Crater size-shape profiles for the moon and mercury: Terrain effects and interplanetary comparisons

New crater size-shape data were compiled for 221 fresh lunar craters and 152 youthful mercurian craters. Terraces and central peaks develop initially in fresh craters on the Moon in the 0–10 km diameter interval. Above a diameter of 65 km all craters are terraced and have central peaks. Swirl floor texture is most common in craters in the size range 20–30 km, but it occurs less frequently as terraces become a dominant feature of crater interiors. For the Moon there is a correlation between crater shape and geomorphic terrain type. For example, craters on the maria are more complex in terms of central peak and terrace detail at any given crater diameter than are craters in the highlands. These crater data suggest that there are significant differences in substrate and/or target properties between maria and highlands. Size-shape profiles for Mercury show that central peak and terrace onset is in the 10–20 km diameter interval; all craters are terraced at 65 km, and all have central peaks at 45 km. The crater data for Mercury show no clear cut terrain correlation. Comparison of lunar and mercurian data indicates that both central peaks and terraces are more abundant in craters in the diameter range 5–75 km on Mercury. Differences in crater shape between Mercury and the Moon may be due to differences in planetary gravitational acceleration (gMercury=2.3gMoon). Also differences between Mercury and the Moon in target and substrate and in modal impact velocity may contribute to affect crater shape.     

The velocity structure of the lunar crust

Seismic refraction data, obtained at the Apollo 14 and 16 sites, when combined with other lunar seismic data, allow a compressional wave velocity profile of the lunar near-surface and crust to be derived. The regolith, although variable in thickness over the lunar surface, possesses surprisingly similar seismic properties. Underlying the regolith at both the Apollo 14 Fra Mauro site and the Apollo 16 Descartes site is low-velocity brecciated material or impact derived debris. Key features of the lunar seismic velocity profile are: (i) velocity increases from 100–300 m s^–1 in the upper 100 m to 4 km s^–1 at 5 km depth, (ii) a more gradual increase from 4 km s^–1 to 6 km s^–1 at 25 km depth, (iii) a discontinuity at a depth of 25 km and (iv) a constant value of 7 km s^–1 at depths from 25 km to about 60 km. The exact details of the velocity variation in the upper 5 to 10 km of the Moon cannot yet be resolved but self-compression of rock powders cannot duplicate the observed magnitude of the velocity change and the steep velocity-depth gradient. Other textural or compositional changes must be important in the upper 5 km of the Moon. The only serious candidates for the lower lunar crust are anorthositic or gabbroic rocks.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.     

Hypervelocity impacts into ice‐topped layered targets: Investigating the effects of ice crust thickness and subsurface density on crater morphology

Many bodies in the outer solar system are theorized to have an ice shell with a different subsurface material below, be it chondritic, regolith, or a subsurface ocean. This layering can have a significant influence on the morphology of impact craters. Accordingly, we have undertaken laboratory hypervelocity impact experiments on a range of multilayered targets, with interiors of water, sand, and basalt. Impact experiments were undertaken using impact speeds in the range of 0.8–5.3 km s^?1, a 1.5 mm Al ball bearing projectile, and an impact incidence of 45°. The surface ice crust had a thickness between 5 and 50 mm, i.e., some 3–30 times the projectile diameter. The thickness of the ice crust as well as the nature of the subsurface layer (liquid, well consolidated, etc.) have a marked effect on the morphology of the resulting impact crater, with thicker ice producing a larger crater diameter (at a given impact velocity), and the crater diameter scaling with impact speed to the power 0.72 for semi‐infinite ice, but with 0.37 for thin ice. The density of the subsurface material changes the structure of the crater, with flat crater floors if there is a dense, well‐consolidated subsurface layer (basalt) or steep, narrow craters if there is a less cohesive subsurface (sand). The associated faulting in the ice surface is also dependent on ice thickness and the substrate material. We find that the ice layer (in impacts at 5 km s^?1) is effectively semi‐infinite if its thickness is more than 15.5 times the projectile diameter. Below this, the crater diameter is reduced by 4% for each reduction in ice layer thickness equal to the impactor diameter. Crater depth is also affected. In the ice thickness region, 7–15.5 times the projectile diameter, the crater shape in the ice is modified even when the subsurface layer is not penetrated. For ice thicknesses, <7 times the projectile diameter, the ice layer is breached, but the nature of the resulting crater depends heavily on the subsurface material. If the subsurface is noncohesive (loose) material, a crater forms in it. If it is dense, well‐consolidated basalt, no crater forms in the exposed subsurface layer.     

