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Origin of the “Late Heavy Bombardment”
A Proposal submitted to NASA's “Origins of Solar Systems” Program, 25 May 2007
Principal Investigator:
Clark R. Chapman ([email protected])
Southwest Research Institute (SwRI)
Suite 300, 1050 Walnut St.
Boulder, CO 80302
Co-Investigator:
Henry (Luke) Dones (SwRI)
Collaborators:
William F. Bottke (SwRI)
Harold Levison (SwRI)
I. BACKGROUND, OVERVIEW, AND OBJECTIVES
The Late Heavy Bombardment (LHB) is one of the most profound, and least understood, events in
Solar System history. A prime discovery of the Apollo era (Tera et al. 1974), this dramatic lunar
bombardment ~3.9 Ga has been hypothesized to have created the crater-saturated surfaces on
Mercury, Mars, and even some outer Solar System satellites (cf. Smith et al. 1981). If it happened on
the Moon, as seems increasingly likely, it must have affected the early Earth even more dramatically,
perhaps influencing the crustal organization of our planet and the beginnings of life. Within the
Origins Program, we have been researching some critical aspects of the LHB: What really are the
constraints, from lunar data, on the magnitude, timing, duration, and impactor size distribution of the
LHB? And what dynamical processes can rather suddenly liberate which impactor population/s ~700
Myr after the origin of the Solar System? Our ultimate goals are to develop secure evidence that this
still-controversial event actually happened, to uniquely determine what the impactors were and what
other planets and satellites were affected, and to understand the implications for planetary evolution.
For instance, if we can learn where the impactors came from, we could infer their probable
compositions and know what volatiles might have been delivered to the Earth and other bodies
around 3.9 Ga.
There have been recent dramatic developments in this topic. One that we will exploit in this
research is development of what we (cf. Levison et al. 2007) call the “Nice model” (Tsiganis et al.
2005; Morbidelli et al. 2005; Gomes et al. 2005) of early planetary evolution, in which a sudden
event in the evolution of Jupiter’s and Saturn’s orbits (crossing the 1:2 mean-motion resonance)
caused a spectacular rearrangement of the outer planets, which in turn explosively scattered both
outer Solar System planetesimals and main-belt asteroids throughout the Solar System. This event
could well have happened hundreds of Myr after planetary accretion. It is quantitatively sufficient to
account for the lunar basins and has duration similar to that inferred for the lunar LHB. Furthermore,
a consensus is beginning to develop, after decades of controversy, that the LHB actually happened.
For example, Trail et al. (2007) report that disturbances in very old terrestrial zircons are clustered
around 3.9 Gy, just before the end of lunar basin formation ~3.85 Gy.
Here we propose a three-year study of several vital remaining LHB issues, organized into three
tasks. This is a good time to tackle these questions because our numerical simulation techniques have
matured to the point that scenarios, many of which were qualitatively articulated decades ago (cf.
Wetherill 1981), can now be definitively tested and examined.
► Task 1. We will dynamically model various plausible scenarios for an LHB resulting from the
Nice model of early Solar System evolution. We will investigate the range of implications of early
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bombardment of the Earth, Moon, and terrestrial planets for observable traits of those bodies and their
earliest geological records.
► Task 2. We will evaluate how bombardment of the satellites of the outer planets, e.g. in a Nice
model-like scenario, will manifest itself in observable properties of those satellites, especially Iapetus.
► Task 3. We will model the evolution of the lunar regolith and megaregolith in order to understand
whether the absence of impact melts >4 Ga proves that a cataclysmic spike in bombardment occurred
as argued by Ryder (1990) and Cohen et al. (2000), or whether repeated ballistic sedimentation
processes associated with basin formation truly produces a "stonewall" effect, restricting the sampling
of old impact melts, as argued by Hartmann (1975, 2003) and Grinspoon (1989).
II. OBJECTIVES AND EXPECTED SIGNIFICANCE: RELEVANCE TO NASA
STRATEGIC GOALS AND ORIGINS
A major goal of NASA's Origins of Solar Systems Program is to understand the formation and
early evolution of planetary systems. We believe that studies of the LHB provide an especially strong
linkage between theories of Solar System formation and some of the oldest, directly observable
attributes of bodies like the Moon, Callisto, and Iapetus. The earliest crustal evolution on Mars may
or may not be visible, depending on whether an LHB happened and on its characteristics. The
predicted consequences of the recently developed “Nice model” for the LHB (see below) are integral
outcomes of early dynamical evolution of the giant planets that may have shaped the structure of the
planetary system that exists today.
Our proposed investigations (involving theory, modeling, and interpretation) address all 5 of the
“major questions” of the 2006 NASA Solar System Exploration Roadmap, particularly the first two,
about the origin and evolution of the planets and minor bodies. The LHB is discussed in the Roadmap
concerning a future lunar South Pole–Aitken Basin Sample Return mission: “The emergence of life
on Earth may have been hindered by the late heavy bombardment, so a better understanding of its
chronology could provide important constraints on the timescales for the development of Earth’s first
life.” We also address Sub-goals 3C.1 (“learning how the Sun’s family of planets and minor bodies
originated and evolved”) and 3C.2 (“understanding the processes that determine the history and future
of habitability in the solar system”) of the 2006 NASA Strategic Plan.
Since the LHB probably played a pivotal role in inhibiting the early evolution of life on Earth and
its end possibly fostered such evolution, it is crucial to understand the fundamental basis for the LHB
and analogous dynamical processes in the early Solar System. Perhaps such processes are unique to
our Solar System; or many may be applicable to extra-solar planetary systems. In any case, the LHB
is within the critical transitional phase from early cataclysmic planetary development epochs (e.g. the
collisional formation of the Moon or stripping of Mercury's mantle) to comparatively tranquil later
times when life could gain a foothold on the Earth, Mars, or other worlds. Few topics for which we
have such detailed planetary data (e.g. the ages of lunar impact melts) are so pertinent to the Origins
theme. And now is the time, when our numerical simulation capabilities have matured to such a high
level of capability, to finally study the relevant dynamical processes that have only been dreamed
about for decades. Finally, we note the explicit encouragement in the Origins Program of joint
research efforts by a strong interdisciplinary team like ours.
III. TECHNICAL APPROACH: TASK STATEMENTS
Task 1. Extending the Nice Model: Implications for the Terrestrial Planets
Background. The stability of the Solar System has long vexed dynamicists. Since the planets have
circled the Sun so many times, it would seem that their orbits have changed little since they formed.
However, we now know that we do not live in a “clockwork universe” (e.g., Duncan & Quinn 1993,
Murray & Holman 2001). The Solar System is marginally stable (Laskar 1996, Lissauer 1999). Plan-
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etary systems can rearrange themselves after long periods of little change (Levison et al. 1998).
The “Nice model” (Tsiganis et al. 2005; Morbidelli et al. 2005; Gomes et al. 2005) provides a
new paradigm for the dynamical evolution of the outer Solar System (Levison et al. 2007). The
investigators’ original goal was to explain the surprisingly large excitation of Jupiter and Saturn’s
orbits. That is, the giant planets’ eccentricities and inclinations are much greater than would be
expected if they formed in the solar nebula; planetesimals left over after the giant planets formed
would be expected to have further reduced the planets’ excitation (Ida & Makino 1992, Levison et al.
2005).
At present, Saturn orbits exterior to the strong 1:2 mean-motion resonance (MMR) with Jupiter.
