Possible long-term decline in impact rates 2. Lunar impact-melt data regarding impact history

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1 Icarus 186 (2007) Possible long-term decline in impact rates 2. Lunar impact-melt data regarding impact history William K. Hartmann a,, Cathy Quantin b, Nicolas Mangold c a Planetary Science Institute, 1700 East Fort Lowell Road, Suite 106, Tucson, AZ , USA b Laboratoire des Sciences de la Terre, UMR CNRS, Université Claude Bernard Lyon 1 - ENS Lyon, Bat. Géode - 6e Etage, 2 rue Raphaël Dubois, Villeurbanne Cedex, France c Orsay Terre, Bat. 509, Université Paris-Sud, Orsay Cedex, France Received 1 March 2006; revised 1 September 2006 Available online 13 November 2006 Abstract Crater counts at lunar landing sites with measured ages establish a steep decline in cratering rate during the period 3.8 to 3.1 Gyr ago. Most models of the time dependence suggest a roughly constant impact rate (within factor 2) after about 3 Gyr ago, but are based on sparse data. Recent dating of impact melts from lunar meteorites, and Apollo glass spherules, clarifies impact rates from 3.2 to 2 Gyr ago or less. Taken together, these data suggest a decline with roughly 700 Myr half-life around 3 Gyr ago, and a slower decline after that, dropping by a factor 3 from about 2.3 Gyr ago until the present. Planetary cratering involved several phases with different time behaviors: (1) rapid sweep-up of most primordial planetesimals into planets in the first hundred Myr, (2) possible later effects of giant planet migration with enhanced cratering, (3) longer term sweep-up of leftover planetesimals, and finally (4) the present long-term leakage of asteroids from reservoirs such as the main asteroid belt and Kuiper belt. In addition, at any given point on the Moon, a pattern of spikes (sharp maxima of relatively narrow time width) will appear in the production rate of smaller craters ( 500 m?), not only from secondary debris from large primary lunar impacts at various distances from the point in question, but also from asteroid breakups dotted through Solar System history. The pattern of spikes varies according to type of sample being measured (i.e., glass spherules vs impact melts). For example, several data sets show an impact rate spike 470 Myr ago associated with the asteroid belt collision that produced the L chondrites (see Section 3.6 below). Such spikes should be less prominent in the production record of craters of D few km. These phenomena affect estimates of planetary surfaces ages from crater counts, as discussed in a companion paper [Quantin, C., Mangold, N., Hartmann, W.K., Allemand, P., Icarus 186, 1 10]. Fewer impact melts and glass spherules are found at 3.8 Gyr than at 3.5 Gyr ago, even though the impact rate itself is known to have been higher at 3.8 Gyr ago than 3.5 Gyr. This disproves the assertion by Ryder [Ryder, G., EOS 71, 313, ] and Cohen et al. [Cohen, B.A., Swindle, T.D., Kring, D.A., Science 290, ] that ancient impact melts are a direct proxy for ancient impact (cf. Section 3.3). This result raises questions about how to interpret cratering history before 3.8 Gyr ago Elsevier Inc. All rights reserved. Keywords: Cratering; Moon, surface; Impact processes; Meteorites; Asteroids, dynamics 1. Background As early as the 1950s, Urey (1952) and Kuiper (1954) speculated that the Moon and planets underwent intense early bombardment, with lower impact rates since then. Quantitative measurements of the time behavior of cratering rates, albeit with * Corresponding author. Fax: address: hartmann@psi.edu (W.K. Hartmann). crude time resolution, have since confirmed this, based on numbers of craters on dated planetary surfaces. The initial measurements were essentially limited to the modern Earth (last 0.5 Gyr, as reflected in numbers of craters of known age), and to the early Moon ( 3.9 to 3.2 Gyr ago, as reflected in samples from Apollo and Luna landing sites). The time behavior of the lunar impact rate is due for re-evaluation, based on three additional data sources: dating of 155 lunar impact-produced glass spherules reported by Culler et al. (2000) (see also Levine et al., 2005, for corrections); dating of some 42 impact melt /$ see front matter 2006 Elsevier Inc. All rights reserved. doi: /j.icarus

2 12 W.K. Hartmann et al. / Icarus 186 (2007) clasts from four lunar meteorite breccias, newly re-analyzed by Cohen et al. (2005); and data on collision rates in the asteroid belt as reflected in impact melts in various classes of meteorites. The impact melts differ from the glass spherules; as discussed below, impact melt rocks and clasts are regarded as crystallizing in lenses of melt under floors of craters larger than some kilometers, whereas glass spherules are ejected from much smaller craters, including the m Wabar craters on Earth. Most authors believe that the time behavior of the impactors, whether asteroidal or cometary, was more or less the same throughout the inner Solar System, because of gravitational scattering processes. (The outer Solar System could be a different story, because of possible inputs from different impactor populations.) In principle, therefore, any determination of the cratering rate on one inner Solar System planet is linked to rates on other planets, albeit through relatively complex relative impact flux ratios and scaling relationships, which involve assumed values of approach/impact velocities, gravity, target effects, etc. These alone may introduce a factor 2 or 3 uncertainty in absolute age cratering rate estimates. We can assume, however, that the general time behavior found in the Earth Moon system, and mirrored approximately in the asteroidal meteorite data, was at least roughly the same throughout the inner Solar System. (Future data at higher time resolution may show differences such as spikes on one planet that differ from spikes