Dynamical sequestration of the Moon-forming impactor in co-orbital resonance with Earth
Introduction
A conflict exists between dynamical models of very early solar system evolution and measurements of isotopic compositions of available solar system material. Dynamical models of recent decades have suggested that the first 50–100 Myr of terrestrial planet formation involved km-size planetesimals and large lunar- to Mars-mass protoplanets (Wetherill and Stewart, 1989, Wetherill and Stewart, 1993, Chambers and Wetherill, 1998, Chambers, 2001, Chambers, 2013). During this period extensive scattering and mixing of these objects may have occurred, both within and between the inner and outer solar system. The prevailing theory for the formation of the Moon suggests that during this period a large protoplanet impacted Earth, resulting in the formation of the Moon out of debris from the collision (Hartmann and Davis, 1974, Hartmann and Davis, 1975, Cameron and Ward, 1976, Thompson and Stevenson, 1983, Canup, 2004, Canup, 2008, Canup, 2012, Stevenson and Halliday, 2014).
The isotopic composition of samples from Earth, the Moon, and enstatite chondrites from the innermost edge of the asteroid belt is all remarkably similar to each other and all dramatically different from isotopic compositions of ordinary chondrites, ureilites, and carbonaceous material from farther out in the solar system. Most numerical models have established that a moon formed by a giant impact would likely have a different proportion of impactor material than Earth (e.g. Canup, 2004, Canup, 2008, Stewart et al., 2013), and should thus have different isotope ratios than Earth if the impactor were formed from material originating even slightly farther out in the solar system. However, the measured terrestrial and lunar isotope ratios are essentially equal (within error bars) for potassium (Humayun and Clayton, 1995); chromium (Lugmair and Shukolyukov, 1998); titanium (Zhang et al., 2012); and oxygen (Young et al., 2016; also see Herwartz et al., 2014). Late accretion of material after formation of the Moon has been invoked to explain recently measured differences in lunar and terrestrial tungsten isotope ratios (Touboul et al., 2015), which may have been more similar when the Moon formed.
Fig. 1 illustrates the data for chromium and oxygen isotopes. From this figure it is clear that the conflict between the dynamics and the geochemistry becomes more exacerbated if the Moon-forming impactor includes material from the main asteroid belt (e.g., ordinary chondrities, ureilites) or, far worse, carbonaceous chondrite-type material from the outer solar system. Melosh, 2009, Melosh, 2014, lamenting the apparent need for an isotopically identical impactor, declared this problem an “isotope crisis” that shed doubt on the giant impact model. Hartmann, 1986, Hartmann, 2014 noted, however, that the original Hartmann and Davis, 1974, Hartmann and Davis, 1975) model of a giant impact argued for a locally-grown impactor and noted that the solar system indeed still contains “local” objects (enstatite chondrites) with virtually Earth-like compositions. Hartmann (2014) thus argued that the answer to the isotope crisis is simply to accept empirically that any Moon-forming impactor was a very local object, which would solve most (but not all) of the isotope crisis. Indeed, a slight offset in lunar oxygen isotopes, relative to Earth has been reported (Herwartz et al., 2014; see their Fig. 1) in the direction of enstatite chondrite. Mastrobuono-Battisti et al. (2015) recently lent support to this when they showed that 10–20% of terrestrial planet giant impacts the impacting object is a local body compositionally similar to the planet being impacted. However, Kaib and Cowan, 2015a, Kaib and Cowan, 2015b) showed that isotopic differences within the measured Earth–Moon range are to be expected in only 5% of potential Moon-forming impactors. Nakajima and Stevenson (2015) discuss circumstances related to the Grand Tack scenario (Walsh et al., 2011) that could increase the probability that the Moon-forming impactor had a similar oxygen isotopic ratio as Earth.
The other component of the isotope crisis has to do with the timing of the Moon-forming impact. If the impactor did originate very close to Earth (to ensure a more plausible likelihood of similar isotopic composition) then a mechanism may be needed to delay the impact. Age estimates for differentiation of Earth's core (Halliday, 2008) and modeling of a late veneer chronology utilizing highly siderophile elements in Earth's mantle (Jacobson et al., 2014) each generally agree that the Moon-forming impact must have occurred between roughly 70 and 130 Myr after condensation of Calcium Aluminum Inclusions (CAIs), the first solids in the solar system. Bottke et al. (2015) independently supported this Moon-formation time scale by combining dynamical simulations, geochemistry, and proposed asteroid impact age distributions. Thus, resolving the isotope crisis may not only require a very local impactor, but a mechanism to sequester this impactor very close to 1 AU for up to 130 Myr after CAIs. New research into the process of planet formation, described below, may suggest that both of these conditions could be natural consequences of the process of terrestrial planet formation and early evolution.
