Earth and Planetary Science Letters 470 (2017) 87–95

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Earth and Planetary Science Letterswww.elsevier.com/locate/epsl

Ejection of iron-bearing giant-impact fragments and the dynamicaland geochemical inﬂuence of the fragment re-accretion
Hidenori Genda a,b,∗ , Tsuyoshi Iizuka b , Takanori Sasaki c,d , Yuichiro Ueno a,d ,Masahiro Ikoma b,eaEarth-Life Science Institute, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan
Department of Earth and Planetary Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japanc
Department of Astronomy, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japand
Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japane
Research Center for the Early Universe, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japanba r t i c l e

i n f oArticle history:
Received 19 August 2016
Received in revised form 10 April 2017
Accepted 18 April 2017
Available online xxxx
Editor: B. Marty
Keywords:
giant impacts
terrestrial planet formationlate veneer
dynamical friction
reduced atmospherea b s t r a c t
The Earth was born in violence. Many giant collisions of protoplanets are thought to have occurred
during the terrestrial planet formation. Here we investigated the giant impact stage by using a hybrid
code that consistently deals with the orbital evolution of protoplanets around the Sun and the detailsof processes during giant impacts between two protoplanets. A signiﬁcant amount of materials (up to
several tens of percent of the total mass of the protoplanets) is ejected by giant impacts. We call theseejected fragments the giant-impact fragments (GIFs). In some of the erosive hit-and-run and high-velocity
collisions, metallic iron is also ejected, which comes from the colliding protoplanets’ cores. From ten
numerical simulations for the giant impact stage, we found that the mass fraction of metallic iron in
GIFs ranges from ∼1 wt% to ∼25 wt%. We also discussed the effects of the GIFs on the dynamical andgeochemical characteristics of formed terrestrial planets. We found that the GIFs have the potential tosolve the following dynamical and geochemical conﬂicts: (1) The Earth, currently in a near circular orbit,
is likely to have had a highly eccentric orbit during the giant impact stage. The GIFs are large enoughin total mass to lower the eccentricity of the Earth to its current value via their dynamical friction.
(2) The concentrations of highly siderophile elements (HSEs) in the Earth’s mantle are greater than what
was predicted experimentally. Re-accretion of the iron-bearing GIFs onto the Earth can contribute to theexcess of HSEs. In addition, Iron-bearing GIFs provide signiﬁcant reducing agent that could transformprimitive CO2 –H2 O atmosphere and ocean into more reducing H2 -bearing atmosphere. Thus, GIFs areimportant for the origin of Earth’s life and its early evolution.
© 2017 Elsevier B.V. All rights reserved.

1. Introduction
According to the classical model for planet formation called“the planetesimal accretion model”, planets are formed in situ in a
protoplanetary disk through successive accretion of km-sized planetesimals (Safronov, 1969; Hayashi et al., 1985). In the terrestrial
planet region in our solar system, if the minimum-mass solar nebula (Hayashi, 1981) is assumed, several tens of Mars-sized protoplanets form (Wetherill, 1985; Lissauer, 1987; Kokubo and Ida,
1998) and they collide with each other to form Earth-sized planets (Chambers and Wetherill, 1998; Agnor et al., 1999). Collisions*

Corresponding author at: Earth-Life Science Institute, Tokyo Institute of Technology, 2-12-1-IE-14 Ookayama, Meguro-ku, Tokyo 152-8551, Japan.
E-mail address: genda@elsi.jp (H. Genda).
http://dx.doi.org/10.1016/j.epsl.2017.04.035
0012-821X/© 2017 Elsevier B.V. All rights reserved.

among protoplanets are called giant impacts, and this stage lastsfor ∼100 Myr (Kokubo et al., 2006; Jacobson et al., 2014). Especially, the last giant impact onto Earth likely produced the Moon,
which meets geophysical and geochemical observations of Moon
(Stevenson and Halliday, 2014). Although the detailed accretion
process of protoplanets is a matter debate (Hayashi et al., 1985;
Walsh et al., 2011; Lambrechts and Johansen, 2012; Levison et al.,2015), giant impacts seem to be a natural consequence for terrestrial planet formation.
Giant impacts are not simply merging events but also include
complex events such as hit-and-run collisions (Agnor and Asphaug,
2004; Genda et al., 2012) and erosive collisions (Leinhardt and
Stewart, 2012). These collisions also more or less produce ejectedmaterials that are gravitationally unbound by protoplanets and orbit around a star. Using the impact conditions obtained by N-bodyorbital calculations of protoplanets (Kokubo and Genda, 2010),

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H. Genda et al. / Earth and Planetary Science Letters 470 (2017) 87–95

a hybrid code that simulates both the orbital evolution and collision process of protoplanets in the giant impact stage, based on the
proto-type of a hybrid code presented in Genda et al. (2011). The
details of the code are described in Section 2, and the simulation
results are shown in Section 3. We show that the production andre-accretion of GIFs are inevitable during the giant impact stage.
In Section 4, we discuss the dynamical effects of the GIFs on the
Earth, and quantitatively examine the geochemical effects of reaccretion of GIFs on the Earth.
2. Hybrid code for giant impact stage

Fig. 1. Schematic view of production and re-accretion of giant-impact fragments(GIFs). (1) Several tens of Mars-sized protoplanets form in the terrestrial-planet
formation region. (2) These protoplanets collide with each other and eject large
amounts of material into the orbital region. (3) The GIFs are re-accreted onto theterrestrial planets on a timescale of 10 Myr after the end of giant impacts. In thisstudy, we simulate orbital evolutions and collisional processes of the protoplanets,
and estimate the amount of GIFs and their compositions. We also discuss the dynamical and geochemical inﬂuence of the re-accretion of GIFs based on analyticalarguments.

