Re-examining the main asteroid belt as the primary source of ancient lunar craters

It has been hypothesized that the impactors that created the majority of the observable craters on the ancient lunar highlands were derived from the main asteroid belt in such a way that preserved their size-frequency distribution (Strom, R.G., Malhotra, R., Ito, T., Yoshida, F., Kring, D.A. [2005]. Science 309, 1847-1850). A more limited version of this hypothesis, dubbed the E-belt hypothesis, postulates that a destabilized contiguous inner extension of the main asteroid belt produced a bombardment limited to those craters younger than Nectaris basin (Bottke, W.F., Vokrouhlický, D., Minton, D., Nesvorný, D., Morbidelli, A., Brasser, R., Simonson, B., Levison, H.F. [2012]. Nature 485, 78-81). We investigate these hypotheses with a Monte Carlo code called the Cratered Terrain Evolution Model (CTEM), which models the topography of a terrain that has experienced bombardment due to an input impactor population. We detail our effort to calibrate the code with a human crater counter. We also take advantage of recent advances in understanding the scaling relationships between impactor size (D_i) and final crater size (D_c) for basin-sized impact craters (D_c > 300 km) in order to use large impact basins as a constraint on the ancient impactor population of the Moon. We find that matching the observed number of lunar highlands craters with D_c ≃ 100 km requires that the total number of impacting asteroids with D_i > 10 km be no fewer than 4 ×10^-6km^-2 . However, this required mass of impactors has <1% chance of producing only a single basin larger than the ∼1200 km Imbrium basin; instead, these simulations are likely to produce more large basins than are observed on the Moon. This difficulty in reproducing the lunar highlands cratering record with a main asteroid belt SFD arises because the main belt is relatively abundant in the objects that produce these "megabasins" that are larger than Imbrium. We also find that the main asteroid belt SFD has <16% chance of producing Nectarian densities of D_c > 64 km craters while not producing a crater larger than Imbrium, as required by the E-belt hypothesis. These results suggest that the lunar highlands were unlikely to have been bombarded by a population whose size-frequency distribution resembles that of the currently observed main asteroid belt. We suggest that the population of impactors that cratered the lunar highlands had a somewhat similar size-frequency distribution as the modern main asteroid belt, reflecting a similar rocky composition and collisional history, but had a smaller ratio of objects capable of producing megabasins compared to objects capable of producing ∼100 km craters. We estimate that the impactor population required to match the lunar highlands had N_>5.5km /N_>70km ≃ 630 , while the modern main asteroid belt ratio is N_>5.5km /N_>70km ≃ 100 .