Runaway growth of planetary embryos facilitated by massive bodies in a protoplanetary disk.

About 30% of detected extrasolar planets exist in multiple-star systems. The standard model of planet formation cannot easily accommodate such systems and has difficulty explaining the odd orbital characteristics of most extrasolar giant planets. We demonstrate that the formation of terrestrial-size planets may be insulated from these problems, enabling much of the framework of the standard model to be salvaged for use in complex systems. A type of runaway growth is identified that allows planetary embryos to form by a combination of nebular gas drag and perturbations from massive companions-be they giant planets, brown dwarfs, or other stars.

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.

Ways that our Solar System helps us understand the formation of other planetary systems and ways that it doesn't.

Models of planetary formation can be tested by comparison of their ability to predict features of our Solar System in a consistent way, and then extrapolated to other hypothetical planetary systems by different choice of parameters. When this is done, it is found that the resulting systems are insensitive to direct effects of the mass of the star, but do strongly depend on the properties of the disk, principally its surface density. Major uncertainty results from lack of an adequate theoretical model that predicts the existence, size, and distribution of analogs of our Solar System, particularly the gas giants Jupiter and Saturn. Nevertheless, reasons can be found for expecting that planetary systems, including those containing biologically habitable planets similar to Earth, may be abundant in the Galaxy and Universe.

Possible consequences of absence of "Jupiters" in planetary systems.

The formation of the gas giant planets Jupiter and Saturn probably required the growth of massive approximately 15 Earth-mass cores on a time scale shorter than the approximately 10(7) time scale for removal of nebular gas. Relatively minor variations in nebular parameters could preclude the growth of full-size gas giants even in systems in which the terrestrial planet region is similar to our own. Systems containing "failed Jupiters," resembling Uranus and Neptune in their failure to capture much nebular gas, would be expected to contain more densely populated cometary source regions. They will also eject a smaller number of comets into interstellar space. If systems of this kind were the norm, observation of hyperbolic comets would be unexpected. Monte Carlo calculations of the orbital evolution of region of such systems (the Kuiper belt) indicate that throughout Earth history the cometary impact flux in their terrestrial planet regions would be approximately 1000 times greater than in our Solar System. It may be speculated that this could frustrate the evolution of organisms that observe and seek to understand their planetary system. For this reason our observation of these planets in our Solar System may tell us nothing about the probability of similar gas giants occurring in other planetary systems. This situation can be corrected by observation of an unbiased sample of planetary systems.

Provenance of the terrestrial planets.

Earlier work on the simultaneous accumulation of the asteroid belt and the terrestrial planets is extended to investigate the relative contribution to the final planets made by material from different heliocentric distances. As before, stochastic variations intrinsic to the accumulation processes lead to a variety of final planetary configurations, but include systems having a number of features similar to our solar system. Fifty-nine new simulations are presented, from which thirteen are selected as more similar to our solar system than the others. It is found that the concept of "local feeding zones" for each final terrestrial planet has no validity for this model. Instead, the final terrestrial planets receive major contributions from bodies ranging from 0.5 to at least 2.5 AU, and often to greater distances. Nevertheless, there is a correlation between the final heliocentric distance of a planet and its average provenance. Together with the effect of stochastic fluctuations, this permits variation in the composition of the terrestrial planets, such as the difference in the decompressed density of Earth and Mars. Biologically important light elements, derived from the asteroidal region, are likely to have been significant constituents of the Earth during its formation.

Formation of planetary embryos: effects of fragmentation, low relative velocity, and independent variation of eccentricity and inclination.

