Ages of large lunar impact craters and implications for bombardment during the Moon’s middle age

Highlights

• Computed ages of several large lunar crater floors using small, superposed craters.

• Ages indicate an extended tail to the Late Heavy Bombardment.

• Ages hint that the impact flux for 3–1 Ga may not be constant.

• Individual secondary crater fields can have widely varying characteristics.

Abstract

Standard lunar chronologies, based on combining lunar sample radiometric ages with impact crater densities of inferred associated units, have lately been questioned about the robustness of their interpretations of the temporal dependance of the lunar impact flux. In particular, there has been increasing focus on the “middle age” of lunar bombardment, from the end of the Late Heavy Bombardment (∼3.8 Ga) until comparatively recent times (∼1 Ga). To gain a better understanding of impact flux in this time period, we determined and analyzed the cratering ages of selected terrains on the Moon. We required distinct terrains with random locations and areas large enough to achieve good statistics for the small, superposed crater size–frequency distributions to be compiled. Therefore, we selected 40 lunar craters with diameter ∼90 km and determined the model ages of their floors by measuring the density of superposed craters using the Lunar Reconnaissance Orbiter Wide Angle Camera mosaic. Absolute model ages were computed using the Model Production Function of Marchi et al. (Marchi, S., Mottola, S., Cremonese, G., Massironi, M., Martellato, E. [2009]. Astron. J. 137, 4936–4948). We find that a majority (36 of 40) of our superposed crater size–frequency distributions are consistent with the Model Production Function. A histogram of the original crater floor model ages indicates the bombardment rate decreased gradually from ∼3.8 Ga until ∼3.0 Ga, implying an extended tail to the Late Heavy Bombardment. For large craters, it also preliminarily suggests that between ∼3.0 and 1.0 Ga bombardment may be characterized by long periods (>600 Myr) of relatively few impacts (“lulls”) broken by a short duration (∼200 Myr) of relatively more impacts (“spike”). While measuring superposed craters, we also noted if they were part of a cluster or chain (named “obvious secondary”), and analyzed these craters separately. Interestingly, we observe a wide variety of slopes to the differential size–frequency power-law, which demonstrates that there can be considerable variation in individual secondary crater field size–frequency distributions. Finally, four of the small, superposed crater size–frequency distributions are found to be inconsistent with the Model Production Function; possible reasons are: resurfacing has modified these distributions, unrecognized secondary craters, and/or the Model Production Function has incorrect inputs (such as the scaling law for the target terrain). The degraded appearance of the superposed craters and indications of resurfacing suggest that the first cause is the most likely.

Introduction

Standard lunar chronologies (Hartmann et al., 1981, Neukum et al., 2001, Stöffler and Ryder, 2001) have been based on combining lunar sample radiometric ages with inferred impact crater densities of features or geological units from which the samples have been interpreted to come. In particular, there has been increasing focus on terrestrial planetary cratering from the declining phases of the Late Heavy Bombardment (LHB, ∼4 Ga; see Table 1 for summary of all acronyms) through the middle of planetary history (∼1 Ga). Lately, however, there has been increasing skepticism that these interpretations of how the impact flux on the Moon has changed with time during this “middle age” of bombardment are robust. There are three critical elements in deriving the lunar impact chronology: the association of the samples with the units on which superposed craters are counted, the measurements of relative crater density, and the sample ages themselves.

First, the Apollo-era lunar sample investigators, and the more recent evaluations and syntheses of that work (Stöffler and Ryder, 2001, Wilhelms, 1987), put together the best sample and terrain associations they could with the available data. But many uncertainties remain or have even arisen as a result of the recently renewed interest in the Moon and data from several lunar spacecraft in the past decade. For example, the earlier assignments of Apollo sample ages to specific basins have been increasingly questioned, in part based on new imaging of the Moon by the Lunar Reconnaissance Orbiter Camera (LROC). The age of Nectaris has long been disputed, but the once accepted age of Serenitatis is now also seriously challenged by interpretations of new images of the Serenitatis region (Spudis et al., 2011). Post-LHB ages are often based on assumptions that the samples are from the sampling localities rather than being ejecta from some distant locations. Alternatively, ages for some distant features (e.g., Copernicus, which is not near an Apollo or Luna site) were derived assuming that they are not local samples but are indeed ejecta from the distant feature, based on circumstantial evidence like a ray crossing the locality.

Second, the crater measurements are also problematical. Ideally, one wants to have a good statistical count of superposed craters on a homogeneous geological unit. But for various reasons (one being the small size of many units, hence a preference to use an age-dating method using the much more numerous small craters), much of the early post-Apollo crater age dating was based on the D_L criterion, which is an estimated diameter (D) for craters degraded to nearly the point of invisibility by smaller superposed craters (Boyce and Dial, 1975, Soderblom and Lebofsky, 1972). This now abandoned method invoked a fairly simplistic theoretical model for crater degradation by saturation cratering in a regolith. Discrepancies are fairly common between results of this technique compared with newer, presumably better, techniques (see discussions by Hiesinger et al., 2000, Hiesinger et al., 2010).

The third element of the crater chronology technique, the sample ages, have minor issues of methodological uncertainties (e.g., Stöffler and Ryder, 2001 and references therein), including overall calibration issues. However, these seem to be less serious than problems with the other two elements – the crater statistics and the associations between the samples and the units studied for crater density.

