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Planetary and Space Science 74 (2012) 179 -193

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Planetary and Space Science
journa l h o m e p ag e: www. e lsevier .com/locate/pss

The present-day flux of large meteoroids on the lunar surface--A synthesis of models and observational techniques
J. Oberst a,b,n, A. Christou c, R. Suggs d, D. Moser e, I.J. Daubar f, A.S. McEwen f, M. Burchell g, ? T. Kawamura h, H. Hiesinger i, K. Wunnemann j, R. Wagner a, M.S. Robinson k
a b c d e f g h i j k

DLR Institute of Planetary Research, Rutherfordstr. 2, 12489 Berlin, Germany Technical University Berlin, Straïe des 17, Juni 135, 10623 Berlin, Germany Armagh Observatory, College Hill, Armagh BT61 9DG, UK NASA/MSFC/EV44, USA MITS Dynetics/EV44, USA Lunar and Planetary Lab, University of Arizona, Tucson, AZ 85721, USA School of Physical Sciences, University of Kent, Canterbury, Kent CT2 7NH, UK ISAS/JAXA, 3-1-1 Yoshinodai, Chuo, Sagamihara, Kanagawa 252-5210, Japan ? ? ? ? Institut fur Planetologie, Westfalische Wilhelms-Universitat, Wilhelm-Klemm-Str. 10, 48149 Munster, Germany ? Museum fur Naturkunde, Leibniz Institute for Research on Evolution and Biodiversity at the Humboldt University Berlin, Invalidenstr. 43, 10115 Berlin, Germany School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287, USA

article info
Article history: Received 2 March 2012 Accepted 5 October 2012 Available online 6 November 2012 Keywords: Moon Meteroids Observation techniques Models

abstract
Monitoring the lunar surface for impacts is a highly rewarding approach to study small asteroids and large meteoroids encountering the Earth-Moon System. The various effects of meteoroids impacting the Moon are described and results from different detection and study techniques are compared. While the traditional statistics of impact craters allow us to determine the cumulative meteoroid flux on the lunar surface, the recent successful identification of fresh craters in orbital imagery has the potential to directly measure the cratering rate of today. Time-resolved recordings, e.g., seismic data of impacts and impact flash detections clearly demonstrate variations of the impact flux during the lunar day. From the temporal/spatial distribution of impact events, constraints can be obtained on the meteoroid approach trajectories and velocities. The current monitoring allows us to identify temporal clustering of impacts and to study the different meteoroid showers encountering the Earth-Moon system. Though observational biases and deficiencies in our knowledge of the scaling laws are severe, there appears to be an order-of-magnitude agreement in the observed flux within the error limits. Selenographic asymmetries in the impact flux (e.g., for equatorial vs. polar areas) have been predicted. An excess of impacts on the lunar leading hemisphere can be demonstrated in current data. We expect that future missions will allow simultaneous detections of seismic events and impact flashes. The known locations and times of the flashes will allow us to constrain the seismic solutions. While the numbers of flash detections are still limited, coordinated world-wide observations hold great potential for exploiting this observation technique. The potential for identification of fresh craters in high-resolution orbital image data has just barely been tapped, but should improve significantly with the LRO extended mission. & 2012 Elsevier Ltd. All rights reserved.

1. Introduction The surface of the Moon is impacted by objects ranging in size from submicron dust to large comets and asteroids. Its large target area allows us to study these ``meteoroids'' and the variations of their flux in time and space. Lunar impacts are also used to address well-known key issues in planetary science. Impact craters and their

n Corresponding author at: DLR Institute of Planetary Research, Rutherfordstr. 2, D-12489 Berlin, Germany. Tel.: ? 49 30 67055 336. E-mail address: Juergen.Oberst@dlr.de (J. Oberst).

ejecta represent ``windows'' into the crust. Studies of crater morphology provide information on the stratigraphy and physical properties of the regolith and crust. Impact statistics are a prime tool used to derive the ages of planetary surfaces. Seismic waves generated by impacts may act as sounding tools of the lunar interior. As the meteoroids impact the lunar surface, their kinetic energy is partitioned into the excavation of craters, the production of plumes associated with a flash of light, and the generation of seismic waves that propagate through the Lunar interior. Different observational techniques are used to examine different effects of the impact process, but the inferences made on the source parameters (e.g., impactor population, energy conversion

0032-0633/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.pss.2012.10.005


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efficiencies) are constrained by the fact that the source process is one and the same. This paper is the distillation of a workshop that brought together the different fields of meteor astronomy, hypervelocity impact physics, dust exosphere modeling, cratering, planetary interior modeling, and space instrumentation under the umbrella of the impact process. It reviews the current state-of the art on the study, both observational and theoretical, of the different effects of the impact phenomenon; highlights areas of investigation, such as the observations of impact flashes and the counting of new small craters on the Moon, where a significant volume of new results is becoming available; and quantifies the mutual consistency of inferences made on the current size distribution of impactors and their resulting craters. Finally it identifies areas, actions and events of high interdisciplinary benefit to advance the field.

2. The impactor population The impactor population in the Earth Moon system is traditionally being monitored by telescopic observations of Near-Earth Objects (NEOs) ( 4 10 m) as well as by observations of the smaller meteoroids ( o 10 m) entering the Earth's atmosphere. 2.1. Near-earth objects Since the discovery of the first near-Earth asteroid over a century ago, the population has grown tremendously allowing statistical studies to be made of their physical and dynamical properties. These, in turn, point to likely scenarios of their origin and evolution. At the time of writing, the Minor Planet Centre (http:// www.minorplanetcenter.net) lists approximately 8000 known near Earth objects (NEOs; asteroids and comets), most of which were discovered over the past decade by the dedicated surveys such as LINEAR or Spacewatch. Bottke et al. (2002) estimated that the NEO population contains $ 960 objects with absolute magnitude H o 18 (1 km across or larger; 1200 discovered to-date) and 24,500 objects with H o 22 (a few hundred m across or larger). McMillan et al. (2010) used Spacewatch survey data to estimate that about a million NEOs with H o 26 (tens of meters across or larger) exist. The number of near-Earth asteroids (NEAs) was recently revised slightly downward by the Wide-field Infrared Survey Explorer (WISE) to 981 7 19 larger than 1 km and 20,500 7 3000 larger than 100 m (Mainzer et al., 2011). 2.2. Large meteoroids Observations of bright meteors in the Earth's atmosphere provide basic context information on the speed, mass- and size distribution, bulk properties, and flux profile of large meteoroids, which for the purposes of this paper are defined as those of mass higher than 0.1 kg. The overall meteor flux has to-date been investigated by: (i) Revelle (2001), based on infrasonic wave data from the Air Force Technical Applications Centre (AFTAC) network, (ii) Brown et al. (2002), based on observations by US Department of Defence/ Department of Energy (DoD/DoE) satellites in geostationary orbit, (iii) Halliday et al. (1996), derived from fireball data (here we discuss their ``asteroidal'' subgroup) gathered by the Meteor Orbit and Recovery (MORP) Project, and others. Meteoroid engineering models have been developed to assess their effects and associated risk to spacecraft (e.g., McNamara et al. 2004). Meteoroids are not randomly distributed in space, but often travel in ``swarms'' or ``streams.'' In streams, the meteoroids generally travel dispersed along a common orbital path; i.e., the

orbital elements a, e, i, O, and o (semimajor axis, eccentricity, inclination, longitude of the ascending node, and argument of periapsis) of the meteoroids are similar, while their sixth orbital element n, the true anomalies, are randomly distributed along the orbit. Meteoroid swarms, on the other hand, show significant clustering along the orbital path; i.e. the true anomalies are also similar. Interestingly, the first definite evidence for the existence of swarms of large meteoroids came from the Apollo seismic soundings (Duennebier et al., 1976). Based on observations of comet 2 P/Encke, Asher and Izumi (1998) proposed that such swarms are the result of resonant trapping, resulting in an increase of the abundance of fireballs within the Taurid shower during certain years (Dubietis and Arlt, 2006). The survival time of streams is generally on the order of 103 to 105 years (e.g., Jones, 1986). Thus, their existence indicates that not enough time has elapsed to randomize the meteoroids orbits since they separated from their parents. Often, these parent bodies can still be found in orbits very similar to those of the observed meteoroids.

