Keith A. Holsapple
2010 Annual Research Report
Holsapple worked on The Analysis and Interpretation of the Deep Impact Event, NASA GRANT# NNX08AG11G
This grant is nearing the end of the funded period. Here both previous and new results are identified, grouped according to specific milestones identified in the proposal.
Milestone 1: We will gather all data published to date on high speed impact cratering for which ejecta velocity measurements are available. We will analyze and correlate the data in the framework of scaling theory, and will publish a modern update to the Housen et al. (1983) paper in the technical literature - to make it available to the community. We expect that this paper would be finished at the end of the first year.
The “Ejecta from Impact Craters, 2010” paper is a significant improvement to the original ejecta scaling laws we developed in the early 1980s (Housen et al. 1983). New data and analysis have provided insights into the effect of target porosity on ejection velocities. Furthermore, these data reveal departures from the commonly-observed power-law scaling behavior. These departures are expected when gravity or target strength affect ejection velocities, and for particles launched from positions close to the impactor. These factors have been included in a new ejecta model that is described in the paper.
During our work under this milestone, ejecta data from the literature and from the authors’ own experiments conducted under this contract were summarized for a variety of target materials. The data were gathered into a comprehensive database and analyzed within the framework of point-source scaling theory. The results provide significant insights into how the ejecta velocity distribution depends on the conditions of an impact event. The dependence of ejection velocity on some variables, such as the impactor velocity and density are fairly well understood and follow the behavior expected from scaling theory.
The dependences on other variables, primarily the properties of the target material, are less understood. We have highlighted those deficiencies as potential areas for fruitful research. For example, one of the least understood target properties is material strength. This is in part due to the fact that strength measurements are often difficult and expensive to perform. This is compounded by a basic lack of understanding of which strength properties (tension, shear, compression) are important and should be measured. Another complication associated with target properties is that the governing strength of many geological materials (certainly rock, but also some cohesive soils) depends on the event size scale. For example, a direct application of laboratory impact experiments in rock would indicate that the surfaces of rocky asteroids smaller than ~70 km diameter should be essentially barren because nearly all ejecta should exceed the escape velocity; a prediction clearly at odds with observations of asteroid surfaces. A general weakening of rock at large scales undoubtedly results in ejecta velocities much lower than those measured in lab experiments that use pristine targets. The effects of size scale on strength should be addressed in future studies of impact ejecta.
Target porosity is of course another fundamental material property with significant effects on the ejecta velocity distribution, especially with regard to Deep Impact. Energy losses during compaction of pore spaces cause a reduction in ejection speeds. Data on ejecta velocities from our experiments in targets with a wide range of porosity, as well as data gathered from the literature, clearly show how ejecta velocities dramatically decrease with increasing target porosity.
New for 2010, submitted for publication:
We have described an important consequence of the effect of porosity in the recent paper (“Craters without Ejecta, 2010”). Our experiments have shown that increased porosity not only causes a reduction in ejection velocities, but also a significant change in the geometry of the material flow field initiated by an impact. In materials with low or moderate porosity, some of the target material is simply driven downward, or down and then back up but not ejected. However, that material represents a minor fraction of the crater volume. Most of the crater is formed by shearing and ejection of the material, which then can potentially contribute to the crater ejecta blanket (if it doesn’t escape the impacted body).
Highly porous materials behave much differently. We have observed that the flow of material in that case is primarily downward. That is, most of the crater volume is formed by compaction as the material is driven down or radially outward and compressed into the wall of the transient crater. In addition, because of the reduced velocities of any ejected material, much of the ejecta can fall back within the crater, leaving only a small mass in the ejecta blanket. As a result, craters on porous bodies can form without significant ejecta blankets. Our initial work in this area led some to believe that the Deep Impact event might not liberate much ejecta. However, we have shown that suppression of ejecta in porous targets only occurs at large size scales, because at small scales the ejected material is still able to escape the crater. The terms “large” and “small” are determined by the porosity and crushing strength of a specific body in question, because those properties determine the ejecta velocities and crater size. Nevertheless, we have determined the set of conditions under which suppression of ejecta should occur for a class of porous silicate materials used in our experiments.
