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Origin of the "Late Heavy Bombardment"
A Proposal submitted to NASA's "Origins of Solar Systems" Program
13 June 2002
Principal Investigator:
Clark R. Chapman ([email protected])
Southwest Research Institute (SwRI)
Suite 426, 1050 Walnut St.
Boulder, CO 80302
Co-Investigators:
Harold Levison (SwRI)
Henry (Luke) Dones (SwRI)
Collaborators:
Barbara Cohen (Univ. of Hawaii)
Martin Duncan (Queen's Univ., Ontario)
David Grinspoon (SwRI)
William Ward (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). It likely affected the early Earth even
more dramatically than the Moon, perhaps influencing the crustal organization of our planet and the
beginnings of life.
Within the Origins Program, we have been researching two critical aspects of the LHB: (1) What
really are the constraints, from lunar data, on the magnitude, timing, duration, and impactor size distribution
of the LHB? (2) What processes can rather suddenly liberate which impactor population/s ~700 Myr after the
origin of the Solar System? Our ultimate goal is to sharpen our understanding of both aspects of the problem
to uniquely determine what the impactors were, what other planets were affected, and thus 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.
We have assembled a research team with diverse talents, and we have made excellent progress in our
first cycle of studying the LHB. We have contributed to a long-delayed, but recently very spirited, reexamination of the Apollo data – particularly concerning impact melts – and have identified major
inconsistencies between histograms of ages of such melts, histograms of other lunar rock resetting ages, the
sharp cessation of the LHB inferred from basin ages, and histograms of resetting ages for several classes of
meteorites (see Appendices A and B, by Chapman, Cohen & Grinspoon). We propose to address these
intriguing issues in this renewal proposal.
We have also evaluated or begun to evaluate several dynamical/physical models for the LHB,
including: (a) the possibility that the LHB was a late stage development, due to evolving resonances, from the
origin of the Moon (Appendix C), (b) the possibility of a major asteroid collisional disruption, (c) the concept
that remnant inner solar system planetesimals were liberated from their storage locations when a fifth
terrestrial planet was ejected from the system, and (d) that the LHB was triggered by the formation of Uranus
and Neptune.
The latter possibility has particularly interesting ramifications. The paper reporting our investigations
of this hypothesis (Levison et al. 2001; Appendix D) considers the effects of a plausible, late formation of
Uranus and Neptune on neighboring icy planetesimals. Their transport would have caused an LHB and also
would have caused Saturn and Jupiter to migrate, having the chain-reaction effect of destabilizing both Jovian
Trojans and main-belt asteroids (we find that the Trojans could not be a major contributor to the LHB, but
main-belt asteroids could have been as important as the outer solar system planetesimals).
An outgrowth of this research (and of work with Dones, E. Thommes, and Collaborator Duncan) has
been an integrated perspective concerning early solar system dynamical processes (called the "Fairy Tale"),
which Levison first presented in an invited talk to the Giant Planet Decadal Survey Committee. A very recent
article (Levison et al. 2002; Appendix E) reviews these ideas. Among the Fairy Tale’s features are: (a) cores
of Jupiter, Saturn, Uranus, and Neptune all form in the Jupiter-Saturn zone; (b) the two cores between Jupiter
and Saturn are inhibited in accreting gas by Jupiter and Saturn but remain dynamically stable for ~700 Myr;
(c) the system goes unstable, ejecting the cores to become Uranus and Neptune; and (d) evolution to their
current locations disupts trans-Saturnian icy planetesimals, scattering them throughout the Solar System
causing, among other things, the lunar LHB.
Here we propose a three-year study of several vital remaining LHB issues, organized into five tasks.
This is a good time to tackle these questions because of the renewed interest in the LHB shown by the 2002
LPSC’s special session on the LHB, and 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. In collaboration with Drs. Cohen and Grinspoon, we will model the evolution of the lunar regolith
and megaregolith in order to understand whether the absence of impact melts >4 Ga in age 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) and Grinspoon (1989).
► Task 2. An implication of the Uranus/Neptune formation hypothesis of Levison et al. (2001) is that an
associated LHB must have affected the satellites of Jupiter and Saturn ~100 times more dramatically than the
Earth-Moon system; we propose to investigate what sizes of moons might have been actually disrupted (and
re-accreted), whether basin-bombardment would have melted the crusts of Ganymede and Callisto, forming
the sub-surface oceans that they apparently possess, and other consequences. Perhaps the damage would have
been so severe that we can rule out any outer solar system sources for the LHB.
► Task 3. Recently Morbidelli et al. (2001) integrated the orbits of remnant planetesimals in the terrestrial
planet zone until ~4.3 Ga, then simply extrapolated to the epoch of the LHB, with equivocal results. We
propose to run 8 simulations of the evolution of accretional left-overs for a full 1 Gyr and determine
definitively whether or not this promising idea can explain late bombardment, in which case a spike would not
be expected. If the extended tail doesn't work, then a spike, from some other cause, would be the dynamically
preferred form of the LHB.
► Task 4. Chambers and Lissauer (2002) and our group have independently proposed that the LHB might
have been caused by a fifth terrestrial planet whose orbit became unstable ~700 Myr after the Solar System
formed. Chambers and Lissauer considered a planet slightly interior to the asteroid belt, i.e., between Mars’
orbit and 2.1 AU. We propose to model scenarios in which an additional planet orbited between Venus and
Earth or between Earth and Mars.
► Task 5. Since Mercury, the Moon, and Mars all have heavily cratered terrains, it is widely assumed that
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all these terrains were created by a common set of impactors. However, plausible niches exist – e.g.,
corotation sites in the Earth-Moon system, somewhat analogous to the Trojan points in the Sun-Jupiter system
– in which additional Earth satellites might have been stored for hundreds of Myr before their orbits became
unstable because of the tidal expansion of the lunar orbit. We propose to explore this “geocentric impactor”
model by means of numerical orbit integrations.