Fernández & Ip (1984) showed that as the giant planets scattered residual planetesimals, Jupiter
would have migrated inward and Saturn, Uranus, and Neptune would have migrated outward. In this
process, the orbital separations of Jupiter and Saturn would have increased by ~1 AU (Malhotra
1995). Originally, Jupiter and Saturn would have been much closer to the 1:2 resonance. Since
resonance crossings can excite eccentricities (e.g., Chiang et al. 2002), the Nice group explored a
scenario in which Saturn began slightly interior to the 1:2 resonance. Tsiganis et al. (2005)
performed 43 simulations of the orbital evolution of compact giant planet systems with a massive
disk of planetesimals exterior to the planets. They find that planetesimals are fed inward, originally
by Neptune, causing gradual migration of the planets. Eventually, Jupiter and Saturn cross the 1:2
MMR and their eccentricities are excited. The newly eccentric Jupiter and Saturn destabilize the
orbits of Uranus and Neptune, causing a drastic rearrangement of the Solar System. The ice giants’
orbits rapidly expand and become eccentric, so that they cross the planetesimal disk and the orbit of
Saturn or, in some cases, even the orbit of Jupiter. About two-thirds of the 43 runs were “successful,”
meaning that all of the planets survived. In half of the successful runs (“class A” runs), neither Uranus
nor Neptune closely approach a gas giant. In the other half (“class B” runs), one or both of the gas
giants encounter Saturn. In many cases, “Uranus” and “Neptune” exchange orbits. In both class A
and class B runs, the disk later circularizes the orbits of the giant planets, but Tsiganis et al. find that
class B scenarios provide a better match to their present-day orbits.
The relevance of the Nice model to the LHB is that the instability in the ice giants’ orbits
unleashes a flood of planetesimals throughout the Solar System (Gomes et al. 2005; Fig. 1). In the
Nice model, the final configuration of the planets depends primarily on the mass of the external disk.
However, the time at which the resonance crossing occurs, and thus the small bodies are released,
also depends on parameters such as the initial distance of Jupiter and Saturn from the 1:2 resonance.
Gomes et al. find crossing times ~200-1100 Myr after the planets formed, bracketing the time (~700
Myr) at which the LHB occurred. Thus the Nice scenario can produce an LHB. Figure 1.1, from
Gomes et al. (2005), shows a sample evolution. Panel (a) shows the compact system of planets and
the disk 100 Myr into the run. Panel (b) shows the system one million years prior to the resonance
crossing, and panel (c) shows that planetesimals have been scattered all over the system only two
million years after the resonance crossing. In panel (d), at 1100 Myr, the planets have reached their
final orbits, and 97% of the disk’s mass has been removed, generally due to ejection by Jupiter.
Gomes et al. estimate that about 40 of every billion planetesimals (i.e., “comets”) in the disk would
ultimately strike the Moon. For a 35M disk, this corresponds to 8-9 × 1021 g hitting the Moon (Fig.
1.2), which is comparable with estimates of the total mass of the impactors that made the later lunar
basins (Zahnle & Sleep 1997, Levison et al. 2001). These cometary impactors arrive quickly; Gomes
et al. estimate that half of those striking the Moon do so in the first 3.7 Myr after resonance crossing
and 90% arrive within 29 Myr.
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The rapid phase of
planetary migration also
would have caused both
mean-motion resonances
and secular resonances like
the 6 to sweep across the
asteroid belt (Liou &
Malhotra 1997, Gomes
1997, Ito & Malhotra 2006;
see Fig. 1.3). This sweeping
would have placed many
asteroids on Earth-crossing
orbits, making them
potential lunar impactors
(Levison et al. 2001). The
Fig. 1.1 (left): Four snapshots of one of the simulations discussed by Gomes et al.
original Nice model
(2005). The outer planets remain in a slowly evolving, compact configuration (panels a
and b, at 100 and 879 Myr, respectively) until Jupiter and Saturn cross the 1:2
calculations did not include
resonance 880 Myr after the beginning of the simulation. The orbits of Uranus,
the gravitational effects of the
Neptune, and objects in the planetesimal disk become unstable, and a flood of small
bodies is unleashed (panel c, 882 Myr). Another 200 Myr later, the system has settled
terrestrial planets on the small
down and the giant planets follow stable orbits similar to their present orbits (panel d,
bodies, which are important
1100 Myr).
for asteroids, but generally not
Fig. 1.2 (right): Panel (a): The evolution of the orbits of the giant planets for the same
for comets. To determine the
simulation shown in Fig. 1.1. Each orbit is represented by a pair of curves giving the
aphelion and perihelion distances, respectively. Jupiter and Saturn cross the 1:2 MMR
flux of asteroids that the
at 880 Myr. Uranus and Neptune are scattered outward into the planetesimal disk, and
migration of the giant planets
their orbits are then circularized by dynamical friction. Panel (b): The cumulative mass
of comets (solid curve) and asteroids (dashed curve) that strike the Moon. The comet
would have produced, Gomes
curve is offset so that
its value is zero at the time of the resonance crossing. In this
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et al. performed additional
simulation,
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
10
g
of comets struck the Moon before the resonance crossing and 8 
1021 g of cometary material struck the Moon during the LHB. In the same simulation,
integrations of main-belt
the mass of the asteroid belt
is reduced from ~10 times its current mass to near its
asteroids perturbed by Venus,
current mass, and 8  1021 g of asteroids strike the Moon. The asteroidal impacts occur
over a considerably longer period than do the cometary impacts, but this result is
Earth, Mars, Jupiter, and
sensitive to the assumed state of the asteroid belt prior to the resonance crossing and
Saturn. They found that the
the details of the evolution of the giant planets.
mass of the main belt would
have been reduced by about a factor of 10 during the unstable phase in the Nice model, and infer that
3–8 × 1021 g in asteroids (1 to 3 asteroids out of 10,000) would have struck the Moon during the LHB
(Fig. 1.2). Thus the predicted asteroidal mass striking the Moon during the LHB is comparable to the
predicted cometary mass. Gomes et al. find that the asteroidal spike is more prolonged that the
cometary spike, with 50% of the asteroidal impacts on the Moon occurring within 50 Myr after the
resonance crossing and 90% occurring within 150 Myr. They warn, however, that the results for
asteroids are sensitive to the orbital evolution of the giant planets and the state of the asteroid belt
prior to the LHB. Different parameter choices could result in a less protracted influx of asteroids,
though it probably would still last longer than the cometary influx.
Around the time the Nice model appeared, Strom et al. (2005) used new measurements of the sizefrequency distributions (SFDs) of asteroids to show that the old, heavily cratered surfaces on the
terrestrial planets have crater SFDs consistent with impactors coming directly from the main belt [i.e.,
Main Belt Asteroids, or MBAs]. Young surfaces have a different size distribution that implies
cratering by Near-Earth Asteroids [NEAs] (Figs. 1.5 and 1.6). Strom et al. infer that the impactors on
the old surfaces were delivered directly from the main belt by a mass-independent process during the
LHB, due to a dynamical excitation event like that in the Nice model. By contrast, the SFD of lunar
impactors since the LHB has been determined by slow, size-dependent processes like the Yarkovsky
effect that place MBAs in resonances, ultimately to become NEAs. The results of Strom et al. support
the view, based on compositional evidence, that the LHB impactors were primarily asteroids (Swindle
& Kring 2001, Kring & Cohen 2002). These intriguing results raise questions about the provenance
of impactors both during the LHB and prior to its onset. For example, one can ask:
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► Where do the asteroidal impactors originate, and what is the mix of impactors from different parts
of the belt that strike each of the terrestrial planets as a function of time during the LHB? Bodies can
be transported inward from the belt both by “powerful resonances,” such as the ν6 secular resonance
and the 3:1 mean-motion resonance with Jupiter, and by numerous weak “diffusive resonances”
(Morbidelli & Vokrouhlický 2003). Both play a role during the LHB (Gomes et al. 2005). At present,
most bodies that strike the Earth and Moon originate in the inner main belt (Gladman et al. 1997,
Bottke et al. 2002), but that may not have been the case during the LHB. Two high-inclination
populations – the Hungarias with semi-major axes (a) between 1.77 and 2.06 AU and inclinations (i)
> 15◦ and the Phocaeas, with 2.1 < a < 2.5 AU and i “above” the ν6 resonance (Migliorini et al.
