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New approaches to the Moon’s
isotopic crisis
H. J. Melosh1,2,3
1 Earth, Atmospheric and Planetary Sciences, 2 Physics and
rsta.royalsocietypublishing.org
Review
Cite this article: Melosh HJ. 2014 New
approaches to the Moon’s isotopic crisis. Phil.
Trans. R. Soc. A 372: 20130168.
http://dx.doi.org/10.1098/rsta.2013.0168
One contribution of 19 to a Discussion Meeting
Issue ‘Origin of the Moon’.
Subject Areas:
solar system, geophysics
Keywords:
Moon, origin, isotope, giant impact
Author for correspondence:
H. J. Melosh
e-mail: [email protected]
Astronomy, and 3 Aeronautical and Astronautical Engineering
Departments, Purdue University, West Lafayette, IN 47907, USA
Recent comparisons of the isotopic compositions of
the Earth and the Moon show that, unlike nearly
every other body known in the Solar System, our
satellite’s isotopic ratios are nearly identical to the
Earth’s for nearly every isotopic system. The Moon’s
chemical make-up, however, differs from the Earth’s
in its low volatile content and perhaps in the elevated
abundance of oxidized iron. This surprising situation
is not readily explained by current impact models
of the Moon’s origin and offers a major clue to the
Moon’s formation, if we only could understand it
properly. Current ideas to explain this similarity range
from assuming an impactor with the same isotopic
composition as the Earth to postulating a pure ice
impactor that completely vaporized upon impact.
Several recent proposals follow from the suggestion
that the Earth–Moon system may have lost a great
deal of angular momentum during early resonant
interactions. The isotopic constraint may be the most
stringent test yet for theories of the Moon’s origin.
1. The giant impact hypothesis
The giant impact hypothesis of the Moon’s origin arose
in the aftermath of the successful Apollo missions to
the Moon, which returned hundreds of kilograms of
lunar surface material to the Earth and engendered
a vigorous research programme in lunar science. The
returned Apollo samples (supplemented by the Soviet
Luna sample returns and lunar meteorite finds) did not
fit any of the three classic models of lunar origin (fission,
capture and co-accretion) and initiated a period of deep
confusion about the Moon’s origin lasting from about
1969 to 1984. During this time, a great many detailed
facts about the Moon, its geology, geochemistry and
chronology were gleaned from the lunar rocks, but no
clear picture of its origin emerged.
2014 The Author(s) Published by the Royal Society. All rights reserved.
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Table 1. Bulk silicate composition of the Moon [2].
2
FeO
14.1
MgO
32.9
Al2 O3
4.2
SiO2
45.1
Taylor [4]
4.6
13.1
32.3
6.1
43.9
..........................................................................................................................................................................................................
..........................................................................................................................................................................................................
Wänke & Dreibus [5]
3.8
13.1
32.6
4.6
45.9
O’Neill [6]
3.3
12.4
35.1
3.9
44.6
Kushov & Kronrod I [7]
4.8
10.4
28.5
6.3
50.0
Kushov & Kronrod II [7]
4.3
11.7
29.6
5.9
48.5
Warren [1]
3.0
9.1
35.6
3.8
46.2
bulk silicate Earth; McDonough & Sun [8]
3.6
8.2
38.2
4.5
45.5
..........................................................................................................................................................................................................
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..........................................................................................................................................................................................................
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It is now clear that the Moon is a differentiated body with a bulk chemical composition
generally similar to that of the Earth’s mantle, but compared with the Earth, the Moon is strongly
depleted in volatiles such as Na, K, Rb and especially water. Until recently, bulk chemical
estimates also suggested that the Moon is slightly enriched in refractory elements such as Al
and Ca, although revisions of the Moon’s crustal thickness have now made the Moon seem
more similar to the Earth in these elements. In addition, the Moon’s silicate rocks are believed
to contain about twice as much iron oxide, FeO, as the Earth’s mantle, although Warren [1]
dissents from this difference, as listed in table 1. Table 1, after Khan et al. [2], compares several
estimates of the major oxide abundances in the bulk silicate Moon with a similar estimate for
the Earth’s mantle. The slight enrichment of the Moon in Al and Ca reported in this table has
now been largely or completely erased by the recent discoveries of NASA’s GRAIL mission
that reduced the average crustal thickness of the Moon to 35 km [9]. The volatile element
depletions, however, remain as strong chemical differences between the Earth and Moon, in spite
of more recent discoveries suggesting that the Moon’s interior is not as depleted in water as
initially supposed.