Effect of target properties and impact velocity on ejection dynamics and ejecta deposition

Impact craters are formed by the displacement and ejection of target material. Ejection angles and speeds during the excavation process depend on specific target properties. In order to quantify the influence of the constitutive properties of the target and impact velocity on ejection trajectories, we present the results of a systematic numerical parameter study. We have carried out a suite of numerical simulations of impact scenarios with different coefficients of friction (0.0–1.0), porosities (0–42%), and cohesions (0–150 MPa). Furthermore, simulations with varying pairs of impact velocity (1–20 km s⁻¹) and projectile mass yielding craters of approximately equal volume are examined. We record ejection speed, ejection angle, and the mass of ejected material to determine parameters in scaling relationships, and to calculate the thickness of deposited ejecta by assuming analytical parabolic trajectories under Earth gravity. For the resulting deposits, we parameterize the thickness as a function of radial distance by a power law. We find that strength—that is, the coefficient of friction and target cohesion—has the strongest effect on the distribution of ejecta. In contrast, ejecta thickness as a function of distance is very similar for different target porosities and for varying impact velocities larger than ~6 km s⁻¹. We compare the derived ejecta deposits with observations from natural craters and experiments.     

Photospheric and chromospheric oscillations in the base of coronal holes

In this paper we carry out an analysis of the spatial–temporal line-of-sight velocity variations measured in the chromospheric (H, H) and photospheric (Fei 6569 Å, Fei 4864 Å, Nii 4857 Å) lines at the base of 17 coronal holes. Time series of a duration from 43 to 120 min were recorded with the CCD line-array and the CCD matrix. Rather frequently we observed quasi-stationary upward flows with a measured velocity of up to 1 km s^–1 in the photosphere and up to 4–5 km s^–1 in the chromosphere (equivalent radial velocity of up to 3 km s^–1 and up to 12–15 km s^–1 accordingly) near dark points on the chromospheric network boundary inside polar CH. Line-of-sight velocity fluctuation spectra contain meaningful maxima in the low-frequency region clustering around the values 0.4, 0.75, and 1 mHz. Usually, the spatial localization of these maxima mutually coincides and, in our opinion, coincides with the chromospheric network boundary. Acoustic 3- and 5-min oscillations are enhanced in the coronal hole region and reach 1 km s^–1 in the photosphere and 3–4 km s^–1 in the chromosphere. These oscillations are not localized spatially and are distinguished throughout the entire region observed.     

Lunar velocity structure and compositional and thermal inferences

Seismic data from the Apollo Passive Seismic Network stations are analyzed to determine the velocity structure and to infer the composition and physical properties of the lunar interior. Data from artificial impacts (S-IVB booster and LM ascent stage) cover a distance range of 70–1100 km. Travel times and amplitudes, as well as theoretical seismograms, are used to derive a velocity model for the outer 150 km of the Moon. TheP wave velocity model confirms our earlier report of a lunar crust in the eastern part of Oceanus Procellarum.The crust is about 60 km thick and may consist of two layers in the mare regions. Possible values for theP-wave velocity in the uppermost mantle are between 7.7 km s^–1 and 9.0 km s^–1. The 9 km s^–1 velocity cannot extend below a depth of about 100 km and must decrease below this depth. The elastic properties of the deep interior as inferred from the seismograms of natural events (meteoroid impacts and moonquakes) occurring at great distance indicate that there is an increase in attenuation and a possible decrease of velocity at depths below about 1000 km. This verifies the high temperatures calculated for the deep lunar interior by thermal history models.Paper presented at the Lunar Science Institute Conference on Geophysical and Geochemical Exploration of the Moon and Planets, January 10–12, 1973.     