II. PROGRESS REPORT
● Evidence for a Lunar LHB (see Appendices A, B, and D)
In order to constrain dynamical models for the origin of the LHB, we must first understand what is
really known about the LHB. In fact, virtually all solid evidence for it is derived from lunar rocks, sampled by
both Apollo astronauts and lunar meteorites. Additional constraints, from lunar geochemistry and geophysics,
were evaluated by Dr. Chapman, collaborating with Dr. Dones, resulting in Sect. II ("The Early Impact Record
of the Moon") of Levison et al. (2001; Appendix D). They found that some constraints (degree of lunar
crustal contamination by exogenous impactors, evidence for under-saturation of basins, and evidence of
minimal mantle penetration) were relatively weak, but nevertheless they adopted some plausible baseline
assumptions concerning the LHB: (a) a spike in bombardment rate occurred, which lasted ~100 Myr, and (b)
approximately 6 x 1021 g of material struck the moon during this period.
More recently, inspired by the late Graham Ryder's recent discussions of the LHB, Chapman formed a
collaboration with Drs. Cohen and Grinspoon to critically re-examine the implications of age histograms of
relevant lunar samples believed to have been affected by lunar basin formation. The LHB was first proposed
based on a spike near ~4 Ga in histograms of Ar-Ar and Rb-Sr rock ages, indicating times the rocks were reset
by large impacts and degassed. Ryder (1990), emphasizing that ages of lunar impact melt rocks were more
robust evidence for basin formation, argued that the absence of such impact melts >3.9 Ga meant that preLHB bombardment was light, proving that the heavy bombardment ~3.9 - 3.8 Ga was a true cataclysm. As we
(Chapman et al. 2002a, 2002b; see Appendices A and B) point out, however, collected impact melts are
clearly biased toward recent formation times. Many date from ages later than the last basin impact, indicating
that they were formed in smaller cratering events; yet no melts were collected representing the basins that
must have formed (since they are still partly visible) before Nectaris. Furthermore, we have emphasized that
both degassing ages and impact melt ages cover much longer durations than most estimates of the duration
(~100 Myr) of the LHB from the inferred ages of the basins. Finally, degassing ages of several classes of
meteorites (Bogard 1995), a possible indication of the LHB in the asteroid belt, spread over an even longer
duration (~1 Gyr; see Fig. 1). We suggest that these inconsistencies reflect non-uniform sampling, perhaps
due to processing in the megaregolith and the regolith that have occurred between, for example, formation of
impact melts and their collection by Apollo astronauts. We propose, in Task 1, to model these processes and
learn what the rock ages have to tell us about the LHB.
● A Possible Circumterrestrial Source for the LHB (see Appendix C)
We (led by W. Ward and R. Canup) have been studying a circumterrestrial storage mechanism for
small bodies left over after lunar formation that is similar to the leading model for Neptune’s ring arcs
(Goldreich, Tremaine, and Borderies 1986; Porco 1991; Namouni & Porco 2002). The arcs are confined by a
corotation resonance that causes material to librate. Unlike the high order Neptune case, we have investigated
a low order m = 3 outer resonance with the Moon. The trajectories of arc particles as seen in a reference
frame rotating at the pattern speed of the resonant term, ps
s s
s
s /dt), are closed, where
s
s, and
s denote, respectively, the Moon’s orbital frequency, its epicyclic (radial) frequency, and the
longitude of the lunar perigee. The area enclosed by a trajectory behaves as an adiabatic invariant during the
expansion of the lunar orbit due to tides. Thus, the arcs move out in lock-step with the Moon as it recedes
from the Earth. However, the arcs’ stability is at risk due to viscous diffusion, which attempts to spread them
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beyond the separatrix of the resonance as energy is dissipated. Goldreich et al. proposed that diffusion could
be countered by a nearby Lindblad resonance, which could supply energy. In our case, an m = 2 outer
Lindblad resonance lies in the vicinity. The resonances are split by the difference in apse precession rates of
the Moon and arc particles.
The strength of the confining resonance is determined as follows. The precession rate of the Moon’s
orbit is determined by the solar torque and the quadrupole field of the Earth, while that of the arc particles is
determined by these same torques plus the m = 0 (i.e., secular) portion of the lunar potential. In their original
model of the Neptune ring arcs, Goldreich et al. described the role of the radial eccentricity gradient q r
de/dr, where r is the distance from the central planet and e is the eccentricity, in causing the arc to either
spread or contract; in our case, q decreases by a factor ~8 during the lunar expansion. At some critical value
qc, the angular momentum luminosity due to viscosity vanishes (Borderies, Goldreich, and Tremaine 1982).
For q > qc, the arcs contract; for q > qc, they expand. The value of qc depends on the details of the particles’
interactions and the confining resonance’s dynamics. If the critical value lies somewhere in the range of q
that has obtained during lunar history, the arcs could have been destabilized at some point and become a
source of lunar bombardment. We are continuing to assess the feasibility of this geocentric mechanism as an
alternative to a Solar System-wide flux of LHB impactors.
● Fifth Terrestrial Planet Scenarios for the LHB (see also Task 4)
If the LHB was indeed an impact spike, it requires that either (1) the impactors were created at the
time of the LHB near a dynamically unstable region of the Solar System or (2) the dynamical structure of the
Solar System changed at the time of the LHB, allowing a previously stable region to become unstable. One
possibility is that there was another planet in the terrestrial region whose orbit became unstable and liberated
previously stable asteroids (cf. Chambers and Lissauer 2002).
During the previous cycle, we began studying this model for the LHB; see Task 4 for a discussion of
the work we propose to follow up on this idea. Two of the free parameters of these simulations are the
location and the mass of the fifth terrestrial planet. As we explored parameter space, we found an interesting
system – consisting of Mercury through Neptune in their current orbits plus an additional Mars-mass planet at
0.86 AU – that was stable for 1 billion years. This result was surprising because Laskar (1997) argued that
there was not enough room in the inner Solar System for an additional planet. In addition, it profoundly
affects our understanding of the structure of the Solar System and constrains models of planet formation. We
are currently writing a paper on this system, for submission to Nature.