Geochemist Ted Ringwood [10,11] suggested that the chemical differences between the Earth
and Moon could be explained if one supposed that the Moon formed out of Earth mantle material
that was first vaporized and then re-condensed under conditions that permitted volatiles to
escape. Ringwood did not, however, offer a plausible scenario under which this evaporation could
occur [12] and his idea lay fallow for more than a decade.
Our modern understanding of the Moon’s origin grew out of dynamical studies of planetary
accretion that, over the decades from the 1950s to the 1980s, focused on the likelihood of
increasingly large impacts during the end stages of planetary growth. Urey [13] had posited
growth from cosmic dust falling directly onto growing planets, resulting in very cold internal
temperatures (indeed, he believed that the Moon was an undifferentiated body right up until
Apollo 11 brought back the first samples of igneous rocks). Safronov [14] and Kaula [15]
envisioned multi-kilometre planetesimal impacts that somewhat alleviated the lack of initial
heating of the Earth and Moon, but not until the work of Wetherill [16] and Greenberg et al. [17]
was it appreciated that the final stages of planetary accretion must have occurred through giant,
planetary-scale impacts.
The radical idea that the Moon might have been born during a planetary size impact late in
Earth’s accretion history was first vetted at a conference in 1974, at which Hartmann & Davis [18],
reasoning by an appeal to the hierarchical growth scenario, suggested that a very large impact
might have injected a cloud of dust and debris from the Earth into orbit and thus formed the
Moon. At the same conference, Cameron & Ward [19], reasoning from the large ‘excess’ angular
momentum of the Earth–Moon system compared with the other planets in our Solar System,
went much further and argued that the impactor would have to be as big as Mars to inject the
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CaO
3.7
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source
Ringwood [3]
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necessary angular momentum and at the same time actually orbit material by non-gravitational
accelerations of expanding vapour. These apparently outrageous suggestions were not taken
seriously by most of the lunar science community until a conference on the origin of the Moon in
1984 pointed up the difficulties of the classic origins.
The possibility of a giant impact then received support from numerical simulations [20,21],
which showed that a very large impact (and only a planetary-scale impact) could eject a moonmass of material into orbit around the Earth and give it the observed angular momentum of the
Earth–Moon system. Cameron & Ward [19] had argued that the debris could be injected into orbit
by pressure gradients in a cloud of expanding vapour and that the ejected debris’ orbits would
subsequently be circularized by particle–particle collisions in the dense disc. Stevenson [22]
supported this idea and further proposed that gravitational torques from the massive and highly
distorted Earth–projectile system would also be effective, a mechanism supported by subsequent
numerical simulations. Melosh & Sonett [23] argued that the process of impact jetting during
an oblique collision could produce sufficient amounts of high-temperature vapour and that this
vapour would be an approximately equal mixture of target and projectile material. Because jetting
only incorporates material from near the surface of the impacting objects, they emphasized that
metallic iron would be excluded from the orbiting debris provided that both projectile and target
bodies had already formed cores. Following previous workers [18,19], Melosh and Sonett also
emphasized the fundamental link between the geochemical evidence for volatile depletion and
the essential role of vaporization in injecting material into orbit. Stevenson [24] examined the
dynamics of a two-phase melt and vapour disc orbiting the Earth and again found that such a
disc could plausibly form a satellite closely resembling our Moon.
The first numerical simulations of the moon-forming impact were performed in the aftermath
of the 1984 Kona conference. The model of Benz et al. [20] employed the smooth particle
hydrodynamic (SPH) method, which has subsequently become the method of choice for these
complex simulations that must incorporate self-gravity, thermodynamics and hydrodynamics.
Kipp & Melosh [21] used an Eulerian hydrodynamic simulation, a method that has only recently
become capable of fully addressing these complexities [25].
Subsequent numerical simulations by Canup & Asphaug [26] strongly supported the giant
impact scenario and demonstrated a wide class of conditions under which a planetary-scale
impact could produce a large moon with the angular momentum of our current Earth–Moon
system. These simulations readily explain the presence of a moon in orbit around the Earth, the
depletion of volatiles in its material and the lack or strong depletion of metallic iron in the Moon.
