Constraining Lunar Bombardment History by Modeling Impact Age Distributions

A proposal to the NASA Solar System Workings Program In response to Solicitation NNH17ZDA001N-SSW

Principal Investigator: Oleg Abramov (Planetary Science Institute) Co-Is: David Minton (Purdue University), Stephen Mojzsis (University of Colorado), James Richardson (Planetary Science Institute) Collaborator: Barbara Cohen (Marshall Space Flight Center) Graduate Student: TBD (Purdue University)

TABLE OF CONTENTS

Scientific/Technical/Management Section ...... 1 Introduction ...... 1 Objectives and approach ...... 2 1. Task I – Intergrate impact heating into CTEM ...... 2 1.1 Models of impact heating ...... 3 1.2 Models of ejecta temperatures, volumes, and melt content ...... 4 1.3 Cratered Terrain Evolution Model (CTEM) ...... 4 1.4 Modeling ejecta blankets with the integrated CTEM ...... 6 2. Task II – Model age-resetting within ejecta blankets ...... 6 2.1 First-order age-reset model ...... 7 2.2 Models of Pb diffusion in zircon and apatite ...... 7 2.3 Ar diffusion model ...... 7 3. Task III – Construct the integrated CTEM ...... 8 3.1 Early bombardment history of the ...... 8 3.2 Bombardment scenarios ...... 9 3.3 Running the integrated CTEM ...... 1 0 4. Task IV – Compare model results to lunar Data ...... 11 Model validation and constraints ...... 13 Significance and perceived impact ...... 14 Work plan ...... 15 Investigator roles ...... 15 References ...... 16 Data Management Plan ...... 22 Biographical Sketches ...... 23 Summary of Personnel and Work Effort ...... 28 Current and Pending Funding ...... 29 Budget Justification ...... 35 1. Personnel ...... 35 2. Travel ...... 36 3. Other Direct Costs ...... 37 4. Indirect Costs ...... 37 5. Facilities and Equipment ...... 37 6. Budget Details ...... 38 SCIENTIFIC/TECHNICAL/MANAGEMENT SECTION

INTRODUCTION The history of impact bombardment on the early Moon, as interpreted from sample analyses and crater counting, has been a subject of significant controversy in the field of planetary science for almost four decades. Argon and lead loss (and correlated disturbances in the Rb-Sr system) measured in Apollo and Luna samples from the Moon [e.g., Turner et al., 1973; Tera et al., 1974; Dalrymple and Ryder, 1993, 1996] including both crustal and impact lithologies, suggest that a substantial fraction of the lunar crust was metamorphosed or melted by impact events that occurred ~3.9-4.0 Ga. Moreover, a dearth of impact-related isotope ages older than ~4 Ga is suggestive of a lack of large basin impacts during that time [Tera et al., 1974; Ryder, 1990] Subsequent high- precision 40Ar-39Ar analyses of Apollo 14, 15 and 17, Luna 24, and highlands meteorite impact-melt rocks show a range of ages [Cadogan and Turner, 1977; Swindle et al., 1991; Dalrymple and Ryder, 1993; Cohen et al., 2000; Fernandes et al., 2000; Levine et al., 2004; Cohen et al., 2005; Norman et al., 2006; Zellner et al., 2009a,b; Norman et al., 2010] but few older than 4.0 Ga (see Fig. 1). These observations have been interpreted by some researchers as evidence for a dramatic increase in the number of impacts within a brief time span of 20 to 200 Myr [Tera et al., 1974; Ryder, 1990], during which most or all observed large lunar basins formed in an event called the lunar cataclysm, the terminal cataclysm, or late heavy bombardment (LHB). As an alternative hypothesis, it has been suggested that the basin-generating impact flux on the Moon began with the formation of the solar system and declined monotonically until it finally ended at ~3.7-3.8 Ga [Hartmann, 1975]. Under this scenario the apparent lack of lunar impact melts older than about 4 Ga is due to the “Stonewall Effect,” in which the near-surface regolith layers from which all samples in our collection 1.0 3.95 are derived are strongly biased toward +Apollo+Luna (no Culler et al.) n=276 those melts produced by the last large 0.9 Apollo+Luna ((no Culler et al.) n=211 basins, such as Imbrium [Haskin et al.,

0.8 Meteorites n=65 1998]. Under the “Stonewall” hypothesis,

Apollo+Luna (w/Culler et al.) n=366 no anomalous spike of impacts many 0.7 hundreds of millions of years after the

0.6 formation of the solar system need be invoked, as the upper layers of regolith 0.50 4.25 0.5 0.75 predominantly contain melts from the last handful of large basins. Our current 0.4 0.25 0.85 0.40 1.95 understanding of the evolution of the 2.10 Frequency (Arbritary Unit) (Arbritary Frequency 0.3 1.70 lunar regolith and megaregolith during 2.60 3.50 2.40 2.95 and subsequent to the basin-forming 0.2 epoch is inadequate to distinguish

0.1 between these two very different interpretations of the lunar sample record 0.0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 [e.g., Fernandez et al., 2013]. There has Age (Ga) been a critical need in the lunar science Figure 1. Gaussian probability curve calculated using community for a model of lunar regolith published 40Ar/39Ar impact ages obtained for samples from evolution that can predict the age Apollo 12, 14, 16, and 17 and Luna 16 and 24 missions distribution of impact melts on the lunar and lunar meteorites. From Fernandes et al. [2013]. surface [e.g., Chapman et al., 2007].

