I ran N -body simulations of terrestrial planet accretion to study this process. By running such a large number of them, I could obtain a statistical view of the probabilities of matching different Solar System properties and check for correlations between properties, which were largely absent. The simulations provide information about the mass evolution of the Earth and the provenance of its building blocks, which I then incorporate into a model of core—mantle chemical evolution.
Such bodies, referred to as planetesimals , are massive enough that their gravitational interactions are significant, while their small surface area to volume ratio means they are only weakly affected by aerodynamic forces. Dust grains grow by colliding with one another and sticking together by electrostatic forces. Small particles also physically embed themselves in larger aggregates during high-speed collisions.
The motion of small dust grains is closely coupled to that of the gas, and turbulence causes dust to diffuse over large distances leading to substantial radial and vertical mixing of material within the disk. Particles larger than 1 mm develop significant velocities relative to the gas because gas orbits the star somewhat more slowly than a solid body due to an outward pressure gradient in the disk.
This velocity differential causes particles to migrate radially toward the star, and particles also settle vertically toward the midplane of the disk. This implies that growth through this size range must be rapid, or else much of the solid material in the disk would evaporate when it enters the hot regions close to the star.
The required rapid growth might occur as a result of ongoing pairwise collisions, possibly aided by the concentration of particles into small regions due to turbulent eddies. Alternatively, planetesimals might form via the gravitational collapse of regions containing dense concentrations of solid particles the Goldreich-Ward mechanism.
Both models face substantial challenges. For pairwise collisions to work fast enough, meter-sized objects need to efficiently stick together upon collision rather than breaking up. This has not been demonstrated in laboratory experiments, and theoretical arguments suggest that at the expected collision velocities, it is very difficult for growth to occur. In the absence of direct observations or suitable laboratory experiments, much of what we know about terrestrial-planet formation comes from computer simulations.
Terrestrial-planet formation has been studied extensively using statistical models based on the coagulation equation to study the early stages of growth and N-body simulations to model later stages when the number of large bodies is small. Once planetesimals have formed, their subsequent evolution is dominated by mutual gravitational interactions and collisions as they orbit the central star. Colliding planetesimals typically merge to form a larger body with some mass escaping as small fragments.
Planetesimals also undergo numerous close encounters with one another, which alter their orbits but not their masses. At an early stage, runaway growth takes place, in which large bodies typically grow more rapidly than small ones due to differences in their orbital eccentricities and inclinations.
Runaway growth is followed by oligarchic growth , in which a relatively small number of large bodies grow at similar rates until they have swept up most of the smaller planetesimals. Collisions and radioactive decay heat the large bodies until they melt, causing dense elements such as iron to sink to the center to form a core overlain by a rocky mantle. Subsequent collisions between these embryos lead to the final assembly of the terrestrial planets, on a time scale of up to million years.
The Moon is thought to have formed about 40 million years after the start of the Solar System from debris placed into orbit about the Earth when it collided with a Mars-sized planetary embryo.
A substantial fraction of the Earth's mass is thought to have been accreted via large impacts, so requiring such a cataclysmic event to form the Moon is in principle not a problem, though only a small fraction of giant impacts would lead to the formation of a satellite with the properties of the Moon. Another puzzle is why the Moon has such a similar composition to the Earth - this is not an obvious consequence of the giant-impact theory. The time scale for lunar formation, along with other time scales such as that for asteroids to become large enough to differentiate, is derived by applying radionuclide chronometers to samples of rock.
Such cosmochemistry evidence is becoming increasingly important, and provides a growing number of constraints on the formation of the early Solar System. Planets typically acquire mass from a range of distances within a protoplanetary disk, although the mixture is different for each object, leading to a unique chemical composition.
It is likely that Earth acquired most of its water and other volatile materials from relatively cold regions of the Sun's protoplanetary disk such as the asteroid belt.
Simulations of terrestrial-planet formation are able to reproduce the basic architecture a small number of terrestrial planets with low-eccentricity orbits of the inner Solar System from plausible initial conditions.
