On estimating contributions of basin ejecta to regolith deposits at lunar sites

Abstract— We have developed a quantitative model for predicting characteristics of ejecta deposits that result from basin‐sized cratering events. This model is based on impact crater scaling equations (Housen, Schmitt, and Holsapple 1983; Holsapple 1993) and the concept of ballistic sedimentation (Oberbeck 1975), and takes into account the size distribution of the individual fragments ejected from the primary crater. Using the model, we can estimate, for an area centered at the chosen location of interest, the average distribution of thicknesses of basin ejecta deposits within the area and the fraction of primary ejecta contained within the deposits. Model estimates of ejecta deposit thicknesses are calibrated using those of the Orientale Basin (Moore, Hodges, and Scott 1974) and of the Ries Basin (Hörz, Ostertag, and Rainey 1983). Observed densities of secondary craters surrounding the Imbrium and Orientale Basins are much lower than the modeled densities. Similarly, crater counts for part of the northern half of the Copernicus secondary cratering field are much lower than the model predicts, and variation in crater densities with distance from Copernicus is less than expected. These results suggest that mutual obliteration erases essentially all secondary craters associated with the debris surge that arises from the impacting primary fragments during ballistic sedimentation; if so, a process other than ballistic sedimentation is needed to produce observable secondary craters. Regardless, our ejecta deposit model can be useful for suggesting provenances of sampled lunar materials, providing information complementary to photogeological and remote sensing interpretations, and as a tool for planning rover traverses (e.g., Haskin et al. 1995, 2002).     

Nature of solar-cycle and heliomagnetic-polarity dependence of cosmic rays, inferred from their correlation with heliomagnetic spherical surface harmonics in the period 1976–1985

Correlation of cosmic-ray intensity (I) with the solar magnetic field expanded into the spherical surface harmonics, B_ns(n 9), by Hoeksema and Scherrer has been studied using the following regression equation:

, where are subgroups of B_ns classified in ascending order of n, and τ_i is the time lag of I behind correlation coefficient between the observed and simulated intensities (I_obs, I_sml) in the period 1976–1985 is 0.87 and considerably better than that derived from any single index of solar activity. The lag time τ₃ is greater than others, indicating that the higher order magnetic disturbances effective to the cosmic-ray modulation have a longer lifetime in space than the lower order disturbances. The rigidity spectrum of the cosmic-ray intensity variation responsible for A_I due to the dipole moment is harder than those for others (A₂,A₃), indicating that the lowest order (i.e. largest scale) magnetic disturbances can modulate cosmic rays more effectively than the higher order disturbances. As another result of the present analysis, it has been found that the intensity depends also on the polarity of the polar magnetic field of the Sun; the residual (I_obs−I_sml) of the simulation changes its sign from positive to negative with a time lag (0–5 Carrington rotation periods) behind the directional change of the solar magnetic dipole moment from northward to southward, and has a softer rigidity spectrum than A_iS. The dependence is consistent with the result having been obtained in the previous period, 1936–1976, by one (K.N.) of the present authors. The polarity dependence can be found also in the 22-year variation of the time lags obtained every solar cycle in the period 1936–1985. The theoretical interpretation of these polarity dependences is discussed on the basis of the diffusion-convection-drift model.     

Degree of impactor fragmentation under collision with a regolith surface—Laboratory impact experiments of rock projectiles