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OBJECTIVES AND APPROACH The proposed work would develop a fully three-dimensional regolith/megaregolith evolution model which leverages two existing well-tested and published models: (i) Cratered Terrain Evolution Model (CTEM) [Richardson, 2009], which now includes deposition of proximal and distal ejecta [Huang et al., 2017], and (ii) a two-dimensional model of impact-induced heating of the crust and impact-induced age-resetting [Abramov et al., 2013]. The regolith model will track ages of impact-reset material in several isotopic systems and generate maps of age distributions as a function of depth. The model output will then be compared to the ages of lunar meteorites, which represent a fairly random sampling of the upper regolith. Through this comparison, an assessment of whether the “Stonewall” or “Cataclysm” hypothesis is statistically more likely will be performed. It is important to note that conclusively differentiating between the “Stonewall” and “Cataclysm” hypotheses is not a stated goal of this work, although it is a possible outcome. It is also possible that analysis will reveal that both hypotheses are statistically viable explanations for the impact melt age distribution observed in lunar meteorites. In any case, the proposed project will set the groundwork for high-resolution, sophisticated three-dimensional models of lunar regolith evolution and age-resetting, which will be applicable to specific locations on the Moon such as the Apollo and Luna landing sites. This work addresses the following fundamental problem: What is the age and volume distribution of impact melts in the uppermost layers of lunar regolith? Under the Stonewall hypothesis, the surface should be dominated by material that was isotopically disturbed (meaning, for instance, that it experienced Pb or Ar loss) by the more recent impacts, and the apparent dearth of >~4.0 Ga ages seen in Fig. 1 does not imply a post-~4.0 Ga increase in the impactor flux. If, however, the upper regolith contains a fairly representative sampling of melts from many generations of impacts, then the distributions seen in Fig. 1 may reflect the real cadence of impacts, lending support for the Cataclysm hypothesis. There is likely some bias towards the most recent impact events in the near-surface, and this modeling effort will quantify this effect to assess the statistical likelihood of a cataclysmic spike. The proposed work will seek to quantify the distribution of surface material by modeling the evolution of the large impact-dominated megaregolith [Hartmann, 1973; Langevin and Arnold, 1977; Housen et al., 1979] under a variety of early bombardment scenarios, and, in a more approximate way, the post-bombardment evolution of the surficial regolith reworked by small impacts (impact gardening). In Task I, we will integrate impact heating into CTEM, allowing for calculation of post-impact temperature distributions within the crater and its ejecta blanket. In Task II, a 1-D ejecta cooling model will be used to model the heat-driven resetting of pertinent radiogenic systems, mapping out the relevant temperature and ejecta thickness parameter space. In Task III, the global regolith model will be constructed and run for several bombardment scenarios, drawing on results from Task I and II. In Task IV, the results of the regolith model will be compared to recorded melt ages in lunar meteorites using statistical methods. Model validation and testing against known constraints will be very important for every step of this project.

1. TASK I – INTERGRATE IMPACT HEATING INTO CTEM Task summary: An existing analytical model of impact heating (Fig. 2) will be integrated into CTEM, allowing for calculation of temperature distributions within craters and their ejecta blankets. The model will be tested by running it for impactors from 1 to 200 km in diameter in 1- km increments, assembling a library of volumes, temperature distributions, and melt fractions of

- 2 - ejecta blankets to be compared against available constraints. In preparation for calculating the degree of age-resetting, an existing two-dimensional model for calculating post-impact temperature distributions [Abramov and Mojzsis, 2009a, Abramov et al, 2013, Abramov and Mojzsis, 2016] will be coupled with the CTEM, which uses the Maxwell-Z model [Maxwell and Seifert. 1974; Maxwell, 1977] and an empirically-derived geometric model for crater rays [Huang et al., 2017] to simulate ejecta transport and deposition.

1.1 MODELS OF IMPACT HEATING The first step in the process is the production of temperature distributions associated with a wide range of transient craters. Parameters of projectiles that produce these craters, including diameters, densities, velocities, and impact angles are described in Task III. The analytical method described in Abramov and Mojzsis [2009a], based on the Murnaghan equation of state [Kieffer and Simmonds, 1980], will be used, and an example temperature distribution is shown in Fig. 2. This method has been previously applied to the Moon by Abramov and Mojzsis [2009b]. This model has been extensively tested, as detailed in the “Model validation and constraints” section. The diameter and depth of the transient crater formed by a given impact will be calculated using Pi-scaling laws [e.g., Schmidt and Housen, 1987]. Anorthosite, the main component of the ancient lunar highlands crust, will be used as a primary lithology for all thermal calculations. Thermal conductivity, heat capacity, density, and clast content will represent mean values derived from samples of lunar ejecta blankets [e.g., Hemingway et al., 1973]. The model will have a geothermal gradient of 13 °C km-1 based on the heat flux estimated for the early Moon of ~30 mW m-2 [e.g. Toksőz and Solomon, 1973; Spohn et al., 2001] and a surface boundary with the mean lunar equilibrium surface temperature of -50 °C as estimated by Vasavada et al. [1999]. As standard procedure, however, sensitivity tests will be performed for all parameters that are not well constrained, and appropriate error ranges will be carried through all subsequent calculations. Latent heats for Melt Radial Distance (km) 5 10 15 20 calculating impact-induced

0 20 0

7 0 melting and vaporization are Vapor 8 2 0 27 1 33 implemented using the method of 2 45 500 Jaeger [1968]. A velocity- dependent shock-decay exponent 4 70 120 will be used [Ahrens and

6 95 O’Keefe, 1987]. An impact angle Depth (km) of 45° will be assumed in the

8 120 proposed investigation because it is the most probable impact 10 trajectory [Gilbert, 1893; Impactor: 1.0 km Impact velocity: 20 km s-1 Shoemaker, 1962]. In addition, a Transient crater diameter (rim-to-rim): 12.8 km broad range of impact angles Final crater diameter (rim-to-rim): 18.5 km have been tested (see “Model Figure 2. Graphical illustration of how ejecta temperatures will validation and constraints”), and be calculated. Transient crater (white line), with dimensions it was found that an impact angle derived from Pi-group scaling laws, is superimposed on a post- of 45° provides a good statistical impact temperature distribution. The excavation depth is approximation. indicated by a dashed line). From Abramov et al. [2013].