Genda et al. (2015a) estimated that a large amount of materials(several Mars masses in total) is ejected by giant impacts throughout the giant impact stage, which is consistent with the previous
estimate (Stewart and Leinhardt, 2012). Ejection of materials by
collisions seems to be ubiquitous not only during the giant impact
stage, but also during the protoplanet formation stage (Bonsor etal., 2015; Carter et al., 2015).
If giant impacts take place in extrasolar systems, they would
leave observational signatures. Indeed, detection of tens of infraredexcess of solar-type stars with ages of 10–100 Myr has been reported recently (Zuckerman et al., 2011). This infrared excess is
attributed to the infrared emission of dusts in a debris disk. Thesedusts are heated by the star (e.g., Olofsson et al., 2012), and thesewarm debris disks (> ∼200 K) are located roughly 1 to several AU
from the central stars, which corresponds to our terrestrial planet
region. Thus, observed infrared excesses can be explained by debris
produced during giant impact events (Jackson and Wyatt, 2012;
Genda et al., 2015a; Kenyon et al., 2016).
Here, we focus on the ejected materials produced by giant impact events during terrestrial planet formation (Fig. 1); we hereafter refer to the ejected materials as giant-impact fragments(GIFs). The GIFs may have effects on the characteristics of formed
terrestrial planets, which have not been well investigated. For example, while the current Earth’s orbit is nearly circular, the protoEarth likely had a highly eccentric orbit just after the end of
the giant impact stage (Kokubo et al., 2006). We propose that
the GIFs can decrease its eccentricity via dynamical friction withplanets, provided a suﬃcient amount of GIFs are ejected and distributed in the terrestrial planet region. Moreover, if the GIFs
contain metallic iron that is ejected from the cores of colliding
differentiated protoplanets, re-accretion of the GIFs on the Earthshould have effects on the redox state of the early Earth’s environment because metallic iron acts as a reductant. Since almost
all highly siderophile elements (HSEs; Re, Au, Os, Ir, Ru, Pt, Rh
and Pd) are partitioned into the iron cores of protoplanets, reaccretion of metallic iron in GIFs would be a potential source ofexcess HSEs in the current Earth’s mantle (Kimura et al., 1974;
Chou, 1978).
Here we perform the self-consistent simulations of successive
giant collisions among protoplanets and calculate the mass of GIFs
with a focus on their iron contents. To that end, we have developed

Our hybrid code consists of two parts: an N-body code for describing the orbital evolution of protoplanets around the Sun and
an impact code for describing a collision between two protoplanets. In the N-body code, we use the modiﬁed fourth-order Hermite
scheme with an individual time step (Kokubo and Makino, 2004).
This allows us to calculate the orbits of protoplanets accurately,
considering their mutual gravitational interactions without missing collisions between them. In the impact code, we utilize thecode developed in Genda et al. (2015b). In this code, the standard smoothed particle hydrodynamics (SPH) method (Lucy, 1977)
is used, which is a ﬂexible Lagrangian method of solving hydrodynamic equations and has been widely used to simulate giant
impacts between protoplanets (Canup, 2004).
The numerical simulation is started with the N-body code under a certain initial condition where protoplanets are located in
the terrestrial planet forming region, and the orbital evolution of
protoplanets is integrated. When the surfaces of any two protoplanets contact or overlap in the N-body code, we switch fromthe N-body code to the SPH code. By using impact parameters(the impact velocity and the impact angle) obtained by the orbital
calculation and planetary conditions of the colliding protoplanets(their masses, core–mantle ratios, and spin states), we calculate
the collision between two protoplanets. We use 10,000 SPH particles with equal mass for the two colliding protoplanets. During
the impact simulation, the gravities of the Sun and the other protoplanets that act on the SPH particles are included, and orbital
evolutions of the other protoplanets are also calculated.
Next, we analyze the outcome of the collision, and determine
the masses of the gravitationally bounded clumps after the collision (Genda et al., 2015b), whose masses are deﬁned as M 1 , M 2 ,M 3 . . . in order from the largest body. We set the lower limit of thenumber of SPH particles (= 10 particles) for a clump. We classify
the impact event into two types by comparing the largest and second largest bodies (M 1 and M 2 ). If M 1 / M 2 is less than 100, wedeﬁne this collision as a hit-and-run impact, and we include boththe largest and the second largest bodies as protoplanets in thesubsequent N-body calculation. Otherwise, we deﬁne it as a singlemain-body-remaining impact, and we only include the largest bodyas a protoplanet. It is noted that not only a simple merging impact,
but also an impact that destroys the impactor (smaller protoplanet)
are classiﬁed into a single-main-body-remaining impact.
We also determine the mass of GIFs (M GIFs ) and its composition(i.e., iron fraction). Here we deﬁne the materials other than protoplanet(s) after the collision as GIFs. Therefore, M GIFs = M tot − M 1
for a single-main-body-remaining impact, and M GIFs = M tot − M 1 −M 2 for a hit-and-run impact, where M tot is the sum of mass forcolliding two protoplanets. Some of the ejected fragments soon
re-accrete onto the protoplanets, or orbit near the protoplanet(s),making a disk structure, but we do not regard these types offragments as GIFs. By using the data of the mass, position, andvelocity for post-impact protoplanets(s), we switch the code fromthe SPH code to the N-body code. For simplicity, we remove theejected materials (i.e., GIFs) produced by each collision from thesubsequent N-body calculation. We calculate the orbits of the pro-