Some meteorites consist of a mix of components of various parent bodies that were presumably brought together by past collisions. Impact experiments have been performed to investigate the degree of target fragmentation during such collisions. However, much less attention has been paid to the fate of the impactors. Here, we report the results of our study of the empirical relationship between the degree of projectile fragmentation and the impact conditions. Millimeter‐sized pyrophyllite and basalt projectiles were impacted onto regolith‐like sand targets and an aluminum target at velocities of up to 960 m s^?1. Experiments using millimeter‐sized pyrophyllite blocks as targets were also conducted to fill the gap between this study and the previous studies of centimeter‐sized rock targets. The catastrophic disruption threshold for a projectile is defined as the energy density at which the mass of the largest fragment is the half of the original mass. The thresholds with the sand target were 4.5 ± 1.1 × 10⁴ and 9.0 ± 1.9 × 10⁴ J kg^?1, for pyrophyllite and basalt projectiles, respectively. These values are two orders of magnitude larger than the threshold for impacts between pyrophyllite projectiles onto aluminum targets, but are qualitatively consistent with the fact that the compressive and tensile strengths of basalt are larger than those of pyrophyllite. The threshold for pyrophyllite projectiles and the aluminum target agrees with the threshold for aluminum projectiles and pyrophyllite targets within the margin of error. Consistent with a previous result, the threshold depended on the size of the rocks with a power of approximately ?0.4 (Housen and Holsapple 1999). Destruction of rock projectiles occurred when the peak pressure was about ten times the tensile strength of the rocks.     

Catastrophic fragmentation as a stochastic process: sizes and shapes of fragments

It is rather difficult to understand theoretically and to analyse the experimental data concerning the mass and shape distributions of fragments created by catastrophic collisions. The fragmentation process is discussed as being a purely stochastical phenomenon; the size and shape distributions obtained in this way are compared with the results of laboratory experiments. The results are presented of some computer simulations of random volume fragmentation processes; they are a 3-D generalization of the numerical experiments described in Grady and Kipp (J. Appl. Phys. 58(3), 1210–1222, 1985). The features of the size distribution are discussed, comparing it with the expectations of the Mott-Linfoot and Grady-Kipp theories. In the literature the shape of fragments is defined in terms of the ratios B/A and C/A, where A, B, C are defined as the sizes of a fragment along three orthogonal axes. The definition of the shape of a fragment cannot be considered unique, since it is not obvious in which order to define the three axes when the fragments are not ellipsoidal. A few possible methods are introduced explicity, and the resulting differences are discussed. In this light, the shape results (the mean values and the distribution of the axial ratios) obtained in recent laboratory experiments are rediscussed and critically reviewed. For what concerns the stochastical modelling, the results of various simulations, corresponding to different assumptions regarding fragmentation properties are presented. It is shown that the main features of the shape distributions from laboratory experiments cannot be satisfactorily reproduced. Comparison of the results with the outcomes of the semiempirical fragmentation model by Paolicchi et al. (Icarus 121, 126–157, 1996), as well as with some results coming out from hydrodynamical simulations, shows how only a “global” and physical model, not a purely statistical one (neither global nor “local”), can afford to reproduce the observed data.     

Velocity of finer fragments from impact

We describe the method and the result of a new experiment to obtain velocity distribution of fine ejecta fragments, from a few to a hundred microns in size, produced from basalt targets by impacts of nylon projectiles at a velocity of 3.7 km s⁻¹. The size distribution of holes perforated by the ejecta fragments on thin films and foils placed around the targets was investigated, and the size-velocity relation was determined with the aid of an empirical formula for threshold penetration (McDonnell and Sullivan, Hypervelocity Impacts in Space, Unit for Space Sciences, University of Kent, 1992). The velocity of the fastest fragments, at a given size, is from the extrapolation of the size-velocity relation for 1–100 mm fragments (Nakamura and Fujiwara, Icarus92, 132–146, 1991; Nakamura et al, Icarus100, 127–135, 1992). The laboratory results are also compared with those obtained from the study of secondary craters around large lunar craters (Vickery, Icarus67, 224–236, 1986, Geophys. Res. Lett. 14, 726–729, 1987). All these data provide a smooth size-velocity relationship in the normalized fragment size range of four orders of magnitude.     

Fragment ejection velocities and the collisional evolution of asteroids

We have applied the algorithm developed by Petit and Farinella (Celest. Mech. 57, 1–28, 1993) to model the outcomes of impacts between asteroids of different sizes, to show that a crucial feature of these models is the assumed relationship between velocity and mass of fragments ejected after a shattering impact. Not only how the mean velocity depends upon mass is important to determine the extent of fragment reaccumulation, but also the distribution of velocities about the mean values. The available experimental evidence on this issue is still sparse, and does not constrain the collisional models well enough to allow us to make reliable predictions on the outcomes of impacts between bodies of size much larger than the laboratory targets. As a consequence, when the collisional outcome models are used as an input for simulations of the asteroid collisional history since the origin of the solar system, the results show a strong sensitivity to the assumed velocity vs mass relationship. This sensitivity is stronger in the diameter range (a few tens to a few hundreds of km) where the self-gravitational reaccumulation of fragments is most effective, but may also extend to much smaller sizes.     