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1.2 MODELS OF EJECTA TEMPERATURES, VOLUMES, AND MELT CONTENT The process of calculating ejecta blanket properties begins with the temperature distributions for impact craters described in subsection 1.1. In the preliminary study presented here, the temperature of the ejecta associated with a given impact crater was calculated by volumetrically averaging the temperatures to which non-vaporized material within the excavation zone of the transient crater (Fig. 2) was heated. This method allowed the calculation of mean ejecta blanket temperatures as a function of crater diameter, as shown by the preliminary results presented in Fig. 3a. Ejecta and melt volumes were computed and recorded, and their ratio was used to estimate the fraction of melt in the ejecta (Fig. 3b). Final Crater Diameter (km) 20 100 1000 4000 2500 -1 Impact angle = 45°, v = 20 km s-1 Impact angle = 45°, vi = 20 km s 1 i 2000 0.8 1500 0.6

1000 0.4

500 Earth, granitic target 0.2 Fraction of melt in ejecta

Mean Ejecta Temperature (°C) Earth, basaltic target Earth, granitic target 0 0 a. 10 100 1000 10000 b. 1 10 100 500 Final Crater Diameter (km) Projectile Diameter (km) Figure 3. Preliminary results for the Earth, obtained from a simplified version of the model illustrated in Fig. 2. a) Mean ejecta temperature as a function of crater diameter on the Earth for indicated lithologies. Ejecta temperatures for expected to be significantly lower for the Moon. b) Fraction of melt in impact ejecta as a function of crater and projectile diameters on Earth. From Abramov et al. [2013].

1.3 CRATERED TERRAIN EVOLUTION MODEL (CTEM)

Initial surface N = 0.6×105 km-2 N = 1.2×105 km-2 Di>1 m Di>1 m A B C

elevation (m)

1 km

N = 1.8×105 km-2 N = 2.4×105 km-2 N = 3×105 km-2 Di>1 m Di>1 m Di>1 m D E F

Figure 4. Example of a local-scale CTEM run. (A) The test crater is placed on a fresh lunar surface. (B–F) Each frame in this sequence shows the topography of the simulated surface after the accumulation of the number of impactors indicated above each frame. From Minton et al. [2015].

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The Cratered Terrain Evolution Model (CTEM) [Richardson, 2009; Minton et al. 2015; Huang et al., 2017] is a mature, well-tested, and well-constrained numerical modeling code that simulates the physical evolution of a surface being bombarded by impactors with specified properties (e.g, size frequency distribution, flux over time, velocities, densities). CTEM models a given planetary surface as a grid of points (heretofore referred to as pixels), where the number of pixels in the grid is set by the user. Each pixel contains a variety of data, one of which is the current elevation at that location, allowing the construction of a Digital Elevation Model (DEM) of the surface. For each impact that is modeled, the DEM of the surface is altered to represent the topographic changes brought about in the formation of a crater. All major crater degradation processes are included: unstable slope collapse, impact ejecta, and diffusive erosion. A sample run is shown in Fig. 4. A major recent advance in CTEM is regolith tracking [Huang et al., 2017], which is accomplished by modeling impact-driven material transport and mixing processes. This addition includes treatments of the reworking zone of locally derived material, as well as both continuous proximal and discontinuous distal ejecta (crater rays). The analytical solution is applied to a discretized model of the excavation flow-field’s hydrodynamic streamlines [Maxwell and Seifert 1974; Maxwell 1977], in order to compute excavated mass as a function of distance from the impact site and ejection velocity. Finally, these discrete, ejected mass segments will be followed in post- ejection flight through a set of ballistics equations in order to (i) compute ejecta blanket thickness h as a function of distance from the final crater rim, as described by a simple kinematic model of the ejecta flow field called the Maxwell-Z model [Maxwell and Seifert, 1974; Maxwell, 1977], and (ii) Estimate the amount of ejecta lost to space. These streamlines are described by the following equation in polar coordinates: 1/(Z-2) r = r0(1 – cos θ) (1) where r0 is the radial distance from the center of the crater, r0 = 1 is the transient crater rim, θ is measured from local vertical below the point of impact, and Z~3 [Melosh, 1989]. A set of four streamlines is computed from the four corners of the 1x1 pixel ejecta block that define a four-sided stream tube. Every stream tube originates in the impact point, dips under the surface, then emerges some fraction of the way to the transient crater rim, so each ejecta block contains a mix of material along that curved path (Fig. 5). Ejecta blanket thickness for this calculation is cross-checked against established ejecta scaling laws based on observations of lunar craters [McGetchin et al., 1973].

Figure 5. Schematic cross section view of the ejecta emplacement model within CTEM. The redder the color of a streamline, the higher the ejection speed (and, generally, temperature) of a streamline. The horizontal dotted lines denote ejecta layers deposited by previous impacts. The mixture of isotopic ages within a single ejecta block will be determined by the relative abundances of material of different ages and the degree of resetting by this impact. From Huang et al. [2017].

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Integration of thermal modeling into CTEM can be described as follows. By overlaying a provenance map of the thermal profile of the material contained in the transient crater volume (Fig. 2), and calculating the volume of intersection with any particular stream tube, we can determine an average temperature in each set of adjacent streamlines. This sets the temperature profile of the ejecta blanket at time of emplacement. A reset age will be assigned in several isotopic systems based on temperatures and locations within the ejecta blanket. Each pixel in CTEM will contain information about any resetting of greater than 1% that occurred, at a vertical resolution of 1 m.

