Rebuttal to the comment by Malhotra and Strom on “Constraints on the source of lunar cataclysm impactors”

?uk et al. (?uk, M. Gladman, B.J., Stewart, S.T. [2010]. Icarus 207 590-594) concluded that the the lunar cataclysm (late heavy bombardment) was recorded in lunar Imbrian era craters, and that their size distribution is different from that of main belt asteroids (which may have been the dominant pre-Imbrian impactors). This result would likely preclude the asteroid belt as the direct source of lunar cataclysm impactors. Malhotra and Strom (Malhotra, R., Strom, R.G. [2011]. Icarus) maintain that the lunar impactor population in the Imbrian era was the same as in Nectarian and pre-Nectarian periods, and this population had a size distribution identical to that of main belt asteroids. In support of this claim, they present an Imbrian size distribution made from two data sets published by Wilhelms et al. (Wilhelms, D.E., Oberbeck, V.R., Aggarwal, H.R. [1978]. Proc. Lunar Sci. Conf. 9, 3735-3762). However, these two data sets cannot be simply combined as they represent areas of different ages and therefore crater densities. Malhotra and Strom (Malhotra, R., Strom, R.G. [2011]. Icarus) differ with the main conclusion of Wilhelms et al. (Wilhelms, D.E., Oberbeck, V.R., Aggarwal, H.R. [1978]. Proc. Lunar Sci. Conf. 9, 3735-3762) that the Nectarian and Imbrian crater size distributions were different. We conclude that the available data indicate that the lunar Imbrian-era impactors had a different size distribution from the older ones, with the Imbrian impactor distribution being significantly richer in small impactors than that of older lunar impactors or current main-belt asteroids.     

Comment on “Constraints on the source of lunar cataclysm impactors” (Cuk et al., 2010, Icarus 207, 590-594)

Cuk et al. (Cuk, M., Gladman, B.J., Stewart, S.T. [2010]. Icarus 207, 590-594) argue that the projectiles bombarding the Moon at the time of the so-called lunar cataclysm could not have been mainbelt asteroids ejected by purely gravitational means, in contradiction with a conclusion that was reached by Strom et al. (Strom, R.G., Malhotra, R., Ito, T., Yoshida, F., Kring, D.A. [2005]. Science 309, 1847-1850). We demonstrate that Cuk et al.’s argument is erroneous because, contrary to their arguments, the lunar highlands do register the cataclysm impacts, lunar class 1 craters do not represent the size distribution of the cataclysm craters, and the crater size distributions on the late-forming basins are quite similar to those of the highlands craters, albeit at a lower number density due to the rapid decline of the impact flux during the cataclysm.     

The SMART-1 lunar impact

The SMART-1 spacecraft impacted the Moon on 3rd September 2006 at a speed of 2 km s⁻¹ and at a very shallow angle of incidence (∼1°). The resulting impact crater is too small to be viewed from the Earth; accordingly, the general crater size and shape have been determined here by laboratory impact experiments at the same speed and angle of incidence combined with extrapolating to the correct size scale to match the SMART-1 impact. This predicts a highly asymmetric crater approximately 5.5-26 m long, 1.9-9 m wide, 0.23-1.5 m deep and 0.71-6.9 m³ volume. Some of the excavated mass will have gone into crater rim walls, but 0.64-6.3 m³ would have been ejecta on ballistic trajectories corresponding to a cloud of 2200-21,800 kg of lunar material moving away from the impact site. The shallow Messier crater on the Moon is similarly asymmetric and is usually taken as arising from a highly oblique impact. The light flash from the impact and the associated ejecta plume were observed from Earth, but the flash magnitude was not obtained, so it is not possible to obtain the luminous efficiency of the impact event.     

Distributions of boulders ejected from lunar craters

We investigate the spatial distributions of boulders ejected from 18 lunar impact craters that are hundreds of meters in diameter. To accomplish this goal, we measured the diameters of 13,955 ejected boulders and the distance of each boulder from the crater center. Using the boulder distances, we calculated ejection velocities for the boulders. We compare these data with previously published data on larger craters and use this information to determine how boulder ejection velocity scales with crater diameter. We also measured regolith depths in the areas surrounding many of the craters, for comparison with the boulder distributions. These results contribute to understanding boulder ejection velocities, to determining whether there is a relationship between the quantity of ejected boulders and lunar regolith depths, and to understanding the distributions of secondary craters in the Solar System. Understanding distributions of blocky ejecta is an important consideration for landing site selection on both the Moon and Mars.     