H. Genda et al. / Earth and Planetary Science Letters 470 (2017) 87–95

toplanets until the next collision. These iterative calculations arecontinued for 200 Myr. In all the simulations below, we assume
that no nebular gas remains. In this hybrid code, we can trace
the changes in the mass, spin state (obliquity and spin rate), andcomposition (core–mantle ratio) of protoplanets during the giant
impact stage.
Although introducing GIFs in N-body calculation would be important for many aspects, it is very CPU time consuming to carryout the N-body calculation with large number of fragments. Asa ﬁrst step, here we carried out the N-body simulations without
GIFs, but we estimated the mass and composition of GIFs producedby each giant impact and we qualitatively discuss the effects of
GIFs on the dynamical and geochemical aspects in Section 4.
For the initial condition of protoplanets, we follow the classicalplanetesimal accretion model. In the stage of protoplanet formation
through successive accretions of planetesimals, the growth modeof a protoplanet is oligarchic, and its mass is given by the isolation
mass (Kokubo and Ida, 2000). If the minimum-mass solar nebula(Hayashi, 1981) is assumed, several tens of Mars-sized protoplanets
form in the terrestrial planet formation region. In this study, we
put 16 Mars-sized protoplanets with a total mass of 2.3 M ⊕ from
0.5 to 1.5 AU for the initial conditions, where M ⊕ is the Earthmass. This initial condition is the same one that Kokubo and Genda(2010) used.
All the protoplanets are assumed to be initially differentiatedwith a 30 wt% iron core and 70 wt% silicate mantle. In our
SPH simulations, we use the Tillotson EOS (Tillotson, 1962) withthe parameter sets of granite for the mantle and of iron forthe core (Melosh, 1989). Although peridotite is more appropriate for the mantle materials, there is no available parameter setof peridotite for the Tillotson EOS. Instead, for many giant impact simulations (e.g., Benz et al., 1987; Canup and Asphaug, 2001;
Agnor and Asphaug, 2004), the parameter set of granite or basalt
was used. We expect there to be no signiﬁcant difference in behavior among the shocked states of peridotite, granite and basalt
during a giant impact because they have similar density–pressure
relations in shocked states (e.g., Artemieva and Ivanov, 2004).

89

Fig. 2. Orbital evolutions of protoplanets for two different initial angular distributions of protoplanets (Runs 3 and 5). Top and middle panels show temporal changes
in the semi-major axes a (red curves) and pericenter q and apocenter Q distances(green curves) of protoplanets for Runs 3 and 5, respectively. Bottom panel showsthe error of the total energy (potential and orbital energies of protoplanets) for theorbital calculation, considering the energy loss due to the removal of the ejectedmaterials in our simulation. (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)

3. Numerical results of the giant impact stage
We have performed ten runs with different initial angular distributions of the protoplanets. Fig. 2 shows the orbital evolutionof the protoplanets for 200 Myr in the typical two runs (Runs 3
and 5). Considering the energy loss due to the removal of GIFs
in our simulation, we have conﬁrmed that the error of the totalenergy for the orbital calculation in 200 Myr is typically within
0.01%.
As shown below, Runs 3 and 5 are the typical cases resulting
in a high and low content of metallic iron in GIFs, respectively.
The number of protoplanets decreases with time, which indicatesthat single-main-body remaining giant impact events happen. In
these simulations for Runs 3 and 5, giant impacts occur 23 and 25
times, respectively. In total for 10 runs, 245 giant impacts occur.
We found 52% of giant impact events (= 127/245) are hit-andrun events, which is consistent with the previous studies (49% in
Kokubo and Genda, 2010, and 38% in Chambers, 2013).
The numbers of the planets that survived after 200 Myr are 5
and 4 for Runs 3 and 5, respectively. From ten runs, we found thatthe average number and the standard deviation of the ﬁnal planets
is 4.2 ± 0.8, which is identical within the uncertainty to the previous results obtained by N-body calculations, that is, 3.4 ± 0.6 and3.6 ± 0.8 reported in Kokubo et al. (2006) and Kokubo and Genda(2010), respectively. In detail, the average number obtained hereis slightly larger than those in the previous studies. In our hybrid
code, since we removed the ejected materials produced by eachcollision, the total mass of the protoplanetary system decreases

Fig. 3. Mass versus semi-major axis for all protoplanets at the end of the simulations(t = 200 Myr). Circles indicate numerical results, while square symbols show theterrestrial planets of our solar system for comparison.

with time. It has already been shown in Kokubo et al. (2006) thata lighter protoplanetary disk results in a larger number of ﬁnal
planets, which would be responsible for the larger average number obtained here. Our result (4.2 ± 0.8) is also consistent with therecent results obtained by N-body calculations with fragmentation
model (4.2 ± 0.9 in Chambers (2013) and 3.8 ± 0.9 in Quintana etal. (2016)).
Fig. 3 shows the mass and semi-major axis for all planets ﬁnally formed. Typically, 1 or 2 Earth-sized planets are formed in
the middle of the terrestrial planet region (∼1 AU), and another2 or 3 small planets are formed at the both edges of the terrestrial planet region, which is consistent with the previous studies(Kokubo and Genda, 2010; Chambers, 2013). These small planetsare likely survivors, that is, they experienced no giant impact or a
few hit-and-run giant impacts.
Fig. 4 shows the snapshots for three types of giant impacts
happened in Run 3. Those giant impacts correspond to the 8th(Coll#8), 19th (Coll#19), and 23rd collisions (Coll#23), respectively.
Fig. 5 shows the mass (and the number of SPH particles) of the