Small compositional differences between the Earth and Moon (such as the Moon’s putative high
iron oxide content) could be explained by differences between the proto-Earth and the projectile
(now often called ‘Theia’) [27].
All of the initial numerical simulations of the Moon’s origin were constrained by the thenperceived need to nearly match the angular momentum of the Earth–Moon system [28]. The other
major constraint was that the final mass in an orbiting proto-lunar disc must be at least equal to,
or perhaps twice as large as, the current Moon’s mass to account for viscous dissipation in the
disc and consequent de-orbiting of some material as the disc spreads. All of these simulations
agreed in finding that a Mars-mass impactor striking obliquely at a velocity not much larger than
the Earth’s escape velocity best satisfies these two constraints.
Given these constraints, all of these previous simulations found that the projectile, while
contributing about 10% to the mass of the Earth (roughly equal to the ratio of the mass of Mars
to the mass of the Earth), contributed between 70 and 90% to the mass of the Moon-forming
disc (summarized by Canup et al. [25]). These highly unequal contributions of the projectile
material to the Earth and Moon were not initially regarded as a serious problem: indeed, this
was seen as a way to explain the larger iron abundance in the bulk Moon. Mcfarlane [27], on
geochemical grounds, even argued that the Earth could not have contributed more than about
50% of the mass of the Moon. However, we now recognize this asymmetric mass contribution
as a looming problem; a problem brought on by high-precision measurements of isotopes in the
Earth and Moon.
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2. Isotopic similarity of the Earth and Moon
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rsta.royalsocietypublishing.org Phil. Trans. R. Soc. A 372: 20130168
There were signs of an isotopic problem with the then-understood giant impact hypothesis as
early as 2001. Three-isotope (16 O, 17 O and 18 O) oxygen measurements on the SNC (Shergottie,
Nakhlite and Chassigny Martian) meteorites indicated a significant offset between the Martian
and terrestrial mass-fractionation lines [29]. Older oxygen isotopic measurements with large
error bars could accommodate this small difference between Earth isotopes and Mars (assuming
that the modern planet Mars is a proxy for the Moon-forming impactor Theia), but these new
measurements indicated that, lacking some homogenization mechanism, Mars itself could not
have been the impactor. This can, of course, be reconciled if the actual impactor is isotopically
nearly identical to the Earth (as the enstatite meteorites nearly are), but as error bars shrank,
the O-isotopic similarity between the Earth and Moon came to seem anomalous. A very small
difference in the 17 O ratio between the Earth and lunar rocks of about 12 ± 3 ppm has recently
been reported [30] (as well as a larger difference from enstatite chondrites), but that still leaves the
Earth–Moon system as more similar in O isotopes than any other two bodies in the Solar System.
The Earth–Moon similarity contrasts sharply with the O-isotope trends of most meteorites, which
are substantially different from the Earth–Moon system and from each other. Nor is there any
apparent trend with distance from the Sun, for while Mars’ O-isotopes lie above the Earth–
Moon mass-fractionation line, the still more distant Vesta’s O-isotopes (represented by the HED
meteorite clan) lie well below that line.
Adding to the eerie similarity between oxygen isotopes of the Earth and Moon, many other
isotopic systems show a near identity of the two bodies. In 1995, Humayun & Clayton [31,32]
showed that 39 K and 41 K are nearly identical in the Earth and Moon, although this similarity
is not unique to the Earth–Moon system, because this identity is found in nearly all Solar
System bodies and is surprisingly independent of K depletion in the rocks. In 1998, Lugmair
& Shukolyukov [33] extended the similarity between the Earth and Moon to the 53 Mn–53 Cr
system. In 2007, this similarity was further extended to 28 Si, 29 Si, 30 Si [34] and more tellingly
to the radiogenic 182 W, 184 W system [35], although that study did report a slight excess of
182 W/184 W that was not statistically significant. The similarity in the W system indicates that the
impactor and proto-Earth must have had a nearly identical history of iron–silicate differentiation,
a situation that is hard to envision in the context of current models for terrestrial planet formation.
Finally, in 2012, Zhang et al. [36] showed that the highly refractory element Ti also shows near
identity of 47 Ti and 50 Ti between the Earth and Moon. The difference between the abundance
of these two isotopes in the Earth and Moon is only about 1/150 of the difference between the
Earth and carbonaceous chondrites, again underlining the eerie similarity between the Earth
and Moon.
