Elsevier

Icarus

Volume 275, 1 September 2016, Pages 239-248
Icarus

Dynamical sequestration of the Moon-forming impactor in co-orbital resonance with Earth

https://doi.org/10.1016/j.icarus.2016.04.007Get rights and content

Highlights

  • We explore Earth's co-orbital resonance as a potential source of the Moon-forming impactor.

  • Mars-mass co-orbital companions of Earth at 1 AU can persist for up to 250 Million years.

  • Escaping companions can impact Earth, with an average impact time of 101 Million years.

  • Several models resulted in formation of a super-Earth, with at least Earth and Venus colliding.

  • Configurations that remained stable included unusual hierarchical coorbital systems.

Abstract

Recent concerns about the giant impact hypothesis for the origin of the Moon, and an associated “isotope crisis” may be assuaged if the impactor was a local object that formed near Earth. We investigated a scenario that may meet this criterion, with protoplanets assumed to originate in 1:1 co-orbital resonance with Earth. Using N-body numerical simulations we explored the dynamical consequences of placing Mars-mass companions in various co-orbital configurations with a proto-Earth of 0.9 Earth-masses (M). We modeled 162 different configurations, some with just the four terrestrial planets and others that included the four giant planets. In both the 4- and 8-planet models we found that a single Mars-mass companion typically remained a stable co-orbital of Earth for the entire 250 million year (Myr) duration of our simulations (59 of 68 unique simulations). In an effort to destabilize such a system we carried out an additional 94 simulations that included a second Mars-mass co-orbital companion. Even with two Mars-mass companions sharing Earth's orbit about two-thirds of these models (66) also remained stable for the entire 250 Myr duration of the simulations. Of the 28 2-companion models that eventually became unstable 24 impacts were observed between Earth and an escaping co-orbital companion. The average delay we observed for an impact of a Mars-mass companion with Earth was 102 Myr, and the longest delay was 221 Myr. In 40% of the 8-planet models that became unstable (10 out of 25) Earth collided with the nearly equal mass Venus to form a super-Earth (loosely defined here as mass ≥1.7 M). These impacts were typically the final giant impact in the system and often occurred after Earth and/or Venus has accreted one or more of the other large objects. Several of the stable configurations involved unusual 3-planet hierarchical co-orbital systems.

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)

  • N.A. Kaib et al.

    The feeding zones of terrestrial planets and insights into Moon formation

    Icarus

    (2015)
  • N.A. Kaib et al.

    Brief follow-up on recent studies of Theia's accretion

    Icarus

    (2015)
  • T. Kleine et al.

    182Hf-182 W isotope systematics of chondrites, eucrites, and martian meteorites: Chronology of core formation and mantle differentiation

    Geochim. Cosmochim. Acta

    (2004)
  • S.J. Kortenkamp

    Trapping and dynamical evolution of interplanetary dust particles in Earth's quasi-satellite resonance

    Icarus

    (2013)
  • S.J. Kortenkamp et al.

    Transformation of Trojans into quasi-satellites during planetary migration and their subsequent close-encounters with the host planet

    Icarus

    (2011)
  • S.J. Kortenkamp et al.

    Survival of Trojan-type companions of Neptune during primordial planet migration

    Icarus

    (2004)
  • H.F. Levison et al.

    The long-term dynamical behavior of short-period comets

    Icarus

    (1994)
  • H.F. Levison et al.

    Origin of the structure of the Kuiper belt during a dynamical instability in the orbits of Uranus and Neptune

    Icarus

    (2008)
  • G. Lugmair et al.

    Early solar system timescales according to 53Mn-53Cr systematics

    Geochim. Cosmochim. Acta

    (1998)
  • M. Nakajima et al.

    Melting and mixing states of the Earth's mantle after the Moon-forming impact

    Earth Planet. Sci. Lett.

    (2015)
  • B.L. Quarles et al.

    Dynamical evolution of the Earth-Moon progenitors – Whence Theia?

    Icarus

    (2015)
  • P. Wajer

    Dynamical evolution of Earth's quasi-satellites: 2004 GU9 and 2006 FV35

    Icarus

    (2010)
  • P.H. Warren

    Stable isotopes and the noncarbonaceous derivation of ureilites, in common with nearly all differentiated planetary materials

    Geochim. Cosmochim. Acta

    (2011)
  • G.W. Wetherill

    Steady state populations of Apollo-Amor objects

    Icarus

    (1979)
  • G.W. Wetherill et al.

    Accumulation of a swarm of small planetesimals

    Icarus

    (1989)
  • G.W. Wetherill et al.

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

    Icarus

    (1993)
  • C. Beauge et al.

    Co-orbital terrestrial planets in exoplanetary systems: A formation scenario

    Astron. Astrophys.

    (2007)
  • E. Belbruno et al.

    Where did the Moon come from

    Astron. J.

    (2005)
  • E. Belbruno et al.

    Formation of the Earth impactor and Moon

  • W.F. Bottke et al.

    Dating the Moon-forming impact event with asteroidal meteorites

    Science

    (2015)
  • C.J. Burke et al.

    Planetary candidates observed by Kepler IV: Planet sample from Q1-Q8 (22 months)

    Astrophys. J. Suppl.

    (2014)
  • A.G.W. Cameron et al.

    The origin of the Moon

  • R. Canup

    Forming a moon with an Earth-like composition via a giant impact

    Science

    (2012)
  • J.E. Chambers

    A hybrid symplectic integrator that permits close encounters between massive bodies

    Mon. Not. R. Astron. Soc.

    (1999)
  • B.F. Collins et al.

    Co-orbital oligarchy

    Astron. J.

    (2009)
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