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H. Genda et al. / Earth and Planetary Science Letters 470 (2017) 87–95

Fig. 4. Snapshots of three giant impacts (Coll#8, #19, and #23) taking place in Run 3. Green and red particles represent mantle materials and iron materials, respectively. The
ﬁlled black circles in the bottom-right corner of each panel are 5000 km in diameter. (For interpretation of the references to color in this ﬁgure legend, the reader is referredto the web version of this article.)
Table 1
Total mass of GIFs and their iron content for various numerical resolutions.
# of SPH
particles

Coll#8
M GIFs[M tot ]f Fe

Coll#19
M GIFs[M tot ]f Fe

Coll#23
M GIFs[M tot ]

f Fe

104
105
106

0.009
0.012
0.017

0%
0%
0%

0.45
0.52
0.61

4.9%
6.9%
8.8%

0.32
0.33
0.33

27.2%
27.1%
27.5%

Note: M GIFs is the total mass of GIFs ejected by each giant impact, M tot is the summation of the target’s and impactor’s mass, and f Fe is the fraction of metallic ironin GIFs.

Fig. 5. The mass of the largest and second largest bodies, and GIFs after giant impacts. Three giant impacts (Coll#8, #19, and #23) are considered. If the data points
are on the dashed line, these clumps have different number of SPH particles. The
data points that have 1 in the value of horizontal axis correspond to total mass of
single SPH particle.

largest and the second largest bodies (M 1 and M 2 ) and GIFs obtained by analyzing the collision outcome. In Coll#8, two Marssized protoplanets collide at a low velocity (v imp = 1.04v esc ) witha 47◦ impact angle, where v imp and v esc are the impact velocity and the two-body surface escape velocity, respectively, anda 0◦ impact angle corresponds to a head-on impact. Two colliding protoplanets merge together, and a small amount of GIFs
(2.2 × 1022 kg) is ejected. All SPH particles in GIFs are gravitationally separated from each other (Fig. 5). Since each iron core completely merges, the GIFs contain no iron particles. In Coll#19, twoMars-sized protoplanets collide at a high velocity (v imp = 2.6v esc )with a 14◦ impact angle, and they do not merge, which is classiﬁed as a hit-and-run impact. In Fig. 5, the largest and second
largest clumps survive the giant collision. Due to the high impact
velocity in Coll#19, a lot of GIFs (3.7 × 1023 kg) are ejected, andGIFs consist of small 4 clumps and a lot of the other single SPH
particles. GIFs are ejected not only from their mantles, but also
from their iron cores. In this collision, 4.9% of the mass in GIFs
is iron material. In Coll#23, different sized protoplanets collide ata high velocity (v imp = 3.2v esc ) with a 33◦ impact angle. The im-pactor (smaller protoplanet) is pulverized, and almost all of the
impactor’s materials from both mantle and core (1.3 × 1024 kg) areejected. Since M 2 is much smaller than M 1 , this collision is classiﬁed as a single-main-body-remaining impact. On the other hand,
the target core remains intact.
The number of SPH particles (104 particles) used here for giant impact simulations would not be enough to precisely estimate
the masses of the largest and the second largest bodies and GIFs.
According to Genda et al. (2015b), higher-resolution impact simulation of planetesimals tends to result in more erosive and disruptive collision. Here we carried out additional high-resolution
simulations (105 and 106 SPH particles) for three types of giant
impacts (Coll#8, Coll#19, and Coll#23). Table 1 lists the total massand composition of GIFs for different numerical resolutions.
For simple merging event (Coll#8), the mass of GIFs (M GIFs ) increases by a factor of 2, but it is still a small fraction of M tot .
For hit-and-run event (Coll#19), both M GIFs and the fraction of
metallic iron in GIFs ( f Fe ) increase by 50%. For impactor-destroying
event (Coll#23), neither M GIFs nor f Fe depends on the numericalresolutions. Although the dependence of M GIFs on the numericalresolution is different among various types of giant impacts, M GIFs
tends to increase with the numerical resolution. In this sense, theresults obtained by using 104 SPH particles give us the lower estimate in the mass of GIFs.
Fig. 6 shows a plot of the mass of GIFs ejected by each giant impact in Runs 3 and 5. Sometimes, catastrophic high-impact-velocity

H. Genda et al. / Earth and Planetary Science Letters 470 (2017) 87–95

Fig. 6. The total mass of ejected materials by each giant impact during 200 Myr for
Runs 3 and 5. The green bars represent the total mass of ejected materials, while
the red bars represent that of iron components. Three bars indicated by Coll#8, #19
and #23 represent collisions shown in Fig. 4. (For interpretation of the references tocolor in this ﬁgure legend, the reader is referred to the web version of this article.)

