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The physics of planetesimal formation

Physical processes involved in the planetesimal formation are discussed with special attention given to the nature of aerodynamic interactions between solid bodies and gas in the solar nebula. It is emphasized that the model of planetesimal formation by gravitational instability of a dust layer yields predictions that are simple but almost certainly wrong. It is suggested instead that the formation of planetesimals began with the process of coagulation of grains into larger aggregates, and that gravitational forces became more important than gas drag only after objects as large as many meters in diameter had formed.

Weidenschilling, Stuart J.↗

Formation of the terrestrial planets from planetesimals

Formation of the terrestrial planets from planetesimals is discussed. The following subject areas are covered: (1) formation of the original planetesimals; (2) growth of planetesimals into planetary embryos; and (3) growth of runaway planetary embryos into terrestrial planets.

Wetherill, George W.↗

Xenon fractionation in porous planetesimals

The distinctively fractionated Xe on Mars and earth may have its root in a common source from which both planets accreted. Beginning with Ozima and Nakazawa's (1980) hypothesis that terrestrial Xe fractionation was caused by gravitational separation of adsorbed solar nebular gases inside large porous planetesimals, it is pointed out that Xe would have been trapped as the planetesimal grew and pores were squeezed shut by lithostatic pressure. It is shown that enough fractionated Xe to supply the earth could have been trapped this way. The degree of fractionation is controlled by the lithostatic pressure at the pore-closing front and so would have been roughly the same for all large planetesimals. The predicted degree of fractionation agrees well with that preserved in terrestrial and Martian Xe. Relative to Xe, this source is strongly depleted in other noble gases. In contrast to the original Ozima and Nakazawa hypothesis, the present hypothesis predicts the observed fractionation, and it allows planetary accretion to occur after the dissipation of the solar nebula.

Zahnle, Kevin↗

Accretional evolution of a planetesimal swarm. I - A new simulation

This novel simulation of planetary accretion simultaneously treats many interacting heliocentric distance zones and characterizes planetesimals via Keplerian elements. The numerical code employed, in addition to following the size distribution and the orbit-element distribution of a planetesimal swarm from arbitrary size and orbit distributions, treats a small number of the largest bodies as discrete objects with individual orbits. The accretion algorithm used yields good agreement with the analytic solutions; agreement is also obtained with the results of Weatherill and Stewart (1989) for gravitational accretion of planetesimals having equivalent initial conditions.

Spaute, Dominique↗

Accretion rates of protoplanets. II - Gaussian distributions of planetesimal velocities

In the present growth-rate calculations for a protoplanet that is embedded in a disk of planetesimals with triaxial Gaussian velocity dispersion and uniform surface density, the protoplanet is on a circular orbit. The accretion rate in the two-body approximation is found to be enhanced by a factor of about 3 relative to the case where all planetesimals' eccentricities and inclinations are equal to the rms values of those disk variables having locally Gaussian velocity dispersion. This accretion-rate enhancement should be incorporated by all models that assume a single random velocity for all planetesimals in lieu of a Gaussian distribution.

Greenzweig, Yuval↗

What initiated planetesimal formation?

The physical structure of primitive (chondritic) meteorites, even after some geological processing and modification, is thought by most to contain clues as to the first stage of accretion of solid matter into objects that might be called planetesimals. However, theoretical understanding of the processes responsible for this important stage is shaky. We note what we believe are fundamental obstacles for the Goldreich-Ward version of rapid and direct planetesimal formation via gravitational instability in a settled particle layer, and describe an alternative scenario which might lead from grainy nebula gas to primitive planetesimals in a way that has intriguing connections to the meteorite evidence.

Cuzzi, J. N.↗

Transportation of volatile elements in thermally evolving planetesimals: An important role of metallic iron