1.4 MODELING EJECTA BLANKETS WITH THE INTEGRATED CTEM The integrated CTEM will be initially run for impactors from 1 to 200 km in diameter in 1-km increments to test the code and compile a library of temperature distributions within impact ejecta blankets. This range was chosen because impactors smaller than 1 km do not yield significant quantities of melt nor significantly contribute to the megaregolith, and 200 km is the approximate maximum impactor diameter based on size-frequency distribution and delivered mass constraints (see Section 3.1), as well as the approximate size of the projectile that formed South Pole-Aitken Basin. CTEM is run from the UNIX command line and can be automated with relative ease using scripting. The CPU time required to generate a library of 200 ejecta blanket properties from post- impact temperature distributions sampled at resolutions of 2000 × 2000 pixels is approximately six hours using the PSI computer cluster (see “Facilities and Equipment” section for details), based on prior individual runs. Before proceeding, the output of the model will be tested against observations of impact ejecta blankets, as described in the “Model validation and constraints” section.

2. TASK II – MODEL AGE-RESETTING WITHIN EJECTA BLANKETS Task summary: Use existing one-dimensional model of age-resetting within cooling impact ejecta blankets (Fig. 6) to create a library of the degree of age-resetting in the depth-temperature parameter space. Apply library results to the ejecta blankets modeled in Task I to create maps of isotopic resetting within heterogeneous ejecta blankets. Calculate mean degree of resetting in the isotopic systems considered. A library of age-resetting within impact ejecta blankets will be constructed using an existing one- dimensional model [Abramov et al., 2011] based on HEATING 7.3, a general-purpose, three- dimensional, finite-difference heat transfer program written and maintained by Oak Ridge National Laboratory. HEATING materials library contains thermal and physical parameters for anorthosite. The model consists of hot ejecta overburden, modeled on a 1000-node grid with a radiative upper boundary, overlying a 2000-node original surface with an initial temperature of -50 °C. Thickness and initial temperature of the ejecta are specified as inputs. Temperatures between 200 °C and 1600 °C (chosen based on known diffusion behavior in systems of interest) and ejecta thicknesses between 1 m and 6000 m (an approximate maximum for South Pole-Aitken Basin, McGetchin et al., 1973) will be tested. Temperatures will be varied in increments of 50 °C, and depths by 1 m (for ejecta thicknesses of 1-10 m), 10 m (for ejecta thicknesses of 10-100 m), and 100 m (for ejecta thicknesses of 100-6000 m). The model will be run until the entire ejecta blanket cools to temperatures at which no further age-resetting is occurring. Based on preliminary runs within the parameter range of interest, this time period can range from less than a year to over 104 years, depending on the initial thickness and temperature of the blanket. Typical model run times range from 1 to 20 minutes, and 2800 runs are planned to map out the parameter space, implying total CPU time between ~2 and ~34 days. Runs will be divided between multiple CPUs on the PSI compute cluster to decrease total run time.

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2.1 FIRST-ORDER AGE-RESET MODEL As a first-order estimate of impact-induced age resetting, all material within the ejecta blanket that was melted by the impact will be tagged as fully reset, while material that was not melted will be treated as non-reset. This provides a good estimate for whole-rock radioisotopic systems where diffusion does not play a significant role and resetting takes place by disturbance only (i.e., U-Pb, Pb-Pb, and Rb-Sr).

2.2 MODELS OF PB DIFFUSION IN ZIRCON AND APATITE In addition to age-resetting in whole rocks, described in the Introduction, isotopic disturbances within mineral grains, particularly zircons and apatites, have been increasingly used as indicators of the lunar bombardment history [e.g., Pidgeon et al., 2010; Liu et al., 2012]. Of particular interest is a study by Nemchin et al. [2009], which examined four Apollo 14 and reported that the U- Pb system was completely reset at ~3.9 Ga in apatites, but undisturbed in zircons. This provides a constraint on the thermal history of the samples, and suggests that a difference in “thermal stability” of zircon and apatite can help resolve the impact history of the Moon. Preliminary results from the model are shown in Fig. 6 for zircon and apatite. Model results suggest that that there is a fairly narrow parameter space that yields partial Pb-loss. In the case of zircon grains (Fig. 6a), only a temperature of 1200 °C results in partial Pb-loss in zircon grains within the ejecta. Other initial temperatures tested (300 °C, 600 °C, and 900 °C) result in no appreciable Pb-loss. In the case of apatite (Fig. 6b), initial temperatures of 1200 °C and 900 °C resulted in complete Pb loss throughout most of the ejecta blanket, 300 °C resulted in zero Pb-loss, and only 600 °C resulted in partial Pb-loss. The effects of shock damage in zircons on Pb diffusion were also evaluated, using observations from Wittmann et al. [2006] and diffusion equations for radiation-damaged zircons [Cherniak et al., 1991]. It was found that the effects were minimal [Abramov et al., 2011], because the shock pressure associated with the onset of age-resetting in zircon is essentially the same as the shock pressure associated with the onset of damage (20-30 GPa). The same is true for apatite, in which age-resetting begins at significantly lower shock pressures than the onset of damage [Cherniak et al., 1991; Nemchin et al., 2009].

Figure 6. Percentage of Pb-loss in 50-µm mineral grains within a cooling 100-m thick impact ejecta blanket of various initial temperatures. a) zircon b) apatite. From Abramov et al. [2013].