3. Predictions for the moon 3.1. General considerations The lunar surface comprises an area of approx. 3.8 Ò 107 km2, much larger than coverage by all terrestrial ``fireball'' camera systems combined. The surface of the Moon is a target for showers with southern hemisphere radiant, for which terrestrial observations are scarce. Depending on observation techniques, time-varying biases can be avoided or corrected. The probability for an impact at a given location on the Moon will depend on velocities and approach orbits of the meteoroids. As the meteoroid flux is far from uniform, the relationship is intricate. Earth and Moon jointly move about the sun at the considerable speed of 30 km/s. Owing to the Lunar rotation (synodic rotation: 29.5 days), the numbers of meteoroid encounters and the relative encounter speeds of the meteoroids will vary significantly over the lunar surface during the lunar day. While this effect should clearly be detectable in time-resolved impact observations, owing to the Earth and Moon's rotation, the effect will even out, however, over time and will not be revealed in the cratering record. In contrast, with the Moon moving about the Earth at a speed of 1 km/s, we expect an additional smaller hemispheric variation of the impact flux during the lunar day. As the Moon is locked in its orbit, this effect may become visible in a relative surplus or deficit of craters on the lunar leading or trailing hemisphere. 3.2. Gravitational focusing The flux of meteoroids in the Earth-Moon system is affected by gravitational focusing and acceleration of the projectiles when approaching the Earth-Moon system. The former increases the effective target area of the Earth or the Moon from R to R* according to qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ð Ð ÑÑ ?1î Rn Ì R 1 ? 2g = v2 R 1 while the latter accelerates the meteoroid from vN to vr according to v2 Ì v2 ? 2GM =r r 1 ?2î

Here, R and R* are the actual and effective radii of the target body respectively, vr is the velocity of a meteoroid at distance r from the body of mass M, vN is the velocity of the meteoroid at infinity and G is the gravitational constant. R* and vN are sometimes called the ``impact radius'' and the ``geocentric'' velocity of the


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meteoroid, respectively. Note that high values of vN result in vr E vN, R* E R, i.e. these effects are more pronounced for slowmoving objects. At typical speeds of 20 km s Ð 1 for the Earth and 17 km s Ð 1 for the Moon the above formulas yield. Dv Ì vr Ð vN $ 3 km s Ð 1, R*/R $ 1.14 and v $ 0.15 km s Ð 1, * R /R $ 1.01 with parameter values taken from Section 4.1. Clearly, B the effect is significant for the Earth but negligible for the Moon . The Earth's gravity field will affect the orbits of impactors to the Moon and thus change the impact conditions. Previous studies point out that such gravitational effect will focus more impactors on the lunar nearside and create nearside/farside asymmetry (e.g., Wiesel, 1971). On the other hand, Bandermann and Singer (1973) claim that whether the Earth gravity will act as a lens or a shield depends on the encounter velocities of the impactors and the distance between the Earth and the Moon. Recent numerical simulation using the present Earth-Moon condition and debiased NEO model conclude that such nearside/ farside asymmetry is negligible (Gallant et al., 2009; Le Feuvre and Wieczorek, 2011). Le Feuvre and Wieczorek found $ 0.1% enhancement for the nearside which is small enough that it does not affect the global cratering. While the nearside/farside asymmetry is insignificantly small with present setting, Gallant et al. (2009) point out that, in the very distant past, the Earth could have served as a gravitational shield for the Moon. They concluded that for Earth-Moon distance less than 30 Earth radii, shielding will reduce the nearside crater production by a few percent. 3.3. Polar vs. equatorial flux Theoretical and numerical studies predict the existence of flux asymmetries on the Moon (Morota and Furumoto, 2003; Wieczorek and Le Feuvre, 2009; Gallant et al., 2009; Ito and Malhotra, 2010), which can affect crater chronology (Morota et al., 2005; Le Feuvre and Wieczorek, 2008). Larger meteoroids typically approach from low inclination heliocentric orbits, resulting in the flux at low latitudes exceeding that at high latitudes. The heliocentric velocity of the Moon must be taken into account to reveal the meteoroids radiant positions in the planet's equatorial coordinate system. Recent numerical simulations predict such latitudinal variation of the cratering rate (Le Feuvre and Wieczorek, 2008; Gallant et al., 2009). Le Feuvre and Wieczorek (2008) used a model population of impactors to estimate a polar-to-equator ratio of 0.90. The primary cause of this latitudinal asymmetry was found to be the significant number of impactors with low inclination. An independent study by Gallant et al. (2009) also predicts that fluxes at low latitudes (0-301) are higher by 10% compared to high latitude (60-901). These authors also studied the effect of impact velocity and concluded that the asymmetry is higher for the high impact velocity. 3.4. Leading/trailing edge effects Being tidally locked, the synchronous rotation state causes the leading side of the Moon to intercept more impactors than the trailing side. In addition, the synchronous rotation causes a bias in relative impact velocity of surrounding impactors in that head-on collisions at the leading side will generally occur at higher impact velocities compared to the trailing side. As crater size increases with impact velocity or impact energy, such difference in relative impact velocity leads to an apparent increase for numbers of craters for given size on the leading side. Theoretical modeling implies that the degree of the asymmetry depends on the velocity of the impactors around the satellite and the orbital velocity of the satellite (Wood, 1973; Shoemaker and Wolfe, 1982; Horedt