● The LHB due to Scattered Planetesimals and Asteroids when Uranus and Neptune Formed (see Appendix
D)
The time and place of the formation of Uranus and Neptune remain uncertain (Levison & Stewart
2001). We (Levison et al. 2001, Appendix D) have numerically simulated Wetherill’s (1975) idea that the
formation of Uranus and Neptune ~3.9 Ga destabilized the orbits of comet-like bodies in the outer Solar
System, thereby causing the lunar LHB. For this scenario to produce the late lunar basins, our numerical
modeling shows that the Uranus–Neptune region must have contained planetesimals totaling ~5 times the
current mass of these planets, in accord with other dynamical estimates (see Appendix E).
Our Uranus/Neptune model for the LHB was inspired by Wetherill’s (1975) original idea, although
we do not invoke tidal disruption of planetesimals by the terrestrial planets. As a side effect of the scattering
of planetesimals, we find that Jupiter migrates inward and Saturn outward, causing resonances (particularly
6 secular resonance) to sweep through the asteroid belt. If the mass of the main belt 3.9 Ga was greater
than ~10 times its current mass, LHB impacts actually would have been dominated by asteroids. The arrival of
Uranus and Neptune in their current configuration could have been so late either because (a) planet formation
is intrinsically slow in the outer Solar System or (b) they could have formed closer to the Sun, possibly
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between Jupiter and Saturn (see below and Appendix E), occupied stable orbits for hundreds of Myr, and then
been gravitationally scattered outward (Thommes et al. 1999, 2002). This model predicts a huge impact flux
onto the moons of the outer Solar System, including the Galilean satellites (see Task 2).
● The Levison et al. "Fairy Tale" about Early Solar System History (see Appendix E)
As an outgrowth of work funded by another grant on the origin of Uranus and Neptune (Thommes et
al. 1999, 2002; Levison and Stewart 2001) and our own work on the LHB, we have proposed a new scenario
for the formation of Uranus and Neptune that includes an explanation of the LHB on the Moon and terrestrial
planets. The simplest form of this model includes the following steps: (1) Four icy giant-planet cores of 1015 M grow in the Jupiter-Saturn zone due to oligarchic growth (Ida and Makino 1993; Kokubo and Ida 1998,
2000). (2) The inner- and outermost cores start to accrete gas and open gaps. We identify these cores with
proto-Jupiter and proto-Saturn. (3) Waves generated at resonances in the gas ring between proto-Saturn and
proto-Jupiter force the gas into the gaps surrounding each of the two planets. The ring between the two planets
is removed. As a result, the cores between the gas giants cannot accrete gas. (4) The resulting Jupiter-corecore-Saturn system is stable for 700 Myr and then goes unstable. The cores, which we identify with Uranus
and Neptune, are ejected from between the gas giants. (5) Uranus and Neptune get scattered outward.
Interaction with a massive trans-Saturnian particle disk leads them to evolve to their current locations, and
dynamically excites the Kuiper Belt (Thommes et al. 1999, 2002). During this process disk particles are
scattered throughout the solar system. Some of these strike planets and satellites. For the Moon, this event
represents the LHB (see Appendix E).
III. TASK STATEMENTS
Task 1. Modelling (Mega)regolith Evolution to Understand Impact Melt Sampling Biases
Background. Tera et al. (1974) first proposed a "terminal cataclysm" or Late Heavy Bombardment (LHB)
based on an apparent spike in lunar rock resetting ages; the LHB 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). 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, to Imbrium at 3.85 Ga (with ~10 basins forming in that interval and only the last basin,
Orientale, still younger), thus defining an especially abrupt post-spike decline or cessation of bombardment by
large projectiles (half-life ~50 Myr; Wilhelms 1987). The validity of this evidence depends on (a) the degree
to which the rock ages 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) and
Grinspoon (1989), for example, ascribe 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 orginally used to argue for a lunar LHB,
Bogard (1995) has suggested that an LHB occurred contemporaneously in the asteroid belt (on the HED
parent body and possibly on ordinary chondrite parent bodies).
Chapman et al. (2002a, 2002b) have critically examined these arguments (see Progress Rept., Sect. II;
Appendices A and B) 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 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 or with the inferred sharp cessation of bombardment by basin-forming
projectiles. Such discrepancies do not necessarily disprove that a cataclysm happened: they could well be the
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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 reset samples and exaggerate effects of the most recent basins (e.g. Imbrium, cf. Haskin
et al. 2002a).
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 are 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.) All of these processes must differ between the Moon and smaller asteroids, which we must bear in
mind when comparing age histograms for meteorite parent bodies with those for lunar rocks.
Objectives. In this task, we propose (with Collaborators B. Cohen and D. Grinspoon) to evaluate more
rigorously and quantitatively than has been done before whether lunar impact melt samples are representative
of the bombardment rate by large cratering and, especially, basin-forming projectiles. Secondary objectives
are to evaluate (a) how robust associations of rocks with particular basins are likely to be and (b) effects on
age histograms of differences between lunar and meteorite parent-body regolith processes. The overall goal is
to establish what constraints really exist on the commencement of the Late Heavy Bombardment and its
duration. In other words, how securely do we know the rapidity of the decline in bombardment rate during the
4 - 3.8 Ga period, and how robustly do we know that there was a cataclysmic spike (i.e. a relative lack of preNectarian bombardment) as distinct from just a rapid cessation of an early high bombardment rate?
Technical Approach. The 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
aspects of the problem and then to vary parameters in order to understand the broad nature of where impact
melts are emplaced and how they subsequently move around on and below the lunar surface until they are
collected. Chapman (cf. Chapman & McKinnon 1986) has previously developed a 2-D code, to study lunar
surface processes and saturation cratering, that clicks through time-steps starting with an uncratered surface
until the surface is multiply saturated with craters. The shape of the input production function can be varied
and the emplacement of ejecta blankets represented. Collaborator Grinspoon (1989) has studied the LHB
using a 2-D analytic model which he is converting into a numerical model. Cohen, requesting support in a
complementary proposal, will lead our joint effort to combine Chapman's and Grinspoon's 2-D approaches
and then extend them for the first time into the third dimension to model the megaregolith. By parameterizing
the results of published models for basin geometry, impact melt production, and ejecta emplacement (cf.