An earlier investigation of the formation of approximately 10(26) g planetary embryos from much smaller planetesimals (G.W. Wetherill and G.R. Stewart 1989, Icarus 77, 350-357) has been extended to include the effects of collisional fragmentation, the low relative velocity regime in which the effects due to solar gravity are important, and independent perturbations of eccentricity and inclination. In agreement with this earlier work, it if found that at 1 AU runaway growth occurs on a approximately 10(-5)-year time scale as a consequence of equipartition of energy between large and small planetesimals. It is now seen that the runaway is initiated after approximately 10(4) years, when the relative velocities of the larger bodies temporarily fall into the low-velocity regime, lowering their inclinations and increasing their gravitational capture rates. After approximately 2 X 10(4) years, relative velocities between most bodies emerge from the low-velocity regime, and these higher velocities tend to inhibit further runaway growth. This rapid runaway growth is self-regulated, however, by these same higher velocities, causing fragmentation of the smaller bodies. The velocities of the collision fragments are reduced by gas drag, facilitating their capture by the growing runaway embryos. Variations in which different fragmentation models are used, or long-range forces between nonrunaway bodies are absent, give similar results. When fragmentation is not included, the time scale for growth increases to approximately 3 X 10(5) years as a result of loss of the self-regulating process described above.

Occurrence of Earth-like bodies in planetary systems.

Present theories of terrestrial planet formation predict the rapid ;;runaway formation'' of planetary embryos. The sizes of the embryos increase with heliocentric distance. These embryos then merge to form planets. In earlier Monte Carlo simulations of the merger of these embryos it was assumed that embryos did not form in the asteroid belt, but this assumption may not be valid. Simulations in which runaways were allowed to form in the asteroid belt show that, although the initial distributions of mass, energy, and angular momentum are different from those observed today, during the growth of the planets these distributions spontaneously evolve toward those observed, simply as a result of known solar system processes. Even when a large planet analogous to ;;Jupiter'' does not form, an Earth-sized planet is almost always found near Earth's heliocentric distance. These results suggest that occurrence of Earth-like planets may be a common feature of planetary systems.

Occurrence of giant impacts during the growth of the terrestrial planets.

Three-dimensional Monte Carlo simulations of the accumulation of the terrestrial planets in the absence of gas drag produced results that are in general agreement with the number and distribution of the present planets. The accumulation process appears to be characterized by impact of bodies as large as three times the mass of Mars at velocities of about 9 kilometers per second. These giant impacts on Earth may have supplied the material and angular momentum that formed the moon, should have heated Earth to the melting point, and may have been responsible for the differences in the content of inert gases of the atmospheres of Earth and Venus.

Effect of food intake and fasting on gastrointestinal lead absorption in humans.

The effect of food intake versus brief fasting on gastrointestinal absorption of lead was measured in five healthy men who were living in a metabolic unit and eating constant lead diets. Lead absorpiton was assessed by the difference between dietary intake and output of 1) lead tracers composed of nonradioactive isotopes which were ingested as a single dose either with food or during a 16-hr fast, 2) lead tracers ingested with meals for relatively long periods (2 to 124 days), and 3) total led in ingested foods. Absorption estimated by 1) was confirmed by increments in tracer concentrations in blood. Lead tracers were given as nitrate, cysteine complex, or sulfide. Absorption was 10.3 +/- 2.2% (SD) for food lead; 8.2 +/- 2.8% for tracers ingested with food; and 35 +/- 13% (P < 0.01) percent for tracers ingested without food. The increased absorption of lead when ingested without food should be considered when the hazards of exposure to lead are determined.

The Earth and planetary sciences.

During the last two decades the earth sciences community has become persuaded that the earth is a dynamic body; an engine driven by its internal heat. The major surface manifestation of this dynamism has been fragmentation of the earth's outer shell and subsequent relative horizontal movement of the pieces on a large scale. The driving force is convection within the earth, but much remains to be learned about the nature of the convection and the composition of the earth's interior. The other terrestrial planets show evidence of once having been hot, but their surfaces suggest long-term stability and lack evidence of continuing convection.

Magnitude of lead intake from respiration by normal man.

Lead metabolism of five normal men was studied in a hospital metabolic unit in order to measure the daily intake of lead by respiration in urban adults. Subjects ingested a constant diet, and samples of blood, urine, feces, and diet were analyzed periodically for lead isotopic abundances by mass spectrometry. Three men were fed daily a stable isotope tracer of lead for 83 to 124 days in order to distinguish ingested from respired lead. Also, three men lived in rooms with filtered, low-lead air for 25 to 50 days in order to examine the response of blood lead levels to a change in airborne lead exposure. The quantity of respired lead intake was determined from the lead balance data, labeling of blood lead with a dietary lead tracer, and the response of blood lead levels and lead balances to exposure to low-lead air. The results indicate that these men absorbed a mean of 14 +/- 4 (S.D.) microgram/day of lead while exposed to the ambient levels of about 2 microgram/m3 of airborne lead. About twice this amount was absorbed from the diet.