and Neukum, 1984; Zahnle et al., 1998, 2001). A lower encounter velocity of the impactors and a higher orbital velocity of the satellite lead to a larger leading-trailing asymmetry. In the case of the Moon this asymmetry was expected to be small because of the low orbital velocity ( $ 1 km/s). Based on analytical studies, the apex/antapex ratio of cratering rates is predicted to be 1-2, while those of Galilean satellites are estimated to be 5-50. Recent numerical simulations of candidate impactors drawn from a debiased Near-Earth Object (NEO) model also show a small asymmetry of $ 1.3 for the Moon (Le Feuvre and Wieczorek, 2008; Gallant et al., 2009; Ito and Malhotra, 2010). Such an asymmetry was previously thought to be undetectable or easily obscured by the age variations across the lunar surface. 3.5. Models of the impact process When a cosmic object strikes the moon at high velocity, a crater is formed. A small portion of the object's pre-impact kinetic energy is released as seismic energy that propagates through the lunar interior and can be detected by seismic stations. Also, upon impact, a light flash can be recorded by appropriate camera stations either on Earth or on other spacecraft 3.5.1. Crater scaling laws As a first-order approximation, the size of the resulting crater depends on the kinetic energy of the projectile; however, properties of the impacting object (rock, iron or ice composition, impact velocity and angle) and the target (strength, porosity, gravity, and material composition) also play an important role. As with other rocky solar system bodies, lunar craters fall into classes, which depend on size (e.g., Dence, 1965; Melosh, 1989). There are simple bowl-shaped craters (diameters o 15 km, Pike, 1977), larger more complex craters with central peaks or rings and finally large basins (e.g., see Spudis, 1993). The process of crater formation has been studied in detail among field observations and experimental work in particular by numerical modeling (e.g., O'Keefe and Ahrens, 1993; Melosh and Ivanov, 1999; Ivanov, 2005; Collins et al., 2008a; Senft and Stewart, 2008). The impact generates an excavation flow that produces a cavity, growth stops when it is no longer possible to displace further material against its own cohesive strength (strength dominated regime, see Holsapple, 1993 or O'Keefe and Ahrens, 1993 ) or weight (gravity dominated). On the Moon, small craters ( o 200 m) are strength dominated (Melosh, 1989) representing almost perfectly bowl-shaped depressions. Simple craters between 200 m and 15 km on the Moon are controlled by gravity (Pike, 1977; Melosh, 1989); however, the buoyant forces are not strong enough to cause a collapse of the entire cavity. For larger craters, the initial transient crater is modified to form the final, observed crater. Inward slumping of the oversteepened crater wall results in the formation of a breccia lens inside the crater and, thus, a slight increase in crater diameter and decrease of crater depth. The complex morphology of craters 4 15 km is the result of a much more comprehensive gravity-driven collapse (Pike, 1977; Melosh, 1989) that first starts at the deepest point of the transient crater. The crater floor rises upwards while the crater wall sags inwards and forms a terraced rim zone. The mass movements accompanying the crater collapse yield a significant increase of the crater diameter and a decrease of crater depth due to structural uplift in comparison to the shape of the transient crater. Due to the different degree of collapse at strength, simple, and complex craters and involved enlargement of the transient crater, the size of the final crater structure is an inappropriate measure of the size of an event (Holsapple, 1993).


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Consequently, quantifying the size of an impact event, or more precisely the kinetic energy of the projectile required to produce a crater of a given size, has to be carried out in two steps. (I) For the larger, complex craters estimate the size of the transient crater from the morphology and size of the final crater (Croft, 1985; McKinnon and Schenk,1985; Holsapple, 1993). (II) scaling laws are used to calculate the kinetic energy and/or momentum of the impactor (in terms of velocity, mass, size, and angle of incidence) required to excavate the estimated transient crater size (Schmidt and Housen, 1987; Holsapple, 1993; Housen and Holsapple, 2003, 2007). Because the majority of impacts occur at an oblique angle of incidence it is common when predicting crater size to replace in any scaling relationship, the impact velocity U by its vertical component (Chapman and McKinnon, 1986): numerical models have shown that this assumption holds true for specific cases (Elbeshausen et al., 2009). However, if there are greater uncertainties in the problem this is often neglected altogether.

In principle this can all be tested using man-made impacts on the Moon. Gehring and Warnica (1963) predicted that the impacts of spacecraft on the lunar surface would produce observable flashes if in the dark region (i.e. beyond the terminator), but for many years no reliable reports were made. However, in 2006 the Smart 1 spacecraft struck the Moon and produced an observed flash (Veillet and Foing, 2007). Unfortunately this flash saturated the detector, so its intensity and thus a value of Z were not obtained. More recently, the LCROSS mission to the Moon included a deliberate impact on the lunar surface at 2.5 km s Ð 1 by a Centaur upper stage (Schultz et al., 2010). A second spacecraft was closely following behind the impactor and observed the impact. No signal was observed in the visible spectrum even though the mission team had anticipated one with an expected Z of 10 Ð 5-10 Ð 6 (see Schultz et al., 2010 and references therein). A flash was however observed in the near infrared and the impact did produce a vapor cloud whose expansion was compatible with a temperature of $ 1000 K (Gladstone et al., 2010).

3.5.2. Impact flash simulations To turn the observed lunar light flashes into a proper flux of impactors, requires converting the observed luminous energy into an impact energy. This then allows an impactor mass to be found if a mean impact speed is assumed. The fraction of impact kinetic energy, which is emitted as luminous energy is commonly called Z (luminous efficiency). It is not possible to calculate this from first principles, so laboratory experiments have been conducted to determine it. Early laboratory experiments showed that the light energy (E) scaled with impactor mass (m) and speed (v) according to E Ì cmavb, where the constants c, a and b depended on projectile and target materials. This relation for E implies that Z depends on vb Ð 2, i.e. unless b Ì 2 there is no single value of Z. Experiments seem to show that a is equal to 1, or very similar, leaving just the variables c and b to be determined in most experiments. However, extrapolating from the impactor masses of say 10 Ð 16 kg in a typical dust experiment in the laboratory to the masses of particles impacting the Moon with enough energy to produce a light flash detectable at the Earth (i.e. perhaps m scale impactors) involves a significant step, even if c and b are well constrained. Worse, estimates of Z made in various experiments vary. Light gas gun experiments at about 5 km s Ð 1, give Z $ 10 Ð 5 to 10 Ð 4, but experiments over wider speed regimes show not only that Z has a speed dependence of vb Ð 2 as stated, but b ranges from 3.3 to 8.3 depending on the materials involved (see Burchell et al., 2010 for a recent review). Even at a low value of b of 3.65 (suggested by Burchell et al., 1996 for impacts of iron micro-particles onto ice), Z rises from 6 Ò 10 Ð 6 at 2 km s Ð 1, to 1 Ò 10 Ð 4 at 10 km s Ð 1 and 2.4 Ò 10 Ð 3 at 72 km s Ð 1. Given that many of the reported lunar impacts are during various meteor showers, each of which can have very different mean impact speeds, this dependence of Z on impact speed is clearly important. It is also possible to estimate Z by observing lunar impacts and assuming impact speeds and an impactor size distribution. This was done for the Leonid meteor shower of 1999 (Bellot Rubio et al., 2000; Ortiz et al., 2006). Using a similar technique, Moser et al. (2010) determined Z for other showers. The meteor shower (Moser et al., 2010) and various laboratory experiments (Swift et al., 2010) can be combined into a single data set and a fit made to the data--this then permits an estimate of Z over a wide range of impact speeds. Another important aspect of impact light flash, is that the mean temperature of the flash is equivalent to 2000-6000 K (again see Burchell et al., 2010), with the lower temperatures associated with the lowest speed impacts (typically 2000-3000 K at 4-5 km s Ð 1). This suggests that much of the emitted luminous energy will be in the infrared.