collisions, which produce GIFs greater than 0.03 M ⊕ , take place.
Fig. 6 also shows the composition of the GIFs, that is, the fractionsof rock and iron materials. We found that some giant impacts ejectsigniﬁcant amounts of metallic iron (red bars). Even in the case ofa low-velocity impact such as the canonical Moon-forming impact,
it was reported that a small amount of iron material was ejectedfrom the impactor’s core into a proto-lunar disk (e.g., Canup andAsphaug, 2001). It was also reported that high velocity collisions
among planetesimals and protoplanets during the stage of protoplanet formation, which is followed by the giant impact stage,
produce a lot of debris, and some of them are metallic iron fromdifferentiated planetesimals (Carter et al., 2015). Therefore, it isreasonable to expect a signiﬁcant amount of ejected metallic iron
for intermediate or high velocity giant impacts.
It has been reported that the standard SPH method usedhere has diﬃculty in picking up hydrodynamical instabilities (e.g.,
Agertz et al., 2007) such as Rayleigh–Taylor and Kelvin–Helmholtz
instability. These instabilities create the mixed layer at the core–mantle boundary to some extent, and would enhance the amountof metallic iron in GIFs. In this sense, the amount of ejected metallic iron obtained here would be a lower estimate.
Fig. 7 shows the total mass of GIFs during the giant impact stage in each run. A large amount of materials (from 0.3
to 0.8 M ⊕ ) are ejected. On average, GIFs of 0.51 M ⊕ are produced, which is consistent with the previous estimate (0.42 M ⊕ )in Genda et al. (2015a), where they performed giant impact simulations by using the impact conditions obtained separately by
the N-body calculations for the orbital evolution of protoplanets
done by Kokubo and Genda (2010). Although the average mass ofejected materials produced by a single giant-impact event is small(a few percent of the two colliding protoplanets), the cumulative
amount of the ejected materials is not negligible relative to thetotal mass of the protoplanetary system (2.3 M ⊕ ). For each run,
GIFs contain iron materials (0.6–25 wt% of GIFs), and in particular,catastrophic high-impact-velocity collisions between protoplanets
in Runs 3, 6 and 9 produce large amounts of ejected iron materials.
4. Dynamical and geochemical effects of GIFs on the Earth
4.1. Circularization of the Earth’s orbit via dynamical friction of GIFs
In many orbital simulations of protoplanets in the giant impact
stage (Chambers and Wetherill, 1998; Kokubo et al., 2006), the ec-

91

Fig. 7. Cumulative mass of the GIFs in Earth mass units for ten runs with different initial orbital conﬁgurations of protoplanets. The colors of each bar show thecomposition of the ejected materials (green: rocky material from the protoplanets’
mantles, red: iron material from their cores). (For interpretation of the references tocolor in this ﬁgure legend, the reader is referred to the web version of this article.)

centricities of the terrestrial planets ﬁnally formed are rather high(∼0.1) compared with the present ones of the Earth and Venus(∼0.01). Such high eccentricities are a natural consequence of the
giant impact stage; otherwise protoplanets in separate orbits neverundergo orbital crossing. To date, two mechanisms for damping
such high eccentricities have been proposed: the drag force of theremaining nebular gas (Kominami and Ida, 2002) and the dynamical friction due to the planetesimals that are yet to accrete onto
the protoplanets during the oligarchic growth stage (O’Brien et al.,2006). In Section 3, we have found that a large quantity of GIFs areinevitably produced during the giant impact stage, which suggeststhat the GIFs may be able to damp the high eccentricities of fullygrown terrestrial planets like remaining planetesimals can do. We
should emphasize that our scenario is self-suﬃcient, so that we
do not require the remaining nebular gas nor planetesimals during
the giant impact stage to explain the current low eccentricities of
the terrestrial planets.
According to Schlichting et al. (2012), remaining planetesimals
with a total mass of 0.01 M ⊕ can damp the excited eccentricity of
the Earth to the present level. In the limit of eﬃcient dampingof eccentricities of planetesimals due to their mutual collisions,they estimated a total mass of the remaining planetesimals thatis required to damp the eccentricities of the planets by comparing the eccentricity damping timescale for the terrestrial planets
through dynamical friction with remaining planetesimals (t damp ) to
the accretion timescale of the remaining planetesimals (t acc ). The
condition t acc > t damp must be fulﬁlled for the eccentricities of theplanets to be fully damped. Such a condition is derived asΣpl  Σtp

v
v esc

2
,

(1)

where Σ pl and Σ tp are the mass surface densities of remaining
planetesimals and the terrestrial planets, respectively, and v andv esc are the velocity dispersion and escape velocity of the terrestrial planets, respectively. Since v / v esc is ∼0.1–0.3 during the giant
impact stage in by N-body simulations (Chambers, 2001), Σpl /Σtp
is estimated to be 0.01–0.1. Therefore, Schlichting et al. (2012) concluded that remaining planetesimals with roughly 0.01 M ⊕ candamp the Earth’s eccentricity.
Although detailed simulations including gravitational interactions between protoplanets and remaining small bodies such as

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H. Genda et al. / Earth and Planetary Science Letters 470 (2017) 87–95