Melosh 1989, Cintala & Grieve 1998, Haskin et al. 2002b), the three of us can specify the degree of resetting
or melting of model elements, and then follow their emplacement as ejecta and subsequent movement within
the megaregolith (as well as possible later resetting, melting, or destruction) as basin-forming impacts
proceed. By running the model with different choices of parameters, within allowable ranges, we can learn
about the plausible range of uncertainties in outcomes. The result of this phase of the 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, for which Chapman will take prime responsibility in the collaboration with Cohen
and Grinspoon, 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 basin-produced impact melts will remain at
depth forever. But those located within the upper tens of meters, plus a few rare ones at greater depth reached
by a large cratering event, have a chance of being collected at the immediate surface. The question is whether
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the population traits and characteristics of rocks actually sitting on, or very near, the surface have been
modified by regolith evolution, which is dominated by an impactor size distribution that is much steeper than
the one that characterizes megaregolith evolution. The fundamental tool to be utilized will also be based on
the 2-D cratering code previously developed by Chapman, but it will model effects at scales of millimeters to
meters rather than hundreds-of-meters-to-tens-of-km applicable to the megaregolith. Moreover, the model's
extension into the third dimension will have to be parameterized differently because of the steep size
distribution: rare, but important events that penetrate to the base of the surficial regolith occur very rarely,
while the surface is repeatedly sandblasted by small meteorites. We will rely on analytical results for stirring
depths timescales, and stochastic variations thereof, previously derived by Housen, Chapman, et al. 1979a,b)
and by the Orsay group (cf. Langevin & Arnold 1977). We will also parameterize the effects of bombardment
by the millimeter/centimeter-scale impacts that erode and pulverize rocks exposed at the lunar surface. While
the immediate lunar surface is a comparatively dangerous place for a rock to be and 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 modelled by others.
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 are the processes that
form highland breccias and then spall them off the lunar surface to become lunar meteorites of the materials
within the lunar megaregolith? Different factors no doubt affected the USSR's automated collection of lunar
samples. Finally, a combination of human subjectivity plus well-formulated 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 propose only a modest degree of preliminary analysis
of these issues here.
Modelling 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. McCay et al. 1989) – the
degree to which meteorites might be more, or less, representative of bombardment history than are lunar
rocks. For more background on this Task than we have space for here, please see Appendix A.
Task 2. Consequences of Uranus/Neptune Formation LHB on Jupiter/Saturn Satellites
If the LHB was caused by small bodies beyond Jupiter, such as the Uranus-Neptune planetesimals
considered by Levison et al. (2001), the moons of the giant planets would have had an even heavier
bombardment than the Moon. Such a bombardment would have profoundly affected these satellites,
presumably long after they had formed, in ways possibly still manifest today, especially for ancient crusts like
Callisto’s. Since we wish to know where the LHB impactors originated, we might be able to find evidence
for, or rule out, certain models by investigating the diverse effects of impactors from different source regions
on bodies throughout the Solar System.
In the context of the model of Levison et al. (2001), we estimate that the rate of large impacts on the
Galilean satellites during the LHB was of order 100 times the rate of impacts on the Moon at that time
(Zahnle et al. 1998, 2002; Levison et al. 2001). Thus the 12 late lunar basins (i.e., craters >300 km diameter)
translate to some 1000 basins on each Galilean satellite. At present-day rates, ~1 basin is expected to form in
4 Gyr on Europa, Ganymede, or Callisto; thus the LHB represents a fluence 1000 times greater than what has
come since. The LHB would have geometrically saturated the Galilean satellites with basins multiple times,
perhaps depleted surfaces of ice (Levison et al. 2001; D. Stevenson, pers. comm.), probably disrupted 1000km moons such as Saturn’s Tethys and Dione, and might even have disrupted the Galilean satellites
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(depending, of course, on the uncertain size distribution of the largest impactors); disrupted moons would
reaccrete.
The bombardment also could have melted satellite surfaces to considerable depth. For example, of the
~1000 basins that we estimate would have formed on Callisto, perhaps 100 would be Imbrium-scale [(2 ± 1) x
1033 ergs, Zahnle and Sleep 1997]. If 5% of the impact energy went into melting Callisto’s surface (assumed
to be made of ice), the resulting mass of liquid water per impact is 3x1022 g. If we approximate the melted
region as a hemisphere, the maximum depth is 250 km. Thus LHB impacts could possibly have melted much
or all of Callisto’s surface to such depths, which is intriguing in view of Galileo data suggesting that
Ganymede and Callisto may have internal oceans at depths >80 km (Schenk 2002), but <150-200 km (Zimmer
et al. 2000, Kivelson et al. 2002).
We do not propose detailed modeling of the effects of basin-forming impacts on the Galilean
satellites. However, we do propose to follow up on the model of Levison et al. (2001, Appendix D) by
computing impact and catastrophic disruption rates for the satellites of the giant planets in scenarios in which
the LHB impactors come from the outer Solar System. These will include our original model, in which Uranus
and Neptune form late, and several cases modeled by Thommes et al. (1999, 2002), in which Uranus and
Neptune form in the Jupiter-Saturn region, are scattered outward, and then have their orbits circularized
(Levison et al. 2002, Appendix E). The impact rate calculations will use the same formalism1 that we have
used in studying current impact rates in the outer Solar System (Zahnle et al. 1998, 2001, 2002). The basins
would have been formed by impactors with diameters, d, of tens or hundreds of km. As a baseline, we will
assume that the impactors’ size distribution is similar to that of the best-characterized small body population
in the outer solar system, Kuiper Belt Objects (KBOs). The KBO cumulative size distribution follows a power
law with index q = 3et al. 2001, Trujillo et al. 2001), and q = 2.5 for
et al. 2002). Since satellite disruption is caused by the larger impactors, we will
study variations in the impactors’ size distribution (both the slope and an upper cutoff ). Such preliminary
calculations should yield insights about geological/geophysical attributes of outer solar system satellites
severely bombarded by an LHB.