The stochastic nature of planetary accretion, however, means that a precision comparison between the Solar System and theoretical models in not possible. The number and masses of terrestrial planets are predicted to vary from one planetary system to another due to differences in the amount of solid material available and the presence or absence of giant planets, as well as the highly stochastic nature of planet formation.
The presence of a giant planet probably frustrates terrestrial-planet formation in neighboring regions of the disk, leading to the absence of terrestrial planets in these regions or the formation of an asteroid belt. These predictions will be tested by ongoing and future space missions designed to search for extrasolar terrestrial planets, such as COROT and Kepler. Schematic illustration of orbital repulsion on the a — e plane. This implies that they repeat the orbital repulsion while growing.
Consequently, the orbital separation of protoplanets is always kept larger than about 5 r H. This is one of the important factors that realize oligarchic growth of protoplanets. Orbiting the sun, planetesimals sometimes collide with each other to form protoplanets.
In this section we review the basic physics of accretionary evolution of planetesimals. Runaway growth of planetesimals and oligarchic growth of protoplanets are demonstrated by showing N -body simulations. In the orderly growth mode, all the particles grow equally; in other words, mass ratios between particles tend to be unity. On the other hand, in the runaway growth mode, larger particles grow faster than smaller ones and their mass ratios increase monotonically. Which growth mode is relevant to planetesimal accretion was controversial around the end of the last century.
In the early stages of planetesimal accretion, the growth mode of planetesimals is runaway growth, where larger planetesimals grow more rapidly than smaller ones and their mass ratios increase with time [ 21—23 ]. We illustrate the basic processes of runaway growth of planetesimals by showing the results of N -body simulation of planetesimal accretion. Figures 7 and 8 show an example of runaway growth [ 24 ]. For simplicity, the calculation in this section is gas-free.
The circles represent planetesimals and their radii are proportional to the radii of planetesimals. It is clearly shown that a planetesimal grows in the runaway mode. Note that the eccentricity and the inclination of the largest body is always kept small due to dynamical friction from smaller bodies. These small eccentricity and inclination values facilitate runaway growth [ 23 , 25 ].
The evolution of the mass distribution of planetesimals is shown in Fig. The cumulative number of bodies n c against mass is plotted. The mass distribution relaxes to a distribution that is well approximated by a power-law distribution.
This index can be derived analytically as a stationary distribution [ 26 ]. Note that runaway growth does not necessarily mean that the growth time decreases with mass, but it does mean that the mass ratio of any two bodies increases with time.
The runaway body keeps growing and then isolates from the continuous power-law mass distribution. In this stage, the runaway body predominantly grows as a sink of the mass flow from the continuous power-law mass distribution.
Protoplanets are formed through runaway growth of planetesimals. In the late runaway stage, protoplanets grow while interacting with one another. Kokubo and Ida [ 20 ] investigated this stage and found oligarchic growth of protoplanets: similar-sized protoplanets grow keeping their orbital separation larger than about 5 r H , while most planetesimals remain small. Through oligarchic growth, a bi-modal protoplanet—planetesimal system is formed at the post-runaway stage. We present an example of an N -body simulation that shows oligarchic growth [ 12 ].
In this calculation, the 6-fold radius of planetesimals is used to accelerate the accretion process. The use of the 6-fold radius of planetesimals does not change the growth mode of planetesimals but shortens the growth timescale about 6 times [ 21 ].
The accretion propagates from small to large a. This is because the accretion timescale is smaller for smaller a since the surface number density of planetesimals is higher and the orbital period is smaller for smaller a [see Eq. Note that at large a the protoplanets are still growing. The result of the N -body simulation is consistent with the estimation based on the oligarchic growth model described below. Figure 10 shows the isolation mass of protoplanets against the semimajor axis for the standard disk model for solar system formation [ 24 ].
This suggests that they are leftover protoplanets. In order to complete Venus and Earth, whose masses are one order of magnitude larger than that of protoplanets, further accretion of protoplanets is necessary. However, their growth timescale is longer than the age of the solar system.