1998; see Fig. 1.4) – currently contribute only about 10% to the flux of NEAs (Bottke et al. 2002,
2004). Prior to the LHB, the Hungaria and Phocaea regions, and a zone between them identified by
Bottke et al. (2007), could have harbored a larger population, relative to the main belt, than they do
now. These regions thus might have been important sources of impactors during the LHB.
Interestingly, Kring & Cohen (2002) find that the compositions of “several of the [LHB] projectiles
… are similar to those of some iron meteorites and enstatite chondrites,” although Tagle (2005)
argues that the Serenitatis impactor was an ordinary chondrite. Gaffey et al. (1992; also see Binzel et
al. 2004) argue for a connection between the Hungarias, E-type asteroids, and enstatite chondrites.
During the rapid migration phase of Jupiter and Saturn in the Nice model, the ν6 resonance might
have swept across the entire main belt (Gomes 1997, Levison et al. 2001, Gomes et al. 2005, Ito &
Malhotra 2006; see Fig. 1.3), possibly implying an important role for outer-belt, volatile-rich
asteroids during the LHB. Strom et al. state that the lower crater densities on the circum-Caloris
plains on Mercury, compared with the lunar highlands, implies that the Mercurian plains “probably
formed near the tail end of the LHB,” although endogenic crater-erasure processes (e.g. volcanism)
cannot be ruled out. Ito & Malhotra (2006) find that fragments from a disrupted asteroid in the ν6
resonance reach all the terrestrial planets at about the same time, while a disruption event further from
the resonance can result in a progressive delay in the arrival of impactors at Mars, Earth, Venus, and
Mercury. With the MESSENGER flybys of Mercury beginning in January 2008, the cratering history
of this largely unexplored planet will be of great interest.
► Did comets play any role in the LHB on the terrestrial planets? From the good match shown in Fig.
1-6, Strom et al. infer that “either
comets played a minor role or their
impact record was erased by laterimpacting asteroids.” In the Nice
model, the comets and fast-arriving
(“class 1”) asteroids strike the
terrestrial planets on similar
timescales, while “class 2” asteroids
trickle in later. The cometary influx
is not sensitive to the free parameters
in the Nice model, and a substantial
cometary contribution to the lunar
LHB appears likely. But the cometary
Fig. 1.3 (left): The region of the main belt swept by the 6 resonance (top)
population could have a size
and the 6 (bottom) is very sensitive to the amount that Saturn migrates. The
distribution similar or identical to that
lines represent the results from an analytic model, while the crosses were
calculated numerically. From Gomes (1997).
of the asteroids, for example if both
result from collisional evolution.
Fig. 1.4 (right): Schematic representation of the (semi-major axis, inclination)
distribution of the Mars-crossing asteroid population, from Migliorini et al.
The most important mean motion and secular resonances are also
► Strom et al. assert that “the previous (1998).
shown. The main belt (MB), Phocaea (PH), Hungaria (HU), and dynamically
evolved (EV) populations are shown.
crater record has been obliterated by
[the LHB].” This raises the hotly
debated issue of whether the lunar basins tabulated by Wilhelms et al. (1987), which are mainly preNectarian, are saturated or instead represent all basins formed after the lunar crust solidified.
Hartmann (1984) argues that the coincidence of similar high crater/basin densities reached on the
heavily cratered surfaces of most planets and satellites argues that they are all essentially in
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equilibrium and thus
evidence of the earlier
histories has been
destroyed. While it is
well understood
(Chapman &
McKinnon 1986) that a
kind of quasiequilibrium is achieved
that roughly maintains
the shape of a shallowsloped production
function, that does not
mean that such a
Fig. 1.5 (left). Representative crater size-frequency distributions (SFD), expressed as “R” plots,
for old, heavily cratered terrains (red) and young, lightly cratered terrains on the terrestrial
surface is actually “in
planets, inner Solar System, from Strom et al. (2005). The older terrains have a bigger fraction
production.” The
of large craters than the younger terrains.
visible craters are
Fig. 1.6 (right). Inferred impactor SFDs, calculated by applying a Schmidt-Housen cratersimply those of the
scaling relation to data like those in Fig. 2.1, along with SFDs for near-Earth and main-belt
asteroids deduced from ground-based surveys, from Strom et al. (2005), who conclude that the
latter stages of what
heavily cratered terrains were impacted by bodies with an SFD like that of MBAs, while younger
could be a protracted
terrains were cratered by bodies with an NEA-like SFD.
period of saturation
cratering, the earlier phases of which might have had a different production function. Further
modeling of saturated terrains can shed light on the evolution of the size-frequency distribution of the
impactors with time (Bottke & Chapman 2006).
Objectives. The published calculations for the Nice model suggest that the LHB would have had
two phases – the first due to comets (and asteroids quickly swept by the ν6 resonance), and the
second due to higher inclination asteroids. Gomes et al. (2005) and Morbidelli & Bottke (2006) argue
that the Nice model is consistent with the known properties of the LHB, including recent work
suggesting that asteroids were more important than comets in producing the late lunar basins (Kring
& Cohen 2002, Strom et al. 2005). However, it is not at all clear how robust the results of Gomes et
al. are, since the second phase of asteroidal impacts is sensitive to the evolution of the giant planets
and the dynamical state of the asteroid belt. We propose to analyze the 29 successful runs of the Nice
model, for which the data will be provided by Collaborator Levison, and to carry out a few additional
runs of the Nice model in which the terrestrial planets are included throughout the entire integration.
Using the time histories of the positions and velocities of the giant planets and planetesimals from the
Nice model runs, we then propose to calculate the rates of crater and basin production on each of the
terrestrial planets and the Moon caused by asteroids and comets from the onset of the LHB (~3.9 Ga)
until ~3.5 Ga. We will then use plausible production functions (e.g. Bottke et al. 2005a have argued
that the present MBA SFD was established very early in Solar System history) as input to the
CRASAT numerical crater saturation model (Bottke & Chapman 2006) to determine how crater
density evolves with time on the terrestrial planets. These calculations will constrain the range of
plausible impact histories for both the terrestrial planets (this Task) and satellites of the outer planets
(Task 2) during the LHB.
Technical Approach. We will perform a series of orbital integrations of asteroids and comets,
using both existing and new runs of the Nice model as a starting point. Our work will improve on that
of the study by Gomes et al. (2005) in that we will analyze a wide range of scenarios, rather than just
one representative case; our dynamical modeling of the asteroid belt will be more realistic; and we
will consider the possibility that the asteroid belt extended inward to 1.7 or 1.8 AU at the time of the
LHB. The calculations by Tsiganis et al. (2005) did not include asteroids, so Gomes et al. (2005)
modeled the main belt by applying an artificial smooth drag force on the orbits of Jupiter and Saturn
(Malhotra 1993) to simulate the sweeping of the main belt by resonances. In other words, Gomes et
al. did not use the detailed histories of the giant planet orbits at all. We will employ the approach of
Petit et al. (2001), who studied the dynamical excitation of the main belt by first simulating the
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evolution of massive embryos in the terrestrial planets’ region via their mutual interactions and
perturbations by Jupiter and Saturn. Petit et al. then simulated the belt by using the recorded states of
the massive bodies to gravitationally perturb test particles. In our case, the planets (the giant planets
in the existing calculations, Venus through Neptune or Mercury-Neptune in the new calculations) will
perturb the asteroid belt. The new integrations will use the numerical codes “SyMBA” (Duncan et al.