4. Detection techniques and results 4.1. Accumulations of craters over time The derivation of ages of geologic units on the lunar and any other planetary surface by their superimposed crater sizefrequency distributions involves two steps: (1) The crater sizefrequency distribution in a mapped geologic unit is measured. The frequency of a specific reference crater diameter or a diameter range in this distribution is a measure for the relative age of the geologic unit: the higher the crater frequency, the higher the age ? of the geologic unit (Opik, 1960; Baldwin, 1964). Standard techniques of measuring crater distributions and representation of results in graphical form for the purpose of relative age dating were established in a workshop of the Crater Analysis Techniques Working Group in Flagstaff in September 1977 (Crater analysis techniques working group, 1979). In a second step (2), crater frequencies are converted into absolute model ages (e.g., BVSP, 1981; Neukum, 1983; Neukum and Ivanov, 1994; Neukum et al., 2001; Hartmann and Ivanov, 2007). The radiometric ages of rock materials collected at the Apollo and Luna landing sites are used to correlate these ages with crater frequencies measured for the geologic units from which the samples were collected. Note that there may be a significant difference between the landscape's age or crater retention age and the radiometric age of the geologic unit. The crater retention age is generally a lower limit on the age of the geologic unit, but may be quite close in the case of craters larger than a few hundred meters diameter on the lunar maria. In the approach by Neukum (1983); Neukum and Ivanov (1994), and Neukum et al. (2001), crater size-frequency distributions measured on mapped geologic units on the lunar surface can be fitted by a polynomial of 11th degree that represents a model of the lunar production distribution. Previously, straight lines with a specific slope in specific diameter ranges had been used to fit crater distributions (e.g., Neukum, 1983; Neukum and Ivanov, 1994, and references therein). Neukum and others derived the lunar production distribution by normalizing crater distributions measured in different diameter ranges and on geologic units of different ages vertically to one another in log N (N: crater frequency), i.e. normalizing all distributions to one age. The authors used this procedure to show that (a) all distributions could be aligned along a continuous curve and, as a consequence, that (b) the shape of the lunar crater production distribution is more or less constant with time, and (c) that lunar crater distributions measured in geologic units of different ages could be fitted by the same 11th degree polynomial (Neukum, 1983;


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Neukum and Ivanov, 1994; Neukum et al., 2001). The lunar production distribution or production function polynomial is used to directly compare the relative age of geologic units by the crater frequencies at a specific reference crater diameter, usually 1 km or 10 km (e.g., Greeley et al., 1993; Hiesinger et al., 2000, 2003; 2010; Wagner et al., 2002, 2010; Morota et al., 2011). The relationship between the crater size-frequency distribution and the properties of the crater-generating projectile population can be made by crater scaling laws (see section above). Neukum and others have shown that the shape of the lunar crater distribution (and also of crater distributions on the terrestrial planets Mars and Mercury) and the size distribution of Main Belt Asteroids (MBA) are remarkably similar, implying that craters on the Moon were primarily created by the impacts of asteroids (Strom and Neukum, 1988; Neukum, 1983; Neukum and Ivanov, 1994; Neukum et al., 2001). Note, however, that the shape of Near Earth Objects (NEO) size distribution was recently shown to be somewhat different than previously believed (Mainzer et al., 2011). Also, the stability of the lunar production function with time is an open question. Neukum (1983); Neukum and Ivanov (1994); Neukum et al. (2001) concluded that the lunar production function is more or less time-invariant and, therefore, that the size distribution of impactors did not change significantly with time. On the other hand, Strom et al. (2005); Head et al. (2010) discussed that the shape of crater distributions changed with time and distinguished between pre-mare and post-mare crater distributions created by different asteroid families. Recently, Marchi et al. (2009); Le Feuvre and Wieczorek (2011) presented and discussed different approaches. Both groups derived model production functions from the size distribution of Main Belt Asteroids (MBA) and Near Earth Objects (NEO) using crater scaling. Marchi and others (2009) and LeFeuvre and Wieczorek (2011) used different orbital distributions for the impactors and different scaling relations for the strength to gravity transition as well as for the porous to non-porous transition in the target material (see LeFeuvre and Wieczorek, 2011, for details). Marchi et al. (2009) found a good fit for MBA-derived crater distributions in the oldest regions (Nectaris basin and older) while crater size distributions in younger regions seem to agree better with a size distribution both by MBAs and NEOs. Marchi et al. (2009) showed that their model production function agreed within less than a factor of 2 with the production function by Neukum and co-workers (e.g., Neukum and Ivanov, 1994; Neukum et al., 2001). LeFeuvre and Wieczorek (2011) found a much better agreement between their model production function and the production function by Neukum (1983) and Neukum and Ivanov (1994) over a wide range of diameters (100 m-300 km) under the assumption of a flux constant for the last $ 3 Ga, with discrepancies between the model production functions being on the order of 20-30% in crater frequency. Cratering chronology models for the Moon can be derived by correlating radiometric and exposure age data of lunar rock and soil samples with crater frequencies measured for geologic units at the landing sites (Neukum, 1983; Neukum and Ivanov, 1994; ? Stoffler and Ryder, 2001; Neukum et al., 2001; Hiesinger et al., 2010). The rate of crater formation (e.g., for reference diameter of 1 km, Fig. 1) over time is represented by (1) a smooth exponential decay during an early period of heavy bombardment until about 3-3.3 Gyr ago and by (2) a more or less constant cratering rate since then in the approach by Neukum (1983); Neukum and Ivanov (1994); Neukum et al. (2001). The disagreement between the radiometric age of the young ray crater Copernicus and its superimposed crater frequency reported by, e.g., Neukum and Ivanov (1994) could recently be corrected by measurements on new LROC image data by Hiesinger et al. (2010) who found an excellent agreement between the model age of a specific ejecta

Fig. 1. The lunar cratering chronology model (Neukum, 1983), based on the correlation between radiometric and exposure ages of rocks returned by the Apollo (Ap11-Ap17) and Luna missions (L-16, L-24) and the crater frequencies of the geologic units were the rock and soil samples were collected. The cumulative crater frequency (Crater analysis techniques working group, 1979) is taken at the reference diameter of 1 km. The chronology function and its coefficients correlating cumulative crater frequency and absolute age are included in the diagram. New counts of geological units on the young bright ray crater Copernicus mapped in images of Lunar Reconnaissance Orbiter (LRO) performed by Hiesinger et al. (2012) revealed a much better correlation between the radiometric age of Copernicus and crater frequency compared to previous measurements.

unit and radiometric ages of Copernicus ejecta material (see also Jaumann et al., this issue). From the described crater chronology, an estimate of the current meteoroid flux can be made. Neukum (1983) estimates that at the current day lunar craters are formed at a rate given by log n Ì ?Ð3îlog D ? 4:88 ?3î

where n is the cumulative number of craters with diameters D or larger (D is measured in meters) occurring on the entire Lunar surface per year (valid for the size range of 1 m o D o 1000 m). The equation predicts, there should be 76 fresh craters with sizes of 10 m or larger on the entire Lunar surface every year, an estimate which has been questioned in some discussions about the role of secondary impacts in the record of crater counts (Shoemaker, 1965; Wilhelms et al., 1978; Bierhaus et al., 2001; Hartmann, 2005; McEwen et al., 2005; McEwen and Bierhaus, 2006; Wells et al., 2010; Robbins and Hynek, 2011; Strom et al., 2011). A direct verification of this elementary relationship appears highly desirable. In the lunar chronology model presented by Marchi et al. ? (2009), the authors used radiometric data by Stoffler and Ryder (2001) to calibrate their model. Their model function is the same as the one used in the Neukum lunar chronology model but with different coefficients, similarily reflecting an early smooth exponential decay in impact rate and a subsequent constant impactor flux (Marchi et al., 2009). Like the two versions of production functions by Neukum and co-workers (1994, 2001) and by Marchi and colleagues, the chronologies agree within less than a factor of 2 (Marchi et al., 2009), with the highest discrepancies in model ages between the two models ocurring for ages younger than $ 3 Ga, while for ages higher than $ 3 Ga the agreement is very good (within an order of 0.05 Ga). Marchi et al. (2009) infer that one of the likely causes for differences in the very young ({1 Ga) ages between the two models could be a non-constant impactor flux which is not described in a chronology equation like the one used by Neukum and Ivanov (1994). Formation of dynamical families in the asteroid belt could have been the case for a recent increase in projectile flux in the last $ 0.4 Ga (Marchi et al., 2009).