2.3 AR DIFFUSION MODEL Though the cataclysm concept was initially formulated from U-Pb ages of highlands rocks (Tera et al., 1974), the most complete and self-consistent record of lunar bombardment we currently have comes from the 40Ar-39Ar dating of impact-melt rocks (see Fig. 1). This is largely because of the

- 7 - extensive work that has been done on multiple types of samples (Apollo, Luna, meteorites, glasses), but importantly also because of the consistency in the state of the samples – all the samples in this dataset have been fully melted and recrystallized by impact. This enables us to directly compare our models to these data. Age resetting in the Ar-Ar system in whole rocks will be modeled using an approach similar to that employed for Pb diffusion in zircon and apatite (Section 2.2). Materials that undergo complete melting will be considered reset and tagged with an appropriate impact age. Additional outgassing due to heating within hot ejecta blankets will be modeled by coupling the thermal cooling models of ejecta blankets with the diffusion equations of McDougall and Harrison [1988]. These well- constrained, laboratory-derived diffusion equations, require as inputs (i) temperature and (ii) time spent at that temperature, which will be predicted by the model.

3. TASK III – CONSTRUCT THE INTEGRATED CTEM Task summary: Populate the model lunar surface with impacts within total mass, bombardment flux, size-frequency distribution, and positional constraints. Add an appropriate ejecta blanket for each impact, containing older as well as newly-age-reset material in proper proportions.

3.1 EARLY BOMBARDMENT HISTORY OF THE MOON In addition to sample analysis results, discussed on the Introduction, one of the main constraints on the Moon’s early bombardment history is the abundance, size distribution, and relative ages of large lunar craters. There are at least ~45 identified lunar basins, ~30 of which are pre-Nectarian [Ryder, 2002]. Recent modeling efforts suggest that a substantial fraction of these could come from either the main asteroid belt or an extension of the inner main belt dubbed the “E-Belt” [Minton and Malhotra 2011, Morbidelli et al. 2010; Bottke et al. 2012]. Pre-mare terrains on the Moon appear to be cratered by a population with a size-frequency distribution and velocity typical of objects originating in the main asteroid belt [Strom et al., 2005; Richardson, 2009; Head et al., 2010], and geochemical signatures [Kring and Cohen, 2002; Tagle, 2005; Joy et al., 2012] likewise point to the as a primary source. Bottke et al. [2012] infer that were a minor player in the early bombardment of the Moon, based on the excellent match between the asteroid-only model results and lunar crater counts. Dynamical models [e.g., Figure 7. The LHB would have deposited ~1.8-3.5 km of ejecta on the Moon. “Cumulative” refers to multiple impacts Gomes et al., 2005; Bottke et al., within each size bin. Assumptions: Mass flux of 1022 g, 2012] and analytical estimates asteroid belt SFD, impact velocity of 20 km s-1. Unpublished [e.g., Minton and Malhotra, 2010] results by PI Abramov, based on the methods in Abramov et suggest that the median impact al, [2013]. velocity on the Moon was

- 8 - approximately 20 km s-1. The size/frequency distribution of the asteroid belt is unlikely to have changed significantly since the bombardment epoch [Bottke et al., 2005], and thus the size/frequency distribution of the asteroid belt will be adapted for the impactor population in this study, and velocities and densities typical of asteroids will be used. Another parameter relevant to the early bombardment history of the Moon is the mass delivered to its surface by impactors. The total mass delivered to the Moon during the basin-forming epoch is estimated at 1.1 × 1022 g based on the lunar cratering record [Hartmann et al., 2000; Ryder et al. 2000] and 9.0 × 1021 g based on dynamical modeling [Gomes et al., 2005]. For the purposes of the proposed work, the average value of 1.0 × 1022 g will be adopted as a baseline estimate, and other values will be tested. Combining the expected SFD, delivered mass, and a preliminary version of the ejecta model described in Task I allows for an estimate of the total amount of megaregolith formed as large-scale ejecta by impactors larger than 1 km in diameter (Fig. 7), yielding a range of 1.8-3.5 km, which is in excellent agreement with previous estimates (Fig. 8).

3.2 BOMBARDMENT SCENARIOS After libraries of ejecta properties and the corresponding age-resetting are compiled, simulations of the early lunar bombardments designed to help understand the lunar sample record (Fig. 1) will be conducted. Specifically, the effects of the following three scenarios of early bombardment flux on the Moon will be examined: (i) A “Uniform” test case, capturing a declining post- accretionary bombardment flux based on cratering history models of Hartmann et al. [1981] and Neukum [1983]. (ii) A “Cataclysmic” case, characterized by a spike in the number of impacts, in which all visible pre-mare craters (including all basins) formed Figure 8. A schematic cross section of the top portion of the over an interval of ~200 Myr lunar crust [Heiken et al., 1991] showing the difference in grain [Ryder, 1990]. (iii) A “Semi- size and degree of reworking with depth as a result of impact Cataclysmic” scenario, which is cratering. Depths are inferred from seismic measurements and characterized by both declining sound speed. post-accetionary bombardment and a spike in impact flux some time between 4.2 and 3.9 Ga. This is based on recent models of giant planet migration, which suggest that it is difficult for the main asteroid belt to supply enough material to form all pre-mare craters, and perhaps only surfaces younger than Nectarian-age (roughly 1/3 of the observed basins)

- 9 - are associated with this event [Minton and Malhotra, 2011; Bottke et al., 2012; Fassett et al., 2012]. We will therefore adopt a scenario that we dub “Semi-Cataclysmic” in which the first 2/3 of basins formed prior to the beginning of the terminal cataclysm, and the last 1/3 during the later ~200 Myr bombardment. A variation of this scenario, which we will also test, is dubbed the “Sawtooth” hypothesis [Bottke et al., 2012; Morbidelli et al., 2012], in which a sudden increase in the number of impacts at ~4.2 Ga is followed by a graduate decline.