Some isotopes do show differences between the Earth and Moon. For example, Paniello et al.
[37] find an enrichment of heavy isotopes of Zn in lunar rocks which they attribute to the depletion
of the volatile element Zn in a hot proto-lunar disc. Furthermore, some small isotopic differences
may be expected between the Earth and Moon if, as is widely believed, the Earth received a ‘late
veneer’ of chondritic material that supplied its inventory of highly siderophile elements, while the
Moon escaped such an addition [38]. This late veneer could comprise between 0.1% and perhaps
as much as 0.8% of the mass of the bulk silicate Earth and could plausibly explain the small
differences in 17 O recently detected between Earth and Moon rocks [30], as well as affecting
other isotopic systems. Small, post-impact, differences in isotopic ratios such as 182 W/184 W occur
on the Earth itself [39,40], so at some high level of precision we should expect isotopic divergences
between the Earth and Moon that are more indicative of post-formation events than of their
original heritage.
The obvious conclusion of all these isotopic similarities is that the Moon is almost entirely
derived from the Earth’s mantle. But what are we to make of the likely difference in FeO
abundance between the Earth and Moon, and the volatile depletions of the Moon? We have
the peculiar circumstance that the Earth and Moon, while apparently nearly identical in most
isotope ratios, are substantially different in their bulk chemistry. Furthermore, if the Moon is
4
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(a) The Earth and impactor had identical isotopic compositions
An easy and general solution would be to assume that the impactor was simply identical to
the Earth in isotopic composition. Volatiles would be lost from the hot, partially vaporized
orbiting disc by evaporation into space and the isotopic similarity becomes a non-problem. This
solution presently seems implausible, given the wide range of oxygen isotopic compositions of
the meteorites, but in fact we do not know the isotopic composition of bodies inside the orbit
of Earth. It would be very revealing to discover that Venus or Mercury lie on the same massfractionation line as the Earth and Moon. Unfortunately, until a meteorite from either of these
bodies is identified [41], or samples are returned, this possibility remains speculative. Possibly
the impactor was a close relative of the Earth [42] that accreted in a location similar to that
of the Earth. All scenarios of this type have difficulty, however, in explaining the similarity of
the W isotopes, that imply a history of accretion and differentiation that is very similar to that
of the Earth.
(b) Are the existing numerical simulations adequate?
Nearly all of the current simulations use the SPH method, a meshless Lagrangian numerical
technique that, for a long period of time, seemed to be the only way to handle the extreme
distortions of an impact while including the shifting forces of massive, self-gravitating masses of
material. None of the simulations so far published are truly converged in the sense that an increase
in resolution gives precisely the same results of lower resolution computations. However, Canup
et al. [25] have shown that SPH and a conventional Eulerian hydrocode (CTH with adaptive mesh
refinement) give nearly identical results and that resolution is not a major issue.
Adequate equations of state are a continuing issue. Hydrocodes cannot properly represent
the outcomes of collisions without an adequate model for the response of candidate geologic
materials to impact shock and pressure release cycling. Recent improvements in the ANEOS
analytical equation of state package have incorporated molecular species [43], but observations
of SiO2 and other silicates at planetary shock conditions [44–46] now indicate that such
models overestimate the shock pressure for vaporization by about a factor of 2, so that much
improvement, as well as expansion of existing equations of state to more realistic materials, is
urgently needed.
The importance of an adequate equation of state was clearly demonstrated by Wada et al.
[47], who argued that, if the orbiting lunar disc is entirely vapour, it is quickly perturbed by
strong internal shocks and loses much of its mass onto the Earth within hours. A stable, Moonforming disc requires the presence of a condensed liquid or solid phase to prevent the formation
of these instabilities. This subject has not, to date, received the attention from the Moon-origin
community that it deserves, and more work of this kind is needed to properly understand the
long-term stability requirements of the Moon-forming disc. In particular, the results of Wada et al.
are somewhat at odds with the standard model of viscous disc evolution [48], which predicts that
a small fraction of the disc’s mass should spread outwards as angular momentum is exchanged
within the disc.
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3. Proposed solutions to the puzzle
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rsta.royalsocietypublishing.org Phil. Trans. R. Soc. A 372: 20130168
entirely derived from the Earth’s mantle, and if the giant impact models can only place about
30% of Earth mantle material into the orbiting debris disc, then where does that leave the giant
impact hypothesis? At first sight, this would rule out the giant impact scenario. However, none
of the other older models of the Moon’s origin can accommodate these facts either. Evidently,
the recent high-precision isotopic determinations in lunar rocks have created a crisis for both the
giant impact origin, and every other origin scenario.
