Core formation by giant impacts

Abstract

The timing and mechanisms of core formation remain unresolved questions in our knowledge of the Solar System's early state. Because no known nebular processes separate iron from silicates during planetesimals formation, it is believed that the terrestrial planets formed from planetesimals containing approximately solar abundances of iron and silicates. At some stage of planetary growth, iron separated from the silicates to form cores. We propose that once a planet reaches a certain minimum mass, large impacts characteristic of late accretion can trigger core formation. Our model overcomes two major difficulties of core formation: large-scale segregation of molten iron into diapirs and displacement of the cold, elastic interior of the planet by the iron. Large, high-speed impacts on relatively large planets (>∼10 23 kg) result in melting beyond the transient crater's dimensions, forming a large, intact melt region with a radius up to a few times the projectile's radius. Both the iron and silicates melt. Iron rapidly settles to the melt region's base because of its high density. The accumulated iron forms a large, negatively buoyant mass that stresses the underlying material. If the generated stress is larger than the maximum long term stress that the cold interior can support, the iron rapidly flows to the planet's center, displacing the cold interior and forming (or adding to) a core. To investigate, we developed an analytical melting model based on the Hugoniot equations, the empirical relationship for the decline of particle velocity with distance, and the linear shock-particle velocity relationship. Using this melting model coupled with a Monte Carlo simulation of accretion, we examined the ability of giant impacts to trigger core formation. The melt forms an intact region only if the melt fraction that is not excavated from the crater is >∼0.5–0.6. This does not occur until a planet is of approximately lunar mass or greater and is struck by a planetesimal of about one-tenth its mass. If the maximum long-term stress that the planet's cold interior can withstand is 2 kbar, consistent with conditions at the Earth's surface, planets must be approximately the mass of Ceres before impacts induce core formation. However, core formation occurs only if an intact melt region forms at this stage and if planetesimals with impact speeds greater than about 7.25 km sec −1 exist during this stage of accretion, both of which are unlikely. If the approach velocity of the planetesimals is small, the planet must grow to ∼10 24 kg ( ∼ 1 6 − 1 4 the Earth's mass) before a giant impact will induce core formation. If a small fraction of the planetesimals have approach velocities greater than a few kilometers per second, impact-induced core formation occurs in planets with masses between 1 and 6 × 10 23 kg. By the time a planet grows to Mars size, it has a nearly 100% probability that a giant impact triggered core formation. A Mercury-mass planet has about a 75% probability. Giant impacts do not explain whole-body differentiation of asteroid-sized planets.