on other planets, due to specific orbital patterns among asteroid fragment families; the same data may confirm Solar Systemwide spikes.) At a more detailed level, the shape of the time dependence curve will depend on the size of the impactors involved, and hence the craters being measured, especially if viewed at high time resolution. For example, if a 1-km asteroid breaks up in the belt and feeds a shower of fragments toward a resonance, the largest fragment might be 100 m in size, and the largest crater that could be produced in the inner Solar System in that shower could thus be 2 km across. In that case, craters of D 2km would show a spike in production rate, but larger craters would not. Furthermore, because of the Yarkovsky effect, fragments smaller than a few meters across will drift toward the resonances and experience orbit evolution much faster than fragments larger than 10 m, not to mention that carbonaceous, stone, and iron fragments will have different time profiles from each other (Hartmann et al., 1999). The final time dependence of cratering and spike profile will thus be different for small craters than for large craters. In a related effect, Strom et al. (2005) and Morbidelli and Bottke (2006) described how orbital migration of giant planets in the first few hundred Myr, involving resonance effects among them, might have caused Jupiter resonances to destabilize belts of interplanetary bodies, causing non-yarkovsky dependent ejection of small and large bodies into the inner Solar System. Strom et al. posited a shift from non-size dependent effects to size-dependent effects. At a detailed level, there is no single time dependence for cratering at all sizes. We concentrate on the first-order curve for bodies 500 m (ideally averaged over the Moon), showing the decline from early intense bombardment to current cratering in the last few hundred Myr. 2. Evidence from crater counts Crater counts subsequent to the early Kuiper/Urey work confirmed a high early cratering rate declining toward a more constant rate in later time. This behavior was identified even before the Apollo missions, from combining terrestrial and lunar crater counts. In 1965, Hartmann used then-new Canadian crater discoveries to estimate crater production rate in the Earth Moon system, and applied this in order to estimate (surprisingly correctly!) that the lunar mare lava plains are about 3.6 Gyr old. This work noted the decrease must have been rapid in pre-mare time and more slow since then, because any such early age for lunar maria required a rapid decrease in flux in the first 1 Gyr. Hartmann (1966) quantitatively evaluated the Moon s early intense bombardment by noting that the pre-mare crater density is 32 times the post-mare crater density, but that the pre-mare craters formed in an estimated 1/7 of the total time interval. Thus, in pre-mare time, the cratering rate on the Moon had to average roughly two hundred times the average post-mare rate. After Apollo/Luna missions dated various landing sites on the Moon, both Hartmann (1970a, 1970b, 1972) and Neukum (1983) showed that the older landing sites had higher crater densities than the somewhat younger landing sites, confirming that the cratering rate declined very rapidly from 3.8 to 3.1 Gyr ago. Hartmann s (1972, Figs. 3, 4) comparison of Apollo sites indicated a drop in crater density by about a factor 10 from highland sites to the youngest mare sites, with a suggested half-life of <100 Myr in rate of cratering around 3.8 Gyr ago, 300 Myr around 3.1 Gyr ago, and leveling out by 2 Gyr ago. Hartmann s (1970a) schematic curve suggested that a sawtooth fine structure might be found in the curve due to impactors derived from discrete major collisions in the asteroid belt a behavior confirmed recently by the apparent spike in L-chondrite production about 500 Myr ago (see Section 3.6). Analysis of the Apollo data and highland crater densities suggested the cratering rate before 3.8 Gyr ago reached at least two orders of magnitude higher than the average rate in the last 2 Gyr (Hartmann, 1970b, Fig.2;Hartmann, 1972, Fig.5). Neukum (1983), followed by Neukum and Ivanov (1994) and Neukum et al. (2001), derived an empirical equation characterizing the time dependence of cratering from around 3.8 Gyr ago until today, showing the steep early decline and a more constant later value, as discussed further in Section 3.4. While the high, steeply declining cratering rate before 3.1 Gyr ago comes directly from the Apollo/Luna data, the long-term gradual trends have remained less certain. 3. Evidence from impact melt materials Impact melts found in lunar rock and soil samples can be dated and used to estimate the rates of impacts at different times (Ryder, 1990; Taylor et al., 1991; Stöffler and Ryder, 2001). Emphasis in those works was on impact melts as evidence for a cataclysm, or an overwhelming spike in impact rates at 3.9 ± 0.1 Gyr ago, during which most large multi-ring basins were thought to have formed within as little as 200 Myr (Stöffler and Ryder, 2001). Cohen et al. (2000, 2002) added im-