The regimes of the east-west and the radial anisotropies of cosmic rays in the heliosphere

The observations obtained over the last 23 y suggest that there are two distinct physical states of the heliosphere. One state covers the period 1957–1970 when the diurnal anisotropy consists of the azimuthal component only. One may define this period as the regime of the East-West (co-rotation) anisotropy. The period 1971–1979 is characterized by the appearance of a radial anisotropy, which attains a maximum amplitude in 1976, when the solar activity is minimum. There appears to exist an inverse correlation between the amplitude of the radial anisotropy and solar activity. The amplitude of the EastWest anisotropy varies with time during this latter period and may also be rigidity-dependent. In 1976 the amplitude of the East-West anisotropy is zero for the underground muon data obtained at Embudo and has a lower value for the neutron monitor data obtained at Deep River. On the other hand, the amplitude of the radial anisotropy depends weakly upon the primary rigidity. The period 1971–1979 thus defines the regime of the radial anisotropy. The physical state of the heliosphere is very stable during the regime of the East-West anisotropy and extremely dynamic during the regime of the radial anisotropy. The heliosphere appears to switch from one physical state to another following the onset of the solar polar field reversal.     

Neutrinos from SN1987A: flavor conversion and interpretation of results

After recent results from solar neutrino experiments and KamLAND we can definitely say that neutrinos from SN1987A underwent flavor conversion, and the conversion effects must be taken into account in the analysis of the data. Assuming the normal mass hierarchy of neutrinos we calculate the permutation factors p for the Kamiokande-2, IMB and Baksan detectors. The conversion inside the star leads to p=0.28–0.32; the oscillations in the matter of the Earth give partial (and different for different detectors) regeneration of the original signal, reducing this factor down to 0.15–0.20 (at E=40 MeV). We study in details the influence of conversion on the observed signal depending on the parameters of the original neutrino spectra. For a given set of these parameters, the conversion could lead to an increase of the average energy of the observed events up to 50% and of the number of events by a factor of 2 at Kamiokande-2 and by a factor of 3–5 at IMB. Inversely, we find that neglecting the conversion effects can lead up to 50% error in the determination of the average energy of the original spectrum and about 50% error in the original luminosity. Comparing our calculations with experimental data we conclude that the Kamiokande-2 data alone do not favor strong conversion effect, which testifies for small difference of the original and spectra. In contrast, the combined analysis of the Kamiokande and IMB results slightly favors strong conversion effects (that is, large difference of the original spectra). In comparison with the no-oscillation case, the latter requires lower average energy and higher luminosity of the original flux.     

Catastrophic disruption experiments: recent results

This paper presents a review of the progress in the field of catastrophic disruption experiments over the past 4 years, since the publication of the review paper by Fujiwara et al. (Asteroids II, pp. 240–265, University of Arizona Press, Tucson, 1989). We describe the development of new techniques to produce shattering impacts relevant to the study of the collisional evolution of the asteroids, and summarise the results from numerous experiments which have been performed to date, using a variety of materials for both the impactor and the targets. Some of these, such as ice-on-ice, loose aggregates and pressurised targets, are quite new and have provided novel and exciting results. Some of the gaps existing previously in the data on fragment ejection-angle distributions, as well as translational and rotational velocity fields (including fine fragments) have been filled, and these new results will be surveyed.     