GIFs are needed to conﬁrm the above conclusion, dynamical friction by such a large quantity of GIFs—0.3–0.8 M ⊕ obtained inour simulations—is a promising mechanism for damping the eccentricities of the excited terrestrial planets. Note that not allof the GIFs contribute to damping the eccentricities of formedplanets. Some of the GIFs produced early in the giant impact
stage re-accrete on protoplanets before the Earth is completely
formed (i.e., the last giant impact), and small GIFs (∼ μm) produced via mutual collisions among GIFs can also be easily blownout by solar radiation pressure. The half-life of such a debris
disk produced by giant impacts is estimated to be the order of
10 Myr in the cases of both re-accretion (Jackson and Wyatt, 2012;
Bottke et al., 2015) and blowing-out (Genda et al., 2015a). Therefore, the large fraction of GIFs produced early in the giant impact
stage cannot survive until the last giant impact (∼100 Myr), but
the GIFs produced in the late stages can survive and would contribute to damping the Earth’s eccentricity.
4.2. GIFs as a potential source of excess HSEs in the Earth’s mantle
Highly siderophile elements (HSEs) are strongly depleted in the
Earth’s mantle relative to chondrites, but their relative abundances
are nearly chondritic despite their signiﬁcantly different silicate–
metal partitioning coeﬃcients (Mann et al., 2012). The observed
HSE signature has led to the widely held hypothesis that the HSEs
were almost completely stripped from the Earth’s mantle throughmetal-silicate segregation as well as sulﬁde-silicate segregation
and, after core formation, a small amount of materials enriched in
HSEs was supplied to the Earth (Kimura et al., 1974; Chou, 1978;
Rubie et al., 2016) via the late-accretion (or “late veneer”, which
has sometimes been used as the synonym with “late-accretion”).
As the source for the late veneer, chondrites in the outer asteroid belt (Drake and Righter, 2002) and leftover planetesimals after
the giant impact phase (Schlichting et al., 2012) have been proposed. The former is further considered as a potential source of
the Earth’s volatiles (e.g., Albarède, 2009).
Here, as an alternative, we argue that the excess abundances of
HSEs in the Earth’s mantle can be attributed to the re-accretionof GIFs. The protoplanets gravitationally capture the GIFs on atimescale of 10 Myr after the end of each giant impact (Genda
et al., 2015a), whereas the terrestrial magma ocean largely solidiﬁes in several Myr around 1 AU (Hamano et al., 2013). There isa debate about the single timing for completion of Earth’s coreformation, that is, there would be multiple stages of Earth’s coreformation. Since giant impacts are one of the major processes thatlead to core formation, here we assumed that major phase of coreformation ended by the stage of the GIFs’ re-accretion after the last
giant impact.
According to our simulations, the GIFs contain 0.6–25 wt% ofiron (Fig. 7). Consequently, a substantial amount of HSEs in metallic iron materials of GIFs with nearly chondritic relative proportions would be delivered to the mantle by GIF re-accretion. For
example, in Runs 1, 5 and 8 (the cases for low concentration ofiron), GIFs of ∼0.4 M ⊕ are produced and their iron contents are a
few percent. If 10% of the GIFs re-accrete onto the Earth after thelast giant impact, the relative abundances of HSEs compared to CI
chondrites are as much as 3 × 10−3 , which is consistent with theabundance of HSEs in the Earth’s mantle (1 × 10−3 to 4 × 10−3 ;Walker, 2009).
If the metallic iron of re-accreting GIFs simply sinks into the
Earth core, HSEs in Fe of GIFs cannot be left behind in the Earth’s
mantle. A signiﬁcant fraction of HSEs delivered by the GIF-metals
should reside in the silicate Earth if the metals oxidized during or
after the re-accretion process. The oxidation of re-accreted metals would occur on the Earth’s surface if the Earth had ocean
on the surface, and would occur in the Earth’s mantle because

the Earth’s mantle would have been oxidized during the main
phase of Earth’s accretion and core growth as indicated by moderately siderophile element systematics (Wade and Wood, 2005;
Rubie et al., 2011). The mantle oxidation could be caused either by
disproportionation of ferrous Fe to ferric and metal Fe during silicate perovskite crystallization followed by the metal segregation(Wade and Wood, 2005; Frost et al., 2008) or by a transition fromvolatile-depleted to volatile-enriched accreting materials (Rubie etal., 2011).
The oxidative reaction eﬃciently proceeds especially when thesize of metallic iron in GIFs is small. If the size of metallic iron in
GIFs is planetary sized (∼1000 km), most of re-accreting metallic
iron cannot be oxidized. Due to the limit of the resolution for our
numerical simulation, we cannot directly calculate the size of irondroplets ejected by giant impacts that is smaller than the size ofa single SPH particle. Nevertheless, we can roughly estimate thetypical size of iron droplets by considering the balance between
surface tension of liquid iron and the local kinetic energy during
fragmentation. According to Melosh and Vickery (1991), the typicalsize (d) of molten droplets ejected by an impact is given byd≈

40σsurfρ1/3 

D imp
v imp

2/3
,

(2)