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(c) Material equilibration between the orbiting disc and proto-Earth
6
M
[Amoon (0) − Aearth (0)]e−mexch /m∗
M+m
(3.1)
Aearth (mexch ) = Aequil −
m
[Amoon (0) − Aearth (0)]e−mexch /m∗ ,
M+m
(3.2)
and
where
m∗ =
1
,
1/m + 1/M
(3.3)
from which it is easy to deduce the fractional decrease in concentration
Amoon (mexch ) − Aearth (mexch )
= e−mexch /m∗ .
Amoon (0) − Aearth (0)
(3.4)
.........................................................
Amoon (mexch ) = Aequil +
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In the face of this isotopic crisis, Pahlevan & Stevenson [49] made the ingenious suggestion that
the orbiting disc and the hot, post-impact Earth can efficiently exchange material through a cloud
of vapour surrounding both the hot molten disc and the Earth. Focusing on the oxygen isotopes,
they argued that the vapour pressure of O-containing silicate species was high enough to permit
significant exchange and that the disc would remain hot long enough to permit equilibration of
O-isotopes.
Unfortunately, there are several problems with this proposal. A geochemical objection is that,
while O-species might be volatile enough for substantial exchange between the Earth and protoMoon, the similarity of Ti isotopes [36] requires much higher temperatures for equilibration
because the vapour pressure of TiO species is very low at the temperature of ca 3000 K proposed
by Pahlevan and Stevenson. The low volatility of TiO species would require substantially longer
equilibration times (more than a year [36], as opposed to one week for forsterite vapour [49])
than envisioned in the original Pahlevan and Stevenson proposal. It is possible that exchange of
minor refractory species such as TiO might take place through fine dust in the solid state, but this
idea needs to be developed quantitatively. A second, physics-based, objection is that the isotopic
equilibration requires an unlikely exchange process that permits large amounts of material to
cycle between the hot, post-impact Earth and the orbiting disc without substantially altering its
angular momentum.
This latter objection is based on the fact that the post-impact Earth must have been spinning
with a period substantially longer than the orbital period of the ejected proto-lunar disc. If all of
the angular momentum of the present Earth–Moon system is concentrated back into the Earth,
its rotational period would have been approximately 4 h (this estimate is approximate because it
assumes that the moment of inertia of the rapidly rotating Earth is equal to that of the present
Earth—in fact, a highly oblate rapidly rotating planet would have a higher moment of inertia
and thus a longer period, so this is a conservative estimate). However, for the Earth to match
the rotation rate of an orbiting disc, its rotational period must be close to 1.5 h. So if the angular
momentum of the disc were to equilibrate with the Earth, the disc could not maintain its orbital
velocity and the bulk of its mass would collapse back onto the Earth, leaving too little material in
orbit to form our Moon.
It is easy to estimate how much mass must be exchanged between the Earth and an orbiting
proto-lunar disc to equilibrate isotopes to any given degree. I follow the model of Pahlevan &
Stevenson [49], but unlike them I write the equations in terms of the amount of mass exchanged
mexch to illustrate this process. Figure 1 shows a schematic of the model: we consider two isotope
reservoirs, the proto-Earth and the orbiting disc, in which the concentration of isotopic species A,
which is a function of mass exchanged A(mexch ), in the proto-Earth of mass M is Aearth while in
the orbiting disc of mass m the concentration is Amoon . The total amount of isotope A is conserved,
so we impose the constraint MAearth + mAmoon = constant. If we let the completely equilibrated
concentration (which can be approached but never actually attained) be Aequil , it is easy to show
that, as a function of mass exchanged, the concentration in each reservoir is given by
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proto-lunar disc
mass m
proto-Earth
mass M
Amoon
Aearth
dm
mass exchange
Figure 1. Isotopic equilibration by exchange of a parcel of mass dm between an orbiting disc of mass m and the post-impact
proto-Earth of mass M. The isotopic concentrations of species A in the disc is Amoon and in the Earth is Aearth .