1998; Levison & Duncan 2000) and “Mercury” (Chambers 1999). In different runs of the Nice model,
the regions of the asteroid belt that are destabilized will vary, as will the timing of resonance
sweeping. We will consider various initial excitation states for the belt, including eccentricity and
inclination distributions similar to those of the current (bias-corrected) belt (Jedicke & Metcalfe 1998,
Jedicke et al. 2006), and other cases in which typical eccentricities and inclinations in the belt are
small prior to the LHB. Since the LHB will excite the belt, reality should lie between these two
limits. The calculations will be carried out for 300–500 Myr after the resonance crossing. From the
orbital histories of the asteroids and comets whose orbits we integrate, we will determine the rates of
asteroidal and cometary impacts on Mercury, Venus, the Moon, Earth, and Mars as a function of time.
We will then use a modified version of a numerical model (CRASAT) we have developed that
tracks how the SFD of a cratered surface evolves with time due to impacts (Bottke & Chapman
2006). In the CRASAT code, craters are defined by their rims; when a user-specified fraction of a
crater’s rim has been removed by overlapping craters, we assume it is no longer recognizable.
Planetary impacts by asteroids and comets recorded in our orbital integrations will determine the
locations of impacts on each planet and their impact speeds and angles to the vertical (Zahnle et al.
2001). We will supplement these “direct impacts” with a larger sample of impacts calculated with
Kessler’s generalization of Opik's equations that gives the statistical probability of collision between
a planet and small body (Kessler 1981, Nesvorný et al. 2004). This approach allows for latitudinal
variations in cratering rate and, for the Moon, an apex-antapex asymmetry (Le Feuvre & Wieczorek
2006). We will use a Schmidt-Housen scaling law, modified for crater collapse, to compute crater
diameters, given assumed impactor sizes (e.g., Ivanov 2001, Holsapple et al. 2002).
We will initially assume an asteroidal SFD (not depending upon an asteroid’s distance from the
Sun) based on recent surveys (cf., O’Brien & Greenberg 2005). The SFD of cometary nuclei is not as
well-constrained, but appears to be “shallow” (top-heavy) for small comets (Lamy et al. 2004,
Whitman et al. 2006) and steep for large comets (see Task 2). We will also consider the possibly
evolving size distributions for these populations as a result of collisional evolution (e.g. following the
modeling by Bottke et al. 2005b). We will initially assume that the planets are blank slates at the
time the LHB begins. Later, we will perform simulations in which we assume that a population of
craters and basins (such as South Pole-Aitken on the Moon) pre-dates the LHB. These calculations
will enable us to address questions such as: What is the provenance of the impactors on each planet?
What are the relative contributions of asteroids and comets? How long does the impact spike last at
each planet? Do these spikes occur at the same time, or is there a measurable delay as the asteroidal
impactors march inward from the belt to Mars-crossing orbit and then to Mercury-crossing? Are the
crater populations on Mercury, the Moon, and Mars consistent with the Nice model? How large are
the total expected populations of craters and basins on all the terrestrial planets, some of which might
be marginally visible (e.g. buried craters, Frey 2006)?
Task 2. Impact and Orbital Histories of Outer Planet Satellites
Background. Jupiter blocks the passage into the inner Solar System of the vast majority of small
bodies that form beyond its orbit (Wetherill 1994). Thus, if comets contributed significantly to the
lunar LHB (Wetherill 1975, Levison et al. 2001, Gomes et al. 2005), the regular satellites of the giant
planets would have suffered a much heavier bombardment than the Moon. Such a bombardment
would have profoundly affected them, long after they had formed, in ways possibly still apparent
today, especially for ancient crusts like those of Callisto and Iapetus. Since we wish to know where
the LHB impactors originated, we might be able to find evidence for, or rule out, certain models by
modeling the diverse effects of impactors from different source regions on bodies throughout the
Solar System.
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The present-day impact rate by ecliptic comets, derived from the Kuiper belt/scattered disk
(Duncan et al. 2004), is estimated to be 35-90 times higher on the big moons of the outer Solar
System – the Galilean satellites, Titan, and Triton – than their rate striking the Moon (Zahnle et al.
1998, 2003; Levison et al. 2001)1. Gomes et al. (2005) estimate that 8.4 × 1021 g of comets struck the
Moon during the LHB. This translates to 3-8 × 1023 g in comets striking each big moon, a mass
equivalent to a single impactor ~1000 km in diameter. The mid-sized moons of Saturn and Uranus,
including distant Iapetus, should have suffered 1-10 times as many cometary impacts as the Moon.
Iapetus, in fact, has at least seven impact basins on its leading face, including one 800 km in diameter,
the largest known in the Saturn system (Giese et al. 2007; cf. Moore et al. 2004, Bruesch & Asphaug
2004). We do not know how many of the ~12 late lunar basins (i.e., craters > 300 km diameter,
Wilhelms et al. 1987) were made by ecliptic comets. If half the lunar basins have a cometary origin,
then 200-500 basins would have formed on each Galilean satellite. At current rates, 3 or 4 basins are
expected to form in 4 Gyr on Europa, Ganymede, or Callisto; thus the LHB represents a fluence about
100 times greater than what has come since. Some of the possible effects of the LHB on moons of the
outer planets include the following.
► Geometrical saturation by basin-forming impacts. Five hundred 300-km basins would cover
Callisto’s surface twice over if they were uniformly distributed over the moon’s surface, or ~5 times
over if we include larger basins (Valhalla has a rim diameter of ~1000 km and rings extending to
almost 4000 km [Passey & Shoemaker 1982, Schenk et al. 2004]).
►Extensive melting of surfaces. Of the 500 basins that we estimate would have formed on Callisto
during the LHB, perhaps 50 would be roughly Imbrium-scale (~1000 km). For an Imbrium-scale
impact on Callisto, we estimate that 5% of the impact energy, or 1032 ergs, goes into melting the
moon’s surface (Levison et al. 2001). If we assume that Callisto’s surface is made of ice, the resulting
mass of water is 3 ×1022 g. If we approximate the melted region as a hemisphere, the maximum depth
is 125 km. Thus it seems possible that impacts during the LHB would have melted much or all of
Callisto’s surface to a depth of 100–150 km. In this view, most of the basins that formed during the
LHB would be (at best) difficult to recognize at present.
► Catastrophic disruption. Smith et al. (1982) inferred that Dione and the moons interior to it were
disrupted by impacts and then reassembled in the early days of the Saturn system. Amalthea in the
Jovian system, Umbriel and its Uranian ilk, and the Neptunian moons discovered by Voyager would
have undergone similar histories (Smith et al. 1986, 1989). While recent model estimates of
disruption rates for mid-sized moons (e.g., Lissauer et al. 1988, Zahnle et al. 2003) are lower than the
estimates of Smith et al., clearly moons of the outer planets smaller than ~100 km have almost
certainly been disrupted and reassembled at some point in Solar System history (e.g., Colwell et al.