Discoveries of extrasolar planetary systems with numerous Earth-size planets (see catalogs by Burke et al., 2014, Rowe et al., 2015, Mullally et al., 2015) have brought renewed interest to the process of terrestrial planet formation and early evolution, and interactions of local planet-size bodies that may no longer exist in our solar system. Several independent groups have utilized modern techniques to examine these processes and found interesting results unseen in modeling from a generation ago (e.g., Safronov, 1972, Wetherill and Stewart, 1989, Wetherill and Stewart, 1993). For example, Beaugé et al. (2007) modeled terrestrial planet formation in theoretical extrasolar systems and reported the formation of co-orbital planets, with a terrestrial planet forming in a 1-to-1 orbital resonance with a pre-existing giant planet. Collins and Sari (2009) found that relatively narrow terrestrial planet accretion zones within a protoplanetary disk can produce not just a single dominant protoplanet but numerous large protoplanets forming in mutual co-orbital resonance with each other. Cresswell and Nelson, 2008, Cresswell and Nelson, 2009 studied formation of somewhat larger planets (sub Neptune-mass) and found as many as 30% of their simulated planetary systems emerging with long-lived co-orbital planets. While co-orbital planets have not yet been confirmed (also see Goździewski and Konacki, 2006), these new theoretical models provide a type of qualitative motivation for the investigation described in this paper.
With an eye on the isotopic similarities between Earth and the Moon, Belbruno and Gott, 2005, Belbruno and Gott, 2008 suggested that the Moon-forming impactor may have originated in co-orbital resonance with Earth until eventually escaping the resonance and impacting Earth. In this scenario the co-orbital resonance could provide the necessary dynamical safe haven to delay the timing of the last giant impact with Earth. We acknowledge that some isotopic properties may depend on the objects’ mass (e.g., Si; Armytage et al., 2012) and time-scale of accretion and differentiation (e.g., W; Kleine et al., 2004). Likewise, a co-orbital origin does not necessarily imply that Earth and a companion would have similar chemical properties. Chambers, 2001, Chambers, 2013) demonstrated that the late stage of planet formation is likely a stochastic process. Two objects growing in the vicinity of each other may not necessarily incorporate material from different regions in the same proportions. We point out that all models of Moon formation that invoke a Mars-mass impactor, regardless of where it originates, suffer from these same issues. In light of the recent work on co-orbital planet formation described above, we argue that of all the possible locations where a protoplanet isotopically similar to the proto-Earth could have formed the most plausible and/or least objectionable location may be within Earth's co-orbital region.
With these caveats acknowledged, we ask, “If an isotopically similar protoplanet could form in co-orbital resonance with Earth would this provide a dynamical basis for delaying the moon-forming impact?”
Section snippets
Methods and results
Our simulations begin at a point when the inner solar system has evolved to hold 4 terrestrial planets and one or two remaining Mars-mass protoplanets. This state is generally thought to have been achieved roughly 30–50 Myr after CAIs (see Morbidelli et al. (2012) for a review and Chambers (2013) for more recent work). We model the consequences if – following Beaugé et al. (2007) and Collins and Sari (2009) – these last one or two protoplanets formed as co-orbital companions with Earth, the
Summary and discussion
We make the initial assumption that ∼30–50 Myr after CAIs the inner solar system contained the 4 terrestrial planets and one or two remaining Mars-mass protoplanets. Furthermore, we anticipate that one of these protoplanets will be the Moon-forming impactor. This working hypothesis is similar to the recent study of Quarles and Lissauer (2015). They modeled the orbital evolution of such a system assuming a final remaining protoplanet was located between about 0.8 and 1.2 AU. In contrast, we seek
Acknowledgments
S.J.K. acknowledges support from the National Aeronautics and Space Administration under grant NNX14AN23G. We thank Nathan Kaib and Billy Quarles for detailed reviews that helped significantly clarify and correct the manuscript. We are also grateful to Alessandro Morbidelli both for pointing out a misconception we had in the original manuscript and for his editorial patience.
References (71)
- et al.
Silicon isotopes in lunar rocks: Implications for the Moon's formation and the early history of the Earth
Geochim. Cosmochim. Acta
(2012) Simulations of a late lunar-forming impact
Icarus
(2004)Lunar-forming collisions with pre-impact rotation
Icarus
(2008)Making more terrestrial planets
Icarus
(2001)Late-stage planetary accretion including hit-and-run collisions and fragmentation
Icarus
(2013)- et al.