Task 3. Late-Stage Evolution of Accretional Remnants in Terrestrial Planets Zones
The “null hypothesis” about the LHB is that it was the tail end of accretion. Recent work by
Morbidelli et al. (2001) hinted, but did not prove, that basin formation due to leftovers of accretion could not
extend until 3.9 Ga. We believe that we can now settle this question. Since the terrestrial planets formed
through collisions, it is natural to ask whether small bodies remaining near 1 AU, when accretion was
essentially over, produced the lunar basins. Three of the four models detailed by Wetherill (1975) involved
such accretional leftovers. (The fourth invoked Uranus-Neptune planetesimals, which we studied in Levison
et al. 2001.) The main question with models involving small bodies in the inner Solar System is whether
enough impactors remain some 700 Myr after the Earth and Moon formed (Wetherill 1975, Hartmann et al.
2000).
This issue must be addressed in the context of terrestrial planet formation models. In simulating
terrestrial planet formation, it is now possible to directly numerically integrate more than 100 planetary
“embryos” for hundreds of Myr (Chambers & Wetherill 1998, 2001; Agnor, Canup, and Levison 1999;
Levison and Agnor 2002). Following Wetherill’s (1992) suggestion, it is commonly assumed in recent
models that the asteroid belt’s original mass of solids was comparable to the terrestrial planets. Thus runaway
1
We use a statistical, “Öpik-type”, formalism for computing impact rates. Such an approach is generally adequate for
computing impact rates on bodies in low eccentricity orbits, provided the impactors’ orbits are computed with a direct
integration or sophisticated analytic theory, rather than with a Monte Carlo model (Morbidelli & Gladman 1998, Dones et
al. 1999, Gladman et al. 2000).
8
accretion might have occurred in the belt as well. For example, Petit et al. (2001) performed nine simulations
in which O(100) dynamically cold embryos with masses roughly from a lunar mass to a Martian mass were
distributed 0.5 - 4 AU, 1.5 - 4 AU, or 0.5 - 3 AU. They followed the orbital evolution of 100-1000 test
particles (“asteroids”) in the terrestrial planets region and the asteroid belt. Petit et al. find that almost all
embryos and asteroids are eliminated by mutual interactions and Jupiter’s influence. After 100 Myr, the
terrestrial planets are largely formed, but a small-body population remains among the terrestrial planets, on
eccentric and highly inclined orbits, which is a few times more numerous than the present-day asteroid belt.
Morbidelli et al. (2001) considered how these leftover bodies might impact the Moon. They followed
200 test particles, “cloned” from the survivors of the Petit et al. calculation, for another 100 Myr. (i.e.
between 100-200 Myr after the Solar System’s formation, or ~500 Myr prior to the LHB). Using formalism
of Farinella and Davis (1992), they find that f = 0.5% of the small bodies would impact the Moon within 500
Myr, based on their finding that the population decays with an e-folding time of 77 Myr. The median speed of
these impactors would have been ~30 km/s, higher than current impact speeds for Near-Earth Asteroids
(Gladman et al. 2000) or ecliptic comets (Levison et al. 2001), so a 20 km impactor would make a 300 km
lunar basin. Since Wilhelms (1987) tabulated a total of NB = 45 definite/probable/possible basins, Morbidelli
et al. infer that N = NB/f ~ 104 leftover bodies >20 km could have produced all the basins.
This model has attractive features: Petit et al.’s (2001) survivors appear adequate to make the lunar
basins; are not so numerous as to present a problem with preserving Vesta's crust (Davis et al. 1985); and a
related model can deliver water to Earth from the outer asteroid belt (Morbidelli et al. 2000). But the model
has a major problem: an extrapolation from their simulation of ~200 Myr to the ~700 Myr epoch of the LHB
predicts that it is unlikely that a “terminal lunar cataclysm” (as the authors state) or even one big basin such as
Imbrium can happen as late as 3.9 Ga. However, Morbidelli et al.’s extrapolation may be too pessimistic.
Instead of their assumed exponential decay, more gradual power-law or logarithmic decays are commonly
found at late times in simulations of small-body dynamics (Holman &Wisdom 1993, Gladman et al. 1996,
Duncan & Levison 1997, Evans & Tabachnik 1999).
We propose to settle the question of whether accretional leftovers can produce the LHB by
performing eight 1-Gyr simulations of terrestrial planet formation, starting with 100 planetary embryos, the
giant planets, and 500 test particles. Our initial conditions will be broadly consistent with results of runaway
growth studies of lunar- to Mars-sized embryos (Weidenschilling et al. 1997, but cf. Rafikov 2001). We will
neglect eccentricity damping mechanisms such as dynamical friction with smaller planetesimals (Wetherill &
Stewart 1993; Agnor, Canup, and Levison 1999) and resonant interactions with gas (Agnor & Ward 2002,
Kominami & Ida 2002); such simplifications have generally worked in terrestrial planet accretion models (e.g.
Wetherill 1990; Agnor, Canup, and Levison 1999; Chambers 2001).
In our simulations the embryos will have an average mass <m> = 0.04M (i.e., 0.37 Martian masses
or 3.3 lunar masses) and semi-major axes, a, 0.5 – 3 AU, with surface density proportional to a-3/2, comparable
to minimum mass nebular models with 2M interior to 1.5 AU (Weidenschilling 1977). Their spacing in a
will be ~5rH, where the Hill radius rH = a (<m>/M )1/3 = 0.0025 – 0.0148 AU, with e’s and i’s Rayleighdistributed with mean values of order rH/a. The embryos’ initial angles (mean anomaly, argument of
pericenter, longitude of ascending node) will be selected randomly in four simulations in each of at least 2
sets of simulations with slightly initial masses and eccentricity/inclination distributions.
The orbits will be integrated using our full N-body, symplectic algorithm SyMBA (Duncan, Levison,
and Lee 1998), modified to handle orbits with perihelia close to the Sun (Levison & Duncan 2000). This code
has the speed of the symplectic map invented by Wisdom & Holman (1991), but also accurately handles close
encounters between massive bodies. We will employ a time step of 3 days (i.e., 43 steps/orbit at 0.5 AU).