2000), and larger moons like Enceladus and Miranda may have been (Zahnle et al. 2003).
► Stochastic density variations. By contrast with the monotonic decline in Galilean satellite densities
with distance from Jupiter, the regular satellites of Saturn show no clear pattern. The “ring moons”
interior to Mimas' orbit, as well as Hyperion (Thomas et al. 2007), have densities well below that of
solid water ice, and thus may have substantial voids resulting from catastrophic
disruption/reassemblage events. The mid-sized satellites and Titan have higher but widely varying
densities. Smith et al. (1981) conjectured that “the stochastic character of accretion” of a mixture of
rocky and icy planetesimals might explain the lack of a trend in density. Pollack and Consolmagno
(1984) argued that the mid-sized Saturnian moons formed with similar densities, with the “stochastic
component” being due to catastrophic disruption of some of them.
► Dynamical effects. The large mass flux passing through a planetary system during a heavy
bombardment event could threaten the dynamical stability of planetary satellites. At minimum, both
1
These estimates ignore atmospheric shielding for Titan, which sharply reduces the number of craters <~20 km (e.g., Artemieva
& Lunine 2005, Korycansky & Zahnle 2005, Lorenz et al. 2007), but does not affect the basin-forming impacts on which we focus.
9
direct impacts on satellites and gravitational scattering by interloping planetesimals could excite the
satellites’ eccentricities and inclinations (e.g., Morris & O’Neill 1988, Beaugé et al. 2002, Stern et al.
2003). Tsiganis et al. (2005) find that regular satellites of the outer planets can survive in the Nice
model (and maintain small eccentricities and inclinations), but that irregular satellites would not
survive. Mosqueira & Estrada (2006) point out that Iapetus’ low eccentricity (0.028) “may be the
main constraint for such a scenario,” since eccentricity damping in Iapetus is expected to be
negligible (damping timescale > 1013 years) because of its large distance from Saturn (Peale et al.
1980). In this task we focus on Iapetus’ orbit as the key constraint on the Nice model.
.
Objectives. We will perform orbital integrations of planetesimals (and, in the “class B” runs
described in Task 1, “Uranus” and/or “Neptune”) that undergo encounters with the giant planets
during the LHB. These integrations will determine the changes produced in the satellite orbits by
physical impacts and gravitational scattering, and will narrow the range of tenable LHB models
involving stray bodies from the outer Solar System.
Technical Approach. The orbital histories of the planetesimals (‘comets’) previously calculated in
the Nice model (Task 1) will be used to produce a database of the orbital distributions of bodies that
pass within the Hill spheres of the giant planets. There are ~105 – 106 such encounters with each
planet in each 1000-5000 particle run of the Nice model (on average, each planetesimal passes within
the Hill sphere of each planet dozens of times, making a total of ~100-200 encounters per
planetesimal with all planets; also see Beaugé et al. [2002] and Nesvorný et al. [2004]). In the Nice
model simulations, every planetesimal has a mass of order the lunar mass. These weighty bodies are
fine for modeling the evolution of the planetary orbits, but we need a more realistic mass distribution
for the disk planetesimals to model satellite evolution. Planetesimals’ effects on the satellites’ orbits
are roughly a random walk, so orbital changes scale as the square-root of the typical planetesimal
mass. Beaugé et al. (2002) developed an algorithm to calculate effects of planetesimals on satellites
by assigning the planetesimals masses after the fact.
We will follow the approach of Beaugé et al. (2002). We will first construct functional fits of the
distributions of planetocentric semi-major axis, eccentricity (e), and inclination for the planetesimals
that encounter each planet in the Nice model integrations2. Nesvorný et al. (2004) provide details of
this procedure. These fits specify the relative number of planetesimals crossing each satellite’s orbit
and the distribution of velocities at “infinity” (Zahnle et al. 1998, 2001, 2003; Levison et al. 2000;
Beaugé et al. 2002; Nesvorný et al. 2004). Next, we will integrate the orbits of a huge number of noninteracting planetesimals that interact gravitationally with the planets and the satellites, but not with
each other. Each planetesimal will be integrated for one passage through the Hill sphere of a giant
planet. Most planetesimals follow hyperbolic orbits with respect to the planets; these cross the Hill
sphere in 1-5 years. A few undergo temporary capture onto weakly bound orbits (e < 1), typically for
one or a few crossing times. A very few are captured for tens or hundreds of years (Kary & Dones
1996).
How many planetesimal orbits do we need to integrate? If we assume that the planetesimals in the
35M disk in the Nice model follow an SFD with an index of 4 (i.e., dN/dr ~ r-4, where r is the radius
of the planetesimal), the disk would contain 2 × 109 planetesimals with diameters greater than 20 km,
assuming bodies of unit density. With 100-200 passages through the planetary Hill spheres per
planetesimal, these bodies would undergo > 1011 planetary encounters in all. However, we need not
follow them all. To first order the orbits of the satellites and planetesimals during the encounter are
Keplerian orbits around the planet. We can use the well-developed formalism for calculating the
“Minimum Orbit Intersection Distance” (Gronchi 2005) to determine a lower bound on the satelliteplanetesimal distance of closest approach. We can then use criteria, based on analytic and numerical
studies of gravitational encounters in different regimes (e.g., Heggie & Rasio 1996, Kobayashi & Ida
2
Nesvorný et al. (2004) show that the distributions of the other orbital elements of the planetesimals – the ascending node, argument of
pericenter, and mean anomaly – are accurately fit by uniform distributions. Vokrouhlický et al. (2007) find that this is also the case for
the planetesimals that encounter the giant planets in the Nice model.
10
2001, Heggie & Hut 2003), to determine which encounters potentially have large enough effects on
the satellites (say, eccentricity changes > 10-4) that we need to integrate them. Once
we impose these restrictions, we estimate that we will need to follow “only” 108 encounters3.
The computing time we require is similar to that used in recent studies carried out on ordinary
workstations. For example, Ito & Malhotra (2006) integrated ~104 bodies for > 3 ×109 time steps, i.e.,
for > 3 ×1013 steps in all. In our study, by contrast, we will integrate a vast number of bodies for a
very short time. We plan to use SyMBA (Duncan et al. 1998) to perform most of the integrations. In
some cases, we will include the Sun as a perturber of the satellites4. As a rule, with SyMBA will need
to use a time step of about 1/20 the orbital period (P) of the innermost satellite (Levison & Duncan
2000). To keep the computing time manageable, we will
choose the satellites we need to include judiciously; e.g.,
when we study Iapetus, we will include Titan (which has P
= 16 days) but not satellites interior to Titan (Mimas has P
< 1 day). Thus in this case the time step will be 0.8 days.
The complete passage of a planetesimal through the Hill
sphere will typically take tens to hundreds of time steps.
Thus we will require ~1011 - 1012 time steps per simulation.
We will perform at least thirty such simulations using five
or more realizations of the Nice model and various
assumptions about the SFD of the planetesimals,
including: (1) a monodispersion (e.g., only 100- or 1000km planetesimals); (2) single or double-power laws
(Bernstein et al. 2004), including cases in which the mass
primarily resides in the largest bodies (for a single power
law, dN/dr ~ r-q, with q < 4, Shoemaker & Wolfe 1982,
Tremaine & Dones 1993) and others with equal mass per
decade of size (q = 4) or most of the mass in the smallest
bodies (q > 4), as with present-day Kuiper belt objects
larger than ~100 km (Trujillo et al. 2001, Gladman et al.