The figure below shows a result of our recent work. The data points in the figure represent the population of small solar-system bodies for which we have estimates of both body size (Db) and porosity. We have shown that suppression of ejecta occurs only if the target material is sufficiently crushable. Geological materials, such as soils or rock piles, that typically have porosities in the range of 30% to 40%, do not crush easily and therefore do not exhibit much permanent compaction of pore space during impact events (some compaction does occur, but it represents a minor fraction of the crater volume). Therefore, only bodies above the gray band in the figure are candidates for ejecta suppression. Furthermore, as noted, suppression only occurs at sufficiently large size scales. The two solid lines in the figure are from model calculations (explained in the attached preprint) for two values of a parameter, h, that is the ratio of the volume of material in the ejecta blanket to the volume of the crater. When h is sufficiently small (perhaps 0.1 to 0.25), ejecta blankets would be suppressed. The results show that roughly 1/3 of the objects in the figure are candidates for suppression of ejecta.
The bulk porosity is plotted as a function of body diameter for the population of objects for which estimates of porosity and size are currently available. The solid curves (for two values of h = volume in ejecta blanket/volume of crater) delineate the regions in this map where suppression of ejecta can occur. Bodies near a given curve would show suppression of ejecta only for the largest craters. Those further above a curve would exhibit suppression for a wider range of crater sizes. Suppression of ejecta only occurs when craters are formed mostly by compaction, which requires target porosities greater than about 30-40%. Thus, large bodies, whose porosities are probably low due to gravitational compression, should exhibit craters with significant ejecta blankets.
Our results are consistent with interpretations of imagery of all small bodies that have currently been imaged in detail. Mathilde and Hyperion, both show evidence of a lack of crater ejecta. Small bodies, such as Phobos or Deimos display considerable ejecta. More importantly, our ejecta model shows one reason why the Deep Impact event would produce significant ejecta, even given the likely very high porosity of Tempel 1: the relatively small size size of the comet places it in the regime where ejecta are not suppressed. (An additional reason for production of ejecta is given below).
Milestone 2: We will apply the new ejecta scaling results to model the DI crater and ejecta plume using various candidate and end-member classes of materials. We will construct results showing the nature, the spatial distribution, the brightness and the temporal evolution of an ejecta plume for different material assumptions. Specifically, we will calculate time histories of the total mass of material in the plume as a function of time, the mass that would be observable (taking into account opacity), and the plume position. We will compare those results to the DI observations. During the first year we will collect the relevant DI observations from the literature and refine the model for calculating the plume properties that provided the preliminary results described in Holsapple and Housen (2006). Calculations using this model will begin when the first milestone is nearly complete, and will continue through the second year.
This task was completed in the first two years, and the results are contained in an Icarus publication. The abstract of that paper :
We apply recently updated scaling laws for impact cratering and ejecta to interpret observations of the Deep Impact event. An important question is whether the cratering event was gravity or strength-dominated; the answer gives important clues about the properties of the surface material of Tempel 1. Gravity scaling was assumed in pre-event calculations and has been asserted in initial studies of the mission results. Because the gravity field of Tempel 1 is extremely weak, a gravity-dominated event necessarily implies a surface with essentially zero strength. The conclusion of gravity scaling was based mainly on the interpretation that the impact ejecta plume remained attached to the comet during its evolution. We address that feature here, and conclude that even strength-dominated craters would result in a plume that appeared to remain attached to the surface. We then calculate the plume characteristics from scaling laws for a variety of material types, and for gravity and strength-dominated cases. We find that no model of cratering alone can match the reported observation of plume mass and brightness history. Instead, comet-like acceleration mechanisms such as expanding vapor clouds are required to move the ejected mass to the far field in a few-hour time frame. With such mechanisms, and to within the large uncertainties, either gravity or strength craters can provide the levels of estimated observed mass. Thus, the observations are unlikely to answer the questions about the mechanical nature of the Tempel 1 surface.