3 Possible long-term decline in impact rates 2 13 pact melt data from six lunar meteorites in a quest to reveal time dependence effects outside the Apollo sample suite. They refined their analysis recently (Cohen et al., 2005), but have not given much emphasis to the long-term behavior after 3 Gyr ago. Meanwhile, Culler et al. (2000) analyzed Apollo 14 (Fra Mauro) glass spherules specifically to derive the time behavior of the impact flux from 3.5 Gyr ago until today, suggesting a decline from 3.0 to 0.5 Gyr ago, followed by an increase. Levine et al. (2005) similarly studied Apollo 12 (Oceanus Procellarum) glass spherules. Here we synthesize data from those papers to offer a new estimate of the impact rate time dependence Impact melts as a proxy for impacts: Relevance of the cataclysm controversy Consider a newly formed lunar surface. The first impacts spray glassy material around the surface and form near-surface lenses of impact melts, and as long as the craters, glasses, and melts are sparsely scattered, the melt materials give a good record of the impacts. After a few craters of kilometer-scale (or any diameter D big enough to form substantial impact melts) accumulate, however, sandblasting by much smaller craters (or any size D /100) efficiently begins to grind and garden the earlier impact materials, especially glasses, scattered in the upper meters of regolith. As craters begin to saturate the surface, any given spot has a high probability of being hit more than once, so that full-fledged gardening begins. The melt materials become more densely mixed into the surface regolith, and new craters begin to destroy older craters and their melt materials. Sporadic big craters may excavate into the underlying layer of pristine deep-seated bedrock and scatter ancient igneous rocks, but at the same time pulverize any nearer-surface lenses of impact melts in crater floors. There are always reservoirs of deep ancient igneous bedrock to be added to the surface regolith, but ancient impact melts can only undergo attrition. The natural end result is that the impact melt/glass record of the earliest cratering diminishes as crater populations accumulate. Thus, in principle, we must be cautious because impact melts and glasses may not be a good proxy record for the earliest cratering. This principle is illuminated by an ongoing controversy over what happened in the first 600 Myr. The Apollo/Luna data on impact melt rocks (Ryder, 1990; Stöffler and Ryder, 2001; Taylor et al., 1991) show few melts before 4.0 Gyr ago, followed by an extremely strong, narrow spike containing some 75 85% of the melts at 3.9 ± 0.2 Gyr. [Another 10% or so are between 3.8 and 3.7 Gyr ago, and others are dotted more sparsely down to today cf. summary Fig. 8 in review by Hartmann (2003).] Ryder chose these large-scale samples of melt as a proxy for large-scale impacts (km-scale craters or basins) that produce impact melt sheets. Ryder and others asserted that the data affirm an interplanetary cataclysm in which all lunar basins were formed within a 200 Myr period, 3.9 Gyr ago a cataclysm first proposed by Tera et al. (1974) on the basis of scarcity of Apollo lunar samples from before 4 Gyr ago. An additional effect comes into play here. Only big craters produce igneous impact melt rocks (Melosh, 1989), whereas craters of all sizes produce impact glasses. Therefore, by the above arguments, impact glasses will be particularly slanted toward recent craters, whereas impact melt rocks will sample larger, typically older craters although they, too, suffer from attrition of the oldest samples by later cratering and gardening. This issue of ancient impact melts as a proxy for ancient impacts has a distinct relevance to the use of impact melts to measure longer-term time behavior of the impact flux. Ryder (1989, 1990) explicitly assumed that lack of impact melts at any age (especially before 4 Gyr ago) means lack of impacts at that time (cf. Section 3.3 below) in other words, impact melts are a proxy for impacts, regardless of age. Ryder s (1989) early study states this fundamental assumption: A heavy bombardment from 4.5 to 4.0 Ga would have produced a large number of impact melt rocks [but] there is no evidence of any impact melt rocks older than 3.92 Ga, from which he infers the Moon accreted rapidly and then underwent negligible impacting for 500 Myr. Ryder and other authors pursuing this model visualize a Solar System in which all planetesimals were swept up within 100 Myr of the beginning ( Gyr ago), followed by 500 Myr of little or no cratering, after which a cataclysm of cratering formed about twenty lunar multi-ring basins and most lunar upland craters (cf. Cohen et al., 2000; Stöffler and Ryder, 2001). Ryder s (1989) title called this early quiet and late cataclysm. Ryder s later work softened this image somewhat, asserting that it was hard to know the impact rate before 4.0 Gyr ago, but the idea is implicit or explicit in several papers on this subject. Ryder continued to assert that absolute ages of individual multi-ring impact basins on the Moon are quite precisely known from sample measurements, and that they formed within a 200-Myr window (see Stöffler and Ryder, 2001). Some other authors are more conservative even on that point, suggesting that the impact melts before 4.1 Gyr ago were destroyed by subsequent cratering, and that identification of specific rock samples with specific impact basins is questionable (e.g., Haskin, 1998; Hartmann, 2003). When Cohen et al. (2000) used lunar meteorite breccias to evaluate impact melt dates from lunar regions outside those sampled by Apollo/Luna, such as the lunar far side, their data (Figs. 1a and 1b) was striking for showing no large spike at 3.9 Gyr, but rather a broad concentration of impacts from 4.1 to about 2.4 Gyr, and fewer impact melts thereafter. The lack of a spike at 3.9 Gyr might seem to refute a global lunar cataclysm at 3.9 Gyr, yet they inferred support for the lunar cataclysm hypothesis (as per their title). Their argument went back to the lack of impact melts in their sample before 4.1 Gyr ago, which they interpreted (as did Ryder, 1989, 1990) as confirming sparse cratering at that time, and hence a dramatic onset of cratering at 3.9 Gyr. The logic of Cohen et al. (2000) appears somewhat internally inconsistent, however. To accept lack of lunar meteorite impact melts before 4 Gyr ago as significant implies that their impact melt record at 3.9 Gyr must also be significant, yet they show no spike in impacts comparable to Ryder s at the time of the putative cataclysm. It might be said, therefore, that their data argue against a global cataclysm.