3.3 RUNNING THE INTEGRATED CTEM The regolith model will be used to track the generation and transport of material that is reset in the various isotopic systems considered (U-Pb, Rb-Sr, and Ar-Ar) for each of our bombardment flux scenarios. Tracking multiple isotopic systems allows us some flexibility and redundancy in approaching the problem of understanding the lunar sample record. For instance, if we encounter difficulties in modeling any one particular isotopic system, we will still be able to produce results using the others. A common element that will be used for all bombardment scenarios is a stochastic cratering model [Richardson et al., 2005; Abramov and Mojzsis, 2009a], which populates all or part of a planetary surface with craters as a function of time within a probability field of constraints established from both models and observations (Section 3.2). For the Uniform scenario, the stochastic cratering model will generate impacts at a rate such that 45 basins will be produced between 4.5-3.7 Gy ago, matching the flux curves reported by Hartmann et al. [1981] and Neukum [1983]. In the Cataclysmic scenario, basin formation will be restricted to between 4.0-3.8 Gy ago, as in Ryder [2002]. In the Semi-Cataclysmic scenarios, ~33 basins will be formed in a decaying profile between prior to the beginning of the terminal cataclysm, while the remaining ~12 will occur during the cataclysm, for the flux curve of Bottke et al. [2012]. The model will only include individual impactors greater than 1 km in diameter, since impactors smaller than that do not produce significant amounts of melt (Fig. 3b), and likely delivered a relatively insignificant amount of mass (Fig. 7). Moreover, impactors smaller than 1 km do not significantly contribute to the formation and overturn of the several km-deep megaregolith (Fig. 8), but rather extensively rework the upper few meters of the lunar surface, forming the regolith layer [Chapman et al., 2007]. Combining the size-frequency distribution of the impactor population with estimates of the total mass delivered yields an estimate of ~200,000 impacts by projectiles > 1 km in diameter. The model will use results from Task I and II to assign an ejecta layer with appropriate properties to every , resulting in ~1,000 model layers per CTEM pixel, based on expected ejecta overlap. Each CTEM pixel will contain a record of impact melt ages, expressed as weight percentages, for each isotopic system. The initial starting surface will be the Moon’s primordial anorthositic crust. This is because no impact, with the exception of South Pole–Aitken basin, is expected to have excavated significant amounts of the lunar mantle (based on the excavation depth expression of Croft, [1980]). A typical model run can be summarized as follows: (i) An impact of a magnitude stochastically calculated from SFD and mass delivered constraints takes place at a random location on the Moon. Impact locations will be recorded to assess the degree of overlap between impact craters. (ii) The associated ejecta blanket temperature distribution, geometry, and melt content is pulled from a pre- assembled library (Task I). (iii) The shape of the excavation zone within the transient crater is calculated from Pi-group scaling laws as shown in Fig. 2. (iv) Ejecta incorporating material within the excavation zone (lunar crust and/or regolith from previous model iterations, as well as newly- formed melt) are used to form a new model layer. (v) A library of age-resetting within ejecta

- 10 - blankets (Task II) is used to calculate further age-resetting within the hot ejecta blanket as a function of location within the blanket. These results will be recorded into the CTEM pixels now covered by ejecta. The temporal resolution at which age data will be recorded into each model layer will be 1 Myr, which is significantly smaller than the typical error bars for meteorite age data. At this resolution, it is estimated that the model will run at a rate of 1 impact per second at a typical CTEM spatial resolution of 2000 x 2000 (corresponding to a global resolution of 2.24 km px-1), resulting in a total run time of ~2.3 days. The final output file would be a very reasonable ~2.5 GB, which can be further reduced by compression. Impact gardening by small impacts during the bombardment is included in the model in an approximate way [Huang et al., 2017], but is unlikely to significantly affect the results, as the present-day impact gardening rates on the Moon overturn only ~ 1 cm of the surface every 10 million years [Arnold, 1975]. Even if the impact gardening rate during impact bombardments was 1,000 times the present rate it would have been insufficient to overturn ejecta blankets of tens to thousands of meters associated with the craters in the proposed model at the relevant timescales. We will compile the age distributions of impact melts in the uppermost layers of the model, representing the mean post-bombardment surface. Impact gardening since ~4 Ga would have been expected to rework the upper ~4 m of the surface, forming a layer of regolith from which most lunar meteorites are derived (see Task IV). Therefore, the age-resetting results in the model layers forming the upper ~4 m will be averaged out. This is unlikely to significantly affect the results, however, given that it is only a small fraction of ~2 km of ejecta expected (Fig. 7; Fig. 8). The results will be qualitatively examined at this point; for example, if a spike or at least a dearth of pre-4.0 Ga ages similar to that shown in Fig. 1 is observed under the Uniform scenario, then, to first order, credence is lent to the Stonewall hypothesis. However, a more rigorous assessment of the results will be conducted through comparison to data from lunar meteorites, described in Task IV.

4. TASK IV – COMPARE MODEL RESULTS TO DATA Task summary: Compile age data of impact melts from lunar meteorites of appropriate age range and composition, and perform statistical comparisons to model results. Since the product of the regolith model described above will represent an average of melt age distributions as a function of depth, comparing it to Apollo and Luna samples, which are likely dominated by several large near-side basins would not be a statistically rigorous approach. Rather, model results will be statistically compared to lunar meteorites, which represent a mostly random (with the exception of a few possible cases of source crater pairing and relatively minor biases favoring the equatorial regions and the western hemisphere) sampling of the upper layers of the megaregolith [Gladman et al. 1995; Le Feuvre and Wieczorek, 2008; Gallant et al., 2009]. The Lunar Meteorite Compendium [Righter and Gruener, 2013; Korotev et al., 2017] currently lists 126 known lunar meteorites (this number excludes known pairings). The cosmic ray exposure ages of these meteorites indicate that they were ejected from the Moon between a few hundred and ~20 million years ago, with a median of a few 105 years. Based on the estimated frequency of impacts of a given size, as well as cosmic ray exposure ages, Warren [1994] estimated that most lunar meteorites originate at remarkably shallow depths of ≤3.2 m, and thus essentially sample the surface. The majority of lunar meteorites (75) are classified as feldspathic regolith breccias, with the remainder being mare basalts (14) and fixed feldspathic/basaltic breccias (37). Significantly, none of the lunar meteorites are coherent samples of the lunar crust, which further constraints their origin