Anisotropic gravitational radiation in the problems of three and four black holes

The momentum flux in merging binary black holes is rediscussed using the actual orbit integrations. The terminal velocity acquired by the centre of mass of the system is found to be greater than the estimate of Fitchett (1983) by a factor of 1.45. The actual value in km s^–1 is still uncertain but may be as high as 2000 km s^–1. The centre of mass velocity kick at a black hole merger is incorporated in the orbit integration of few black hole systems. Assuming that the symmetric break-up mode of such systems corresponds to the classical double radio sources, we determine that the centre of mass velocity kick can be about 1000 km s^–1 at most.     

Expansion velocities of cometary gas

Heating processes are expected to strongly affect the structure and dynamics of cometary comas. A radial expansion velocity of less than 1 km s^–1 in the inner coma is quite compatible with a few km s^–1 in the outer regions of large comets.     

The photospheric velocity field of Procyon

BUSS observations of the profiles of two well observed spectral lines in the ultraviolet spectrum of CMi (Procyon; F5 IV–V) are analysed with a Fourier transform method in order to determine values of various parameters of the velocity field of the upper photosphere. We find a microturbulent line-of-sight velocity componentL = 0.9 ± 0.4 km s^–1, a macroturbulent velocity componentL _M = 5.3 ± 0.2 km s^–1, and a rotational velocity componentv _R sini=10.0±1.2 km s^–1. In these calculations a single-moded sinusoidal isotropic macroturbulent velocity function was assumed. The result appears to be sensitive to the assumed shape of the macroturbulence function: for an assumed Gaussian shape the observations can be described withv _R sini=4 km s^–1 andL _M = 11.6 ± 2.7 km s^–1. A comparison is made with other results and theoretical predictions.     

The MEMIN research unit: Scaling impact cratering experiments in porous sandstones

Abstract– The MEMIN research unit (Multidisciplinary Experimental and Modeling Impact research Network) is focused on analyzing experimental impact craters and experimental cratering processes in geological materials. MEMIN is interested in understanding how porosity and pore space saturation influence the cratering process. Here, we present results of a series of impact experiments into porous wet and dry sandstone targets. Steel, iron meteorite, and aluminum projectiles ranging in size from 2.5 to 12 mm were accelerated to velocities of 2.5–7.8 km s^?1, yielding craters with diameters between 3.9 and 40 cm. Results show that the target’s porosity reduces crater volumes and cratering efficiency relative to nonporous rocks. Saturation of pore space with water to 50% and 90% increasingly counteracts the effects of porosity, leading to larger but flatter craters. Spallation becomes more dominant in larger‐scale experiments and leads to an increase in cratering efficiency with increasing projectile size for constant impact velocities. The volume of spalled material is estimated using parabolic fits to the crater morphology, yielding approximations of the transient crater volume. For impacts at the same velocity these transient craters show a constant cratering efficiency that is not affected by projectile size.     

Hydrocode modeling of oblique impacts: The fate of the projectile

Abstract— All impacts are oblique to some degree. Only rarely do projectiles strike a planetary surface (near) vertically. The effects of an oblique impact event on the target are well known, producing craters that appear circular even for low impact angles (>15° with respect to the surface). However, we still have much to learn about the fate of the projectile, especially in oblique impact events. This work investigates the effect of angle of impact on the projectile. Sandia National Laboratories' three‐dimensional hydrocode CTH was used for a series of high‐resolution simulations (50 cells per projectile radius) with varying angle of impact. Simulations were carried out for impacts at 90, 60, 45, 30, and 15° from the horizontal, while keeping projectile size (5 km in radius), type (dunite), and impact velocity (20 km/s) constant. The three‐dimensional hydrocode simulations presented here show that in oblique impacts the distribution of shock pressure inside the projectile (and in the target as well) is highly complex, possessing only bilateral symmetry, even for a spherical projectile. Available experimental data suggest that only the vertical component of the impact velocity plays a role in an impact. If this were correct, simple theoretical considerations indicate that shock pressure, temperature, and energy would depend on sin²θ, where θ is the angle of impact (measured from the horizontal). However, our numerical simulations show that the mean shock pressure in the projectile is better fit by a sin θ dependence, whereas shock temperature and energy depend on sin^3/2 θ. This demonstrates that in impact events the shock wave is the result of complex processes that cannot be described by simple empirical rules. The mass of shock melt or vapor in the projectile decreases drastically for low impact angles as a result of the weakening of the shock for decreasing impact angles. In particular, for asteroidal impacts the amount of projectile vaporized is always limited to a small fraction of the projectile mass. In cometary impacts, however, most of the projectile is vaporized even at low impact angles. In the oblique impact simulations a large fraction of the projectile material retains a net downrange motion. In agreement with experimental work, the simulations show that for low impact angles (30 and 15°), a downrange focusing of projectile material occurs, and a significant amount of it travels at velocities larger than the escape velocity of Earth.     