The CPU time for our calculation scales as aNE2 + bNTP, where NE is the number of embryos and NTP is the
number of test particles. The NE2 dependence limits how many we can follow, so we do not include
planetesimals smaller than a lunar mass, nor collisional fragmentation of embryos, which may slightly
9
overestimate the embryos’ final e’s and i’s. Embryos will merge when they collide in our simulations, with
the new body’s orbit calculated assuming conservation of momentum. Such assumptions are typically
employed in terrestrial planet formation simulations.
We anticipate that the embryos will evolve into a system broadly similar to the present-day system of
terrestrial planets. For instance, Chambers (2001) found that within 200 Myr, similar embryos had formed
systems of three or four planets, with the largest planet containing ~½ of the mass. Besides the impacts of
embryos (or planets) with embryos and test particles, which SyMBA records, we will use a statistical
formalism like that in Farinella & Davis (1992) and Bottke et al. (1994) to compute the impact probabilities
and velocity distributions as a function of time. Using the test particles as proxies for basin-forming
impactors is reasonable, since even the largest (South Pole-Aitken) had a mass of only ~10-4 lunar masses. We
will thus determine how the lunar impact rate due to accretional leftovers varies during the first Gyr of Solar
System history. Assuming a size distribution, we will then calculate when basins are likely to form and
whether large basin formation 3.9 Ga is plausible.
Task 4. Fifth Terrestrial Planet Scenarios for LHB
If the LHB was a spike, it was most likely caused by a change in the dynamical structure of the Solar
System, which would have destabilized a population of small bodies that were previously stable. One
possibility is that a fifth terrestrial planet went unstable, liberating previously stable asteroids (Sect. II). There
is a huge range of initial conditions to explore. The planet could be almost anywhere, with almost any mass.
For example, Chambers & Lissauer (2002) have investigated a fifth planet between Mars and the inner edge
of the main asteroid belt. Early asteroids could also be in many places within the main belt, in possible stable
regions between the terrestrial planets (Evans & Tabachnik 1999), or in Trojan points of the terrestrial planets
(Tabachnik & Evans 2000). We chose to study an extreme possibility – that a fifth terrestrial planet between
Earth and Venus liberated asteroids in the Trojan swarm of Mars (Martian Trojans still exist: Mikkola &
Innanen 1994, Tabachnik & Evans 1999).
Our first step was to conduct a successful plausibility study in our first cycle, to determine whether
our scenario could work without worrying about its likelihood, or needing to produce a complete, consistent
picture. We performed a series of 6 integrations, for times up to 1 Gyr, of the orbits of the seven planets from
Venus2 through Neptune in their current orbits and an additional planet between Earth and Venus. We varied
the extra planet’s mass, initial semi-major axis, and eccentricity and discovered that our systems were
dynamically stable for times from <100 Myr to 1 Gyr, a spread that covers the ~700 Myr between Solar
System formation and the LHB. Hence, such a system could well have caused the LHB. We show the
evolution of one system (Fig. 2), which lasted 300 Myr (reasonably close to 700 Myr, given that we studied
just 6 systems), in which the extra planet has half a Martian mass.
We continued our simulations, starting with the system in Fig. 2 at the point at which the additional
planet crossed the orbit of Venus. However, since this was a plausibility study, we changed the mass of the
extra planet and placed massless test particles in stable Trojan orbits of Mars. We could not dislodge the test
particles from Mars' Trojan points without disrupting the orbits of the rest of the terrestrial planets (e.g.
kicking Mars onto an Earth-crossing orbit). Therefore, we tried simulations with Mars in an initial low
eccentricity orbit and were able to produce an impact spike. Fig. 3 shows the number of test particles on
Earth-crossing orbits as a function of time with a lunar-mass extra planet. Notice that the temporal evolution
of these objects resembles the impact flux of the LHB. Also, Mars' orbit is perturbed enough to explain its
moderately large eccentricity.
2
The time step required by the integrator is a constant fraction of the shortest orbital period in the
problem. Thus, we saved over a factor of two in the amount of CPU time by not including Mercury.
10
Thus, the idea is viable that the LHB was caused by a terrestrial planet going unstable. However,
much work must still be done. First, the simulation discussed above was a patchwork in which we changed
the mass of the extra planet and added particles in the middle of the simulation. And we found only one
plausible solution. So we propose to perform a series of simulations, from start to finish, in which we explore
more of the possible parameter space. We will place the extra planet between Earth and Venus; as before, we
will vary its mass and semi-major axis from run to run. Since our plausibility study suggested that Mars
should start with a small eccentricity, each run will start with an integration of this system using the WisdomHolman mapping (Wisdom & Holman 1991) with an additional drag force on Mars designed to decrease its
eccentricity and inclination, but not its semi-major axis; we will adjust Mars’ eccentricity from run to run.
Adding massless test particles to the stable Mars Trojan orbits using the stable region found by Tabachnik &
Evans (1999), we will evolve the system for at least 1 Gyr or until the evolution is clearly inconsistent with an
LHB, using SyMBA (Duncan et al. 1998) modified to handle close encounters with the Sun (Levison &
Duncan 2001).
Task 5. Geocentric Model for LHB: Late Remnants from Lunar Origin
Ryder (1990; also see Alfven & Arrhenius 1972) suggested that the LHB might have been caused by
projectiles in geocentric orbit, perhaps created by collisional breakup of additional moons, in which case
cratering of Mercury, Mars, etc. would be unrelated to lunar bombardment. Ryder later abandoned the idea of
geocentric impactors (see Sect. 5 of Hartmann et al. 2002) for lack of a specific idea of how the putative
10
orbital periods. If the tidal dissipation
factors were the same as now, the Moon already would have reached a semi-major axis ~44R by the time of
the LHB, almost ¾ of its current distance from the Earth. Thus, ignoring the effects of mutual interactions
between the Moon and other hypothetical bodies orbiting the Earth, the Moon would overtake debris at
distances as large as 44R. However, the measured rate of the Moon’s recession implies that if the Earth’s
dissipation parameter Q had been constant, the Moon would have been at the Earth’s surface < 2 Ga (see
reviews by Boss & Peale 1986, Burns 1986, and Peale 1999). Thus, on average, Q must have been larger in
the past for the Moon to have formed ~4.5 Ga, and it was probably a bit closer to the Earth, ~30-40R distant,
at the time of the LHB.