Making the terrestrial planets: N-body integrations of planetary embryos in three dimensions
Icarus
(1998) - et al.
A population of main belt asteroids co-orbiting with Ceres and Vesta
Icarus
(2012) Atlas of the mean motion resonances in the solar system
Icarus
(2006)- et al.
Satellite-sized planetesimals and lunar origin
Icarus
(1975) - et al.
Precise determination of the isotopic composition of potassium: Application to terrestrial rocks and lunar soils
Geochim. Cosmochim. Acta
(1995)
The feeding zones of terrestrial planets and insights into Moon formation
Icarus
Brief follow-up on recent studies of Theia's accretion
Icarus
182Hf-182 W isotope systematics of chondrites, eucrites, and martian meteorites: Chronology of core formation and mantle differentiation
Geochim. Cosmochim. Acta
Trapping and dynamical evolution of interplanetary dust particles in Earth's quasi-satellite resonance
Icarus
Transformation of Trojans into quasi-satellites during planetary migration and their subsequent close-encounters with the host planet
Icarus
Survival of Trojan-type companions of Neptune during primordial planet migration
Icarus
The long-term dynamical behavior of short-period comets
Icarus
Origin of the structure of the Kuiper belt during a dynamical instability in the orbits of Uranus and Neptune
Icarus
Early solar system timescales according to 53Mn-53Cr systematics
Geochim. Cosmochim. Acta
Melting and mixing states of the Earth's mantle after the Moon-forming impact
Earth Planet. Sci. Lett.
Dynamical evolution of the Earth-Moon progenitors – Whence Theia?
Icarus
Dynamical evolution of Earth's quasi-satellites: 2004 GU9 and 2006 FV35
Icarus
Stable isotopes and the noncarbonaceous derivation of ureilites, in common with nearly all differentiated planetary materials
Geochim. Cosmochim. Acta
Steady state populations of Apollo-Amor objects
Icarus
Accumulation of a swarm of small planetesimals
Icarus
Formation of planetary embryos: Effects of fragmentation, low relative velocity, and independent variation of eccentricity and inclination
Icarus
Co-orbital terrestrial planets in exoplanetary systems: A formation scenario
Astron. Astrophys.
Where did the Moon come from
Astron. J.
Formation of the Earth impactor and Moon
Dating the Moon-forming impact event with asteroidal meteorites
Science
Planetary candidates observed by Kepler IV: Planet sample from Q1-Q8 (22 months)
Astrophys. J. Suppl.
The origin of the Moon
Forming a moon with an Earth-like composition via a giant impact
Science
A hybrid symplectic integrator that permits close encounters between massive bodies
Mon. Not. R. Astron. Soc.
Co-orbital oligarchy
Astron. J.
Cited by (6)
Radial mixing and Ru–Mo isotope systematics under different accretion scenarios
2018, Earth and Planetary Science LettersCitation Excerpt :The Moon has an identical or very similar isotopic composition to the Earth for many elements (e.g., Dauphas and Schauble, 2016, and references therein), which is striking considering the range in isotopic compositions exhibited by meteorites. Theories to explain this phenomenon include: 1) isotopic equilibration between the Earth and Moon via the proto-lunar disk (Pahlevan and Stevenson, 2007), which may not explain isotopic similarities in refractory elements; 2) collisions that result in the Earth and Moon containing similar fractions of the proto-Earth and the Moon-forming impactor, “Theia” (e.g., Canup, 2012; Ćuk and Stewart, 2012), which require specific dynamical conditions; or 3) the proto-Earth and Theia having identical isotopic compositions, which either requires them to have similar provenance/location (e.g., Quarles and Lissauer, 2015; Kortenkamp and Hartmann, 2016) or requires isotopic homogeneity in the inner disk (e.g., Dauphas et al., 2002a, 2014a, 2014b). However, the latter theory does not explain the nearly-identical lunar and terrestrial 182W isotopic anomalies as these anomalies are sensitive to differentiation timescales (Dauphas and Schauble, 2016; Dauphas et al., 2014a; Nimmo and Kleine, 2015).
Workshop Summary: Exoplanet Orbits and Dynamics
2023, Publications of the Astronomical Society of the PacificCollision chains among the terrestrial planets. III. formation of the moon
2021, Planetary Science JournalOrigin of the Moon
2021, arXivAsteroid (469219) 2016 HO<inf>3</inf>, the smallest and closest Earth quasi-satellite
2016, Monthly Notices of the Royal Astronomical Society