An expanding high velocity hi cloud probably ejected from the galactic nucleus

An object located approximately atl=8°,b=–4° with a mean radial velocity of –212.3 km s^–1 has been observed in the 21 cm neutral hydrogen line. The mean weighted velocity dispersion is 11.2 km s^–1 and the total mass is estimated to be 190R ² (kpc) solar masses. We discuss possible interpretations of the origin and nature of this object. The most likely interpretation is that we observe an expanding object which has been ejected from the galactic nucleus.     

Proper motion measurements of umbral and penumbral structure

Horizontal proper motions of penumbral structure and umbral dots have been measured from a 17-min-long time series of sunspot images by numerical techniques. In the penumbra, inflows are seen to occur predominantly in the inner region, with an average velocity of 290 m s^–1. Penumbral outflows take place mostly in the outer part, where they reach velocities as high as 1.5 km s^–1, with an average velocity of 500 m s^–1. In the umbra, proper motions of 28 bright dots have been measured with an accuracy better than 50 m s^–1. The mean velocity of the umbral dots is 210 m s^–1. Most of the umbral dots display the well-known inward motion away from the peripheral umbra.     

Nondestructive imaging of hypervelocity impact-induced damage zones beneath laboratory-created craters by means of ultrasound travel-time tomography

Since the 1960s, hypervelocity impact experiments have been conducted to study the complex deformation mechanisms which occur in the subsurface of meteorite craters. Here, we present ultrasound tomography measurements of the damage zone underneath seven experimentally produced impact craters in sandstone cubes. Within the framework of the Multidisciplinary Experimental and Modeling Impact Research Network and the NEOShield Project, decimeter-sized sandstone targets were impacted by aluminum and steel projectiles with radii of 2.5, 4, and 5 mm at velocities between ~3.0 and ~7.4 km s⁻¹. The 2-D ultrasound tomography clearly shows a correlation between impact energy and the damaged volume within the target blocks. When increasing impact energies from 805 to 2402 J, a corresponding increase in the damage radius from ~13.1 cm to ~17.6 cm was calculated. p-Wave velocity reductions up to 18.3% (for the highest impact energy) were observed in the vicinity of the craters. The reduction in seismic velocity decreased uniformly and linearly with increasing distance from the impact point. The damage intensities correspond to peak damage parameters of 0.4–0.51 compared to undamaged target blocks. In addition to the damage zone below the crater, we could identify weakened zones at the sandstone walls which represent precursors of spalling. The volume of the damaged subsurface beneath experimentally produced craters determined through ultrasound tomography is larger than that obtained from previously reported p-wave velocity reductions or to microscopic and microcomputed tomography observations of crack densities in experimentally produced craters.     

Explosive events in the solar transition zone

The properties of explosive events in the solar transition zone are presented by means of detailed examples and statistical analyses. These events are observed as regions of exceptionally high velocity ( 100 km s^–1) in profiles of Civ, formed at 10⁵ K, observed with the High Resolution Telescope and Spectrograph (HRTS). The following average properties have been determined from observations obtained during the third rocket flight of the HRTS: full width at half maximum extent along the slit - 1.6 × 10³ km; maximum velocity - 110 km s^–1; peak emission measure - 4 × 10⁴¹ cm^–3; lifetime - 60 s; birthrate - 4 × 10^–21 cm^–2 s^–1 in a coronal hole and 1 × 10^–20 cm^–2 s^–1 in the quiet Sun; mass - 6 × 10⁸ g; and, kinetic energy - 6 × 10²² erg. The 6 examples show that there are considerable variations from these average parameters in individual events. Although small, the events show considerable spatial structure and are not point-like objects. A spatial separation is often detected between the positions of the red and blue shifted components and consequently the profile cannot be explained by turbulence alone. Mass motions in the events appear to be isotropic because the maximum observed velocity does not show any correlation with heliographic latitude. Apparent motions of the 100 km s^–1 plasmas during their 60 s lifetime should be detected but none are seen. The spatial frequency of occurrence shows a maximum near latitudes of 40–50°, but otherwise their sites seem to be randomly distributed. There is enough mass in the explosive events that they could make a substantial contribution to the solar wind. It is hard to explain the heating of typical quiet structures by the release of energy in explosive events.     