4 14 W.K. Hartmann et al. / Icarus 186 (2007) Fig. 1. Age distributions of lunar meteorite impact melts and impact-produced glass spherules. These data, taken together, suggest a gradual decline in lunar impact rate from 3.2 to 2 Gyr ago and perhaps beyond. (a) Ages of 31 impact melts from lunar meteorites, summarized by Cohen et al. (2005). (b) The 19 impact melts with lowest age uncertainties, a subset of preceding sample from Cohen et al. (2005). (c) Ages derived from 155 lunar impact-produced glass spherules, from Culler et al. (2000). Culler et al. (2000) provided similar data on 155 glass spherules from the Apollo 14 site at Fra Mauro, a site interpreted as being on the Imbrium ejecta blanket (their data were corrected and modified somewhat by Levine et al., 2005). Their data did show a spike at 3.85 Gyr (the third tallest spike in their detailed data plot), with fewer spherules before that, but as shown by the histogram of Fig. 1c, their spike is nothing like the overwhelming spike in the Ryder and Taylor impact melt data, which included most of their melt samples from 4.5 to 0 Gyr ago. Virtually all Apollo data analysts interpret that the Imbrium impact occurred around Gyr ago, with Fra Mauro representing the Imbrium ejecta (with radial streaks aligned to Imbrium; Hartmann, 1963), and so Culler et al. suggested that their 3.85 Gyr spike and the relative paucity of older spherules reflects formation of the Imbrium basin, since Fra Mauro is ejecta from Imbrium, or at least radially striated by Imbrium. The corrected Apollo 14 spherule data of Levine, divided into the same 400 Myr bins that Culler et al. used, show a broad peak at 4.0 to 2.8 Gyr ago, with the highest bin being 3.6 to 3.2 Gyr, but a smaller subset of 48 dates with only the smallest error bars, ± <100 Myr, shifts the peak barely to the Imbrium bin, by a ratio of 10 to 8 samples, possibly a reflection of the Fra Maura Imbrium spike at 3.85 Gyr. In general, the impact glass data indicate not a cataclysm at 3.9 ± 0.1 Gyr ago,

5 Possible long-term decline in impact rates 2 15 but a broad peak in impact melts at 3.8 to 3.0 Gyr ago, similar to that in the asteroidal meteorite data. The Apollo 12 glass spherule dating by Levine et al. (2005) shows no spike whatsoever at 3.9 Gyr, but they are less relevant as they come from a post-mare surface. Cohen et al. (2005) provided a more complete analysis of their lunar meteorite impact melt data, somewhat softening their 2000 support for a cataclysm at 3.9 Gyr ago, but still arguing that their data are consistent with such an event. These data sets, taken together, however, offer little direct evidence of a global or Solar System-wide cataclysm 3.9 Gyr ago, and suggest the possibility that the earliest melt materials do not reflect the earliest cratering rates Earliest impact melts and glass spherules: Not a proxy for impacts? Are age distributions such as those in Fig. 1 really a representative proxy for the production rate of craters? The answer probably depends on the crater size being discussed. Reflecting the ideas at the beginning of Section 3.1 above, Culler et al. (2000) state specifically that the craters producing their glass spherules are small and proximal to their collection locality, though they do not specify a size or distance range. They also indicate that their sample site is atop a local ejecta blanket produced by Cone crater, which is 370 m in diameter, 1 km away, and 25 Myr old. This accounts for their tallest and narrowest spike corresponding to Cone crater s age; see their Fig. 2 and further discussion by Levine et al. (2005). Similarly, the Levine et al. Apollo 12 data are from a trench on the side of 14-m Sharp crater, and are dominated by spherules <800 Myr old. The second largest spike in the Culler et al. (2000) data is at 3.2 Gyr (another regional crater that ejected glass spherules?). Their third largest spike, in terms of height and width, is the 3.85 Gyr event (associated with Imbrium ejecta?), but it is not as dominant as in the Apollo/Luna impact melt breccias dated by Ryder. The fourth and only other major spike (as tall and nearly as wide as the previous spike) is at about 0.4 Gyr and is probably associated with the asteroidal breakup event or events that produced the L chondrites (see Section 3.6 below). At any rate, the spikiness in the glass spherule data illustrates a problem in separating long-term impact trends from statistics of individual impacts or waves of impacts. The problem is somewhat subtle. Craters smaller than 200 m are in saturation even in the (relatively young) lunar mare lava plains. This means that craters of D 200 m are gardening the surface, pulverizing and destroying the older glass impact melts. Culler et al. (2000) specifically interpret the reduced spherule numbers for ages older than 3.5 Gyr not in terms of a reduced cratering rate at that time, but as likely due to the effect of lunar gardening combined with the age of the Fra Mauro formation. Even with the corrected data of Levine et al. (2005), the Apollo 14 Fra Mauro broad peak appears to be at about 3.6 Gyr, depending on the binning and screening by error bars, with reduced numbers before that. Similarly, the Apollo 12 histogram of Levine et al. (2005) shows a broad maximum at 3.6 to 2.0 Gyr ago, with reduced numbers before 3.4 Gyr ago (a cutoff due to Oceanus Procellarum lava ages). Similarly, the lunar meteorite impact melt clasts show more or less level or reduced numbers before 3.5 Gyr, compared to the broad peak at Gyr ago. Most data sets, therefore, show a broad peak around 3.5 Gyr ago, with fewer earlier impact melts or glasses. Yet crater counts show that the cratering rate was higher before 3.5 Gyr ago (as described in Section 2 above). We suggest that two important principles follow from these concepts. First, because the sample numbers flatten or decrease as we go back before 3.5 Gyr ago, even though the rate of crater production is known to have increased dramatically as we go back into that time, impact melt and glass spherule abundances before 3.5 Gyr ago cannot be taken as a measure of impact rates. This mismatch between cratering rate and impact melt behavior disproves the assumption of Ryder (1989, 1990) and others who have adopted his logic (e.g., Cohen et al., 2000) that