Adiabatic vibrational frequencies of local and nonlocal convection models of the sun

The eigen-vibrational frequencies of Xiong Da-run's nonlocal and local convection models of solar envelope are calculated and compared. The differences between the observational and theoretical vibrational frequencies are less than 1%. They can be divided into two isolated groups. For modes with l ≥ 60, all the differences between observed and theoretical eigen-vibrational frequencies are distributed in a narrow and inclined belt in the (Δv ≈ v)-diagram. This shows that the theoretical model of solar convective region can approximately reflect the intrinsic structure of the sun in the region of r = (0.70–0.95)R. The discrepancies between the theoretical and observational frequencies come from the outer layers. For modes with l < 60, the theoretical vibrational frequency is smaller than the observational one. This implies that the temperature of the upper part of the convectively unstable region is rather low. The frequency difference is more dispersed in the local convection model than in the nonlocal convection model. For the intermediate- and low-frequency ranges (v < 3000), the difference between the two models is small, while for the high-frequency range (v ≥ 3000) the frequency in the local model is higher than in the nonlocal model. This means that the temperature of the radiation region beneath the convective region is higher in the local convection model than in the nonlocal convection model. The nonlocal model is nearer to the observation than the local model.     

Nature of dark energy and polarization measurements

High sensitivity polarization measures, on wide angular scales, together with data on anisotropy, can be used to fix DE parameters. In this paper, first of all, we aim to determine the sensitivity needed to provide significant limits. Our analysis puts in evidence that there is a class of DE models that polarization measures can possibly exclude soon. This class includes models with DE due to a Ratra–Peebles (RP) potential. Using a likelihood analysis, we show that it is possible to distinguish RP models from ΛCDM and other dynamical DE models, already with the sensitivity of experiments like SPOrt or WMAP, thanks to their negative TE correlation at low-l, when the optical depth τ is sufficiently large. On the contrary, fixing the energy scale Λ for RP potentials or distinguishing between ΛCDM and other DE potentials requires a much lower pixel noise, that no planned polarization experiment will achieve. While reviewing this paper after the referee report, the first-year WMAP data were released. WMAP finds large positive anisotropy–polarization correlations at low l; this apparently excludes DE models with RP potentials.     

Origin of the ten degree Solar System dust bands

The Solar System dust bands discovered by IRAS are toroidal distributions of dust particles with common proper inclinations. It is impossible for particles with high eccentricity (approximately 0.2 or greater) to maintain a near constant proper inclination as they precess, and therefore the dust bands must be composed of material having a low eccentricity, pointing to an asteroidal origin. The mechanism of dust band production could involve either a continual comminution of material associated with the major Hirayama asteroid families, the equilibrium model (Dermott et al. (1984) Nature 312, 505–509) or random disruptions in the asteroid belt of small, single asteroids (Sykes and Greenberg (1986) Icarus 65, 51–69). The IRAS observations of the zodiacal cloud from which the dust band profiles are isolated have excellent resolution, and the manner in which these profiles change around the sky should allow the origin of the bands, their radial extent, the size-frequency distribution of the material and the optical properties of the dust itself to be determined. The equilibrium model of the dust bands suggests Eos as the parent of the 10° band pair. Results from detailed numerical modeling of the 10° band pair are presented. It is demonstrated that a model composed of dust particles having mean semimajor axis, proper eccentricity and proper inclination equal to those of the Eos family member asteroids, but with a dispersion in proper inclination of 2.5°, produces a convincing match with observations. Indeed, it is impossible to reproduce the observed profiles of the 10° band pair without imposing such a dispersion on the dust band material. Since the dust band profiles are matched very well with Eos, Themis and Koronis type material alone, the result is taken as strong evidence in favor of the equilibrium model. The effects of planetary perturbations are included by imposing the appropriate forced elements on the dust particle orbits (these forced elements vary with heliocentric distance). A subsequent model in which material is allowed to populate the inner solar system by a Poynting-Robertson drag distribution is also constructed. A dispersion in proper inclination of 3.5° provides the best match with observations, but close examination of the model profiles reveals that they are slightly broader than the observed profiles. If the variation of the number density of asteroidal material with heliocentric distance r is given by an expression of the form 1/r^τ then these results indicate that γ < 1 compared with γ = 1 expected for a simple Poynting-Robertson drag distribution. This implies that asteroidal material is lost from the system as it spirals in towards the Sun, owing to interparticle collisions.     