The geocentric hypothesis for the LHB ought to be tested dynamically. Simulations of the “Giant
Impact” and its immediate aftermath suggest that the Moon forms from an impact-generated debris disk
(Cameron & Benz 1991; Canup & Esposito 1996; Cameron 1997; Ida, Canup, and Stewart 1997; Canup &
Asphaug 2001). Typically, one or two large moons quickly form from the disk, with many smaller bodies
remaining (Ida, Canup, and Stewart 1997). The small bodies are frequently trapped in resonances, e.g., as
lunar Trojans (Kokubo, Makino, and Ida 2000; Kokubo, Canup, and Ida 2000). Bodies trapped in the 1:1 or
other resonances (see Appendix C) might be stable for long periods of time as the lunar orbit expands,
analogous to KBO’s like Pluto that are trapped in resonances with Neptune (Malhotra 1993, 1995)3.
Canup, Levison and Stewart (1999; hereafter CLS99) investigated the orbital stability of multiple
the Earth’s oblateness were incorporated into a symplectic integrator that used the map of Wisdom & Holman
(1991), but tides raised on the moons by the Earth and solar tides were neglected. The rate of tidal evolution
of the orbital radius of a moon, da/dt, due to tides raised on the Earth by the moon is proportional to ma-11/2
3
Neptune and Pluto are in a 2:3 resonance. Because of the large ratio of the Moon’s mass to that of the Earth (~1/81),
the Moon’s orbit is surrounded by a wide chaotic zone within which most orbits rapidly become unstable. The half-width
of the chaotic zone, which defines the region in which first-order mean motion resonances overlap, is 1.3a where a is
the semi-major axis of the Moon’s orbit (Wisdom 1980). Thus most orbits between 0.63a and 1.37a are unstable. Since
the external 2:3 resonance is located at 1.31a, this implies that the lowest-order stable external resonances are the 1:2 and
2:4 near 1.59a and the 1:3 at 2.08a (Canup, Levison, and Stewart 1999).
11
Q-1 , where m is the mass of the moon and a is the moon’s semi-major axis. For bodies outside synchronous
orbit (~2-2.5R just after the Moon-forming impact), da/dt > 0. Each body tidally evolves at a rate depending
on its orbital radius, mass, and the Q values for the Earth and the body, so that an initially stable configuration
of moons may be destabilized by tidal evolution, eventually leading to mutual collisions. For example, small,
inner moons are left behind by a massive outer Moon tidally evolving outwards. Conversely, a massive inner
moon will overtake, and generally collide with, smaller exterior moons. If such collisions happened ~600
Myr after the Moon formed, they might account for the lunar LHB.
The actual orbital evolution of terrestrial satellites can be even more complex. Even a single satellite
within 5R of the Earth might have its eccentricity pumped to large values by the evection resonance, which
involves solar perturbations (Touma & Wisdom 1998). In addition, tides raised on the Earth by a satellite
affect the satellite’s orbital eccentricity and inclination, generally exciting them to larger values; but tides
raised on a satellite by the Earth generally damp satellite eccentricity, so the net change due to Earth and
satellite tides depends on the relative dissipation in the two bodies. If there is more than one moon, they will
pass through mutual mean-motion resonances. Capture into resonance can occur for orbits that are
converging, and the bodies may ultimately collide with each other, potentially contributing to the LHB.
Capture into resonances causes satellite eccentricities to increase, which may break down the resonance (e.g.
if e
vs. satellite tides. With certain combinations of satellite masses and relative tidal dissipation rates in the
satellites and the Earth, collisions among terrestrial satellites could occur 3.9 Ga. We propose to carry out the
first detailed dynamical study of the potential contribution of circumterrestrial debris to the LHB. We will
investigate several cases, beginning with the Moon and a distribution of smaller bodies whose mass totals
~1023 g. The evolution of all bodies will be explicitly tracked as they tidally evolve and interact. We will
investigate the following LHB scenarios:
(1) Collision of the Moon with previously existing material at a ~ 30-40R . Since this is beyond the
predicted extent of the impact-generated debris disk, such material could, for example, represent small outer
satellites that existed prior to the lunar-forming impact event. As the Moon orbitally evolves outward and
catches up with this outer debris, the debris will likely become captured into mean-motion resonances, so the
actual collisional time scales could be long.
2) Interior debris. We will investigate debris from the Moon-forming impact that remains interior to or near
the Moon’s orbit. Such material can be trapped in resonances such as the 1:1 corotation resonance (i.e., they
can become lunar Trojans). CLS99 demonstrated that such resonances may be stable for a long time if the
ratio of the tidal dissipation in the Moon to that in the Earth is larger than it is now.
(3) External resonances between the Moon and exterior debris. Analytic estimates in CLS99 predict that
external resonances with the Moon should destabilize on much shorter time scales than those needed to
explain the LHB, even for significant satellite dissipation. However, the process critical for the timing of
collisions – tidal dissipation within the satellites – was not included in the numerical integrations.
Furthermore, the analytic theory for eccentricity growth in resonance used by CLS99 breaks down when
orbits cross and eccentricities grow. Therefore, we must analyze the timing of collisions as external
resonances destablize.
We propose to expand on the work developed in CLS99 in two ways. (1) Whereas CLS99 used the
Wisdom-Holman map, which is not designed to handle close encounters, we will include the tidal acceleration
terms in SyMBA (Duncan, Levison, and Lee 1998; Levison & Duncan 2001). With SyMBA, we can model
the actual collisions between circumterrestrial debris and their timing, as well as multiple non-colliding close
encounters. (2) We will incorporate dissipation in the satellites into our numerical model (using the constant
time-delay parameterization, similar to that used for tides on the Earth in CLS99) and investigate the entire
plausible range of tidal dissipation rates (satellite and Earth Q-values ranging ~10 - 500).
12
For each of our three scenarios, we will run a suite of simulations that consider a fully-formed Moon
and numerous other bodies representing potential LHB impactors. We can probably complete ~100 1-Gyr
integrations during each year of this grant.