Isolation mass of protoplanets against the semimajor axis with the mass of planets in the solar system and the ice line dotted. The oligarchic growth model of protoplanets is now generally accepted as the standard process of planet formation, though it still has some discrepancies. The generalized oligarchic growth model is used to study the diversity of extrasolar planets together with the core accretion model, as will be shown in Sect. It is generally accepted that the final stage of terrestrial planet formation is the giant impact stage, where protoplanets planetary embryos formed by oligarchic growth collide with one another to complete planets [ 20 , 28 ].
This stage is being actively studied as many small extrasolar planets are discovered. Though protoplanets perturb each other, the protoplanet system is orbitally stable when disk gas exists, since its gravitational drag damps their eccentricities see Sect.
However, it is observationally inferred that disk gas depletes on a timescale of 1—10 million years [ 13 ]. Thus, in the long term, the protoplanet system becomes unstable through mutual gravitational perturbation after the dispersal of the gas disk. Figure 11 shows the orbital instability timescale of a protoplanet system consisting of 10 equal-mass 0. The semi-logarithm dependence on the initial orbital separation of protoplanets is clearly shown. Timescale of orbital instability against the initial orbital separation of protoplanets.
The solid line shows the result of Chambers et al. After a protoplanet system becomes orbitally unstable, the giant impact stage of protoplanets begins. As this process is stochastic in nature, it is necessary to quantify it statistically in order to clarify it.
Kokubo et al. Figure 12 shows an example where three terrestrial planets are formed from 16 protoplanets [ 31 ]. In the standard disk model, two Earth-sized planets typically form in the terrestrial planet region.
The effects of the surface density distribution of the disk are unified using M tot. This result shows that protoplanet accretion proceeds globally, in other words, over the whole terrestrial planet region. Thus the large-scale radial mixing of material is expected.
Time evolution of the semimajor axes solid lines and pericenter and apocenter distances dotted lines of planets left. The size of circles is proportional to the physical size of planets. Average spin angular velocity against planet mass left and normalized cumulative distribution of obliquity with the isotropic distribution dotted line right of all planets formed in the 50 runs of the standard model.
Prograde spin with small obliquity, which is common to terrestrial planets in the solar system except for Venus, is not a common feature of planets assembled by giant impacts. It should be noted, however, that the initial obliquity of a planet determined by giant impacts can be modified substantially by stellar tide if the planet is close to the star Mercury and by satellite tide if the planet has a large satellite Earth.
So far, we have discussed the dynamics and accretion of solid rocky and icy planets. In the solar system, gas giant planets, Jupiter and Saturn, exist. They called this the Nice model , after the city in France where they first discussed it. As the planets interacted with the smaller bodies, they scattered most of them toward the sun. The process caused them to trade energy with the objects, sending the Saturn, Neptune, and Uranus farther out into the solar system. Eventually the small objects reached Jupiter, which sent them flying to the edge of the solar system or completely out of it.
Movement between Jupiter and Saturn drove Uranus and Neptune into even more eccentric orbits, sending the pair through the remaining disk of ices.
Some of the material was flung inward, where it crashed into the terrestrial planets during the Late Heavy Bombardment. Other material was hurled outward, creating the Kuiper Belt. As they moved slowly outward, Neptune and Uranus traded places.
Eventually, interactions with the remaining debris caused the pair to settle into more circular paths as they reached their current distance from the sun. Along the way, it's possible that one or even two other giant planets were kicked out of the system. Astronomer David Nesvorny of SwRI has modeled the early solar system in search of clues that could lead toward understanding its early history.
The solar system didn't wrap up its formation process after the planets formed. Earth stands out from the planets because of its high water content, which many scientists suspect contributed to the evolution of life. But the planet's current location was too warm for it to collect water in the early solar system, suggesting that the life-giving liquid may have been delivered after it was grown. But scientists still don't know the source of that water.
The asteroid belt makes another potential source of water. Several meteorites have shown evidence of alteration, changes made early in their lifetimes that hint that water in some form interacted with their surface. Impacts from meteorites could be another source of water for the planet.
0コメント