Ordinary chondrites are considered to have experienced thermal metamorphism in small bodies. We are interested in behaviors of volatile elements in such a kind of thermally evolving planetesimals. Volatile elements generally have high vapor pressures at high temperature. In porous bodies, with a high gas permeability, volatile elements are transported efficiently over a long range. Behavior of volatile elements transported by permeable gas flow can be handled by an equation whose form is similar to that of the equation of thermal diffusion. We can follow transportation of heats and volatile elements in planetesimals, when parameters in these equations, initial conditions and chemical behavior of volatile elements are given. Recently, we discovered that nitrogen in equilibrated H-chondrites is mainly trapped in taenite (f.c.c. Fe-Ni), probably dissolved in interstitial sites. Fegley suggests that metallic iron cannot trap nitrogen in the solar nebula gas due to its very low nitrogen partial pressure. Approximately 1 bar of nitrogen pressure is required to explain the nitrogen content in taenite. We may expect high nitrogen gas partial pressure (possibly produced by vaporization of nitrogen-bearing solids such as organic materials) at the interior of thermally evolving planetesimals. Kinetic behavior of nitrogen in taenite suggests that it can easily be equilibrated with the ambient nitrogen gas at temperatures of approximately 500 C or higher. We consider that nitrogen is trapped in taenite through a nitrogen redistribution process occurred during the thermal metamorphic event.

Hashizume, K.↗

Infalling Planetesimals in Pre-Main Sequence Stellar Systems

These are exciting times in the study of planetary system formation with a steadily expanding inventory of exo-planet detections, and imaging of dust disks around nearby young and main sequence stars. While these discoveries imply that our Solar System is far from unique, linking the data for the protoplanetary and debris disks to mature planetary systems requires a demonstration that disk evolution proceeds via planetesimal production and growth to the formation of planets. Theoretical studies of planet formation indicate that planetesimals grow, via runaway accretion, to lunar-sized (approx. = 2000 km) embryos in 10(exp 5) years. Recent gas giant planet formation studies have suggested that most of the action in planet formation occurs over 1-16 Myr, with formation of planets similar to Jupiter in t less than 10 Myr, within the time interval that infrared (IR) and optical emission line studies have demonstrated that circumstellar material remains detectable around both solar mass and intermediate mass stars. Direct imaging of exo-planetesimals is not feasible with current and foreseeable technology, since such bodies have substantially less surface area than micron-sized grains distributed in a disk, and thus are inefficient IR emitters. However, such bodies may be indirectly detectable.

Grady, Carol A.↗

Studies of Planet Formation Using a Hybrid N-Body + Planetesimal Code

The goal of our proposal was to use a hybrid multi-annulus planetesimal/n-body code to examine the planetesimal theory, one of the two main theories of planet formation. We developed this code to follow the evolution of numerous 1 m to 1 km planetesimals as they collide, merge, and grow into full-fledged planets. Our goal was to apply the code to several well-posed, topical problems in planet formation and to derive observational consequences of the models. We planned to construct detailed models to address two fundamental issues: (1) icy planets: models for icy planet formation will demonstrate how the physical properties of debris disks - including the Kuiper Belt in our solar system - depend on initial conditions and input physics; and (2) terrestrial planets: calculations following the evolution of 1-10 km planetesimals into Earth-mass planets and rings of dust will provide a better understanding of how terrestrial planets form and interact with their environment.

Kenyon, Scott J.↗

Terrestrial planet and asteroid formation in the presence of giant planets. I. Relative velocities of planetesimals subject to Jupiter and Saturn perturbations

We investigate the orbital evolution of 10(13)- to 10(25) -g planetesimals near 1 AU and in the asteroid belt (near 2.6 AU) prior to the stage of evolution when the mutual perturbations between the planetesimals become important. We include nebular gas drag and the effects of Jupiter and Saturn at their present masses and in their present orbits. Gas drag introduces a size-dependent phasing of the secular perturbations, which leads to a pronounced dip in encounter velocities (Venc) between bodies of similar mass. Plantesimals of identical mass have Venc approximately 1 and approximately 10 m s-1 (near 1 and 2.6 AU, respectively) while bodies differing by approximately 10 in mass have Venc approximately 10 and approximately 100 m s-1 (near 1 and 2.6 AU, respectively). Under these conditions, growth, rather than erosion, will occur only by collisions of bodies of nearly the same mass. There will be essentially no gravitational focusing between bodies less than 10(22) to 10(25) g, allowing growth of planetary embryos in the terrestrial planet region to proceed in a slower nonrunaway fashion. The environment in the asteroid belt will be even more forbidding and it is uncertain whether even the severely depleted present asteroid belt could form under these conditions. The perturbations of Jupiter and Saturn are quite sensitive to their semi-major axes and decrease when the planets' heliocentric distances are increased to allow for protoplanet migration. It is possible, though not clearly demonstrated, that this could produce a depleted asteroid belt but permit formation of a system of terrestrial planet embryos on a approximately 10(6)-year timescale, initially by nonrunaway growth and transitioning to runaway growth after approximately 10(5) years. The calculations reported here are valid under the condition that the relative velocities of the bodies are determined only by Jupiter and Saturn perturbations and by gas drag, with no mutual perturbations between planetesimals. If, while subject to these conditions, the bodies become large enough for their mutual perturbations to influence their velocity and size evolution significantly, the problem becomes much more complex. This problem is under investigation.

