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Register a new userThe equilibrium size-frequency distribution of small craters reveals the effects of distal ejecta on lunar landscape morphology
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Small craters of the lunar maria are observed to be in a state of equilibrium, in which the rate of production of new craters is, on average, equal to the rate of destruction of old craters. Crater counts of multiple lunar terrains over decades consistently show that the equilibrium cumulative size-frequency distribution (SFD) per unit area of small craters of radius >r is proportional r^(-2), and that the total crater density is a few percent of so-called geometric saturation, which is the maximum theoretical packing density of circular features. While it has long been known that the primary crater destruction mechanism for these small craters is steady diffusive degradation, there are few quantitative constraints on the processes that determine the degradation rate of meter to kilometer scale lunar surface features. Here we combine analytical modeling with a Monte Carlo landscape evolution code known as the Cratered Terrain Evolution Model to place constraints on which processes control the observed equilibrium size-frequency distribution for small craters. We find that the impacts by small distal ejecta fragments, distributed in spatially heterogeneous rays, is the largest contributor to the diffusive degradation which controls the equilibrium SFD of small craters. Other degradation or crater removal mechanisms, such cookie cutting, ejecta burial, seismic shaking, and micrometeoroid bombardment, likely contribute very little to the diffusive topographic degradation of the lunar maria at the meter scale and larger.
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We present a study on the relationship between the ratio of the depth of a crater to its diameter and the diameter for lunar craters both on the maria and on the highlands. We consider craters younger than 1.1 billion years in age, i.e. of Copernican period. The aim of this work is to improve our understanding of such relationships based on our new estimates of the craterss depth and diameter. Previous studies considered similar relationships for much older craters (up to 3.2 billion years). We calculated the depths of craters with diameters from 10 to 100 km based on the altitude profiles derived from data obtained by the Lunar Orbiter Laser Altimeter (LOLA) onboard the Lunar Reconnaissance Orbiter (LRO). The ratio h/D of the depth h of a crater to its diameter D can diverge by up to a factor of two for craters with almost the same diameters. The linear and power approximations (regressions) of the dependence of h/D on D were made for simple and complex Copernican craters selected from the data from Mazrouei et al. (2019) and Losiak et al. (2015). For the separation of highland craters into two groups based only on their dependences of h/D on D, at D<18 km these are mostly simple craters, although some complex craters can have diameters D>16 km. Depths of mare craters with D<14 km are greater than 0.15D. Following Pikes (1981) classification, we group mare craters of D<15 km as simple craters. Mare craters with 15<D<18 km fit both approximation curves for simple and complex craters. Depths of mare craters with D>18 km are in a better agreement with the approximation curve of h/D vs. D for complex craters than for simple craters. At the same diameter, mare craters are deeper than highland craters at a diameter smaller than 30-40 km. For greater diameters, highland craters are deeper.
Planetary impact events eject large volumes of surface material. Crater excavation processes are difficult to study, and in particular the details of individual ejecta fragments are not well understood. A related, enduring issue in planetary mapping is whether a given crater resulted from a primary impact (asteroid or comet) or instead is a secondary crater created by an ejecta fragment. With mapping and statistical analyses of six lunar secondary crater fields (including Orientale, Copernicus, and Kepler) we provide three new constraints on these issues: 1) estimation of the maximum secondary crater size as a function of distance from a primary crater on the Moon, 2) estimation of the size and velocity of ejecta fragments that formed these secondaries, and 3) estimation of the fragment size ejected at escape velocity. Through this analysis, we confirmed and extended a suspected scale-dependent trend in ejecta size-velocity distributions. Maximum ejecta fragment sizes fall off much more steeply with increasing ejection velocity for larger primary impacts (compared to smaller primary impacts). Specifically, we characterize the maximum ejecta sizes for a given ejection velocity with a power law, and find the velocity exponent varies between approximately -0.3 and -3 for the range of primary craters investigated here (0.83-660 km in diameter). Data for the jovian moons Europa and Ganymede confirm similar trends for icy surfaces. This result is not predicted by analytical theories of formation of Grady-Kipp fragments or spalls during impacts, and suggests that further modeling investigations are warranted to explain this scale-dependent effect.
We use numerical modeling to investigate the combined effects of impact velocity and acoustic fluidization on lunar craters in the simple-to-complex transition regime. To investigate the full scope of the problem, we employed the two widely adopted Block-Model of acoustic fluidization scaling assumptions (scaling block size by impactor size and scaling by coupling parameter) and compared their outcomes. Impactor size and velocity were varied, such that large/slow and small/fast impactors would produce craters of the same diameter within a suite of simulations, ranging in diameter from 10-26 km, which straddles the simple-to-complex crater transition on Moon. Our study suggests that the transition from simple to complex structures is highly sensitive to the choice of the time decay and viscosity constants in the Block-Model of acoustic fluidization. Moreover, the combination of impactor size and velocity plays a greater role than previously thought in the morphology of craters in the simple-to-complex size range. We propose that scaling of block size by impactor size is an appropriate choice for modeling simple-to-complex craters on planetary surfaces, including both varying and constant impact velocities, as the modeling results are more consistent with the observed morphology of lunar craters. This scaling suggests that the simple-to-complex transition occurs at a larger crater size, if higher impact velocities are considered, and is consistent with the observation that the simple-to-complex transition occurs at larger sizes on Mercury than Mars.
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. 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. We investigate these hypotheses with a Monte Carlo code called the Cratered Terrain Evolution Model (CTEM). We find that matching the observed number of lunar highlands craters with Dc~100 km requires that the total number of impacting asteroids with Di>10 km be no fewer than 4x10-6 km-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 Dc>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, but had a smaller ratio of objects capable of producing megabasins compared to objects capable of producing ~100 km craters.
We compare the number of lunar craters larger than 15 km across and younger than 1.1 Ga to the estimates of the number of craters that could have been formed for 1.1 Ga if the number of near-Earth objects and their orbital elements during that time were close to the corresponding current values. The comparison was performed for craters over the entire lunar surface and in the region of the Oceanus Procellarum and maria on the near side of the Moon. In these estimates, we used the values of collision probabilities of near-Earth objects with the Moon and the dependences of the crater diameters on the impactor sizes. According to the estimates made by different authors, the number density of known Copernican craters with diameters D>15 km in mare regions is at least double the corresponding number for the remaining lunar surface. Our estimates do not contradict the growth in the number of near-Earth objects after probable catastrophic fragmentations of large main-belt asteroids, which may have occurred over the recent 300 Ma; however, they do not prove this increase. Particularly, they do not conflict with the inference made by Mazrouei et al. (2019) that 290 Ma ago the frequency of collisions of near-Earth asteroids with the Moon increased by 2.6 times. For a probability of a collision of an Earth-crossing object (ECO) with the Earth in a year equaled to 10^-8, our estimates of the number of craters agree with the model, according to which the number densities of the 15-km Copernican craters for the whole lunar surface would have been the same as that for mare regions if the data by Losiak et al. (2015) for D<30 km were as complete as those for D>30 km. With this collision probability of ECOs with the Earth and for this model, the cratering rate may have been constant over the recent 1.1 Ga.
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