.Milestone 3: This task will investigate the ejecta velocity distribution and the question of plume detachment for low-strength materials. This is an area that has been virtually unexplored experimentally and is critically important to the interpretation of the DI observations. We will design and conduct impact experiments in appropriate materials with tailored strengths (some candidate materials are described in the Boeing Work Statement). In all cases we will make measurements of the material strengths using common geological material techniques. We will record high-speed digital movies to look at the question of the lift-off of the ejecta plume from the target surface, to quantify the ejecta velocity distribution, and to correct the simple model given in Eq. (1). Because of the importance of this task, and the current lack of relevant data, it will be initiated during the first year and will continue through the final year at some level depending on the results of the initial experiments.
The primary experiments were accomplished earlier:
Impacts were performed in a quarter
space fixture into a highly porous silicate target material consisting of a
mixture of fine quartz sand, water and perlite, which is a naturally occurring
siliceous volcanic rock. The bulk density of the target was 0.34 gm/cm3,
with a corresponding porosity of 87%, well within the estimates for DI. The
projectile impacted normally to the target surface near the interface between
the target material and the front window.
A high-speed camera was positioned to view normally to the front
window. Running at 104
pictures/sec, the camera recorded a cross-sectional view of the crater growth
and the evolution of the ejecta plume.
In order to facilitate visualization of the material flow, colored particles of perlite were emplaced at the target/window interface in a rectangular array. The figure at the left shows the completed target with the array of colored marker particles. The projectile in this test was a polyethylene cylinder 12.1mm in diameter and height, with a mass of 1.328 gm. It was launched to a speed of 1.8 km/s. The target chamber was evacuated to a pressure of ~20 mm Hg.
At 200µs after the impact the transient crater was considerably deeper than wide. Fine white material, presumably severely crushed perlite, was seen moving radially along the target window interface. Subsequent images showed the transient crater continuing to grow with a depth much greater than its diameter.
The next figure shows a later series of images from the same impact. For impacts into a moderately porous material, like dry sand, the ejecta curtain is well known to form a sheet that moves out along the target surface closely attached to the rim of the transient crater. In contrast, the upper image in this figure shows a high-speed vertical plume of fine ejecta. Later on, after several ms, coarser material appeared in the vertical plume and another plume formed, at approximately 45°, which is reminiscent of dry sand. This plume tended to follow the crater rim, which formed at a time of roughly 50 ms. Surprisingly, the vertical plume continued to evolve and in fact lasted for more than twice the crater formation time. Although the ejection speeds in the vertical plume decreased with time, its persistence and direction appear to be a unique aspect of cratering in highly porous materials. Given its long duration, the plume cannot be the result of the usual material flow field established during passage of the impact generated shock.
This behavior is strikingly similar to the observations of the DI event. This may be a characteristic of the so-called "anomalous behavior" of highly porous materials subjected to shock waves. That strange behavior occurs when very porous material is heated so much in the shock that, although the pressure is in compression, the density actually increases because of the thermal expansion. This may be the significant feature for the interpretation of the DI event. It has not been previously identified nor studied in the planetary community and looks to be a very significant factor in plume outbursts triggered by an impact.
Although the transient
crater was quite deep, the final crater was more bowl-shaped. This was due primarily to fall-back of
some of the material in the vertical plume, but also from collapse of material
at late times due to the low target strength.
A basic part of this milestone is to examine the interpretations of the DI ejecta plume made by others. In particular, it has been noted that the DI ejecta plume did not detach from the crater rim to a height of more than 750 m, otherwise a lower edge of the plume would have been observed in the mission images. This fact has been used by others to calculate an upper bound on the strength of the DI surface material of only 65 Pa. The logic used in this argument is that craters formed in cohesive materials should exhibit a lower bound on the ejection velocity, vmin
rvmin2 = Y (1)
where r is the density of the surface material and Y is the strength. Based on our previous experience with impacts in cohesive targets, we believe that Eq. (1) is incorrect and that ejecta can occur with speeds well below the presumed vmin cutoff given in Eq. (1). If so, then the derived strength values for Tempel are incorrect as well.