The LHB and the shape of the impact flux curve for the Moon during ensuing eons has become a matter of much current interest for several reasons. First, there has been a re-examination of the LHB itself (cf. review by Chapman et al. (2007)), with a few investigators continuing to doubt that a “narrow spike” LHB or “terminal cataclysm” occurred at all (Hartmann, 2003, Neukum and Ivanov, 1994). More recently, Morbidelli et al. (2012) have proposed a “saw-tooth” LHB with a wider “spike” and overall lower bombardment rates. This has been hypothesized in the context of a theoretical model for an early extension of the main belt asteroid (MBA) population (the “E-belt”) inward to 1.7 AU from the current inner edge of the belt (Bottke et al., 2012) and new crater measurements of Pre-Nectarian terrains (Marchi et al., 2012). Focusing more on the end of the LHB, there has been a re-examination of what had been traditionally viewed as a change-over in the crater size–frequency distribution (SFD) characteristic of the LHB (what Strom et al. (2005) termed “Population 1”) to the post-LHB bombardment by “Population 2” crater SFDs due to the currently observable population of near-Earth Objects (NEOs) (Strom et al., 2005; implications have recently been debated by Ćuk et al., 2010, Ćuk et al., 2011 and Malhotra and Strom (2011)). In addition, Fassett et al. (2012) have argued that the shape of the crater SFD changed mid-way through the Nectarian rather than at the end of the LHB, calling into question the origin of impactors during the later stages of the LHB. Finally, other researchers have been trying to assess evidence from other various sources (e.g., ancient terrestrial spherule beds [e.g., Simonson and Glass, 2004]) to establish the bombardment rate on Earth, Mercury, and other bodies during the 2–3 Gyr following the LHB (cf. Bottke et al., 2012).

There are widespread implications for understanding the impact flux curve in the inner Solar System during this middle age. If there are substantial departures from lunar chronologies like the smooth curves of Neukum and Ivanov, 1994, Marchi et al., 2009, and Le Feuvre and Wieczorek (2011) then they might correlate with recognizable episodes or durations in the Earth’s geological history. Furthermore, a better understanding of the lunar chronology, as translated to Mercury via dynamical and crater-scaling considerations, might better constrain the possibly very young ages of some volcanic features on Mercury (Marchi et al., 2011, Prockter et al., 2010). There are many other consequences for planetary science, as the Moon is our best witness plate for recording the ancient bombardment by asteroids and comets in the inner Solar System.

In this work, we investigated the ages of distinct features on the Moon that were formed during this period from the ending stages of the LHB toward the present. We employed a methodology introduced by Baldwin (1985), which addressed essentially the same issues still considered today: what was the bombardment rate on the Moon in its middle age. Although his results have substantial statistical uncertainties and were based on the inferior 1960s Lunar Orbiter IV photographs, Baldwin concluded that the impact rate fell to a minimum about 3.1 Ga, and had a fairly abrupt increase in the last 0.3–0.4 Gyr to about double the rate at 3.1 Ga. Other studies have yielded similar, or occasionally discordant, results, but have been based on phenomena that may not be recording impacts by projectiles of sizes that make the craters Baldwin counted (e.g., Culler et al. (2000) studied impact spherules, McEwen et al. (1997) studied farside rayed craters, and Cohen et al. (2005) studied impact melts).

As detailed below, we have a sample of 40 craters of roughly 90 km diameter, ranging from young to old, and we measured the population of small, superposed craters (hereafter also “SSCs”) on their floors. This approach is different from those used previously or currently in the following ways. For our measurements we used the LROC Wide Angle Camera (WAC) mosaic, which is much superior to the Lunar Orbiter images others have employed in the past (e.g., better coverage in both space and pixel scale – especially of the farside, more uniform incidence angle, and reduced image artifacts). Furthermore, we avoided measuring craters on large crater walls, rims, and ejecta blankets, commonly included by others (Baldwin, 1985, Hiesinger et al., 2012). Despite the fact that these are plausibly portions of the original crater, they have sloping crater walls or hilly terrains, which are not valid sampling areas, at least for small craters, because of visibility issues (due to atypical and bad lighting geometry) and mass-wasting problems (which may be greatly enhanced on slopes, thus freshening the surface by a process not active on flat terrains). Furthermore, ejecta blankets are not necessarily solid materials (so scaling relations may be differ from those pertaining to most surfaces), rough at the scales of small craters (making identification difficult), and susceptible to older craters “showing through” (leading to spurious ages). Finally, we segregated SSCs formed in clusters and chains (“obvious secondaries”; hereafter also “OSs”) from the others ultimately used to analyzed the crater floors (hereafter also “CFs”), as they are very likely secondary craters.

As we will describe, we have found a number of issues associated with this methodology. Inevitably, especially for younger craters, we have issues of small counting statistics. Although Baldwin recognized the issue of increased numbers of secondary craters among the smaller superposed craters he counted, we found secondaries to be even more problematic, and did our best to separate primaries from secondaries. Our end product for each of the D ∼ 90 km craters are SFDs for the SSCs (not only totals but also for OSs and for craters classified by degradational state). To these, we generally applied the Marchi et al. (2009) Model Production Function (hereafter also MPF), which assumes an exponentially decreasing (≳3.5 Ga), then constant flux (≲3.5 Ga) for small (D ∼ 1 km) craters, to calculate model ages for the floors. We note that many of the CFs are evidently not the original floors but have been subsequently modified, e.g., by volcanic flooding, ejecta deposits from other craters, and/or mass-wasting of the crater’s interior walls. In the end we have, subject to numerous caveats, a histogram of ages for the lunar terrains analyzed.