Influence of the asymmetrical cratering rate on the lunar cratering chronology

The lunar cratering rate studied over the past 1.1 Gyr, which is a foundation of the lunar cratering chronology, is a decreasing function of the angular distance from the apex of the orbital motion due to the synchronous rotation of the Moon. We here evaluate an influence of the asymmetrical rate upon the age determination.     

Dynamical erosion of the asteroid belt and implications for large impacts in the inner Solar System

The cumulative effects of weak resonant and secular perturbations by the major planets produce chaotic behavior of asteroids on long timescales. Dynamical chaos is the dominant loss mechanism for asteroids with diameters in the current asteroid belt. In a numerical analysis of the long-term evolution of test particles in the main asteroid belt region, we find that the dynamical loss history of test particles from this region is well described with a logarithmic decay law. In our simulations the loss rate function that is established at persists with little deviation to at least . Our study indicates that the asteroid belt region has experienced a significant amount of depletion due to this dynamical erosion—having lost as much as ∼50% of the large asteroids—since 1 Myr after the establishment of the current dynamical structure of the asteroid belt. Because the dynamical depletion of asteroids from the main belt is approximately logarithmic, an equal amount of depletion occurred in the time interval 10-200 Myr as in 0.2-4 Gyr, roughly ∼30% of the current number of large asteroids in the main belt over each interval. We find that asteroids escaping from the main belt due to dynamical chaos have an Earth-impact probability of ∼0.3%. Our model suggests that the rate of impacts from large asteroids has declined by a factor of 3 over the last 3 Gyr, and that the present-day impact flux of objects on the terrestrial planets is roughly an order of magnitude less than estimates currently in use in crater chronologies and impact hazard risk assessments.     

Global survey of lunar regolith depths from LROC images

We performed the first global survey of lunar regolith depths using Lunar Reconnaissance Orbiter Camera (LROC) data and the crater morphology method for determining regolith depth. We find that on both the lunar farside and in the nearside, non-mare regions, the regolith depth is twice as deep as it is within the lunar maria. Our data compare favorably with previous studies where such data exist. We also find that regolith depth correlates well with density of large craters (>20 km diameter). This result is consistent with the gradual formation of regolith by rock fracture during impact events.     

Compositional and temporal investigation of exposed lunar basalts in the Mare Imbrium region

This paper presents an updated stratigraphical and compositional study of the exposed maria within the Imbrium basin on the Moon. Clementine multispectral data were employed to derive TiO₂ and FeO wt% abundance estimates of potentially distinct basaltic flows. Additionally, NASA Lunar Orbiter images were used to estimate flow ages using crater count statistics. Mare Imbrium shows evidence of a complex suite of low to high-Ti basaltic lava units infilling the basin over an 800 million year timescale. More than a third (37%) of identified mare basalts were found to contain 1-3 wt% TiO₂. Two other major mare lithological units (representing about 25% of the surface each) show TiO₂ values between 3-5 and 7-9 wt%. The dominant fraction (55%) of the sampled maria contain FeO between 16 and 18 wt%, followed by 27% of maria having 18-20 wt% and the remaining 18%, 14-16 wt% FeO. A crater frequency count (for diameters >500 m) shows that in three quarters of the sampled mare crater counts range between 3.5 and 5.5×¹⁰⁻² per km², which translates, according to a lunar cratering model chronology, into estimated emplacement ages between ∼3.3 and 2.5 Ga. A compositional convergence trend between the variations of iron and titanium oxides was identified, in particular for materials with TiO₂ and FeO content broadly above 5 and 17 wt%, respectively, suggesting a related petrogenesis and evolution. According to these findings, three major periods of mare infill are exposed in the Imbrium basin; despite each period showing a range of basaltic compositions (classified according to their TiO₂ content), it is apparent that, at least within these local geological settings, the igneous petrogenesis generally evolved through time towards more TiO₂- and FeO-rich melts.     