Twilight effects of solar ionizing radiation

The absorption of solar ionizing radiation during twilight is investigated. Ion production rates are obtained as a function of altitude and twilight intensities and altitude profiles of emissions arising from the fluorescence of solar ionizing radiation are calculated for various solar depression angles. For an atmosphere with an exospheric temperature of 750°K, the predicted overhead intensity from fluorescence of the O⁺(²P — ²D) lines at 7319–7330 diminishes from 175 R at dusk to 10 R at a solar depression angle of 10°. The predicted overhead intensities from fluorescence of the N₂⁺ Meinel and first negative systems are respectively about 175 R and 20 R at dusk diminishing to respectively 1.5 R and 0.1 R at a solar depression angle of 10°.

It is suggested that a charge transfer reaction of O⁺²D in N₂ is a significant source of N₂⁺ ions. This reaction offers a possible explanation for the high apparent rotational temperatures in the first negative system observed by Broadfoot and Hunten. Other excitation and ionization mechanisms are briefly discussed.     

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.     

Meteoritical evidence and constraints on asteroid impacts and disruption

Impact events have played a central role in the life of meteorites. They compacted and lithified the dust from which meteorites are made; produced shock minerals, shock melting, and shock blackening of meteoritic minerals on their parent bodies; turned their parent bodies into rubble; and dispersed at least some pieces of this rubble, sending them to Earth as meteorites. Thus, as well as owing their very existence to the occurrence of catastrophic disruptions, meteorites contain physical ground truth concerning the impact and disruption environment of the solar system. Reviewing these aspects of the impact-meteorite connection, we conclude that impacts severe enough to disrupt asteroids were rare in the earliest stages of the solar nebula, when meteorite parent bodies accreted and were lithified. Likewise, though catastrophic disruptions clearly have occurred over the past several billion years, the small number of exposure events seen in the meteoritic cosmic ray age record indicates that such disruptions at these times also were rare. However, catastrophic disruptions must have been very prevalent during the first billion years of the solar system, resulting in the widespread asteroid macroporosity inferred from the comparison of asteroid bulk densities to meteorite grain densities.     

Colour dependence of zodiacal light models

Colour models of the zodiacal light in the ecliptic have been calculated for both dielectric and metallic particles in the sub-micron and micron size range. Two colour ratios were computed, a blue ratio C_b (0.40 μm, 0.53 μm) and a red ratio, either C_r (0.82 μm, 0.53 μm) or C_r' (0.71 μm, 0.53 μm). The models with a size distribution ∝s^−2.5ds generally show a colour close to the solar colour and almost independent of elongation. Especially in the blue colour ratio there is generally no significant dependence on the lower cutoff size (0.1–1 μm). The main feature of absorbing particles is a reddening at small elongations. The models for size distributions ∝s⁻⁴ds show larger departures from solar colour and more variation with model parameters. Colour measurements, including red and near infra-red, therefore are useful to distinguish between flat and steep size spectra and to verify the presence of slightly absorbing particles.     

Changes in thermospheric molecular oxygen abundance inferred from twilight 6300 A airglow

When the local solar zenith angle, χ_L, is < 105° the 6300 A line is much stronger than expected on the basis of F region ionic recombination alone. Between 95 and 105° the additional intensity is quantitatively explained by production of O(¹D) from photolysis of O₂ in the Schumann-Runge continuum, (λλ 1300–1750 A) using current values for solar flux, atmospheric composition and quenching of O(¹D) by N₂. The Schumann-Runge (SR) component exhibits a large seasonal variation with a maximum in summer. We interpret this variation as implying a seasonal change in thermospheric O₂ abundance; the change seems largely to reflect a variation in O₂ density at the base of the diffusive regime although some contribution may come from changes in thermospheric temperature structure. Large changes in the SR component exist from day to day and with a 27 day period following a major magnetic storm. The photodissociation source becomes inadequate when x_l < 95°; at 90° more than half of the intensity comes from still another source which we identify as local photoelectron excitation of O atoms.     