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Furthermore, the earliest flux could have been different from the smooth exponential decay suggested by, e.g., Neukum and Ivanov (1994). A clustering in radiometric ages of Apollo rock material at about 3.9 Ga was interpreted as a spike in impact rate at that time, termed the Lunar Terminal Cataclysm or Late Heavy Bombardment (LHB) (Marchi et al., 2009, and references therein; see also Jaumann et al., this issue). A possible LHB impact scenario was recently discussed to have been caused by an orbital migration of the large planets Jupiter and Saturn, a scenario described as the Nice Model (e.g., Gomes et al., 2005). The details of an LHB scenario, e.g., if it was a rather short spike or if it represented a prolonged time of intense bombardment lasting from $ 4.1 Ð 3.7 Ga on the Moon are in discussion (e.g., Bottke et al., 2011). LeFeuvre and Wieczorek (2011) took spatial variabilities of impact and cratering rates across the lunar surface into account in their revised lunar chronology model: (1) A higher proportion of low-inclination impactors associated with higher probabilities of an encounter with the Moon at low inclination causes a variation in cratering rate with latitude; the authors derived a ratio of 0.8 between the pole and the equator. (2) Due to the synchronous rotation of the Moon, the cratering rate also varies with longitude, dependent of the distance to the apex of orbital motion, causing a difference in cratering rate higher by a factor of 1.37 at the apex than at the antapex. The factor is dependent of the Earth-Moon distance and, hence, could have been higher in the past when the Moon was closer to Earth. LeFeuvre and Wieczorek (2011) used ? radiometric ages by Stoffler and Ryder (2001) for calibration, except the data points of the Nectaris basin and Crisium mare materials, and included the updated Copernicus data point by Hiesinger et al. (2010). Like Neukum and Ivanov (1994); Marchi et al. (2009), they combined an exponential and a linear term in their chronology function but with three different coefficients than those used in the two previous studies. Their chronology model is in much better agreement with the Neukum and Ivanov (1994) model than the Marchi et al. (2009) model for the last $ 3 Ga. However, their model favors an extension of a constant impactor flux back to $ 3.5 Ga. The Late Heavy Bombardment and a possible reorientation of the Moon could cause that the chronology model by LeFeuvre and Wieczorek (2011) may be inaccurate for units older than 3.5 Ga therefore the authors suggest to use their model with some caution for old units formed within the first $ 1 Ga of lunar history. 4.2. Present-day cratering rate The Lunar Reconnaissance Orbiter camera (LROC) onboard the LRO spacecraft provided, for the first time, discoveries of fresh impact craters that formed in the intervening 40 years since Apollo (Daubar et al., 2011). Daubar et al. found 5 craters of diameters less than 10 m within a surface area of 5700 km2. 4.2.1. Method We compared Lunar Reconnaissance Orbiter Camera (LROC) (Robinson et al., 2010) Narrow-Angle Camera (NAC) images (0.5-m-1.0-m pixel scale; resolution $ 1.5-3 m) to Apollo orbital Panoramic Camera images (Light, 1972), which are scanned at 200 pixels/mm and have varying (2-30 m) resolutions (http:// apollo.sese.asu.edu/ABOUT_SCANS/index.html). These images span elapsed times between 38 and 41 years, depending on exact image dates. Pairs of overlapping images are identified that share similar lighting geometry. Lower incidence and phase angles are preferred for emphasizing albedo differences rather than topography, which is important because the significant albedo difference between bright, extended ejecta and rays and the surrounding dark regolith aids in identifying fresh craters (e.g., Wilhelms et al., 1987). ``Fresh'' in this

case could still mean 4 105 years old. Therefore, we need an adequate high-resolution photo of the same site before the crater formed in order to verify that it formed in recent decades. We avoid the oblique Apollo images and use those that enable identification of fresh craters Z 1 m diameter from bright ejecta at least 10 m wide. The Apollo images are geometrically distorted using manually selected control points in the USGS Integrated Software for Imagers and Spectrometers (ISIS) software (Anderson et al., 2004), to match the geometry of an overlapping LROC NAC frame. The lack of Apollo Pan camera models prevents full geometric reprojection. The warped Apollo image is then blink-compared to the LROC image at full resolution, and each bright, fresh-looking crater present in the LROC image is searched for in the corresponding area in the Apollo image. The area searched must be estimated to understand the rate of new impacts per year. We do this by subtracting null (areas of no overlapping data) and shadowed pixels (where it would not be possible to detect craters) from the warped Apollo images, reducing the area of the equivalent LROC footprint by that fraction, and then counting valid pixels to measure the area. Use of warped Pan images rather than fully re-projected images results in errors of $ 10%. 4.2.2. Results As of March 2011, we have thus far discovered five new impact craters over 5700 km2 on the Moon that formed within the last $ 40 years (Table 1; Figs. 2 and 3). Of those five, three have central craters too small to be measured in the LROC images. For these, we can place only an upper limit on their diameters. The remaining two are slightly less than 10 m across. A few additional new crater candidates could not be confirmed due to the different lighting conditions in the Apollo and LROC frames. Implications of these results are discussed in Section 5. 4.3. Seismic monitoring The real-time monitoring of lunar impacts provides information on the temporal variations of meteoroid encounter rates. A total of 1744 impacts were recorded on long-period seismic instruments during the operational period (1969-1977) of the Apollo Lunar Seismic Experiment Package (ALSEP) network (Nakamura et al., 1982), which formed roughly a triangle of 1000 km base length on the lunar near side. The lunar seismic impact data benefited from the uninterrupted observation time of the Apollo stations, which provided relatively unbiased meteoroid counts for day and night. The seismically observed meteoroids also covered a large mass range: small ( o 1 kg) meteoroids were detected when they impacted close to one of the seismic stations, while the rare larger impacts could be detected anywhere on the entire lunar surface by all four stations of the network (Oberst and Nakamura, 1987a). Artificial impacts, i.e. impacts by spent spacecraft (Saturn IVBoosters and LEM Upper stages) provided useful calibration events,
Table 1 New lunar craters, their locations and approximate sizes; Asterisks (*) mark two-pixel upper limits on diameter, for unresolved craters. Errors are about 1 pixel or $ 0.5 m. LROC image ID (discovery) 1 2 3 4 5 M M M M M 106855508RE 106855508RE 108971316LE 124253664LE 126636371LE Apollo image ID as15_p_9430 as15_p_9430 as15_p_9527 as15_p_9494 as15_p_9508 Latitude Longitude (E) Crater diameter (m) r 2.6* r 2.6* 9.7 r 1.0* 8.0

26.92 26.48 16.92 13.73 15.68

3.94 3.89 40.50 48.44 44.90


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Fig. 2. (L) Apollo 15 Panoramic Camera (AS15-9527) from August 1971; (R) LROC Narrow-Angle Camera (M108971316L) from September 2009 showing new crater. Apollo image has been warped to match the geometry of the raw LROC image. New impact site is circled in red. Scene is approximately 800 m across.