2001, Petit et al. 2006); and (3) a “runaway accretion” case
Fig. 2.1. Orbital evolution due to gravitational
with most of the mass in small bodies but with a small
scattering by Mars-mass planetesimals of a
hypothetical distant satellite7of Jupiter with an
number of Pluto-, Moon-, Mars-, or Earth-sized bodies as
initial semi-major axis of 10 km, and initial
well. In addition, some runs of the Nice model (in fact, the
eccentricity and inclination of zero, from Beaugé
et al. (2002).
ones that produced outer planetary systems most like our
own) involve the passage of “Uranus” or “Neptune” through Saturn’s Hill sphere, so we need to
consider these planetary passages too. They are not as destructive as one might guess, since they
usually occur at distances well outside the regular satellites’ orbits. For example, if Uranus’ closest
approach distance to Saturn were four times Iapetus’ semi-major axis, it should impart an eccentricity
of only 0.005 to Iapetus (Heggie & Rasio 1996).
To illustrate the expected results, in Fig. 2.1 we show the 10-Myr evolution of a hypothetical
distant satellite of Jupiter with an initially circular orbit from Beaugé et al. (2002). While the specific
parameters of this run do not apply (for instance, Beaugé et al. followed only 1000 planetesimals, all
of which had masses of 0.1M), it does illustrate the random-walk nature of the orbital evolution.
In our own calculations we will follow the evolution of the all the classical regular satellites of the
3
We also will use approximate but very fast analytic expressions, such as improved versions of the impulse approximation (Rickman et
al. 2005), in deciding which encounters must be integrated numerically. The impulse approximation assumes that encounters are fast
(i.e., the satellite is effectively stationary during the encounter). Since this assumption is violated in many of the cases we will
investigate,
the impulse approximation is, unfortunately, inadequate for our planned studies of satellite orbit evolution.
4
Including solar perturbations is necessary for distant (irregular) satellites and unnecessary for regular satellites close to their parent
planets. Iapetus is on the boundary, so we will perform experiments to determine the importance of solar perturbations on our results.
To include the Sun as a perturber, we will modify SyMBA in a way similar to how Chambers et al. (2002) adapted the “Mercury” code
(Chambers 1999) to treat planetary accretion in binary star systems.
11
giant planets and selected irregular satellites for 108 years. SyMBA will calculate the result of
gravitational scattering by the perturber and whether a physical impact occurs on the satellite. When
an impact occurs, SyMBA will assume the impact is completely inelastic and will adjust the
satellite’s orbit by using conservation of momentum, i.e., the satellite will receive an impulse v =
mvrel/(m+M), where vrel ≡ v – V; v and V are the pre-impact velocities of the planetesimal and
satellite, respectively; and m and M are the corresponding masses. The impulse produces changes in
the orbital elements of the satellites which can be calculated by Gauss’s equations (e.g., Nesvorný et
al. 2003). For example, the satellite’s eccentricity can change by as much as 2mvrel/[(m+M)V], where
v and V are the pre-impact velocities of the planetesimal and satellite, respectively; m and M are the
corresponding masses, and vrel ≡ v – V. For a head-on impact by a planetesimal on a parabolic orbit,
vrel/V > √2 + 1, so, for m << M, the eccentricity change is ~ 5m/M.5 In some cases we will include
tidal damping, which can rapidly reduce the eccentricity of an inner satellite such as Enceladus (e.g.,
Peale et al. 1980, Squyres et al. 1983). Since the rate of tidal evolution is negligible for distant
satellites, we anticipate that the strongest constraints on the Nice model will be provided by Iapetus.
By including planetesimals as small as 20 km in our integrations, we will be able to estimate the
rate of basin-forming impacts on the satellites at the same time we investigate gravitational scattering
by the planetesimals. (We define a basin to be a crater larger than 300 km. Using Pi-group scaling
[Schmidt & Housen 1987; Holsapple 1993; Holsapple et al. 2002; H. J. Melosh & R. A. Beyer’s
‘Crater’ code at http://pirlwww.lpl.arizona.edu/~jmelosh/crater_c.cgi], a 20-km impactor with unit
density will produce a 270-km crater on Mimas and a 137-km crater on Iapetus, with the difference
arising primarily from the much larger mean impact speed on Mimas.) If the specific energy Q of an
impact exceeds QD* (Benz & Asphaug 1999, Nesvorný et al. 2004), we will assume the satellite is
catastrophically disrupted. (For instance, using Benz & Asphaug’s fits for ice, we find that an
impactor of unit density with diameter d > 32 km will disrupt Mimas, while an impactor with d > 154
km can disrupt Tethys.) Regular satellites will generally reaccrete most of their mass quickly (Burns
& Gladman 1998); thus we will generally assume that the moons are born again with a slate free of
craters.
The main result of these calculations will be a better understanding of the dynamical effects of the
LHB on the regular satellites of the giant planets. We should be able to constrain the distribution of
planetesimal masses if a scenario like that of the Nice model took place, and we may find that some
models that produce the correct planetary orbits lead to “incorrect” satellite orbits. Our simulations
will also provide the most detailed picture to date of the number of basins that would have formed on
each moon during the LHB, their spatial distribution across the moons’ surfaces, and the number of
catastrophic disruption events each moon would have experienced. These spatial distributions can be
used in simulations of crater saturation (Chapman & McKinnon 1986, Hartmann & Gaskell 1997,
Bottke & Chapman 2006; see Task 1).
Task 3. Modeling (Mega)regolith Evolution to Understand Impact Melt Sampling Biases
Background. Tera et al. (1974) first proposed a "terminal cataclysm" or LHB based on an
apparent spike in lunar rock resetting ages. It has more recently been advocated on the basis of a
spike in ages of lunar impact melts, or at least an absence of secure impact melt ages prior to 4 Ga
(Ryder 1990, Bogard 1995, Dalrymple et al. 2001, Cohen et al.. 2000, Kring & Cohen 2002, Cohen et
al. 2005). Dates for lunar impact basins, based on ages for rocks inferred to have been affected by
formation of particular basins, range from Nectaris, at 3.90-3.92 Ga (possibly older), to Imbrium at
3.85 Ga (with ~10 basins forming in that interval, as inferred from stratigraphy, and only the last
basin, Orientale, still younger). The short duration during which the dated basin-forming events
The satellite will receive an impulse δv = mvrel/(m+M) in a completely inelastic impact. For an initially circular satellite orbit, a/a = 2
vT /V, e = [2 cos f vT + sin f vR]/V, and i = cos(f+)vW]/V, where a, e, and i are the initial semi-major axis, eccentricity, and
inclination of the satellite; a, e, and i are the changes in the elements; f and are the true anomaly and argument of pericenter of the
satellite’s orbit; vR, vT, and vW are the radial, tangential, and vertical components of v; and V = |V|. Experiments show that the
efficiency of momentum transfer can be greater or less than our assumed value of unity if ejecta are preferentially thrown backward or
forward, respectively (Yanagisawa et al. 2000). We can easily incorporate variable momentum transfer efficiency into SyMBA if we
find this is warranted.
