Robin M. Canup

Origin of the Moon in a giant impact near the end of the Earth's formation

The Moon is generally believed to have formed from debris ejected by a large off-centre collision with the early Earth. The impact orientation and size are constrained by the angular momentum contained in both the Earths spin and the Moons orbit, a quantity that has been nearly conserved over the past 4.5 billion years. Simulations of potential moon-forming impacts now achieve resolutions sufficient to study the production of bound debris. However, identifying impacts capable of yielding the Earth–Moon system has proved difficult. Previous works found that forming the Moon with an appropriate impact angular momentum required the impact to occur when the Earth was only about half formed, a more restrictive and problematic model than that originally envisaged. Here we report a class of impacts that yield an iron-poor Moon, as well as the current masses and angular momentum of the Earth–Moon system. This class of impacts involves a smaller—and thus more likely—object than previously considered viable, and suggests that the Moon formed near the very end of Earths accumulation.

Forming a Moon with an Earth-like Composition via a Giant Impact

Forming the Moon from Earth It is thought that the Moon formed after a Mars-sized planet hit Earth about 4.5 billion years ago. Computer simulations of this event predict that the Moon was produced primarily from material from the impacting planet. However, the Moon has a similar composition to that of Earth, and the impacting planet would likely have had a different composition. Prior models assumed that the impact left the Earth-Moon system with the same angular momentum as it has today (see the Perspective by Halliday). Ćuk and Stewart (p. 1047, published online 17 October; see the cover) show that the angular momentum of the Earth-Moon system could have decreased by half after the Moon-forming impact, opening the door to new impact models. For example, simulations suggest that high-velocity impacts onto a fast-spinning early Earth can lead to a Moon formed primarily from Earths mantle. Canup (p. 1052, published online 17 October) considered instead lower-velocity impacts by planets comparable in mass to the proto-Earth, which could generate a Moon and an Earth with similar compositions. Computer simulations show that a giant impact on early Earth could lead to a Moon with a composition similar to Earth’s. In the giant impact theory, the Moon formed from debris ejected into an Earth-orbiting disk by the collision of a large planet with the early Earth. Prior impact simulations predict that much of the disk material originates from the colliding planet. However, Earth and the Moon have essentially identical oxygen isotope compositions. This has been a challenge for the impact theory, because the impactor’s composition would have likely differed from that of Earth. We simulated impacts involving larger impactors than previously considered. We show that these can produce a disk with the same composition as the planet’s mantle, consistent with Earth-Moon compositional similarities. Such impacts require subsequent removal of angular momentum from the Earth-Moon system through a resonance with the Sun as recently proposed.

FORMATION OF THE GALILEAN SATELLITES: CONDITIONS OF ACCRETION

We examine formation conditions for the Galilean satellites in the context of models of late-stage giant planet accretion and satellite-disk interactions. We first reevaluate the current standard, in which the satellites form from a ‘‘ minimum mass subnebula ’’ disk, obtained by augmenting the mass of the current satellites to solar abundance and resulting in a disk mass containing about 2% of Jupiter’s mass. Conditions in such a massive and gas-rich disk are difficult to reconcile with both the icy compositions of Ganymede and Callisto and the protracted formation time needed to explain Callisto’s apparent incomplete differentiation. In addition, we argue that disk torques in such a gas-rich disk would cause large satellites to be lost to inward decay onto the planet. These issues have prevented us from identifying a self-consistent scenario for the formation and survival of the Galilean satellites using the standard model. We then consider an alternative, in which the satellites form in a circumplanetary accretion disk produced during the very end stages of gas accretion onto Jupiter. In this case, an amount of gas and solids of at least � 0.02 Jovian masses must still be processed through the disk during the satellite formation era, but this amount need not have been present all at once. We find that an accretion disk produced by a slow inflow of gas and solids, e.g., 2 � 10 � 7 Jovian masses per year, is most consistent with conditions needed to form the Galilean satellites, including disk temperatures low enough for ices and protracted satellite accretion times of � 10 5 yr. Such a ‘‘ gas-starved ’’ disk has an orders-of-magnitude lower gas surface density than the minimum mass subnebula (and for many cases is optically thin). Solids delivered to the disk build up over many disk viscous cycles, resulting in a greatly reduced gas-to-solids ratio during the final stages of satellite accretion. This allows for the survival of Galilean-sized satellites against disk torques over a wide range of plausible conditions.

A common mass scaling for satellite systems of gaseous planets.

The Solar Systems outer planets that contain hydrogen gas all host systems of multiple moons, which notably each contain a similar fraction of their respective planets mass (∼10-4). This mass fraction is two to three orders of magnitude smaller than that of the largest satellites of the solid planets (such as the Earths Moon), and its common value for gas planets has been puzzling. Here we model satellite growth and loss as a forming giant planet accumulates gas and rock-ice solids from solar orbit. We find that the mass fraction of its satellite system is regulated to ∼10-4 by a balance of two competing processes: the supply of inflowing material to the satellites, and satellite loss through orbital decay driven by the gas. We show that the overall properties of the satellite systems of Jupiter, Saturn and Uranus arise naturally, and suggest that similar processes could limit the largest moons of extrasolar Jupiter-mass planets to Moon-to-Mars size.

Lunar accretion from an impact-generated disk

Although the mechanism by which the Moon was formed is currently unknown, several lines of evidence point to its accretion from a circumterrestrial disk of debris generated by a giant impact on the Earth. Theoretical simulations show that a single large moon can be produced from such a disk in less than a year, and establish a direct relationship between the size of the accreted moon and the initial configuration of the debris disk.