low numbers of impact melts before 4.0 Gyr ago equate to low impact rates. [Evidence of cratering before 4.0 Gyr ago exists; for example, even if we choose the lowest error bar data (<100 Myr) in the corrected Apollo 14 Fra Mauro impact glass data of Levine et al. (2005), we find 2 out of 48 (4%) have dates before 4.0 Gyr (namely, 4.09 ± 0.08 and 4.23 ± 0.05 Gyr).] To sum up, glass spherules and impact melt numbers cannot be assumed to be proportional to impact cratering rates, especially during the periods of intense saturation cratering. In short, lack of impact melts lack of impacts. A second principle based on these data is that the glass spherule ages are probably skewed toward younger sources than the larger ( 1 km) craters that produce the lunar meteorites and impact melts that are usually used for dating. This is because even small craters continually produce new glasses, while the older glass spherules are being continually gardened into oblivion by the same small impacts (since craters of D<200 m are in saturation). Thus, tellingly, the glass spherules show more evidence of the known 0.47 Gyr (L chondrite?) impact shower and small recent impact features like Cone and Sharp craters than the impact melt breccias do. To apply this principle, we can say that even if the cratering rate were really constant, the spherules would probably show an increase toward recent time. Therefore, the apparent rate of decrease in glass spherule production from about 3.5 to 1 Gyr ago is probably a lower limit on the real impact rate decrease. In summary, a prudent comparison of the glass spherule data with the impact melt data may be the safest way to examine the overall impact rate behavior, rather than picking one set of impact melt or glass measurements Effects of sample selection procedures on interpretation of cratering rate time dependence and cataclysm As we have noted, lack of impacts melts older than Gyr became conflated with proof of a cataclysm at 3.9 Gyr, as indicated by the logic of Cohen et al. (2000) but the two phenomena may be quite separate. An ongoing question is whether the 3.9 Gyr spike in the Apollo/Luna impact melt samples might be a consequence of the way those samples were selected. Ryder (1990) was specifically looking for the largest,

6 16 W.K. Hartmann et al. / Icarus 186 (2007) basin-scale impacts, and chose his samples according to geochemical and textural criteria in order to date basin-forming events. This raises a question of whether Ryder detected primarily the last large basin(s) on the front site (e.g., Imbrium), and might have found a different time dependence had he used different selection criteria for lunar samples, an issue also raised by the Cohen et al. meteorite data. If the Apollo landing sites had been differently distributed further from Imbrium, the age distribution of Apollo impact melts might have looked more like the curves for Cohen et al. s (2000, 2005) lunar meteorite impact melt clasts. As noted by Cohen et al. (2005), the Apollo and Luna sample sites were all in or near an area called the Procellarum KREEP terrain... identified by the surface expression of elevated thorium levels... Cohen et al. specifically avoided the high-thorium, KREEP-associated lunar meteorites in order to sample other regions of the Moon, and when they did this, the overwhelming 3.9 Gyr spike shown in Ryder s data disappeared. As discussed by Haskin (1998) and Haskin et al. (1998), and illustrated in Fig. 2, high-thorium material is primarily found in the interior and surroundings of the Imbrium impact basin, which they called the High-Th Oval Region. These authors argued that the 3.9 Gyr spike in the impact melt age distribution of the Apollo/Luna high-thorium materials is thus strongly influenced by ejecta from the Imbrium impact. If this is true, one could argue (as did Haskin) that the huge spike in the Apollo/Luna impact melt data of Ryder, far from proving a global or Solar System-wide cratering cataclysm, records a regional lunar front side event (or events) 3.9 Gyr ago perhaps primarily the Imbrium (and Orientale?) event. A similar result shows up by subdividing the 148 samples of impact reset... lunar highland rocks tabulated by Bogard (1995). If we separate those from the Apollo 14 site (recognized as sitting on the high-th Fra Mauro Imbrium ejecta), and those from the more distant Apollo 16 and 17 sites, we find a similar diminution of the cataclysm spike ( Gyr impact-reset ages) as we move away from the Th-rich materials. About 66% of the 35 Apollo 14 samples are in the spike, but only 38% are in the same spike at Apollo sites. (The percentage of very old samples, Gyr in impact-reset age, correspondingly goes up from 0% at Apollo 14 to 19% at the other sites, suggesting access to older impact melts only as we get away from the Imbrium Th-rich ejecta.) Meteorites, representing the main asteroid belt, similarly lack the 3.9 Gyr spike, showing a broader peak of impact melt ages at 4.2to3.5Gyr ago (Hartmann, 2003). The implication of all these data is that a huge 3.9 Gyr spike and paucity of earlier impact melts is not uniform on the Moon, nor is it an accurate record of the impact rate itself in early time. To clarify these issues, it is important to date more lunar meteorite impact melt clasts, as well as more glass samples from lunar upland sites, such as Apollo Four stages of impact history, based on dynamical analyses All sides appear to agree that the impact rate, measured by lunar craters and by Ryder s impact melt rocks, was very high at 3.9 Gyr compared to the present (whether there was a cataclysm or not), and that it declined relatively steeply in the next few hundred Myr. Major questions remain, however: what was the long-term time dependence of the impact rate, how fast did it decline after 3.9 Gyr ago, and did it level out entirely? The Ryder (1989, 1990) assumption, that lack of impact melts between 4.5 and 4.1 Gyr ago = lack of impacts, was used to imply that the events at 3.9 Gyr must have been sud- Fig. 2. Geochemical map of the Moon showing region of high thorium abundance generally coincides almost entirely with the region of the Imbrium basin, especially including its rim and ejecta blanket (see Haskin, 1998; Haskin et al., 1998). Illustration courtesy of R.L. Korotev.