isotope concentration (arb. units)
6
isotopic evolution during exchange
5
4
lunar disc
3
2
proto-Earth
difference = 1%
after mexch = 4.6 m*
1
0
1
2
3
4
5
mexch/m*
Figure 2. The approach of isotope concentrations in the orbiting disc and the proto-Earth as a function of the amount of mass
exchanged. The initial difference is reduced to 1% of the original after a total of about five times the mass of the disc has cycled
between the disc and the proto-Earth. For the purposes of illustration, the initial concentration of isotope A is arbitrarily set to
5 units in the orbiting disc and 2 in the proto-Earth. The Earth/disc mass ratio is 1/80. However, the amount of mass exchange for
a 1% decline in the difference between the isotopic abundance in the proto-Earth and disc is independent of the actual values
of the initial abundances. (Online version in colour.)
Thus, to reduce an initial difference in the concentration of isotope A between the proto-Earth
and the orbiting disc to 1% of its initial concentration, a mass nearly equal to 4.6 times the mass
of the disc itself must be exchanged (because M m for the Earth and Moon, m∗ is nearly equal
to m itself), as illustrated in figure 2.
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A novel proposal suggested that a way out of the isotopic impasse might be through an icerich impactor, perhaps an intruder from the outer Solar System, striking at high speed [53] (also
T. Bowling and B. Johnson 2011, personal communication). Reufer et al. [54] explored a suite of
collisions involving fast, less grazing impacts that included icy impactors, but found that at most
73% of the Moon-forming disc could be derived from the Earth. These computations imposed the
usual constraint on matching the total angular momentum of the Earth–Moon system, but in the
light of the next section this might need to be re-visited.
(e) Is the angular momentum constraint valid?
A fresh, new approach to the Moon-origin problem was initiated by Ćuk & Stewart [55] in a
paper that has shaken the ground beneath all previous approaches. They argued that much of
the initial angular momentum of the Earth–Moon system could have been drained away through
solar tidal torque as the Moon went through a resonance, known as the evection resonance [56],
between the Moon’s perigee precession period and the year. This resonance forces the Moon into a
highly eccentric orbit that is subject to solar tidal torques. Although the efficacy of this resonance
is currently in dispute (J. Wisdom 2013, personal communication), if there is some mechanism
that removes the angular momentum constraint then there may be new ways in which a giant
impact can loft a larger fraction of the Earth’s mantle into orbit.
This new freedom from the angular momentum constraint was exploited by Ćuk & Stewart
themselves [55], who demonstrated that a fast impact with a fast-spinning Earth could, under the
right conditions, loft a disc consisting primarily of Earth mantle material. The most successful
simulations require a retrograde impact (that is, the Earth’s spin on the struck hemisphere is in
the opposite direction to the flight of the impactor). Canup [57] also exploited the lifting of the
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(d) Fast, ice-rich impactors
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Most processes that cycle material from one location to another also exchange
momentum and hence angular momentum in rotating flows. Indeed, viscosity (a measure of
momentum exchange) is generally linked to diffusion (a measure of material exchange) through
the Einstein–Smoluchowski relation, which is a special case of the more general fluctuation–
dissipation theorem. Although the Einstein–Smoluchkowsi relation strictly applies to molecular
processes in kinetic theory, turbulent diffusion is frequently (although not invariably) well
represented by similar statistical models via the eddy diffusion approximation [50]. It is difficult
to envision a process that could exchange as much as five times the disc mass without also
exchanging enough angular momentum to bring the disc down. Stone & Balbus [51] argue
that material convection in Keplerian discs transports angular momentum inward, not outward
as required for the evolution of an accretion disc. In this case, the disc might not collapse
due to viscous dissipation, but the inner portions would then rise to higher altitude as their
angular momentum increases, cutting off exchange of material between the proto-Earth and
disc, which would again thwart the Pahlevan–Stevenson exchange mechanism. The Stone and
Balbus analysis implicitly assumes a homogeneous fluid and it is unclear whether it applies
to a two-phase disc that includes both a gas phase and a liquid that may differentially rotate
and thus develop pressure waves, shocks and other azimuthal instabilities not included in
their analysis. The analysis by Thompson & Stevenson [52] suggests that angular momentum
exchange in a two-phase disc is dominated by gravitational instabilities rather than convective
transfer, which would cause such a disc to spread faster than one dominated by convective
exchange of angular momentum alone. Pahlevan & Stevenson [49] argue that the necessary
isotopic exchange can, indeed, occur on the time scale for evolution of the proto-lunar disc, but
the fact that the Earth and disc must exchange a mass comparable to, or greater than, the mass
of the disc itself while the disc remains in orbit seems incredible and requires a more rigorous
demonstration.