Vertical velocity fluctuations in plage-region magnetic points

Observations of line-of-sight velocities of gases in magnetic fields in weak plages near disk centre confirm the systematic downward velocity of 0.5 km s^–1, and show fluctuations about this mean by a rather uncertain 0.2 km s^–1. Some of the fluctuations show a fairly regular period around 5.5 min.     

The height variation of granular and oscillatory velocities

Previous observations of spatially-resolved vertical velocity variations in ten lines of Fe i spanning the height range 0 h 1000 km are re-analyzed using velocity weighting functions. The amplitudes and scale heights of granular and oscillatory velocities are determined, as well as those of the remaining unresolved velocities. I find that the optimal representation of the amplitude of the outward-decreasing granular velocities is an exponentially decreasing function of height, with a scale height of 150 km and a velocity at zero height of 1.27 km s^–1. The optimal representation of the same quantities for oscillatory velocities is an exponential increase with height, with a scale height of 1100 km and a velocity at zero height of 0.35 km s^–1. The remaining unresolved velocities decrease with height, with a scale height of 380 km and a velocity at zero height of 2.3 km s^–1.     

Damping constant and turbulence in the solar atmosphere

In the region of the formation of weak and medium-strong lines, the microturbulence increases with height (V _ver=0.7–0.9 km s^-1, V _hor= 1.1–1.5 km s^-1), the macroturbulence decreases (V _ver=1.6–1.4 km s^-1, V _hor= 2.4–1.5 km s^-1), and the total velocity field (vertical component) is depth-independent (1.7 km s^-1). The empirical damping constants for Fe, Ti, Cr, Ni lines are equal 1.3₆, 1.7₆, 1.6₆, 1.6₆, respectively. The correlation length (the Kubo-Anderson process has been used) in the solar photosphere is 520–550 km.     

Oscillations and waves in a sunspot

Observations have been made in H of the vertical velocity distribution in a sunspot. Over the umbra the pattern consists of structures of scale-size 2–3. The velocity distribution undergoes oscillations with a period of about 165 s and typical amplitude ±3 km s^–1, but the pattern breaks down after one or two cycles because the period of oscillation varies typically by ±20 s from place to place. Transverse waves develop in the outer 0.1 of the umbral radius and propagate outwards with a velocity of about 20 km s^–1, becoming gradually invisible by or before the outer penumbral boundary; the amplitude is about ±1 km s^–1 at the umbra-penumbra border.The penumbral waves are believed to be basically of the Alfvén type, with 3 × 10^–8 g cm^–3. The umbral oscillations presumably represent gravity waves. In both cases the fluxes are inadequate by two orders of magnitude to account for the sunspot energy deficit.     

Analysis of the hypervelocity impact process from impact flash measurements

Hypervelocity microparticle impact experiments were performed with a 2 MV Van De Graaff dust accelerator. From measurements of the light intensity I and the total light energy E, the relations I=c₁mv^4.1 and E=c₂mv^3.2 were obtained, where m is the projectile mass, ν the projectile velocity and c₁,c₂ are constants, depending on projectile and target material. Using the measured values of the spectral distribution of the light emitted during impact, the temperature of the radiating material was estimated to be between 2500 and 5000 K depending on the projectile velocity. From an analysis of these measurements the angular distribution of secondary particle velocities as well as the relative mass distribution of these particles was determined. Approximately 90% of the detected ejecta mass (ν?1 km/sec) is found between 50° and 70° ejection angle. For ejection angles smaller than 20°, ejecta velocities of up to 30 km/sec were detected when the primary particle velocity was 4.8 km/sec. Using the dependence of the light intensity on pressure in the target chamber, an estimate of the total amount of material vaporized during impact could be derived. It was concluded that at 7.4 km/sec particle impact velocity at least 1.6% of the displaced projectile and crater material was vaporized.