Fig. 3. Locations of new impact craters (white Xs) shown on Clementine 750 nm map of the Moon. Also shown are locations of known artificial (spacecraft) impacts (red circles) (Whitaker, 1972; Robinson et al., in press; Marshall et al., 2011; Roncoli, 2005; Latham et al., 1973; Lawrence, 2010; Burchell et al., 2010), demonstrating that known artificial impacts are not being mistaken for new, naturally occurring impacts.

as the impacts occurred at known places and time. Also, the impact angles, impact velocities, and masses of the space vehicles were known (Latham et al., 1973).

4.3.1. Overall flux The impact seismic signal observed at one single seismic station typically does not reveal the range of the impact from the station or the magnitude of the event (i.e. the observed amplitude of an impact at some unit distance). Hence, statistical methods had been used to estimate the overall meteoroid flux (Latham et al., 1973; Duennebier et al., 1975), making assumptions regarding the magnitude-frequency distribution of impacts as well as the range distribution of impacts with respect to the seismic stations.

Nevertheless, a few large meteoroid impacts could be located by inversion of seismic wave travel times (Oberst and Nakamura, 1989), From the events, a cumulative flux of objects N(E 4 ES) was made, where ES is the ``source energy'' or the kinetic energy of the impactor. The artificial impacts were used to calibrate the natural impacts, i.e. to derive impact energy from seismic amplitude. The Moon flux was derived as N?ES î Ì 11:38Ð0:99 logE
S

?4î
2

The estimated range of masses of these objects is roughly 10 to $ 103 kg.

4.3.2. Variations during the lunar day While the trajectory of a single meteoroid remains unknown, the temporal/spatial distribution of groups of impacts may provide


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Fig. 4. Typical lunar seismogram and distribution of small ( o 1 kg) and large impacts during the lunar day, revealing the different orbital distributions of two populations (see Oberst and Nakamura, 1987b, for details).

significant constraints on the orbital parameters of the meteoroids. Impact events listed in the Passive Seismic Experiment LongPeriod Event Catalogue (Nakamura et al., 1981) were divided into two subgroups, 511 ``small'' and 416 ``large'' impacts (see Oberst and Nakamura, 1987b for details). The distribution of impact times during the lunar day (Fig. 4) indicates that the two groups represent different meteoroid families with differing orbital distributions. In particular, meteoroids associated with small impacts (roughly estimated to be o 1 kg) appear to be approaching from the apex of the Earth/Moon system (Oberst and Nakamura, 1987a). Using a Monte Carlo approach, predictions for impact detection rates at the Apollo stations from given meteoroid orbital distributions were made (Oberst and Nakamura, 1989). Mass distribution, velocity, and impact angles from the vertical were taken into account. The simulation demonstrated that orbital distributions of small and large meteoroids are different indeed, with large meteoroids moving predominantly in prograde orbits of low inclinations and small meteoroids moving in cometarytype high-inclination or retrograde orbits. 4.3.3. Detection of swarms and streams The observed impact rate is far from random. Several detected impact clusters can readily be linked with meteor showers known from terrestrial observations (Oberst and Nakamura, 1988). From the occurrence of impact clusters in space and time (including their recurrence in different years), correlations could be established with the Perseids, Leonids, and Taurids (Oberst and Nakamura, 1987a). The analyses of impacts associated with known showers provide important clues as to what types and velocities of meteoroids are involved among the seismically observed lunar impacts. Obviously, showers of high encounter velocities are favored among the detections. One remarkably strong meteoroid swarm was detected in June 1975 (Duennebier et al., 1976), thought to be associated with the Taurid complex. 4.4. Impact flash detections Observations during the 1999 Leonid meteor storms provided the first video evidence of meteoroid impact flashes on the Moon (Dunham et al., 2000, Ortiz et al., 2000, 2002). While several observatories worldwide have engaged in impact flash observations since, NASA's Marshall Space Flight Center (beginning routine

Fig. 5. Field of view of telescope/video camera system.

lunar impact monitoring in June of 2006, Cooke et al., 2006, 2007) has obtained by far the largest impact flash data set. Contrary to the seismic detections, which require lunar surface equipment, telescopic observations can readily be made from the ground. Fig. 5

4.4.1. Observations and analyses Observations (at NASA Marshall SFC) are made with sensitive video cameras attached to telescopes in the 0.25-0.5 m diameter range (Fig. 6). The night portion of the Moon is observed when the lunar phase is between 10% and 50% illumination (thin crescent to quarter phase; Fig. 5). Moon phases smaller than 10% result in such low elevations of the Moon at twilight that the observation time is very short. Phases greater than quarter have too much glare from the sunlit Moon which affects sensitivity and limiting flash magnitude. These phase limits result in a maximum of 5 evening and 5 morning observation periods per month.


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Fig. 6. NASA MSFC Automated Lunar and Meteor Observatory stations.

Earthshine makes some of the surface features visible which allows determination of approximate impact flash location relative to surface features. The field-of-view (FOV) used by our program is approximately 20 arcmin in the horizontal video axis. The limb of the Moon is placed near one edge of the FOV with the horizontal axis parallel to the central meridian of the Moon. This results in approximately 3.8 million square km or 12% of the lunar surface in the FOV. Roughly 12th magnitude stars are visible in the video with the 1/30 s exposures and video rate readout. The initial observations were made with a 10 in. (0.25 m) f4.5 Newtonian reflector and video camera based on the Sony HAD EXview CCD (StellaCam EX). We added a 14 in. (0.35 m) f8 telescope with focal reducer and the same type of camera in June 2006. The operation of two telescopes allow unambiguous rejection of cosmic ray flashes in the detector by requiring confirmation between both instruments. Widely spaced (100 km) telescopes also reject sun-glints from geosynchronous orbital debris. All telescopes involved have focal reduction optics adjusted to give the same FOV. The Watec 902H2 Ultimate video camera, also based on the Sony EXView HAD chip, is the sensor system of choice. The analog video is fed to a Digital 8 recording deck where it is digitized and passed to a PC via FireWire and recorded to hard disk. The LunarScan software (Gural, 2007) is used to detect the impact flashes in the recorded video and custom software (Swift et al., 2007) is used to perform photometric calibration of the flashes using background stars for calibration and earthshine as a transfer standard.

Fig. 7. Peak flash magnitude distribution. Sample is complete to approximately 10th magnitude.

4.4.2. Results Following 5 years of routine operation a total of 240 impacts were detected from Alabama. On average one can see 1 impact flash for every 2 h of observations but the rate during meteor showers can be dramatically higher. For instance 21 impacts in


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6 h of observations were recorded during the Geminid shower of 2010. In the first 3 years of operation approximately 212 h of clear weather recordings were obtained. From 108 photometric quality impacts observed in the first 3 years of operation, we estimate a flux of 1.34 Ò 10 Ð 7 km Ð 2 h Ð 1 to an approximate detectable impact kinetic energy limit of $ 3 Ò 107 J ( $ 100 g assuming 25 km s Ð 1 impact speed or a detectable magnitude of ? 10). This result makes use of luminous efficiencies determined by Moser et al. (2010); Swift et al. (2010) as given in Fig. 7. Note that the flux determination depends on accurate estimate of observing time, limiting magnitude, and collecting area. We see an asymmetry between the impact rate on the western hemisphere of the Moon (the leading edge, observed during evening observations) and the eastern hemisphere (trailing edge, morning observations) of about 1.45:1 (Fig. 8). Like in the seismic data, the prevalence of well-known meteor showers can be demonstrated. Comparisons of the shower activity can be made with their radiant visibility for our cameras FOV on the Moon for each night of observations. The expected impact flash rate was calculated using known shower radiants and velocities, the reported population index and ZHR (Zenithal

Hourly Rate) at the time of observations (International Meteor Organization, 2009), as well as luminous efficiency vs. velocity from Swift et al. (2010); Moser et al. (2010) (see discussions in above sections). This resulted in the flash rate profile, which was in good agreement with the observations (Fig. 9).