Moon: Origin and evolution of multi-ring basins

This paper summarizes current data and new observations on lunar basin systems. Parts 1–4 review earlier literature and give new crater-counts used to reconstruct basin histories. Among the results are: basin rings are defined by faults, hills, craters, and/or wrinkle ridges; all of these are inter-related; 2 plays a special role in the ratios of ring diameters; flooding occurred in many basins prior to the formation of the familiar front-side maria; 3 km is a typical depth of lava flooding in basins. Parts 5–11 interpret these results in terms of origin and evolution of basins. Polar concentrations of basins and old, large craters are found (Figures 28 and 29). Basins originated by impacts of very early planetesimals left over from or created during formation of the Moon (6). Concentric fractures were produced by the impacts. Concentric rings developed along fractures during subsequent sagging of the basin into partially melted substrata, along the lines of theory and experiments by Lance and Onat (1962) (Figures 36 and 37). There is marginal empirical evidence that some rings formed significantly after their basins (8). The structure of specific rings depended on the nature of volcanic products extruded. Wrinkle ridges, peak-rings, rings of craters, concentric graben, and central peaks are all consequences of basin-forming evolutionary processes (9, Figure 41), Flooding by lava was a final stage in basin evolution. Lava extruded from concentric ring-faults, wrinkle ridges, and crater and basin rims (10). Mascons are directly correlated with the amount of mare lava, but not correlated with basin age or morphology (11). Section 12 summarizes the results and compares them to those of other authors.     

A model independent approach to future solar neutrino experiments

We discuss here what model independent information about properties of neutrinos and of the sun can be obtained from future solar neutrino experiments (SNO, Super-Kamiokande). It is shown that in the general case of transitions of solar ν_e's into νμ and/or ντ the initial ⁸B neutrino flux can be measured by the observation of NC events. From the CC measurements the ν_e survival probability can be determined as a function of neutrino energy. The general case of transitions of solar ν_e's into active as well as sterile neutrinos is considered. A number of relations between measurable quantities the test of which will allow to answer the question whether there are sterile neutrinos in the solar neutrino flux on the earth are derived. Transitions of solar ν_e's into active and sterile states due to neutrino mixing and Dirac magnetic moments or into active left-handed neutrinos and active right-handed antineutrinos due to neutrino mixing and Majorana transition magnetic moments are also considered. It is shown that future solar neutrino experiments will allow to distinguish between the cases of Dirac and Majorana magnetic moments.     

Wavy size distributions for collisional systems with a small-size cutoff

Dohnanyi's [J. geophys. Res. 74, 2531–2554, 1969; in Physical Studies of Minor Planets (edited by T. Gehrels), pp. 263–295. NASA-SP 267, 1971] theory predicts that a collisional system such as the asteroid population should rapidly relax to a power-law equilibrium size distribution, provided all the collisional response parameters are independent of size. However, we have found that Dohnanyi did not include in a consistent way in the theory the possible occurrence of a small-size cutoff in the distribution. We have carried out a number of numerical simulations of the collisional evolution process, showing that the cutoff results in a wavy pattern superimposed on Dohnanyi's equilibrium power law, which affects the distribution up to sizes of tens of km. The pattern arises because particles just above the cutoff are not removed by catastrophic impacts by smaller projectiles, and therefore are created by break-up of larger bodies faster than they are eliminated; larger particles are increasingly depleted up to the size where the smallest shattering projectile exceeds the cutoff, and beyond that the removal rate is reduced and the distribution flattens. Thus, to be effective in producing the waves, the cutoff (or any other persisting “discontinuity” in the particle properties) must be sharp over a size range corresponding to the threshold projectile-to-target ratio for fragmentation. The presence of a small-size cutoff in the real asteroid belt is an open question, since it may be generated by poorly known non-gravitational effects acting on μm-sized dust, and may be affected by influx of cometary debris. However, the observational evidence for a variable characteristic exponent of the size distribution of interplanetary bodies is now strong, and the cutoff effect may provide a simple explanation for this finding.