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Both Ćuk & Stewart [55] and Canup [57] have thus demonstrated that, with the freedom allowed
by loosening the angular momentum constraint, it is possible to form a Moon by impact that
closely resembles the Earth in its isotopic ratios. Both scenarios pass through a hot disc phase from
which volatile elements can presumably be lost. Neither readily explains the Moon’s excess of
FeO, although nor do any other models seem capable of explaining that one remaining difference.
So, is the giant impact scenario again on a secure footing? It may seem so, and yet I am
personally very uneasy about these (and all other!) explanations. The root of my unease boils
down to a somewhat subjective feeling about the ‘naturalness’ of an explanation. By ‘natural’, I
mean that the major features of the outcome (in this case, a moon that is a near isotopic twin of
its primary) should be an almost inevitable result of the formation process. However, both of the
currently successful scenarios by Ćuk & Stewart [55] and Canup [57] require a narrow range of
initial conditions. A bit more mass to the projectile, a slightly different impact angle or velocity,
and the isotopic similarity disappears. Both those papers contain extensive tables of many, many
simulations that, while producing a moon, do not produce one that is isotopically as close to its
primary as is our Moon.
The strongest constraint on the isotopic similarity of our Moon and the Earth is still that from
the oxygen isotopes. The recently reported difference of 12 ± 3 ppm in 17 O [30] shrinks the error
bars still more and further contracts the range of acceptable impact models.
How special a set of initial conditions should we find acceptable? Unfortunately, we have only
one Moon, and so one can always argue that we are simply very, very ‘lucky’ to have one whose
isotopic ratios are so similar to the Earth. But the history of science teaches us that an appeal to
very special circumstances is generally a poor bet (the Earth is not the centre of the Universe, our
Sun is not the only star with planets, etc.). When do we reject a scenario when it becomes ‘too’
improbable? Unfortunately, the annals of science also tell us that the answer to this question is
‘never’: there is always someone advocating a special but highly improbable solution to nearly
every question. Nevertheless, good science suggests that we should not rest on one (or two!)
possible but unlikely solution(s), but continue to seek for one whose probability of occurrence is
much higher. Strange coincidences do (and must!) occur, but they are rare by nature.
The first round of the giant impact scenario had that air of ‘naturalness’. Given that planetaryscale collisions dominate the late stages of accretion, nearly every such impact launched material
into orbit and produced a moon. Not all such moons were like our Moon: most had less mass, but
nevertheless it remains true that nearly every giant impact produces some sort of moon orbiting
the final planet (such a moon may crash at a later stage due to unfavourable tidal interactions,
as probably occurred on Venus). But we now find that the canonical giant impact scenario does
not produce a moon with nearly the same isotopic ratios as its primary. That can happen, but it
requires a rather special set of circumstances. Most such moons receive much more material from
the impactor than from the impactee. Does this tell us that the canonical scenario is wrong or are
we missing something?
Of the face of it, these results might suggest a return to some version of George Darwin’s fission
model of lunar origin [58], in which the Moon spun off the equator of a fast-spinning Earth. But
this scenario leaves unexplained the presence of at least a small core and the depletion of volatile
species in the Moon, facts that the canonical impact model treats well. And then there is the
enhancement of FeO in the Moon. Can some merger of the canonical giant impact and Darwin’s
fission model lead to a moon like our Moon, perhaps through the lifting of the angular momentum
constraint? If something like Darwin’s theory receives new life, the non-zero inclination of the
Moon to the Earth’s equator would seem to be a problem, although some progress has already
been made on this topic [59].
.........................................................
4. Have we now found the answer?
9
rsta.royalsocietypublishing.org Phil. Trans. R. Soc. A 372: 20130168
angular momentum constraint, suggesting that the similarity of the Earth’s and Moon’s isotopes
could be explained if the impactor was nearly the same size as the proto-Earth and thus the final
Earth- and Moon-forming disc received nearly equal contributions from both bodies.
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5. What is needed?
Halliday and Dave Stevenson, for a most stimulating and timely scientific symposium.
Funding statement. My research was supported by NASA’s Lunar Science Institute at the Southwest Research
Institute under grant no. NNA09DB32A.
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