- 11 - to the regolith. This study will be limited to feldspathic regolith breccias, which represent a product of purely impact processes without contamination from a generally more recent volcanic component. All examined feldspathic regolith meteorites contain varying amounts of impact melt: some as veins or clasts, while in others it is a principal component. Of the 75 feldspathic regolith breccia meteorites, 51 have had their impact melt components dated by one or more of the radiogenic methods described in this proposal, resulting in 126 measurements of unique melt ages, out of which 29 are older than 3.7 Ga (see the Lunar Meteorite Compendium and references therein) and thus provide a record of the early bombardment history of the Moon. This is a statistically significant sampling [Cochran, 1977] which will be the baseline for the proposed work, although as future analyses become available, they will be incorporated into this study as well. The model results, with their relatively fine temporal resolution of 1 Myr, will be interpolated to yield a continuous spectrum of impact ages for each radiogenic system examined. Discrete meteorite- derived melt ages will be compared to the model age curves by employing the commonly-used Pearson's chi-squared test, which quantitatively assesses goodness of fit: n (O  E )2 X 2   i i (2) i0 Ei where Oi is an observed frequency, in this case the age of the melt within a lunar meteorite, Ei is expected frequency, in this case the value predicted by the model, and n is the total number of data points. Assumptions are that the observations represent a random sampling and are independent of one another, and are addressed earlier in the text. It is important to note that, although the uncertainties in the ages of the meteorites are quite large and do not, on the surface, indicate a unique impact scenario, this statistical analysis will yield valuable quantitative insights into the probability of a given bombardment scenario. In the unlikely event that a statistically likely bombardment timeline will not emerge, additional comparisons of simulations to “ground truth” would be conducted, for example, by comparing model predictions of regolith age distributions at Apollo landing sites to available data [e.g., Dalrymple and Ryder, 1993; Figure 9. Post-impact temperature distribution after a vertical impact of a 2-km asteroid at 8 km/s on Mars. a) Hydrocode- Haskin et al., 1998; Levine et generated temperature distribution [Pierazzo et al., 2005], b) al., 2005; Norman et al., 2006; Analytically-generated temperature distribution (using methods of Zellner et al., 2009a; Liu et al., Abramov and Mojzsis [2009a]). From Abramov et al. [2016]. 2010; 2012].

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MODEL VALIDATION AND CONSTRAINTS Due to the relative complexity of the models, numerous cross- checks are implemented, and models in this proposal have been constrained and validated with field observations and laboratory experiments to the extent possible. Specific examples include: (i) Use of melt ratios from well-studied Apollo melt breccias, particularly those associated with the Imbrium impact, which was sampled by several Apollo missions, to validate the temperatures in the ejecta deposition model (Abramov et al, 2013). A similar approach was used to validate the CTEM ejecta deposition and material Figure 10. a) Percentage of Pb-loss in 50-µm zircon grains within mixing sub-model [Huang et a 180-km terrestrial impact crater. Pb-loss in the ejecta is not al., 2017] (ii) Ejecta included in this model. b) Extent of age-resetting in zircon grains temperature distributions and within the slightly larger (~250–300 km) Vredefort crater [Moser geometries will be checked et al., 2012]. From Abramov et al. [2016]. against numerical hydrocode results [e.g., Fernandes and Artemieva, 2012] for individual impacts under identical conditions, (iii) Model predictions of mean melt ratios in the lunar regolith will be compared to melt ratios observed in feldspathic regolith breccia lunar meteorites as an additional constraint (this work). (iv) Temperature distributions described in Section 1.1 have been compared to hydrocode simulations and generally agree well (Fig. 9). (v) Generating temperature distributions and predicting melt volumes and the degree of thermal and shock metamorphism for well-studied terrestrial craters such as Vredefort, Sudbury, and Chicxulub. An example of this approach is shown in Fig. 10. (vi) Melt volumes predicted by the post-impact temperature distributions in Section 1.1 have been compared to predictions of the general melt scaling equations of Abramov et al. [2012], which incorporate the results of impact experiments, analytical studies, and hydrocode simulations (Fig. 11), the (vii) lunar record itself -- the final state of a CTEM simulation will be made to match the locations and diameters of known lunar craters listed in the Lunar Crater Database [Öhman et al., 2015] whose relative ages coincide with the bombardment epoch (Imbrian and older). The degree of crater overlap, that is, the probability of an impact occurring into a melt pool from a previous impact, has been approximately evaluated using an existing global thermal cratering model [Abramov and Mojzsis, 2009a; 2010], in which thermal fields for a wide range of craters are introduced into a 3-dimensional model of the lithosphere and allowed to cool by conduction in the subsurface and radiation at the surface. A cursory examination of existing global thermal modeling runs suggests that overlap is negligible except in a few cases of large basins forming in close proximity, and the total degree of overlap is under 10%. However, as part of the proposed project,

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109 a. Impact angle = 45°, v = 20 km s-1 the degree of crater overlap on the Moon will be 108 i quantitatively assessed as described in Section 3.3, 7 ) 10 3 and will be corrected for if necessary. 6 10 To illustrate our concept for modeling Pb loss 105 4 through diffusion, and establish its validity, we used 10 a previously-published simulation of the post-impact 103