5. Measurement comparisons and synthesis 5.1. Current production of small craters If our understanding and models of the production of craters, impact flashes and seismic waves on the lunar surface is correct, then we would expect these to be consistent with the observations and among themselves in so far as the parameters of the source process (natural impacts) are concerned. Therefore we can attempt a general consistency test by first scaling the meteoroid flux models by Halliday et al. (1996); Revelle (2001); Brown et al. (2002) to the case of the Moon through Eqs. (1 and 2). Formally, this is done in three steps: (i) accounting for the gravitational acceleration and focusing of the Earth, (ii) correcting for the smaller target area of the Moon (iii) adding Earth's acceleration but at the Moon's distance, and (iv) accounting for the gravitational acceleration and focusing of the Moon. Steps (iii) and (iv) only add $ 100 m/s and $ 200 m/s respectively to the impact velocity, but we have nevertheless carried out the corrections. The ranges in source energy for which these laws are formally valid have also been corrected for the smaller impact speed at the lunar surface. The following values for the relevant physical parameters were used: RMoon Ì 1738 km, REarth Ì 6478 km (100 km altitude), GMMoon Ì 4903 km3 s Ð 2, GMEarth Ì 398,600 km3 s Ð 2. The results are shown in Table 2. Note that the flux law by Oberst and Nakamura (1989) is formally valid at the lunar surface; therefore, no correction is necessary in this case. To convert source energies to crater radii (Rc), we use the formula of Schmidt and Housen (1987) relevant to hypervelocity impacts on dry sand RC Ì 0:122E0:28 vÐ S
0:21 Ð0:17

g

?5î

Fig. 8. Distribution of 108 impacts observed June 2006-June 2009. Flux asymmetry is 1.45:1. Fluxes are 1.55 Ò 10 Ð 7 in the western hemisphere (left) and 1.07 Ò 10 Ð 7 in the eastern hemisphere (impacts/km2/hr).

Fig. 9. Flash rates after adjustment of Lyrid and Quadrantid population indices. Three letter codes are International Meteor Organization designators for showers.

where Es is measured in Joules, impactor velocity v in m s Ð 1 and the gravitational acceleration g is fixed at 1.62 m s Ð 2. Note that the expression is formally valid for an impactor density of 3 g cm Ð 3. The source energy can also be expressed in terms of the impactor radius r and density as ES Ì (2/3)v2r3. Combining Eq. (1) with Table 2 results in the expressions shown in Table 3. It is important to take note of the formal ranges of validity of the different laws. Those of Revelle (2001); Brown et al. (2002) are similar although the latter was fitted to a significantly larger dataset than the former. As shown in Fig. 11, they agree for crater radii between 20 m and 50 m, yet their different slopes result in significant disagreement for smaller radii. The Oberst and Nakamura (1989) law is formally valid for the lower end of this radius range and is in good agreement with the Halliday et al. (1996) law for the larger crater radii, both predicting 2-3 times fewer craters than the other two laws. Specifically, the Halliday et al. law is the only law formally valid for crater sizes of 5 m or smaller. The fact that Oberst and Nakamura (1989); Halliday et al. (1996); Brown et al. (2002) agree to well within a factor of two for crater sizes between 3.5 and o 10 m implies that these laws are fairly representative of reality in that range. The ``knee'' in the Halliday et al. (1996) law corresponds to a change in slope at 3.5 m, causing it to diverge from the Brown et al. (2002); Oberst and Nakamura (1989) laws for smaller crater radii. For example, it predicts 10 Ð 2 craters of 1 m radius as opposed to an order of magnitude more craters predicted by the other two laws.


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Table 2 Impactor flux laws used in this paper, as a function of the source energy ES. The expressions have been corrected for the difference in gravitational acceleration between the Earth and the Moon (cf. Fig. 10). Source Revelle, 2001 Brown et al., 2002 Halliday et al., 1996 Oberst and Nakamura, 1989 N (E 4 ES) on surface/year 8.56 10.64 7.15 11.50 11.38 Ð Ð Ð Ð Ð 0.72 0.90 0.50 1.00 0.99 Ò Ò Ò Ò Ò log log log log log ES ES ES ES ES Range in ES 1.44 Ò 103-2.99 Ò 107 3.04 Ò 103-7.83 Ò 106 0.105-2.84 2.84-12.6 3 Ò 103-104 Impact velocity (108 J) 14.5 17.3 14.5 14.5 17 Sample size (km s 19 300 79 79 91
Ð1

)

Table 3 Expected numbers of impact craters on the lunar surface according to the flux laws, impact speeds and source energy ranges in Table 1. Source N (R 4 RC) on surface per year 3.84 4.73 3.89 4.99 4.88 Ð Ð Ð Ð Ð 2.59 3.21 1.79 3.57 3.54 Ò Ò Ò Ò Ò logRC logRC logRC logRC logRC Range in RC (m)

Revelle, 2001 Brown et al., 2002 Halliday et al., 1996 Oberst and Nakamura, 1989

20-323 24-215 1.4-3.5 3.5-5.3 24-33

Comparisons to expected bombardment rates and model cratering production functions may be premature with so few data points; however, a preliminary comparison is useful. LRO results reported in the previous section fall between the 10 and 100 year isochrones of the Neukum production function (Neukum, 1983; Neukum et al., 2001), a good match to the actual $ 40 year time interval (Fig. 11). If the lunar Hartmann production function (Hartmann, 1999) is extrapolated to 10 m, it predicts about ten times as many craters as observed. However, we believe it is premature to make any conclusions about the accuracy of those models, given the sparse statistics. 5.2. Flux asymmetries Previous theoretical and analytical studies predicted the apexantapex asymmetry on the Moon to be undetectably small. However, recent studies report observational evidences for the asymmetry (Morota and Furumoto, 2003; Werner and Medvedev, 2010). Morota and Furumoto (2003) discussed the apex-antapex asymmetry from the spatial distribution of rayed craters ( Z 5 km in diameter) on the lunar farside. They showed that the cratering rate of the lunar leading side exceeds that of the trailing side for all studied crater sizes and concluded that the leading-trailing asymmetry on the Moon is 1.44 7 0.2. Based on a comparison with analytical studies, they also estimated that the encounter velocity of the impactors is 12-16 km/s. This implies that in the Copernican period, Near-Earth Asteroids were the dominant impactors on the Moon. The real-time monitoring of impacts may shed additional light on the issue. The apex/antapex asymmetry is obvious in impact flash detections. However, the observed effect is difficult to explain on the basis of today's data on sporadic meteoroid environment. Comparisons with the Meteoroid Engineering Model of McNamara et al. (2004) yielded a 1.02:1 asymmetry. Even though the apex meteoroids are very fast, their flux is lower than the much stronger antapex meteoroids, thus the asymmetry cancels out. With these adjustments, the computed evening/ morning ratio is 1.57 compared to the observed 1.45. Thus, lunar impact flash statistics may, in fact represent a clustering or unusual population indices of meteor showers. A leading-trailing asymmetry was recently also reported from the Apollo seismic data (Kawamura et al., 2011) (Fig. 12). Among the 1744 impact events observed by the Apollo Passive Seismic Experiment (Oberst, 1989), 56 well-defined locations of impact events were used in the statistics. The seismic data represent the current bombardment of the Moon and they represent crater sizes from 1-50 m, which is small compared to those studied in previous studies (Morota and Furumoto, 2003). The seismic data suggest that the cratering rate on the leading side for all impact classes is larger than on the trailing side by a factor of 1.8 7 0.5. This asymmetry implies impact velocities of 3.8-12.9 km/s, which are slower than those estimated from the spatial distribution of the rayed craters or numerical simulations. This might imply that the velocity or size distribution of the impactors for the meter-