7 Possible long-term decline in impact rates 2 17 den and perhaps short-lived, and some writers (Ryder, 1989; Stöffler and Ryder, 2001) imply that lunar samples constrain virtually all lunar basins to have formed within a 200-Myr interval, indicating rapid rise and fall of the cataclysmic cratering. In support of these ideas, it is often noted that recent models of planet accretion (e.g., Levison et al., 2001; Chambers and Cassen, 2002; Gomes et al., 2005; Morbidelli and Bottke, 2006) suggest that 99% or more of the initial planetesimals aggregate into planets on timescales of tens Myr to 100 Myr, and therefore plausible early sources of lunar and planetary cratering were gone by 4.4 Gyr ago. Thus, according to one argument, any intense cratering 3.9 Gyr ago had to be due to an anomalous and unique cataclysm, and any rapid decrease observed in the crater counts at dated Apollo/Luna sites cannot mark a long-term secular decline since accretion, but must mark the rapid fall-off after the cataclysm. Note, however, that to accrete Earth in the usually accepted 50 Myr involves an impact rate probably some 10 8 or 10 9 today s rate (Hartmann, 1980). Therefore, even 1% of the accretion-era value could be of order 10 6 times today s rate, so it remains difficult to argue for a near-zero rate in the first 500 Myr. Indeed, early models of planetesimal evolution (Safronov, 1972; Wetherill, 1975) suggested that near encounters between planetesimals and planets perturbed the former onto more eccentric and inclined orbits so that their half-life against collision with a planet gradually increased as the planets grew. Simulations of the time behavior of impact flux by Wetherill (1975), for example, showed bombardment persisting for several hundred Myr with a gradually lengthening half-life, consistent with a long-term decay in cratering. More recent and sophisticated studies attempted to shed further light on this residual population. For example, Morbidelli et al. (2001) found that a few percent of the initial planetesimal population in the 1 2 AU zone is left on highly inclined orbits... The final depletion of this leftover population would cause an extended bombardment of all the terrestrial planets, slowly decaying with a timescale on the order of 60 Ma. The initial populations of... leftovers would need to be a few times that presently in the main asteroid belt... If this result is adopted, a long-term decline in cratering could have proceeded from before 3.9 Gyr ago to well after that, consistent with the observations. For example, Hartmann (1972), Neukum (1983), and Hartmann and Neukum (2001), using crater counts at dated Apollo sites, derived an observed impact rate, around 3.8 Gyr ago, of a few 100 today s rate. If this were interpreted as part of a gradual loss of planetesimals, it would suggest a decline in impact rate by 10 6 in the first 700 Myr, which translates to a mean half-life of 35 Myr during that period possibly a support for the half-life behavior calculated by Morbidelli et al. (2001). In the same context, Hartmann (1972, Fig. 5, prior to these controversies) measured a half-life of <100 Myr around 4 Gyr ago (using upland crater densities), and 300 Myr for the impact decay rate during the time interval of Apollo landing site ages, about 3.8 to 3.1 Gyr ago. All such discussions, however, are complicated by recent studies of possible resonance effect, in which, as a resonance is reached by a migrating giant planet, it produces sudden scattering of interplanetary populations (Morbidelli and Bottke, 2006), favoring a more cataclysmic event. Gomes et al. (2005), Strom et al. (2005), and Morbidelli and Bottke (2006) present strong cases that planetary migrations, caused by (model-dependent) massive disks of planetesimals, fundamentally destabilized the interplanetary population in the Solar System some Myr after planetary formation, causing a wave of impacts that would have struck all planets and satellites. These results are exciting in terms of explaining various Solar System properties, but we should remain aware that in this work lies a danger of circularity in the arguments, since some of the recent papers about dynamics and decay rates of planetesimal populations assume that a Ryder-style cataclysm has been confirmed, and then look for specific mechanisms that might produce that type of cratering time dependence. (On the other hand, a discovery made during a search for what turns out to be an imaginary effect cannot be dismissed merely because of its motivation!) Precise dating of pre-imbrium basins is crucial to resolve the arguments. Morbidelli and Bottke (2006) noted that the controversial dating of the Nectaris basin alone, for example, strongly influences the uniqueness and magnitude of the cataclysm that is needed in their models. If all basins formed between 3.8 and 4.0 Gyr with none earlier, the cataclysm looks profound; but if the older-looking basins, such as Nectaris and Serenitatis, are admitted as scattered in age at times such as 4.1, 4.2, or even 4.3 Gyr ago, the cataclysm becomes less anomalous and more like a tail-end of an extended planetesimal scattering process, possibly involving planet migrations and resonance effects, and the 3.9 Gyr event(s) become merely the last big basin impact, whose debris was produced late enough to survive the declining post-3.8 Gyr effects of impact gardening and pulverization. To summarize, a significant problem is to understand the impact rate and time behavior of the post-accretion, leftover population, relative to today s impact rate. In terms of the dynamical issues we thus propose a process of at least four stages, more complex than has yet been fully investigated. The first stage is the rapid accretional sweep-up of most planetesimals into planets in the first 100 Myr, leaving behind scattered (high inclination and eccentricity) interplanetary leftovers and possibly uncleared interplanetary zones such as the fringes of the then-more populous main asteroid belt and Kuiper belt. On the Moon, this process probably contributed to buildup of megaregolith, but the detailed record may have been lost because of the cumulative effects of subsequent cratering. The second stage, currently under study and the most complex, involves the final completion of Neptune and Uranus; possible presence of massive planetesimal belts and migration of giant planet orbital elements; sweeping of resonances through previously uncleared zones; and possible sudden, short-lived cataclysmic scattering effects associated with Jupiter Saturn resonant interactions (cf. Strom et al., 2005; Morbidelli and Bottke, 2006). On the Moon, the resulting challenge is to date the major impact basins in order to establish the true duration of their formation. The third stage, overlapping the second stage, is the more gradual sweep-up of the leftover planetesimals independent of any resonance cataclysms (cf. Morbidelli et al., 2001;