where σsurf is the surface tension (∼2 N/m for liquid iron), ρ is thedensity (∼7000 kg/m3 ), D imp is the impactor’s diameter (∼6400
km for a Mars-sized protoplanet), and v imp is the impact velocity(∼10 km/s). We found d ∼ 17 m, which is comparable to the original size of the iron meteorite that made Barringer Crater, Arizona,
USA (d ∼ 40 m). Most of parts of iron droplets with this size burn,and/or is pulverized into much smaller pieces during the Earth’s
atmospheric entry of this iron meteorite (Collins et al., 2005), or
iron droplets are even partially vaporized at the impact onto ocean
or sea ﬂoor (Kraus et al., 2015). Therefore, we expect that metallic Fe is eﬃciently oxidized by water on the Earth’s surface and by
ferric Fe in the mantle, allowing the late addition of HSEs to the
Earth’s mantle by GIFs.
The presence of oceans as far back as 4.3 Ga is indicated byheavy oxygen isotope ratios in Hadean zircons (Cavosie et al.,2005). Yet several recent lines of evidence suggest the existenceof water even before the Moon-forming impact. For example, thediscovery of water in lunar anorthosites indicates that the lunar
magma ocean contained water up to 300 ppm (Hui et al., 2013).
Moreover, the D/H ratios of lunar volcanics that are similar tothat of Earth’s seawater (Saal et al., 2013) imply a common origin for the water on the Earth and Moon. Noble gas abundance
and isotopic compositions suggest that Earth acquired most ofits major volatile elements by accretion of volatile-rich planetesimals and/or protoplanets (Halliday, 2013; Dauphas and Morbidelli,2014). The presence of water in the planetesimals that eventually formed the Earth is also supported by recent theories forthe thermal structure of protoplanetary disks (Oka et al., 2011;
Min et al., 2011). Thus, the inference that the Earth had someamount of ocean during the stage of GIFs re-accretion is reasonable.
Since GIFs also accrete onto Mars and the Moon, HSEs would
be supplied in their mantles. It is reasonably well accepted thatthe abundance of HSEs for the Martian mantle is roughly similar
to that of the Earth’s mantle, and that for the lunar mantle is about
20 times lower than that of the Earth’s mantle (Walker, 2009;
Dale et al., 2012), although there is a debate whether the HSE signatures can be naturally explained by their partitioning between
the silicate and metal (Righter et al., 2015; Sharp et al., 2015) or
require late accretion (Day et al., 2016).
Assuming that all HSEs are supplied via the late accretion, theratios of accreted mass for Earth/Mars and Earth/Moon are es-

H. Genda et al. / Earth and Planetary Science Letters 470 (2017) 87–95

timated as 12–23 and 200–700, respectively (Schlichting et al.,2012). The gravitationally enhanced cross section of a planet σ isgiven by



σ = π R2 1 +

v esc
v rel

2 
,

(3)

1/ 2

provided v rel > ∼2( M p / M ∗ )1/3 (Ida and Nakazawa, 1989), wherev rel is the relative velocities of GIFs, M p and M ∗ are the massesof the protoplanet and central star. If v rel  v esc , the ratio of thecross section between planet 1 and 2 is written asσ1 ρ1 R 1=σ2 ρ2 R 2

4
.

(4)

When the radii and densities of the Earth and Moon are applied
to this equation, the ratio of the cross sections is 300, which isconsistent with the late accretion mass ratio inferred for the Earthand Moon. If this is also applied for the Earth and Mars, the ratioof the cross section is about 17, which is also consistent with theobserved value.
Since the age of core formation on Mars (∼2 Myr, Tang and
Dauphas, 2014; Dauphas and Pourmand, 2011) is much earlier
than the Moon-forming giant impact onto the Earth (>30 Myr,
Kleine et al., 2009), Mars would be a survivor of protoplanets andwould have been exposed to more GIFs during the entire giant impact stage than the Earth and Moon. Meanwhile, Mars should beformed at the outer edge of the terrestrial planet region where giant impact events rarely or never happen. Therefore, total mass of
GIFs at Mars’ orbit should be much smaller than that at Earth’s orbit. Although longer exposure time of GIFs for Mars enhances theaccreted mass of GIFs, lower surface density of GIFs reduces theaccreted mass.
As discussed above, the estimated ratios by late accretion withstrong gravitational focusing can account for HSE contents in the
mantle of the Moon as well as Mars, provided that the relative velocities between the terrestrial planets and accreted materials are
signiﬁcantly low compared to the escape velocities. Such low relative velocities can be achieved by small objects available in theterrestrial planet region rather than those delivered from the outer
asteroid belt.
Furthermore, the late accreted small objects could damp theoriginal high eccentricities of terrestrial planets (see Section 4.1).
Note, however, that if the late veneer has a chondritic composition,accounting for the HSE abundances and eccentricities of the terrestrial planets at the same time requires a typical size of ≤10 m
for the late accreted objects in order to ensure eﬃcient dampingof the relative velocities of planetesimals (Schlichting et al., 2012),
which seems to be too small for leftover planetesimals after the giant impact stage. The GIF late accretion hypothesis can circumvent
this problem. The GIFs would originate mainly from silicate portions of differentiated protoplanets, and therefore have lower HSE
abundances than chondrites (Fig. 7). This relaxes the upper limits
for the total mass and typical size of the late accreted objects.
4.3. Reduction of the primordial atmosphere and ocean by re-accretionof GIFs
The re-accretion of GIFs on the Earth after the solidiﬁcationof magma ocean also has implications for the redox state of the
Earth’s earliest atmosphere. After core–mantle differentiation, oxygen fugacity of the Earth’s uppermost mantle would have been
deﬁned by fayalite–magnetite–quartz (FMQ) buffer, in which H2 O
and CO2 would dominate the magmatic volatile (Trail et al., 2011;
Delano, 2001; Frost et al., 2008). The primordial CO2 -rich atmosphere and the ocean may have been reduced by the impact of93