Melt Volume (km cooling of the ~180-250 km Sudbury crater 102 101 Earth (granite), this work [Abramov and Kring, 2004] and modeled Pb-loss in Earth (granite), Abramov et al. (2012) 100 zircons emplaced within the structure using diffusion 1 2 5 10 20 50 100 300 equations of Cherniak and Watson [2001]. There is a Projectile Diameter (km) rather strong dichotomy – either 100% Pb-loss within zircon grain or none at all, with few areas of b. Impact angle = 45°, Dp = 10 km 105 partial Pb-loss (Fig. 10a). This result is remarkably ) 3 independent of grain diameter. The areas of the crater that have 100% Pb-loss are central uplift

104 (initial temperature of ~1,000 °C) the central melt sheet, as well as the small melt sheet in the annular

Melt Volume (km trough (initial temperature of ~1700 °C). In addition, Earth (granite), this work Earth (granite), Abramov et al. (2012) since the thermal decomposition temperature of 103 10 20 50 100 zircon is 1673 °C [Kaiser and Lobert, 2008], Impact velocity (km s-1) complete loss of grains emplaced within the melt is also likely. The predictions of the model are in very c. -1 Dp = 10 km, vi = 20 km s good agreement with field observations at Vredefort

) crater (Fig. 10b). 3 104 Additional verification of the analytical shock- heating model proposed for this work (Section 1.1) is provided by the Abramov et al. [2012] impact melt-scaling expression. For the purposes of this Melt Volume (km Earth (granite), this work comparison, melt volumes were derived from the Earth (granite), Abramov et al. (2012) Earth (granite), Pierazzo and Melosh (2000) temperature increase (ΔT) in the target predicted by 103 30 45 60 75 90 the shock-heating model. To keep the comparison Impact Angle (degrees) general, a target with no geothermal gradient was and a homogeneous initial temperature of 0 °C was Figure 11. Melt volume comparisons for model validation. (a) Melt volume as a assumed. This allows a comparison to the baseline function of projectile diameter. (b) Melt Abramov et al. [2012] expression which does not volume as a function of impact velocity. (c) include effects of target temperature. The latent heat Melt volume as a function of impact angle. of fusion was included, and melt was defined as material heated above 1087 °C.

SIGNIFICANCE AND PERCEIVED IMPACT The proposed work will make a significant contribution to the knowledge of the thermal history of the Moon, particularly its crust. More specifically, this work will improve our understanding of the lunar (and thus the inner Solar System) bombardment history, and is crucial to the testing of the lunar cataclysm hypothesis, which will in turn have wide-ranging implications for interpreting radiometric ages of lunar samples. Improving our understanding of the lunar bombardment history is also directly relevant to understanding the role played by impacts in shaping the environment of early Earth at the dawn of life. Our regolith evolution model would also give insight into the broader problem of the growth and development of the lunar megaregolith, as well as regoliths of

- 14 - other airless or low-density-atmosphere bodies, such as asteroids, Mercury, Mars, and icy satellites. It would also provide improved constraints on the dynamical models of early Solar System evolution. This work would contribute to the further understanding of impact-induced age resetting with a significantly improved model of age resetting within impact ejecta, modeling age-resetting in additional radioisotopic systems, and statistical comparisons to lunar meteorites.

WORK PLAN A general outline of our yearly goals is as follows: Year 1 (FY19): Complete Task I, building a library of ejecta geometries, temperature distributions, and melt fractions for ejecta blankets. Complete Task II, creating a library of the degree of age- resetting within impact ejecta blankets in the depth-temperature parameter space. Present results from these two efforts at the Lunar and Planetary Science Conference (LPSC). Year 2 (FY20): Complete Task III, in which the integrated CTEM will be run. Test various impact flux scenarios for the early Moon. Present results at LPSC and submit a paper for publication to Earth and Planetary Science Letters. Year 3 (FY21): Complete Task IV, comparing the predictions of the regolith model to recorded melt ages in lunar meteorites using statistical methods. Submit a paper to Icarus describing the results of comparison to lunar meteorites and a synthesis of project results, addressing the broad goal of testing the Cataclysm vs. Stonewall hypotheses.

INVESTIGATOR ROLES Dr. Oleg Abramov (PI) will build libraries of ejecta blanket properties using the integrated Cratered Terrain Evolution Model (CTEM) and age resetting in several radioisotopic systems, construct the regolith model, and perform comparisons to lunar meteoties. Will present results at conferences and in professional manuscripts. PI Abramov will have the overall responsibility in incorporating contributions and input from Co-Is and collaborators toward the common goal of understanding the early bombardment history of the Moon. Dr. David Minton (Co-Investigator) will provide impactor population inputs, particularly projectile diameters, impact velocities, and impactor and target compositions consistent with the state of the art of early solar system dynamics. Co-I Minton will also supervise a graduate student who would be working on this project. Dr. Stephen J. Mojzsis (Co-Investigator) As an expert on geochemistry and geochronology, Dr. Mojzsis will assist with the age-resetting aspect of this project, particularly with the processes of Pb loss within zircon and apatite minerals. Dr. James Richardson (Co-Investigator) will work with PI Abramov on the integration of thermal modeling of post-impact temperatures into CTEM. He will also assist in incorporating work from various team members towards the understanding the development and evolution of regolith on rocky, inner solar-system bodies. Purdue Graduate Student will run develop and execute the intergrated CTEM model runs for various bombardment scenarios, analyze and interpret results, and lead at least one peer-reviewed publication. Dr. Barbara Cohen (Collaborator) will provide expertise in interpreting and understanding the lunar meteorite record, and will offer guidance on Ar dating of lunar impact melts, as well as age- resetting mechanisms in the Ar system.

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