Accretion of the Earth

The origin of the Earth and its Moon has been the focus of an enormous body of research. In this paper I review some of the current models of terrestrial planet accretion, and discuss assumptions common to most works that may require re-examination. Density-wave interactions between growing planets and the gas nebula may help to explain the current near-circular orbits of the Earth and Venus, and may result in large-scale radial migration of proto-planetary embryos. Migration would weaken the link between the present locations of the planets and the original provenance of the material that formed them. Fragmentation can potentially lead to faster accretion and could also damp final planet orbital eccentricities. The Moon-forming impact is believed to be the final major event in the Earths accretion. Successful simulations of lunar-forming impacts involve a differentiated impactor containing between 0.1 and 0.2 Earth masses, an impact angle near 45° and an impact speed within 10 per cent of the Earths escape velocity. All successful impacts—with or without pre-impact rotation—imply that the Moon formed primarily from material originating from the impactor rather than from the proto-Earth. This must ultimately be reconciled with compositional similarities between the Earth and the Moon.

Origin of Saturn/'s rings and inner moons by mass removal from a lost Titan-sized satellite

The origin of Saturn’s rings has not been adequately explained. The current rings are more than 90 to 95 per cent water ice, which implies that initially they were almost pure ice because they are continually polluted by rocky meteoroids. In contrast, a half-rock, half-ice mixture (similar to the composition of many of the satellites in the outer Solar System) would generally be expected. Previous ring origin theories invoke the collisional disruption of a small moon, or the tidal disruption of a comet during a close passage by Saturn. These models are improbable and/or struggle to account for basic properties of the rings, including their icy composition. Saturn has only one large satellite, Titan, whereas Jupiter has four large satellites; additional large satellites probably existed originally but were lost as they spiralled into Saturn. Here I report numerical simulations of the tidal removal of mass from a differentiated, Titan-sized satellite as it migrates inward towards Saturn. Planetary tidal forces preferentially strip material from the satellite’s outer icy layers, while its rocky core remains intact and is lost to collision with the planet. The result is a pure ice ring much more massive than Saturn’s current rings. As the ring evolves, its mass decreases and icy moons are spawned from its outer edge with estimated masses consistent with Saturn’s ice-rich moons interior to and including Tethys.

ON A GIANT IMPACT ORIGIN OF CHARON, NIX, AND HYDRA

It is generally believed that Charon was formed as a result of a large, grazing collision with Pluto that supplied the Pluto-Charon system with its high angular momentum. It has also been proposed that Plutos small outer moons, Nix and Hydra, formed from debris from the Charon-forming impact, although the viability of this scenario remains unclear. Here I use smooth particle hydrodynamics impact simulations to show that it is possible to simultaneously form an intact Charon and an accompanying debris disk from a single impact. The successful cases involve colliding objects that are partially differentiated prior to impact, having thin outer ice mantles overlying a uniform composition rock-ice core. The composition of the resulting debris disks varies from a mixture of rock and ice (similar to the bulk composition of Pluto and Charon) to a pure ice disk. If Nix and Hydra were formed from such an impact-generated disk, their densities should be less than or similar to that of Charon and Pluto, and the small moons could be composed entirely of ice. If they were instead formed from captured material, a mixed rock-ice composition and densities similar to that of Charon and Pluto would be expected. Improved constraints on the properties of Nix and Hydra through occultations and/or the New Horizons encounter may thus help to distinguish between these two modes of origin, particularly if the small moons are found to have ice-like densities.

Lunar Accretion from a Roche-interior Fluid Disk

We use a hybrid numerical approach to simulate the formation of the Moon from an impact-generated disk, consisting of a fluid model for the disk inside the Roche limit and an N-body code to describe accretion outside the Roche limit. As the inner disk spreads due to a thermally regulated viscosity, material is delivered across the Roche limit and accretes into moonlets that are added to the N-body simulation. Contrary to an accretion timescale of a few months obtained with prior pure N-body codes, here the final stage of the Moons growth is controlled by the slow spreading of the inner disk, resulting in a total lunar accretion timescale of ~102 years. It has been proposed that the inner disk may compositionally equilibrate with the Earth through diffusive mixing, which offers a potential explanation for the identical oxygen isotope compositions of the Earth and Moon. However, the mass fraction of the final Moon that is derived from the inner disk is limited by resonant torques between the disk and exterior growing moons. For initial disks containing <2.5 lunar masses , we find that a final Moon with mass contains ≤60% material derived from the inner disk, with this material preferentially delivered to the Moon at the end of its accretion.

CIRCUMPLANETARY DISK FORMATION

The development and evolution of a circumplanetary disk during the accretion of a giant planet is examined. The planet gains mass and angular momentum from infalling solar nebula material while simultaneously contracting due to luminosity losses. When the planet becomes rotationally unstable it begins to shed material into a circumplanetary disk. Viscosity causes the disk to spread to a moderate fraction of the Hill radius where it is assumed that a small fraction of the material escapes back into heliocentric orbit, carrying away most of the excess angular momentum. As the planets contraction continues, its radius can become smaller than the spatial range of the inflow and material begins to fall directly onto the disk, which switches from a spin-out disk to an accretion disk as the planet completes its growth. We here develop a description of the circumplanetary disk, which is combined with models of the planets contraction and the inflow rate including its angular momentum content to yield a solution for the time evolution of a planet-disk system.