The data (Fig. 10) may also be used to predict the number of new craters per km2 in the $ 40 year interval between the Apollo missions and the present, for comparison with the fresh craters identified by the Lunar Reconnaissance Orbiter camera (LROC) (see description above; Daubar et al., 2011). Five craters were found within a surface area of 5700 km2, for three of which only upper limits of crater sizes could be determined. The observed number of craters of 4 m radius or larger (2 craters found; ``X'' symbols) agrees well with the prediction of 7 Ò 10 Ð 4 km Ð 2. This suggests that the search was complete down to that crater size. In contrast, assuming completeness down to a crater radius of 0.5 m (4 craters found; open black rectangle) is not consistent with the predictions, either by the Halliday et al. (1996) law (0.02 km Ð 2 or 100 craters over the search area) or the Oberst and Nakamura (1989)/Brown et al. (2002) laws (0.2 km Ð 2 or 1000 craters over the search area). Hence, either the search does not find the majority of fresh meter-sized craters from Apollo Pan-LROC image comparisons or the theoretical production laws grossly overestimate crater production rates at these sizes. On the other hand, it is not clear that the production laws described above can be extrapolated to such small sizes. Perhaps the adopted impact scaling law (1), despite performing adequately for 10 m class craters, underestimates the sizes of meter-class craters as a function of source energy. In that case, however, the Halliday et al. (1996) law would fall far below the Brown et al. (2002); Oberst and Nakamura (1989) laws and also fail for 5 m radius craters. The inferred flux from the impact flash observations (filled black circle), if assigned a speed of 25 km s Ð 1 (right), corresponds to a crater radius of $ 1.7 m and maps slightly above the extension of the Brown et al. (2002) law. If a higher velocity is assumed (70 km s Ð 1; equivalent to a large contribution of faster meteor shower meteoroids relative to slower sporadics) yields a slightly smaller crater radius (1.4 m) but still quite far from the Halliday et al. (1996) law, which one would expect to be a better match to the data at these small sizes. One possibility for resolving this discrepancy is that the contribution of cometary fireballs at this mass range is underestimated. Halliday et al. (1996) suggested that mass-for-mass, a (faster) cometary meteoroid would produce a brighter fireball than a (slower) asteroidal one and hence, the contribution of cometary fireballs to the total population would be minor (cf. Fig. 1 of that paper). Collecting statistics on new meter-size lunar craters would provide the impetus to re-examine this premise.


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Fig. 10. Cumulative distributions of the area density of lunar craters greater than a given radius that formed over 40 yr (left y axis) and 1 yr (right y axis).

6. Conclusions and future work As for finding new craters, the Apollo panoramic camera images cover only $ 15% of the near side of the Moon (less with favorable illumination), so the specific technique described in Section 4.2 will eventually be restricted by the finite amount of previous data with high enough resolution to detect meter-scale craters (with 10-m scale bright ejecta). Within even that small area, we have as yet searched only a negligible percentage of the available data, the time-consuming comparison of images being the limiting factor. The expected availability of a Pan camera model to enable geometric reprojection of these images will help speed the search. With time and additional person-power we expect to find more new craters. To clarify the present-day Lunar cratering flux we would encourage obtaining improved statistics for new m-sized craters along with complementary observational techniques of meteoroids. We have made routine seismic measurements of meteoroid impacts and visual measurements of their flashes on the Moon for nearly 5 years. Over 240 impacts have been recorded and the flux of meteoroids in the 100 g to kilograms range is consistent with other observations. We found that meteor showers dominate the meteoroid environment in this size range and explain the evening/morning flux asymmetry of 1.5:1. With sufficient numbers of impacts, our data will reveal the population indices of showers. This work has resulted in improvements in our understanding of the luminous efficiency versus velocity for impacts. Continued observations will build up statistics and improve our understanding of the meteoroid complex. Tests have been made on dual camera systems using a Dichroic beamsplitter which allows simultaneous observations using near-infrared (0.9-1.7 mm) and visible light video cameras on one telescope to monitor the Moon simultaneously in the visible and near-infrared spectral regions. Measurements of flash intensity in the visible and NIR simultaneously will allow crude estimates of temperature. A two-camera arrangement also allows detection and confirmation with one single telescope. With more terrestrial stations, longitude coverage is to expand and clear sky statistics will improve. As seismic stations are sent to the Moon (like those proposed for the European Lunar Lander) routine impact flash observations will provide required ground-truth data for inversions of the seismic data and lunar interior models. New seismic observations require the presence of one or several landed platforms on the lunar surface. Despite the numerous orbiting probes since Apollo, no lunar lander mission progressed beyond the study phase--the last unmanned lander

Fig. 11. Comparison of two new craters with measured diameters to model isochrons from Neukum et al., 2001 (solid lines) and Hartmann, 1999 (dashed lines), using the chronology function of Neukum, 1983; Neukum et al., 2001. Data are plotted using the ``Craterstats'' program (Michael and Neukum, 2010).

size craters differ from those for the km-size craters. Additional seismic data will enable us to derive more solid characteristics of the impactor flux. In any case, the recent studies of the historic and current bombardment records support a detectable flux asymmetry on the Moon. None of the observations show an asymmetry in the polar and equatorial flux (Le Feuvre and Wieczorek, 2008; Werner and Medvedev, 2010).


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Fig. 12. (Left) Leading-Trailing flux asymmetry observed from rayed craters (Morota and Furumoto, 2003). (Right) Leading-Trailing flux asymmetry observed with the Apollo seismic data.

being the Luna 24 sample return mission in 1976. Several agencies now are committed to lunar surface missions within the present decade (Zheng et al., 2008; Gardini, 2011; Mitrofanov et al., 2011) which bodes well for the resumption of the lunar seismic monitoring program. One future possibility that is worth mentioning is to carry out these investigations concurrently to characterize the energy partition equation for specific impacts in near-real time. Adding up the inferred mechanical, heat, luminous and seismic energies (a form of energy stoichiometry) should allow one to estimate directly the impactor's kinetic energy and, in the cases of meteor showers where the speed is known, the impactor mass. The resulting distributions can then be directly checked for consistency against, for example, meteor fluxes in the Earth's atmosphere.

Acknowledgments This paper has been prepared following a workshop sponsored by the Europlanet Research Infrastructure (RI) at the German Aerospace Center, Berlin, Germany, October 21-22, 2010. We wish to thank NASA's Meteoroid Environment Office, the Constellation Program Office and the Engineering Directorate at NASA's Marshall Space Flight Center for financial support in making this project possible. Astronomical Research at the Armagh Observatory is funded by the Northern Ireland Department of Culture, Arts and Leisure. J.O. was supported by a grant from the Ministry of Education and Science of the Russian Federation. References
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