8 18 W.K. Hartmann et al. / Icarus 186 (2007) Morbidelli and Bottke, 2006). In the models proposed by Strom et al. (2005) and Morbidelli et al. (2001), these stages may last until 3.7 Gyr ago; crater counts affirm impact rate decline 3.8 to 3.2 Gyr. On the Moon, dating of basins and old large craters, plus the clasts of oldest impact melts from more widely dispersed sites, together with crater counts on more dated surfaces, would clarify the time behavior of this stage. The fourth stage involves the scattering of planetesimals out of the remaining quasi- permanent reservoirs such as the main asteroid belt and the modern Kuiper belt. The impact flux at this stage is more nearly constant, but dynamical models show a long-term decline in asteroid numbers due to collisional clearing of these belts themselves. On the Moon, as we argue here, the dating of lunar impact melts and glass spherules appears to give a record of this phase. Further work is needed in modeling all four stages in order to synthesize our understanding of these processes acting in concert, and the magnitude of cratering rate spikes, or cataclysms, that could rise above the background After 3.9 Gyr: Empirical evidence of a declining impact flux Almost lost in the dynamical literature is the fact that the data sets of both Cohen et al. (2000, 2005) and Culler et al. (2000) give empirical information about the extended lunar impact history after 3.5 Gyr. This information dovetails with, and improves, the earlier attempts to construct lunar impact history from crater counts (Hartmann 1966, 1970a, 1970b; Neukum, 1983; Neukum et al., 2001). A standard model that has been very useful came from the crater-count work of Neukum (1983) who produced not only graphical data on crater density vs time, but fitted it to a numerical expression N(D >1km) = 5.44(10 14 )[e 6.93T 1]+8.38(10 4 )T, where N(D > 1km) = cumulative number of all craters/km 2 larger than 1-km diameter on a lunar surface of age T in Gyr. According to this curve, cratering rate (the differential of the above, not the cumulative number of craters) declines rapidly around 4 to 3.2 Gyr, and levels out and drops by only <10% after about 2.8 Gyr ago. More recent empirical studies of whether the cratering rate changed after 3 Gyr ago conclude that it has been roughly constant to within a factor 2, but give various results about details of possible long-term secular increases or decreases within a factor 2 (Grieve and Shoemaker, 1994; Culler et al., 2000, p. 1785). The impact melt and glass spherule data, as seen in Fig. 1, suggest the decline in cratering rate continued longer and at a more gradual rate than in Neukum s equation. In all three histograms of Figs. 1a 1c, using data on both lunar meteorite impact melts and glass spherules, a broad peak around 3.4 to 2.6 Gyr ago, with gradual decline until 2 Gyr ago or beyond, is apparent. Culler et al. (2000) inferred a decline from 3.0 to 0.5 Gyr. The revision of their Apollo 14 glass spherule data by Levine et al. (2005) shows a smooth decline from 3.6 Gyr ago until 1.2 Gyr ago. The Apollo 12 glass spherule data of Levine et al. (2005) show a decline from around Gyr ago until 1.6 Gyr ago. The lunar meteorite data (Fig. 1, top two graphs) indicate a decline from 3.4 Gyr ago until about 1.8 Gyr ago, with no melts after that. All the data taken together suggest that a long-term decline, neglecting short-lived spikes, continued after about 3 Gyr ago until as recently as 0.5 Gyr ago, although the statistics are sparse. All the glass spherule data, and only the glass spherule data, suggest an increase in melt samples after 1.5 Gyr ago, which we attribute not to a sudden change in the direction of the cratering trend, but to the abundant splashing and preservation of glasses from the smallest, most recent local impact craters, as discussed by Culler et al. (2000) an effect not so prominent in impact melts, which require larger primary craters for their formation. Fig. 3 shows a synthesis of these data. The impact melt and glass spherule data are normalized to 1.00 at an age of 2.6 Gyr ago, where the impact melt and spherule data are judged most convincing. Neukum s equation, being an excellent summary of current cratering data before 3 Gyr ago, is also normalized at 2.6 Gyr ago, when the cratering data are probably fairly reliable, albeit extrapolated to somewhat younger ages than the original Apollo/Luna site crater count data. How can we interpret Fig. 3? As shown by the earliest studies (see Section 1), the average lunar cratering rate before 3.6 Gyr ago had to be >10 times higher than the average rate since then i.e., off scale at the top. This is true whether or not there was a cataclysmic spike at 3.9 Gyr. A comparison of the impact melt/spherule data with the Neukum curve shape suggests that the impact melt and glass spherule data decline more gradually than the Neukum curve, from around 3.5 Gyr ago to around Gyr ago. The normalizing of the Neukum curve at 2.6 Gyr shows that it levels out too soon after 2.6 Gyr ago to match the impact melt/spherule data. We conclude that the new evidence from dating impact melts and spherules implies a long, slow decline in cratering rate, extending well after the pre-lunar-mare intense early bombardment (Hartmann, 1966) or the 3.9 Gyr cataclysm (Tera et al., 1974). The decline continues to at least 0.5 Gyr ago. After this, the impact melt data become too rare to be useful, and the spherule data are dominated by the recent small craters and the L-chondrite breakup The L-chondrite event 470 Myr ago: Implications In Fig. 3, a blip is seen in the glass spherule data around 500 Myr ago. It is more clearly seen as the fourth largest spike in Culler et al. (2000, Fig. 2). This event probably corresponds to the breakup event in the asteroid belt that produced ashowerofl-chondrite meteorites, and perhaps some H chondrites, around that time. The event appears prominently in the record of L-chondrite meteorite ages (cf. Bogard, 1995; Hartmann, 2003, Fig. 8), and in the discovery of fossil L chondrites embedded in Swedish limestones, estimated initially to be 480 Myr old (Schmitz et al., 1997, 2003). A recent Ar Ar study finds agreement between dating of the L-chondrite breakup event recorded in meteorites and the dated mid- Ordovician meteorite shower, both at 469 ± 6Myr(Trieloff et al., 2006). Bogard (1995, Fig. 7) indicates that not only L chondrites, but, to a lesser extent, H chondrites, also show a peak in impact reset ages around Myr.

