotope composition very similar to the proto-Earth. Commonly, some planetesimal-sized bodies with similar provenances to the Earth-like planets are left at the end of the main stage of growth. The most chemically similar planetesimals are typically fragments of protoplanets ejected millions of years earlier. If these similar-provenance bodies are later accreted by the planet, they will represent late-accreted mass that naturally matches Earth's composition. The planetesimal-sized bodies that exist during the giant impact phase can have large core mass fractions, with core provenances similar to the proto-Earth. These bodies are an important potential source for highly siderophile elements. The range of core fractions in leftover planetesimals complicates simple inferences as to the mass and origin of late accretion based on the highly siderophile elements in the mantle.
79 ASTRONOMY AND ASTROPHYSICS↗
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.↗
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↗
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.↗
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.↗
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.↗