5
12
apparently occurred suggests an abrupt post-spike decline or cessation of bombardment by large
projectiles (half-life ~50 Myr; Wilhelms et al.1987). The Nice model can produce such a short halflife by comets and/or low-inclination asteroids but not by higher inclination asteroids. The validity of
the lunar evidence depends on (a) the degree to which the dated samples can be ascribed reliably to
particular basins and (b) the degree to which the prevalence of impact melts of various ages directly
reflects the changing bombardment rates. Hartmann (1975, 2003) and Grinspoon (1989), for
example, attribute the absence of earlier melts to a "stonewall" effect, such that melt rocks produced
prior to Nectaris would have been buried, destroyed, or otherwise undersampled relative to the true
rate at which they were produced. By analogy with the evidence originally used to argue for a lunar
LHB, Bogard (1995, 2006) suggested that an LHB occurred contemporaneously in the asteroid belt
(on the HED parent body and possibly on ordinary chondrite parent bodies), although it appears to be
longer-lived in the asteroid belt than on the Moon. There is also a single Martian meteorite re-set
around 4 Ga (Turner et al. 1997).
Chapman et al. (2007) have critically examined these arguments and have raised serious issues.
For example, the sharp cessation of basin formation depends on best-guess associations of lunar
samples with often distant basins. While the relative stratigraphy is generally well-established,
associations of rocks with basins typically depend on compositional affinities as well as on geological
models from the 1960s/70s – when the missions were planned and the returned samples were
analyzed – which demand reinterpretation from a modern perspective (cf. Grieve 1980).
Furthermore, histograms of impact melt crystallization ages (including melt clasts from lunar
meteorites), and of inferred impact resetting ages, are not in good accord with each other nor with the
inferred sharp cessation of bombardment by basin-forming projectiles. Such differences do not
necessarily disprove that a cataclysm happened; indeed, the Nice model could well yield a sharp spike
for Earth/Moon but a much longer decay of collisional bombardment in the asteroid belt.
Alternatively, the different age-histograms could well be the result of non-uniform sampling. Issues
of collection biases should be evaluated, but Chapman et al. suspect that a prime sampling bias may
be due to megaregolith development processes, which may preferentially hide, destroy, or reset older
samples and exaggerate representation of the effects of the most recent basins (e.g. Imbrium, cf.
Haskin et al. 2002).
While arguments that impact melt histograms are a straightforward reflection of bombardment
history are undone because of obvious sampling biases, there are also serious problems with the
efficacy of Hartmann’s “stonewall.” In particular, it appears that the projectile SFD in the early Solar
System (including the LHB) was “shallow” or top-heavy, dominated by huge basin-forming
impactors. Thus the “churning” of the surficial regolith that we are familiar with (dominated by the
“steep” slope of the modern population of sub-100m impactors) is a bad analog for the evolution of
the megaregolith. The sporadic, huge impacts may have melted and destroyed many pre-existing
rocks, but not in the uniform and repeated way of the modern surficial regolith. Heterogeneous
locations will remain where rocks are not affected because of the large impacts’ stochastic
distribution, and the biggest impacts will often excavate into previously unaffected materials at the
base of the megaregolith. So there is ample opportunity for rocks of all sorts, including impact melts,
to survive...somewhere in the lunar crust. This qualitative statement demands to be evaluated
quantitatively, however.
In addition, processes in the surficial regolith (uppermost meters) must be evaluated in order to
understand additional sorting effects that may affect the sampling of basin-associated rocks and
impact melts at the immediate surface. (Note that both the spallation mechanism by which lunar
meteorites may be derived and the direct sampling by astronauts and machines have obtained most
rocks from the immediate surface. So the evolution of a rock destined for laboratory analysis –
burial, comminution, jostling within the regolith – actively proceeds long after the final basin-forming
event until the rock is eventually collected by an astronaut or launched as a lunar meteorite.) All of
these processes must differ between the Moon and smaller asteroids, with the latter’s small gravity
and perhaps less regolith, which must be considered when comparing age histograms for meteorite
parent bodies with those for lunar rocks.
13
The main question is this: How securely do we know the rapidity of the decline in bombardment
rate during the 4.0 - 3.8 Ga period, and how robustly do we know that there was a cataclysmic spike
(i.e. a relative lack of bombardment in the 4.3 – 4.0 Ga period) as distinct from just a rapid cessation
of an early higher bombardment rate? Many assume that visible pre-Nectarian basins, and South
Pole-Aitken in particular, are very old (similar assumptions have been applied to pre-Noachian
features on Mars). But all we really know is that they are stratigraphically older than Nectaris: they
could be just millions of years older rather than hundreds of millions of years older. The only serious
argument that they must be much older than Nectaris is that made by Baldwin (1987, 2006), who
claims that the old basins required appreciable time to reach their evidently flattened, degraded
morphology given the viscosity of the lunar crust. But an alternative view is that they have been
flattened and filled in not by viscous crustal relaxation but by the bombardment process itself, which
could have happened quickly.
Objectives. In this task, we propose to evaluate quantitatively whether lunar impact melt samples
are representative of the bombardment rate by large cratering- and, especially, basin-formingprojectiles. Secondary objectives are to evaluate (a) how robust are the inferred associations of rocks
with particular basins and (b) effects on age histograms of differences between lunar and meteorite
parent-body regolith processes. The overall goal is to establish what geological constraints really
exist on the commencement of the LHB and its duration.
Technical Approach. Our first step is to develop a parameterized model for the evolution of the
lunar megaregolith during repeated bombardment by projectiles that form large craters and basins.
Our approach is not to simulate in detail, from first principles, the physics of large-scale impacts or
ejecta emplacement. Rather it is to capture the major features of megaregolith processes from
published models of particular phases or elements of the basin-forming process and then to vary
parameters in order to understand the broad nature of where impact melts could be emplaced and how
they subsequently move around on and below the lunar surface until they are collected. P.I. Chapman
(cf. Chapman & McKinnon 1986) previously developed a 2-D code to study lunar surface processes
and saturation cratering; for different choices of production SFD, it clicks through time-steps starting
with an uncratered surface until the surface is multiply saturated with circular craters or remnants of
circles; emplaced ejecta blankets are represented. Collaborator Bottke & Chapman (2006) have
created the new code CRASAT (described in Task 1), based on similar principles, to explore crater
saturation. We propose to extend this approach for the first time into the third dimension to model
the megaregolith. By parameterizing the results of published models for basin geometry (e.g. basin
excavation profiles (Wieczorek & Phillips 1999) as modified with time (Byrne 2006), impact melt
production (volume and spatial emplacement: cf. Cintala & Grieve 1998), and ejecta emplacement
and block size distributions (cf. Melosh 1989, Haskin et al. 2003), we can specify the degree of
resetting, melting, and comminution of rocks within the model elements. We will employ the
fundamental understanding (Melosh 1989 and subsequent literature) of how the 3-D elements in the
pre-existing crustal block are moved and redistributed during the excavation stage of impact
cratering. We can thus follow the spatial emplacement of these elements as ejecta and subsequent
movement within the megaregolith (as well as possible later resetting, melting, or destruction) as
basin-forming impacts continue to occur. By running the model with different choices of parameters,
within allowable ranges, we can learn about the plausible range of uncertainties in outcomes.
We will test various production SFDs, ranging from the top-heavy case represented by lunar basins
and highlands craters to somewhat “steeper” cases, which may have characterized earlier cratering if
the pre-LHB impactors were from a highly collisionally evolved source (Bottke et al. 2005, Charnoz
& Morbidelli 2007). We will vary the location of impact melts from buried melt lenses to surficial
veneers. We will vary basin topography with time using a range of crustal viscosities. The ranges of
parameters in the recent literature are large, but we are looking for first-order answers. For example,
are older materials primarily covered up by later impacts or instead chiefly excavated and distributed
near the surface? How widely are materials redistributed laterally? (The latter question addresses
issues of association between Apollo samples and particular basins.) The result of this phase of the
14
research will be three dimensional pictures (for different parameter choices) of the locations and
characteristics of basin-associated rocks, with different degrees of resetting/melting, at the end of the
LHB.