IV. RELEVANCE TO NASA ORIGINS GOALS
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 Late Heavy Bombardment are an especially
strong linkage between theories of Solar System formation and some of the oldest, directly observable
attributes of bodies like the Moon and Callisto. As we demonstrate in our Progress Report (Sect. II), our first
2½ years of research on this topic under our current Origins grant has led to new concepts concerning the
consequences of formation of the four outer gas giant planets, new perspectives on the earliest (pre-LHB)
history of the lunar crust, and new hypotheses concerning remnant planetesimal populations within the
terrestrial planet zones.
Since the LHB probably played a pivotal role in inhibiting the early evolution of life on Earth (and
perhaps other planets), 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, instead, 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 there is
no time like the present, 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.
V. WORK PLAN, PERSONNEL, PUBLICATIONS, DATA PRODUCTS, EQUIPMENT, AND
BUDGET NOTES
Dr. Clark Chapman, who is P.I. of the predecessor Origins grant nearing completion, will oversee the
entire project, contribute to Task 2 (he has been a Galileo SSI team member specializing in the geology of the
Galilean satellites), and he will be primarily responsible for Task 1. He has extensive experience in modeling
cratering and regolith processes, which is the core technique to be employed. In an interdisciplinary
collaboration, cosmochemist Barbara Cohen (co-author of a Feb. 2002 JGR paper on the LHB and who is
requesting funding via a complementary proposal) and planetary atmospheric scientist David Grinspoon (who
earlier developed an analytical model of the LHB) will help with modeling the formation of basins and
(mega)regolith evolution.
Dr. Hal Levison, expert in numerical simulations of planetary dynamical processes, led our study
(participated in by Drs. Chapman, Dones, and Duncan, among others) of the Uranus-Neptune formation
hypothesis for the LHB and developed (along with Dones, Duncan, and E. Thommes) his "Fairy Tale"
scenario for the early evolution of the giant planets and consequences for the rest of the solar system. In this
proposed research, he will lead Task 4 and contribute to Tasks 2, 3, and 5. He will be assisted by
Collaborator Martin Duncan, dynamicist at Queen's University, who will assist in interpreting the results of
the simulations.
Dr. Luke Dones, a planetary dynamicist and member of the Cassini Imaging Team, replaces Dr. Robin
Canup as Co-I of this research. He has previously researched the LHB in a separate Origins grant. In this
13
work, he will lead research on Tasks 2, 3 and 5 and contribute to the others. Collaborator Bill Ward, who
contributed to the work (with Canup) on the geocentric model for the LHB reported in our Progress Report,
will provide physical insights to Dones et al. in numerically modeling the relevant dynamics, as proposed in
Task 5.
We wish to clarify a programmatic matter. In the last proposal cycle, the Origins Program funded not
only the Chapman et al. research but also a separate grant on LHB research to Dr. Dones, who was then at San
Jose State. Dones has since joined SwRI, so in this proposal we are merging these two research efforts. Note,
however, that in our Progress Report (Sect. II) we discuss only the research that was funded, in whole or in
part, through the Chapman et al. predecessor grant; we do not report herein on the accomplishments of Dr.
Dones under his separate grant.
We expect to work more-or-less continuously on all tasks throughout the three years, emphasizing
synthesis and publication in the third year; we foresee no other significant phasings of one task compared with
another. We will continue to report our results regularly at scientific conferences (for which we have
budgeted just two per year) 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 the "Science Proposal
Budget Notes and Institutional Contributions at Southwest Research" that precede the budget, which explain
in part how, in spite of the unusual accounting procedures that we are mandated to use, our focused research
activities as budgeted are actually very cost-effective.
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APPENDICES
17
Fig. 1. Degassing ages (Kring & Cohen 2002) for several meteorite classes span much longer durations than the ~100 Myr LHB defined
by dated basins (pink bar) and the broader peak in lunar rock degassing ages (blue box).
Fig. 2. The dynamical evolution of the terrestrial planets in a solar system
with an extra planet at 0.86 AU. The mass of the additional planet
is half that of Mars. Each terrestrial planet is designated by a
color, and is represented by two curves. The bottom curve shows the
perihelion distance of the planet with respect to time while the upper
curve shows the aphelion distance. This system remains stable for
~300 Myrs, and then the extra planet (red) goes unstable.
Fig. 3. The temporal evolution of the number of escaped Mars Trojans crossing
the orbit of the Earth (and thus the Moon). The Mars Trojans were
originally on stable orbits, but were destabilized when a lunar-mass
rogue planet perturbed Mars' orbit at t=300 Myr.
Draft Abstract for Cover Page
The Late Heavy Bombardment (LHB) is one of the most significant events in early Solar
System evolution, but three decades after its discovery, we still don't know what bodies caused it,
what processes stored them for ~700 Myr after planetary origin, and how widespread it was in the
Solar System. During the past 3 years, we have analyzed the geophysical and cosmochemical
evidence for the LHB in order to establish constraints that must be met by successful dynamical
models for the LHB. And we have begun to study three plausible, but very different, dynamical
scenarios for the LHB: (a) stirring of main-belt asteroids and outer planet zone planetesimals by the
late formation of Uranus and Neptune (perhaps by ejection from the Jupiter-Saturn zone); (b) stirring
of remnant planetesimals in the inner solar system due to late instability of a fifth terrestrial planet;
and (c) late destabilization of additional satellites left over from the formation of the Moon (a
geocentric LHB that would not have affected other planets). We propose a three-year program of five
tasks: (1) to further constrain the LHB by modeling lunar (mega)regolith processes that might bias
rock age histograms; (2) to analyze the potentially observable consequences of the Uranus-Neptune
hypothesis on the satellite systems of Jupiter and Saturn; (3) to extend to the epoch of the LHB the
numerical simulations of Morbidelli et al. (2001) of late-stage accretional remnants; (4) to further
develop the fifth-planet model; and (5) to perform numerical simulations that will further elucidate
the geocentric model. Our long-term objective is to develop fundamental understanding of early
dynamical processes in planetary systems that can have profound effects on planetary surfaces during
the transition to tranquil times when life may be trying to gain a foothold.