Kinetic analysis of lead metabolism in healthy humans.

The steady state kinetics of lead metabolism were studied in five healthy men with stable isotope tracers. Subjects lived in a metabolic unit and ate constant low lead diets. Their intake was supplemented each day with 79--204 mug of enriched lead-204 as nitrate which was ingested with meals for 1--124 days. The concentration and isotopic composition of lead was determined serially in blood, urine, feces, and diet and less commonly in hair, nails, sweat, bone, and alimentary tract secretions by isotopic dilution, mass spectrometric analysis. The data suggest a three compartmental model for lead metabolism. The first compartment encompasses blood and is 1.5--2.2 times larger than the blood mass. It contains approximately 1.7--2.0 mg of lead and has a mean life of 35 days. This pool is in direct communication with ingested lead, urinary lead, and pools two and three. The second compartment is largely composed of soft tissue, contains about 0.3--0.9 mg of lead, and has a mean life of approximately 40 days. This pool gives rise to lead in hair, nails, sweat, and salivary, gastric, pancreatic, and biliary secretions. Pool three resides primarily in the skeleton, contains the vast quantity of body lead, and has a very slow mean life. Bones appear to differ in their rates of lead turnover. Within the relatively small changes in blood lead observed in the present study, the transfer coefficients between the pools remained constant.

Studies of human lead metabolism by use of stable isotope tracers.

Dynamics of lead metabolism were studied by replacement of a portion of the dietary lead with stable isotope tracers, and maintaining subjects on controlled diets for about 6 months. Results for one subject have been previously reported. Preliminary data are now available for a second subject. Although the data on the two subjects are basically similar, there are also significant differences. The two subjects have different blood lead concentrations (0.25 and 0.18 mug/g). Both subjects received the same dietary and similar atmospheric lead exposure, and the lead concentration of their blood was shown to be nearly in a steady state. The difference in blood lead concentration appears primarily attributable to differences in the fraction of lead absorbed from the gut, although there are also differences in other physiological parameters, as well as probable small differences in their intake of atmospheric lead. The quantity of lead absorbed from a typical urban atmosphere (Pb concentration = 1-2 mug/m(3)) has been shown by our isotopic data and balance studies to be 15+/-3 mug/day. Measurement of the contribution of atmospheric lead to the lead intake of the second subject was also carried out by removal of lead from the atmosphere. Decline in the blood concentration of lead of normal isotopic composition was shown to be equivalent to the removal of 15 g/day. Measurements made during the course of a day show complexities in the absorption and distribution of lead, which are averaged out on a time scale of ca. 5 days.

Lead metabolism in the normal human: stable isotope studies.

Kinetic and metabolic balance studies in a healthy man fed a diet normal in lead content and labeled with lead-204 indicated that approximately two-thirds of his assimilated lead was dietary in origin; the remainder was inhaled. Kinetic analysis shows that the isotopic data can be interpreted by a three-compartment model.

Chondrites: initial strontium-87/strontium-86 ratios and the early history of the solar system.

A sodium-poor, calcium-rich inclusion in the carbonaceous chondrite Allende had a (87)Sr/(86)Sr ratio at the time of its formation of 0.69880, as low a value as that found in any other meteorite. The higher (87)Sr/(86)Sr ratios found in ordinary chondrites indicate that their formation or isotopic equilibration occurred tens of millions of years later.

Asteroidal source of meteorites.

The evolution of asteroidal orbits initially near the Kirkwood Gap at the 1:2 commensurability with Jupiter's period provides a mechanism for the production of meteorites from the asteroid belt without excessive velocity change. The resulting yield ( approximately 10(9) grams per year) and the orbital elements of Earth-crossing objects are in agreement with observational data on meteorites.