Bias-corrected population, size distribution, and impact hazard for the near-Earth objects

Utilizing the largest available data sets for the observed taxonomic (Binzel et al., 2004, Icarus 170, 259-294) and albedo (Delbo et al., 2003, Icarus 166, 116-130) distributions of the near-Earth object population, we model the bias-corrected population. Diameter-limited fractional abundances of the taxonomic complexes are A-0.2%; C-10%, D-17%, O-0.5%, Q-14%, R-0.1%, S-22%, U-0.4%, V-1%, X-34%. In a diameter-limited sample, ∼30% of the NEO population has jovian Tisserand parameter less than 3, where the D-types and X-types dominate. The large contribution from the X-types is surprising and highlights the need to better understand this group with more albedo measurements. Combining the C, D, and X complexes into a “dark” group and the others into a “bright” group yields a debiased dark-to-bright ratio of ∼1.6. Overall, the bias-corrected mean albedo for the NEO population is 0.14±0.02, for which an H magnitude of 17.8±0.1 translates to a diameter of 1 km, in close agreement with Morbidelli et al. (2002, Icarus 158 (2), 329-342). Coupling this bias corrected taxonomic and albedo model with the H magnitude dependent size distribution of (Stuart, 2001, Science 294, 1691-1693) yields a diameter distribution with 1090±180 NEOs with diameters larger than 1 km. As of 2004 June, the Spaceguard Survey has discovered 56% of the NEOs larger than 1 km. Using our size distribution model, and orbital distribution of (Stuart, 2001, Science 294, 1691-1693) we calculate the frequency of impacts into the Earth and the Moon. Globally destructive collisions (∼10²¹ J) of asteroids 1 km or larger strike the Earth once every 0.60±0.1 Myr on average. Regionally destructive collisions with impact energy greater than 4×10¹⁸ J (∼200 m diameter) strike the Earth every 56,000±6000 yr. Collisions in the range of the Tunguska event (4-8×10¹⁶ J) occur every 2000-3000 yr. These values represent the average time between randomly spaced impacts; actual impacts could occur more or less closely spaced solely by chance. As a verification of these impact rates, the crater production function of Shoemaker et al. (1990, Geological Society of American Special Paper 247) has been updated by combining this new population model with a crater formation model to find that the observed crater production function on both the Earth and Moon agrees with the rate of crater production expected from the current population of NEOs.     

Permeability of JSC-1A: A lunar soil simulant

The permeability of lunar soil simulant, JSC-1A, is measured over a range of bulk densities from 1550 to 2000 kg m⁻³. The corresponding viscous flow permeability is 1 × 10⁻¹² m² to 6.1 × 10⁻¹² m² for this bulk density range. Implications of these values on the contamination of regolith by rockets, on barrier/enhancement to bulk flow of ice, and on cratering are discussed. Although the particle size and shape distribution of the JSC-1A are extremely wide, the permeability measurements agree surprisingly well with the Carman-Kozeny equation. The results provide evidence that the Carman-Kozeny model could be applicable to other naturally occurring soils if effective soil properties are considered.     

Photometric anomalies of the lunar surface studied with SMART-1 AMIE data

We present new results from the mapping of lunar photometric function parameters using images acquired by the spacecraft SMART-1 (European Space Agency). The source data for selected lunar areas imaged by the AMIE camera of SMART-1 and the data processing are described. We interpret the behavior of photometric function in terms of lunar regolith properties. Our study reveals photometric anomalies on both small (sub-kilometer) and large (tens of kilometers) scales. We found the regolith mesoscale roughness of lunar swirls to be similar in Mare Marginis, Mare Ingenii, and the surrounding terrains. Unique photometric properties related to peculiarities of the millimeter-scale regolith structure for the Reiner Gamma swirl are confirmed. We identified several impact craters of subkilometer sizes as the source of photometric anomalies created by an increase in mesoscale roughness within the proximal crater ejecta zones. The extended ray systems reveal differences in the photometric properties between proximal and distant ejecta blankets. Basaltic lava flows within Mare Imbrium and Oceanus Procellarum indicate higher regolith porosity for the redder soils due to differences in the chemical composition of lavas.     

Precession of the lunar core

Goldreich (Goldreich, P. [1967]. J. Geophys. Res. 72, 3135) showed that a lunar core of low viscosity would not precess with the mantle. We show that this is also the case for much of lunar history. But when the Moon was close to the Earth, the Moon’s core was forced to follow closely the precessing mantle, in that the rotation axis of the core remained nearly aligned with the symmetry axis of the mantle. The transition from locked to unlocked core precession occurred between 26.0 and 29.0 Earth radii, thus it is likely that the lunar core did not follow the mantle during the Cassini transition. Dwyer and Stevenson (Dwyer, C.A., Stevenson, D.J. [2005]. An Early Nutation-Driven Lunar Dynamo. AGU Fall Meeting Abstracts GP42A-06) suggested that the lunar dynamo needs mechanical stirring to power it. The stirring is caused by the lack of locked precession of the lunar core. So, we do not expect a lunar dynamo powered by mechanical stirring when the Moon was closer to the Earth than 26.0-29.0 Earth radii. A lunar dynamo powered by mechanical stirring might have been strongest near the Cassini transition.     