NASA Discipline Exobiology↗

Studies of Planet Formation using a Hybrid N-body + Planetesimal Code

The goal of our proposal was to use a hybrid multi-annulus planetesimal/n-body code to examine the planetesimal theory, one of the two main theories of planet formation. We developed this code to follow the evolution of numerous 1 m to 1 km planetesimals as they collide, merge, and grow into full-fledged planets. Our goal was to apply the code to several well-posed, topical problems in planet formation and to derive observational consequences of the models. We planned to construct detailed models to address two fundamental issues: 1) icy planets - models for icy planet formation will demonstrate how the physical properties of debris disks, including the Kuiper Belt in our solar system, depend on initial conditions and input physics; and 2) terrestrial planets - calculations following the evolution of 1-10 km planetesimals into Earth-mass planets and rings of dust will provide a better understanding of how terrestrial planets form and interact with their environment. During the past year, we made progress on each issue. Papers published in 2004 are summarized. Summaries of work to be completed during the first half of 2005 and work planned for the second half of 2005 are included.

Kenyon, Scott J.↗

Cascade Model for Planetesimal Formation by Turbulent Clustering.

We use a newly developed cascade model of turbulent concentration of particles in protoplanetary nebulae to calculate several properties of interest to the formation of primitive planetesimals and to the meteorite record. The model follows, and corrects, calculations of the primary planetesimal Initial Mass Function (IMF) by Cuzzi et al. (2010), in which an incorrect cascade model was used. Here we use the model of Hartlep et al. (2017), which has been validated against several published numerical simulations of particle concentration in turbulence. We find that, for a range of nebula and particle properties, planetesimals may be “born big”, formed as sandpiles with diameters in the 10 − 100 km range, directly from freely floating particles. The IMFs have a modal nature, with a well-defined peak rather than a powerlaw size dependence. Predictions for the inner and outer nebula behave similarly in these regards, and observations of inner and outer nebula primitive bodies support such modal IMFs. Also, we present predictions of local particle concentrations on several lengthscales in which particles “commonly” find themselves, which have significance for meteoritical observations of the redox state and isotopic fractionation in regions of chondrule formation. An important difference between these results, and those of Cuzzi et al. (2010), is that particle growth-by-sticking must proceed to at least the 1−few cm radius range for the IMF and meteoritical properties to be most plausibly satisfied. That is, as far as the inner nebula goes, the predominant “particles” must be aggregates of chondrules (or chondrule-size precursors) rather than individual chondrules themselves.

Thomas Hartlep↗

The H-poor nature of incompletely melted planetesimals: The view from acapulcoites and lodranites

The abundance of H in planetary building blocks is of fundamental importance for constraining the evolution of the terrestrial planets. It is commonly assumed that chondrites are the principal sources of Earth’s H; however, recent studies have suggested that primitive achondrites and achondrites may retain a small complement of H. There are few constraints on the H budgets of primitive achondrites, which represent the transition from unmelted to melted planetesimals, but prior work suggests that bulk parent body H contents are several orders of magnitude lower than typical chondritic values. Therefore, to provide further constraints on H retention during the transition from unmelted to melted planetesimals, we have measured the H contents of olivine, orthopyroxene, clinopyroxene, and plagioclase from a suite of acapulcoite-lodranite clan meteorites. Acapulcoite-lodranite clan meteorites represent the “prototypical” primitive achondrite parent body and have bulk major element compositions more akin to the Earth than previously studied primitive achondrites (e.g., the ureilites). We find that the H 2 O contents of olivine (∼5–12 µg/g H 2 O), orthopyroxene (∼3–10 µg/g H 2 O), and clinopyroxene (∼5–8 µg/g H 2 O) are broadly similar, while plagioclase (∼2.5–5 µg/g H 2 O) tends to be offset to lower values. Using a simple, single-stage batch-melting model, we calculate a preferred maximum acapulcoite-lodranite parent body H 2 O content of 38 µg/g, which is similar to other estimates for primitive achondritic and achondritic parent bodies. Furthermore, assuming chondrite-like precursor materials, our data are consistent with efficient loss of H prior to or during the onset of melting of early-formed planetesimals. This requires that Earth’s H-budget was dominated by building blocks that underwent minimal thermal processing.