considerable amount of GIFs, because the average composition of
the metal-bearing GIFs should be more reducing than the FMQ
mantle.
Under the heavy rain of the metal-bearing GIFs during the ﬁrst
100 Myr, metal part of the GIF would have reacted with the ocean
via the reaction, Fe + H2 O → FeO + H2 . In reality, however,
75–99% of the GIFs are not metal but rocky fragments. Therefore,
the reactions between GIFs and the primordial ocean may create
more complex volatiles, which is beyond the scope of this paper.
Instead, here we evaluate the reducing capacity provided by there-accretion of GIFs by estimating the amount of H2 produced by
the impact of GIFs.
First, we assume that the average composition of the GIFs was
similar to that of ordinary chondrites that is considered as therepresentative source materials of terrestrial planets before thecore–mantle differentiation (Rubie et al., 2011). According to theequilibrium calculation of Schaefer and Fegley (2010), the impactof ordinary chondrite would create the highly reducing gasses (H2∼45%, CO ∼25%, H2 O ∼20%, CO2 ∼5%) and other trace components including N2 and CH4 . These volatiles could represent averaged gas composition created by the GIFs and ocean because oursimulation suggests that the impact velocities of GIFs were highenough to vaporize themselves.
In this case, roughly 70% of the reacting water is converted into
H2 and remaining 30% stays in H2 O. Also, the total amount of H2
formed by the GIFs’ impact largely depends on the initial volumeof the ocean before the impact, because the amount of GIFs waslarge enough to react with all of the pre-existing ocean as discussed in Section 4.2. As a result, provided that the initial massof ocean was 3.5 times larger than present, 70 bar H2 atmospherewould be produced during the GIF bombardment, and the presentday volume of ocean was left behind after the impact. This amountof H2 could have sustained over ∼200 Myr, when considering subsequent hydrogen escape into space (see Appendix).
A much higher H2 pressure of atmosphere is possible depending on higher initial ocean mass as well as on higher metal fractionof GIFs. These parameters are highly uncertain, though the simple calculation suggests that very reducing atmosphere could havebeen sustained from 200 to possibly over 1000 Myr timescale after the cessation of GIF bombardment. Thus, when considering there-entry of large amount of GIF, the Hadean and possibly Archean
Earth would have highly reducing atmosphere despite of oxidized
volcanic gas emission.
5. Conclusions
In our solar system, many giant impacts among protoplanets
occurred during terrestrial planet formation. These giant impacts
more or less eject materials into space. In this study, we havesimulated the stage of giant impacts by using a hybrid code thatconsistently deals with the orbital evolution of protoplanets aroundthe Sun and the detailed process of a giant impact between two
protoplanets. The results revealed that a signiﬁcant amount of giant impact fragments (GIFs)—corresponding to ∼0.5 M ⊕ in total—
are ejected by giant impacts throughout the giant impact stage. We
found that GIFs contain a signiﬁcant amount of metallic iron materials (0.6–25 wt% of GIFs), which are ejected from the colliding
protoplanets’ cores.
Based on the numerical results, we have indicated that the GIFs
have signiﬁcant effects on the dynamical and geochemical characteristics of formed terrestrial planets: (1) Dynamical friction causedby GIFs left after the last giant impact can lower the eccentricityof the Earth from a highly eccentric orbit just after the last giant impact (its eccentricity is ∼0.1) to its current value (∼0.01).
(2) Re-accretion of iron-bearing GIFs onto Earth can account for theexcess of highly siderophile elements (HSEs) in the Earth’s mantle

94

H. Genda et al. / Earth and Planetary Science Letters 470 (2017) 87–95

as the source of the late veneer. In addition, the estimated amountof iron-bearing GIFs provides signiﬁcant reducing agent that could
transform primitive CO2 –H2 O atmosphere and ocean into more
reducing H2 -bearing atmosphere. Early reducing atmosphere is important for the origin of Earth’s life and its early evolution.
Acknowledgements
We thank E. Asphaug and D. Stevenson for their helpful reviews,
which led us to greatly improve this paper. We also thank anonymous referees for their constructive reviews. This research was
supported by a grant for the Global COE Program entitled “Fromthe Earth to “Earths” ”, MEXT, Japan. We thank the leader of the
Global COE Program, Professor Shigeru Ida, for providing the opportunity for us to collaborate on this interdisciplinary work.
Appendix A. Calculation of lifetime of H2 atmosphere against
H-escape into space
In order to evaluate the reducing capacity derived from the impact of GIF, we have calculated how long the H2 -atmosphere could
have persisted against hydrogen escape into space. Since we consider a H2 -dominated atmosphere reduced by GIF’s metallic iron inthis paper, the assumption that the escape ﬂux of H2 is controlled
by EUV energy ﬂux (called energy-limited hydrodynamic escape) is
valid (Watson et al., 1981):

φH2 =ε f EUV (t ) R 
4G M ⊕ mH2



m−2 s−1 ,(A.1)

where φH2 is the escape ﬂux of H2 , G is the gravitational constant, R is the planetary radius, and mH2 is the mass of a hydrogenmolecule. Escape eﬃciency ε represents how large a proportion ofreceived EUV energy is available for escaping hydrogen molecules.
We adapt 0.3 for ε (Sekiya et al., 1980). The EUV energy ﬂux
f EUV (t ) would have been several orders of magnitude greater thanits present value (Zahnle and Walker, 1982) at the time of GIF reentry. We used the following time-dependent model for the EUV
energy ﬂux (Ribas et al., 2005),


f EUV (t ) = 0.03t
109 yr−1

W/m2 .

(A.2)

We consider only H2 for the atmospheric species, ignoring theother species for simplicity. By using Eqs. (A.1) and (A.2), we canestimate the timescale for H2 atmospheric loss. If the partial pressure of H2 in the atmosphere is 70 bar, it takes about 200 Myr for
the H2 atmosphere to be completely lost. The presence of CO and
CO2 in the upper atmosphere causes a decrease in the escape eﬃciency (ε ) due to their eﬃcient IR emission (Lammer et al., 2006),
which extends the timescale for H2 atmospheric loss. In this sense,
the timescale estimated here (∼200 Myr) would be a lower one,
although the EUV energy ﬂux is also quite uncertain.
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