The origin of lunar crater rays

Lunar rays are filamentous, high-albedo deposits occurring radial or subradial to impact craters. The nature and origin of lunar rays have long been the subjects of major controversies. We have determined the origin of selected lunar ray segments utilizing Earth-based spectral and radar data as well as FeO, TiO₂, and optical maturity maps produced from Clementine UVVIS images. These include rays associated with Tycho, Olbers A, Lichtenberg, and the Messier crater complex. It was found that lunar rays are bright because of compositional contrast with the surrounding terrain, the presence of immature material, or some combination of the two. Mature “compositional” rays such as those exhibited by Lichtenberg crater, are due entirely to the contrast in albedo between ray material containing highlands-rich primary ejecta and the adjacent dark mare surfaces. “Immaturity” rays are bright due to the presence of fresh, high-albedo material. This fresh debris was produced by one or more of the following: (1) the emplacement of immature primary ejecta, (2) the deposition of immature local material from secondary craters, (3) the action of debris surges downrange of secondary clusters, and (4) the presence of immature interior walls of secondary impact craters. Both composition and state-of-maturity play a role in producing a third (“combination”) class of lunar rays. The working distinction between the Eratosthenian and Copernican Systems is that Copernican craters still have visible rays whereas Eratosthenian-aged craters do not. Compositional rays can persist far longer than 1.1 Ga, the currently accepted age of the Copernican-Eratosthenian boundary. Hence, the mere presence of rays is not a reliable indication of crater age. The optical maturity parameter should be used to define the Copernican-Eratosthenian boundary. The time required for an immature surface to reach the optical maturity index saturation point could be defined as the Copernican Period.     

The surficial nature of lunar swirls as revealed by the Mini-RF instrument

Lunar swirls are optically bright, sinuous albedo features found on the Moon. The Mini-RF synthetic aperture radar on the Lunar Reconnaissance Orbiter has provided a comprehensive set of X- and S-Band radar images of these enigmatic features, including the first radar observations of swirls on the farside of the Moon. A few general remarks can be made about the nature of the lunar swirls from this data set. First, the average radar properties of lunar swirls are identical to nearby non-swirl regions, in both total radar backscatter and circular polarization ratio (CPR). This implies that average centimeter-scale roughness and composition within the high-albedo portions of the swirls do not differ appreciably from the surroundings, and that the high optical reflectance of the swirls is related to a very thin surface phenomenon (less than several decimeters thick) not observable with X- or S-Band radar. Secondly, bright swirl material appears to be stratigraphically younger than a newly discovered impact melt flow at Gerasimovich D. This observation indicates that the swirls are capable of forming over timescales less than the age of the crater. The Mini-RF data set also provides clues to the origin of the lunar swirls. In at least one case, the presence of an enhanced crustal magnetic field appears to be responsible for the preservation of a high-albedo ejecta blanket around an otherwise degraded crater, Descartes C. The degree of degradation of Descartes C suggests it should not be optically bright, yet it is. This implies that the enhanced albedo is related to its location within a magnetic anomaly, and hence supports an origin hypothesis that invokes interaction between the solar wind and the magnetic anomaly.     

Was there ever a Terminal Lunar Cataclysm?: With lunar viscosity arguments

About 30 years ago there was a suggestion by several able scientists at the California Institute of Technology that the Moon had undergone a Terminal Lunar Cataclysm. This meant that most of the early impact cratering had been concentrated strongly at about the time of formation of the Imbrium basin. This solution was discussed in many papers and the idea of a cataclysm gradually faded away. In about 1990 it was again revived by several scientists. The idea of a Terminal Lunar Cataclysm at about the time the Imbrium basin was formed was advanced albeit in a somewhat different manner. The present paper has been written to analyze the various observations and interpretations that have been advanced to permit a cataclysm. It is concluded that the three main proposals, which, if correct, would have permitted a cataclysm to have occurred, are each faulty and not consistent with such a cataclysm. To demonstrate this conclusion it was necessary to determine absolute ages of various lunar features. This meant, in part, determinations of the existence and nature of lunar crustal viscosity consistent with times of formation of six lunar basins. The results of such studies yielded an internally consistent model which requires a long period from the original formation of the Moon at about 4.5 byr to a time slightly earlier than that of the formation of the Imbrium basin at about 3.84 byr. On this model there is no indication of a clustering of events and it is concluded that a Terminal Lunar Cataclysm never occurred.     