The second step is to investigate the role of subsequent processing of the surficial regolith (the
upper meters and tens of meters) that determines the locations and attributes of the rocks that are
actually sampled, ~3.8 Gyr later, by astronauts and other processes. The vast majority of basinproduced impact melts remain at depth forever. But those located within the upper tens of meters,
plus a few rare ones at greater depth reached by large post-mare cratering events, have a chance of
being collected at the immediate surface. The question is how the rocks actually sitting on, or very
near, the surface have been modified by surficial regolith evolution, which is dominated by an
impactor SFD that is much steeper than the one that characterizes megaregolith evolution. For
example, how rapidly are surface rocks comminuted or buried? Are rocks brought to the surface by
some form of “granular convective transport” (Miyamoto et al. 2007, Asphaug 2007)? The
fundamental tool to be utilized will also be based on the 2-D cratering code CRASAT, but its 3-D
extension will model effects at depth scales of millimeters to meters rather than the hundreds-ofmeters to tens-of-km applicable to the megaregolith. Moreover, the model's extension into the third
dimension for the surficial regolith will have to be parameterized differently from the megaregolith
case because of the steep SFD: events that penetrate to the base of the surficial regolith occur very
rarely, while the immediate surface is repeatedly sandblasted by small meteoroids. We will rely on
analytical results for stirring depths, timescales, and stochastic variations thereof, previously derived
by Housen, Chapman, et al. (1977a,b) and by Langevin & Arnold (1977). We will also parameterize
the effects of bombardment by the millimeter/centimeter-scale impacts that erode and pulverize rocks
exposed to space at the immediate lunar surface. While the lunar surface is a comparatively
dangerous place for a rock to be, because such rocks are destroyed on rapid timescales unless they are
reburied, there are also processes (like the "Brazil nut effect"; Asphaug et al. 2001) that preferentially
bring larger elements of a particulate assemblage to the surface. Again, we do not propose to model
the detailed physics of these processes, but rather to use our simple model as a framework in which to
study variations in our parameterization of these effects as separately modeled by others. In this
phase, we are again looking for first-order answers. What are the chances that rocks lying within a
few meters of the surface will be at the surface (collectable) after 3.8 Gy of surficial regolith
evolution?
The final step, before assessing how representative lunar samples may be, is to consider the more
subjective issue of biases in the sample collection process itself. How representative of the materials
within the lunar megaregolith are the processes that form highland breccias and then spall them off
the lunar surface to become lunar meteorites? Different factors no doubt affected the USSR's
automated collection of lunar samples. Finally, a combination of human subjectivity plus wellformulated sampling protocols affected the Apollo astronauts' collections of rocks, soils, and core
samples. We will critically consider whether such final sampling biases are likely to be modest or
significant in comparison with the effects of the physical processes in the megaregolith and surficial
regolith addressed in the first two steps. We will conservatively presume that the collection biases
are relatively unimportant and so we propose only a modest degree of preliminary analysis of these
issues here.
Modeling of asteroidal regoliths is beyond the scope of this proposal, but we will qualitatively
evaluate – in the context of published models for asteroidal regolith evolution (cf. McKay et al. 1989)
– the degree to which meteorites might be more, or less, representative of bombardment history than
are lunar rocks.
IV. IMPACT ON STATE OF KNOWLEDGE
Our ongoing research on the LHB has had important influence on the developing concepts of the
formation and early evolution of the Solar System. The P.I., Co-I, and Collaborators on this proposal
15
have helped shape the evolving concept of the Solar System being fundamentally rearranged about 4
Gy ago, with a planetary-system-wide bombardment having dramatically changed the early geological
(and perhaps biological) evolution of planetary surfaces. Last spring, Drs. Chapman, Levison, and
Bottke participated in the LPI Workshop on Planetary Chronologies, where there was much
discussion of the significance (whether or not it is actually right) of the Nice model for the dynamical
rearrangement of the outer Solar System and resulting late-stage bombardment of planets and
satellites from Mercury to the outer planet satellites. Chapman et al.’s definitive evaluation of
whether lunar data supports or contradicts the terminal cataclysm (LHB) hypothesis, supported by our
earlier Origins grant, is appearing in the July 2007 issue of Icarus. Co-I Dones has helped evaluate
the role of Uranus-Neptune planetesimals in producing the LHB (Levison et al. 2001, 2004), has
studied the effects of such a bombardment on the irregular satellites of the outer planets (Nesvorný et
al. 2004), and (supported by his PGG grant) studied cometary dynamics (Dones et al. 2004, Duncan
et al. 2004). Whereas in some sub-disciplines in planetary science (e.g. the extraterrestrial materials
community) the LHB is deemed a fact, in other sub-disciplines (e.g. the Mars geology community [cf.
Hartmann & Neukum 2001]) it is virtually ignored. Through the interdisciplinary cross-talk that we
have helped foster, a much more critical eye has been turned toward the evidence for the LHB, the
possible dynamical mechanisms that might have been responsible for it, and the implications for the
early evolution for planets, satellites, and small bodies (and the search for palpable evidence of the
earliest planetary histories, not buried by subsequent processes and events). While we cannot forecast
the eventual results of our research, we expect to continue to play a major role in developing an
understanding of the early epochs of planetary formation and evolution.
V. RELEVANCE TO NASA, ORIGINS PROGRAM, AND NRA OBJECTIVES
(These issues are discussed in Part II of this proposal and will not be repeated here.)
VI. WORK PLAN, PERSONNEL, PUBLICATIONS, DATA PRODUCTS, EQUIPMENT,
AND BUDGET NOTES
Dr. Clark Chapman will oversee the project, will be primarily responsible for Task 3, and will
contribute to the other Tasks. He has extensive experience in modeling cratering and regolith
processes, and he has researched ancient terrains on the Moon, Mars, and the Galilean satellites. Dr.
Luke Dones, a planetary dynamicist and member of the Cassini Imaging Team, has previously
researched the LHB (e.g. as co-author of the 2000 Hartmann et al. review chapter on the LHB in the
Origin of the Earth and Moon book). Dones will carry out the numerical simulations in tasks 1 and
2 and will assist in the interpretation of all tasks and publications resulting from them. Dr. Hal
Levison, expert in numerical simulations of planetary dynamical processes, led our earlier study
(participated in by Drs. Chapman and Dones) of an early Uranus-Neptune formation hypothesis for
the LHB and developed (with colleagues in Nice, France, and elsewhere) the “Nice model” for the
early evolution of the giant planets and consequences for the rest of the Solar System. In this
proposed research, Levison will collaborate with us in mining data from previous Nice model runs,
assist in doing the orbital integrations for Tasks 1 and 2, and will help interpret the results.
Collaborator Bill Bottke, a planetary dynamicist, will help us modify and apply the codes he has
developed for analyzing the collisional and dynamical evolution of populations of small bodies as
well as for investigating crater and basin saturation of planetary surfaces.
We expect to work more-or-less continuously on all tasks throughout the three years, emphasizing
synthesis and publication in the third year. We will continue to report our results regularly at
domestic scientific conferences (for which we have budgeted one per year for the P.I. and for the CoI) and by submitting papers to peer-reviewed journals. We have no data requirements and seek no
support for equipment in our budget. We call attention to our Budget Justification, which explains in
part how, in spite of the unusual accounting procedures that we are mandated to use, our cost-shared,
budgeted activities are actually very cost-effective.
16
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