Primitive achondrite↗

No evidence for a strong decrease of planetesimal accretion in old white dwarfs

ABSTRACT A large fraction of white dwarfs are accreting or have recently accreted rocky material from their planetary systems, thereby ‘polluting’ their atmospheres with elements heavier than helium. In recent years, the quest for mechanisms that can deliver planetesimals to the immediate vicinity of their central white dwarfs has stimulated a flurry of modelling efforts. The observed time evolution of the accretion rates of white dwarfs through their multi-Gyr lifetime is a crucial test for dynamical models of evolved planetary systems. Recent studies of cool white dwarf samples have identified a significant decrease of the mass accretion rates of cool, old white dwarfs over Gyr time-scales. Here, we revisit those results using updated white dwarf models and larger samples of old polluted H- and He-atmosphere white dwarfs. We find no compelling evidence for a strong decrease of their time-averaged mass accretion rates for cooling times between 1 and 8 Gyr. Over this period, the mass accretion rates decrease by no more than a factor of the order of 10, which is one order of magnitude smaller than the decay rate found in recent works. Our results require mechanisms that can efficiently and consistently deliver planetesimals inside the Roche radius of white dwarfs over at least 8 Gyr.

Blouin, Simon (ORCID:0000000296321436)↗

Lithium pollution of a white dwarf records the accretion of an extrasolar planetesimal

Tidal disruption and subsequent accretion of planetesimals by white dwarfs can reveal the elemental abundances of rocky bodies in exoplanetary systems. Those abundances provide information on the composition of the nebula from which the systems formed, which is analogous to how meteorite abundances inform our understanding of the early Solar System. We report the detection of lithium, sodium, potassium, and calcium in the atmosphere of the white dwarf Gaia DR2 4353607450860305024, which we ascribe to the accretion of a planetesimal. Using model atmospheres, we determine abundance ratios of these elements, and, with the exception of lithium, they are consistent with meteoritic values in the Solar System. We compare the measured lithium abundance with measurements in old stars and with expectations from Big Bang nucleosynthesis.

79 ASTRONOMY AND ASTROPHYSICS↗

Radial pressure in the solar nebula as affecting the motions of planetesimals

Growing planetesimals and a range of drag laws depending on the Reynolds number and on the ratio of particle size to mean free path are considered. Particles spiral in the direction of positive gradient, thus being concentrated toward toroidal concentrations of gas. The effect increases with decreasing rates of particle growth, i.e., with increasing time scales of planet formation by accretion. In the outer regions, where evidence suggests that comets were formed and Uranus and Neptune were so accumulated, the effect of the pressure gradient is to clear the forming comets from those regions. The large mass of Neptune may have developed because of this effect, perhaps Neptune's solar distance was reduced from Bode's law, and perhaps no comet belt exists beyond Neptune. In the asteroid belt, on a slow time scale, the effect may have spiraled planetesimals toward Mars and Jupiter, thus contributing to the lack of planet formation in this region.

Whipple, F. L.↗

Dynamics of planetesimal formation and planetary accretion

The paper reviews the dynamical processes by which condensed matter in the solar nebula accumulates into planets. The basic processes are: (1) gravitational instability; (2) conversion of the radial gradient of orbital motion into random motion between planetesimals; and (3) collisions, which damp the random motion and result in aggregation and/or fragmentation of planetesimals. Each of these processes is defined analytically, and models, based on these results, of planetary growth, axial rotation rates, and formation of satellite systems are formulated.

Harris, A. W.↗

Thermal evolution of earth and moon growing by planetesimal impacts

Improved estimates of impact energy partitioning are combined with models of planetesimal size distribution and planetary growth to infer the early thermal evolutions of the earth and moon. Binary accretion models of the moon which allow for enhancement of velocities by proximity of the earth do not get hot enough for appreciable melting unless a planetesimal mass distribution starting at a rather high value (earth mass/20 or more) is assumed. This melting occurs deeper than is inferred from petrological and thermotectonic data; hence the results favor formation of the moon as a consequence of a great impact (or great impacts) into the earth.

Kaula, W. M.↗