9 Possible long-term decline in impact rates 2 19 Fig. 3. Synthesis of dating on lunar meteorite impact melts (" s), impact-produced glass spherules (! s), and the Neukum (1983) cratering rate curve (N s). The impact melt and spherule data are normalized to a relative impact rate of 1 at T = 2.4 Gyr ago, when those data are considered most valid. The Neukum curve is fittedtothiscurveatt 3 Gyr ago, when the cratering rate data (measured at Apollo/Luna sites) are considered most valid. The spike from this event is much more pronounced in lunar glass spherule data than in Apollo/Luna impact melts or in the Cohen et al. (2000, 2005) lunar meteorite impact melts. Consistent with the earlier discussion, the spike is strong among the glass spherules because the spherules are weighted toward recent small impacts (the impactors from the L-chondrite event, making some of the small and proximal craters around the Apollo 14 site cited by Culler et al., 2000). Older glasses may be pulverized or diluted in surface layers because of gardening. Nonetheless, Cohen et al. (2002) reported two clasts of 574 ± 87 and 564 ± 25 Myr age in lunar meteorite Dhofar 25 (another 569 Myr age reported in the same paper for a third clast was later withdrawn from the data set as erroneous). At the 1 to 3 sigma level, these may or may not represent the L-chondrite shower or the H -chondrite shower. The stronger showing of the 470 Myr event among the glass spherules than among the impact melt clasts implies that the L-chondrite impactors causing it were mostly smaller than the 5 7 km minimum size of craters needed to produce the meteorite impact melts (cited by Cohen et al., 2005, p. 755). A canonical view (Cohen et al., 2000, 2002, 2005; Melosh, 1989; and others) is that full-fledged igneous impact melt rocks and mineral assemblage clasts require craters larger than this size, whereas smaller local craters can scatter glass spherules. To summarize, the L-chondrite event is recorded on the Moon and the data affirm that spikiness of the curve of impact flux vs time, as mentioned above, depends on the size of the craters being measured. The curve is more spiky for smaller craters (e.g., 200 m) that tend to record very frequent (therefore localized) impact events, which affect the glass spherule record without affecting the impact melt clast record. 4. Calculation of a new time-dependent lunar flux rate We assume the cratering rate from Apollo/Luna sites, being simply and directly observed from cumulative craters on surfaces of well-characterized age, is more reliably known than the cratering rate inferred during the same period from the impact melts and glass spherules. Thus we assume that Neukum s equation of accumulated crater density N(1 km) for craters of D>1 km is relatively reliable for the period about 3.8 to 3.2 Gyr ago (roughly the range of Apollo/Luna landing site ages). Based also on the accompanying paper by Quantin et al. (2007), we suggest a continuing slow decline after that, probably to a lower present-day rate than used in the Hartmann (2005) estimates of cratering rate and isochrons for recent time. (As discussed in the accompanying paper by Quantin et al. (2007), this adjusts Quantin s rate of martian landslide production rate, so that a more constant rate of landslides results a result that is more geologically reasonable.) Thus, starting with Fig. 3, we adjust the Neukum curve to produce a more gradually declining curve. To do this, we tabulated the Neukum (1983) cumulative equation at 200 Myr intervals (Table 1), then tabulatedthe differential crateringwithin the 200 Myr intervals (the actual instantaneous crater production rate in craters/km 2 yr), then adjusted those production rate numbers in order to match the trends in the impact melt and glass spherule data, and also to match the trends inferred from the companion paper. For example, we increased the crater production rate by nearly a factor 2 (relative to the Neukum curve) at 3 Gyr ago, although we match the Neukum crater production rate 2.4 Gyr ago. The main change is that we reduced our cratering rate from the Neukum value by a factor 2 around 600 Myr ago. We note in passing that several papers referenced above treat reported ages for Tycho/Copernicus as useful points in tying

10 20 W.K. Hartmann et al. / Icarus 186 (2007) Table 1 Comparison of lunar time dependence curves Age (Gyr) Neukum cumulative N (1 km) (Moon) (No. craters of D>1km)/km (-1) 2.23 ( 1) (-2) 4.62 ( 2) (-2) 1.88 ( 2) (-3) 6.97 ( 3) (-3) 4.00 ( 3) (-3) 2.86 ( 3) (-3) 2.19 ( 3) (-3) 1.79 ( 3) (-3) 1.53 ( 3) (-3) 1.34 ( 3) (-3) 1.18 ( 3) (-3) 1.02 ( 3) (-3) 8.80 ( 4) (-3) 7.45 ( 4) (-3) 6.19 ( 4) (-3) 5.03 ( 4) (-4) 3.96 ( 4) (-4) 2.98 ( 4) (-4) 2.10 ( 4) (-4) 1.30 ( 4) (-4) 6.06 ( 5) (-5) 3.0 ( 5) (-5) 1.5 ( 5) New cumulative curve (Moon) (No. craters of D>1km)/km 2 down the recent flux. For example, values of 104 ± 4 Myr and 800 ± 15 Myr, respectively, have been inferred from surface exposure ages, degassing ages, and KREEP glasses in Apollo samples (cf. Stöffler and Ryder, 2001, pp. 9 44). The identification of the samples themselves with Tycho and Copernicus is still unconfirmed, however, and we consider that Tycho and Copernicus ages are not well enough established to carry decisive weight. In our newly proposed curve, the total decline in impact cratering from 2.3 Gyr until today is about a factor 3. Our adjusted curve is shown in comparison with the available data in Fig. 3. Fig. 4 shows the new curve not in terms of cratering rate per se, but rather on a plot of cumulative numbers of craters as a function of time, as favored by Neukum (1983) (also in Neukum et al., 2001). The cumulative numbers are compared to Neukum s in Table 1. As can be seen, the net changes in inferred ages are not radical, relative to earlier understandings of uncertainties. The adjustments in age are within the factor 2 to 4 error bars suggested for the overall crater count chronology technique by Hartmann et al. (1999, p. 167) and Hartmann (2005, p. 315). They primarily push back ages of young features. Note that the Neukum equation is traditionally expressed in terms of the number of 1-km craters. As we have discussed, the behavior of the curve may be somewhat diameter-dependent, although at the current levels of uncertainty, these effects may be in the noise level. From about 2.3 Gyr ago to the present, our lunar curve follows an equation Production rate (craters of D>1km/km 2 per 200 Myr) = 4.66(10 5 )T (10 5 ), where T is time in Gyr. This contrasts with the behavior in the Neukum equation, which in this time period is governed mainly by the constant term Production rate (lunar craters of D>1km/km 2 per 200 Myr) = 1.68(10 4 ). Fig. 4. Comparison between the classic Neukum (1983) time dependence equation and the proposed new time dependence. Whereas Fig. 3 shows the crater production rate, this graph shows the integrated cumulative number of craters, expressed as lunar craters of D>1 km formed per km 2, as a function surface age. The graph shows that on the Moon, Mars, and other inner Solar System surfaces with minimal crater densities (where they exist) would be interpreted to have ages typically times as old as in the earlier system.