Global mapping of lunar crustal magnetic fields by Lunar Prospector

The Lunar Prospector Electron Reflectometer has obtained the first global map of lunar crustal magnetic fields, revealing that the effects of basin-forming impacts dominate the large-scale distribution of remanent magnetic fields on the Moon. The weakest surface magnetic fields (<0.2 nT) are found within two of the largest and most recent impact basins, Orientale and Imbrium. Conversely, the largest concentrations of strong surface fields (>40 nT) are diametrically opposite to these same basins. This pattern is present though less pronounced for several other post-Nectarian impact basins larger than 500 km in diameter. The reduced strength and clarity of the pattern for older basins may be attributed to: (1) demagnetization from many smaller impacts, which erases antipodal magnetic signatures over time, (2) superposition effects from other large impacts, and (3) variation in the strength of the ambient magnetizing field. The absence of fringing fields stronger than 1 nT around the perimeter of the Imbrium basin or associated with craters within the basin implies that any uniform magnetization of the impact melt must be weaker than ∼¹⁰⁻⁶ G cm³ g⁻¹. This limits the strength of any steady ambient magnetic field to no more than ∼0.1 Oe at the lunar surface while the basin cooled for tens of millions of years following the Imbrium impact 3.8 billion years ago.     

The early martian evolution—Constraints from basin formation ages

Impact basin formation ages give insight into the early evolution of a planet. The martian basins Hellas, Isidis and Argyre provide an important time-marker for the cessation of the magnetic dynamo and the crustal thickness distribution, both established before 4 Ga ago. No martian surfaces are older than 4.15 Ga based on crater count statistics, and all are younger than the oldest lunar ones. I show that the heavy bombardment period on the Moon and Mars evolved similarly, but endogenic processes have removed the oldest martian basin record. The basin-forming projectile population appears to be different from the impactor population observed today in the inner Solar System. It is yet uncertain whether the heavy bombardment period is cataclysmic or characterized by the decaying flux of planetary formation.     

Identification of the lunar flash of 1953 with a fresh crater on the moon’s surface

A 1953 telescopic photograph of a flash on the Moon is the only unequivocal record of the rare crash of an asteroid-sized body onto the lunar surface. We estimate that this event would create an impact feature up to several km in size and that the diameter of the impacting body would be about 20 m. Such an event would cause regional devastation if it occurred on Earth. Although not detectable with ground- based telescopes, the lunar crater should be visible in space-based images of the Moon. A search of images from the Clementine mission reveals an ∼1.5-km high-albedo, blue, fresh-appearing crater with an associated ejecta blanket at the location of the flash. The identification of this crater offers an opportunity to investigate subsurface unaltered lunar soils.     

Individual lava flow thicknesses in Oceanus Procellarum and Mare Serenitatis determined from Clementine multispectral data

We use multispectral reflectance data from the lunar Clementine mission to investigate the impact ejecta deposits of simple craters in two separate lunar mare basalt regions, one in Oceanus Procellarum and one in Mare Serenitatis. Over 100 impact craters are studied, and for a number of these we observe differences between the TiO₂ (and FeO) contents of their ejecta deposits and the lava flow units in which they are located. We demonstrate that, in the majority of cases, these differences cannot plausibly be attributed to uncorrected maturity effects. These observations, coupled with morphometric crater relationships that provide maximum crater excavation depths, allow the investigation of sub-surface lava flow stratigraphy. We provide estimated average thicknesses for a number of lava flow units in the two study regions, ranging from ∼80 m to ∼600 m. In the case of the Serenitatis study area, our results are consistent with the presence of sub-surface horizons inferred from recent radar sounding measurements from the JAXA Kaguya spacecraft. The average lava flow thicknesses we obtain are used to make estimates of the average flux of volcanic material in these regions. These are in broad agreement with previous studies, suggesting that the variation in mare basalt types we observe with depth is similar to the lateral variations identified at the surface.     

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

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., 2007. 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., 1990. EOS 71, 313, 322-323] and Cohen et al. [Cohen, B.A., Swindle, T.D., Kring, D.A., 2000. Science 290, 1754-1756] 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.