In addition to the experiments described above, we have conducted quarter-space experiments to further investigate the effects of porosity and strength on ejecta. As before, the new experiments were conducted in a quarter space fixture with a highly porous mixture of fine quartz sand, water and perlite. The projectile impacted normally to the target surface near the interface between the target material and the front window. A high-speed digital video camera was positioned to view normally to the front window. Running at 15,000 pictures/sec, the camera recorded a cross-sectional view of the crater growth and the evolution of the ejecta plume. A second camera, running at 120,000 pictures/sec was used to view the projectile and to measure the impact speed.
The figure below shows a sequence of images from the high-speed video of an experiment in which a polyethylene projectile impacted the target at 1.6 km/s. The target material in this case had a porosity of 63%. In our past experiments, the target is placed in an oven to remove the water used to mix the perlite and sand. However in this case, the water (32% by mass) was not removed. This provided some strength to the target material. The images in the figure show the plume of ejecta emitted from the edge of the expanding crater, as usual. The final image, and the inset in the figure, show that the final crater had very steep, nearly vertical walls, again indicating that the target material had significant strength. The cohesion of the material can be estimated from the observed wall height (roughly 0.1 m) to be 0.6 kPa. This is, in fact, a lower bound on the cohesion because any larger value would also provide stability for the steep crater walls.
Impact of a 1.3 gm 1.6 km/s polyethylene cylinder into a 63% porous target having a moisture content of 32%. The sequence of images shows the evolution of the ejecta plume.
The video showed that the ejecta plume never detached from the crater edge. Rather, the ejection velocity steadily decreased with increasing distance from the impact, as typically observed in impact experiments. For a strength of 600 Pa, and a target density of 600 kg/m3, Eq. (1) would indicate a velocity cutoff of 1 m/s. In contrast, ejecta velocities as low as 0.4 m/s were measured. Even slower material was observed, but could not be measured because it traveled outside the field of view of the camera. Additionally, ejecta were observed around the periphery of the crater, indicating even lower ejection speeds.
The fact that the DI plume did detach from the crater rim to a height of more that 750 m indicates that the lowest ejecta speed had to be less than 0.9 m/s. This is greater than the slowest ejecta observed in our experiment. Thus, the surface material on Tempel I could have had a cohesion of 600 Pa (or even larger) and would still not have been observed to detach. That is, the upper bound on the strength of the surface material is at least an order of magnitude larger than claimed.
As note, another feature of the DI ejecta plume is that, in contrast to the ~45° angle usually observed between the plume and the surface, a nearly vertical component of ejecta was also observed. A small vertical component was observed in targets with porosities of 60% in our initial experiments. At larger porosities, the plume because even more dramatic, appearing as a late time “fountain” in ~80% porous targets.
We recently conducted a similar experiment in a target with 83% porosity. This was the same material as in the experiment shown in figure above, except that the target was dried to remove the water in this case. The figure below shows a sequence of images from that event. Interestingly, a vertical plume was not observed in this case. This leads to an important possibility that some material property other than porosity may control the formation of the vertical plume. If so, this could have significant implications for the properties of the surface material on Tempel 1.
Impact of a 1.3 gm 1.8 km/s polyethylene cylinder into an 83% porous target. The sequence of images shows the crater formed without the generating the vertical plume observed in previous experiments by the present investigators and others.
Milestone 4: We will investigate and, if appropriate, conduct experiments with target materials with sufficient volatiles to affect the cratering processes. We will investigate the possibilities of using embedded dry ice or pressurized micro-sphere targets. These experiments are not intended to be simulations of the (currently unknown) processes that may have occurred during the DI event. Rather, we view these experiments as basic demonstrations of how much of an effect the release of volatiles could affect the cratering efficiency. We anticipate conducting these tests during the second and/or third years of the study.
This material is new:
A cratering efficiency (crater mass/impactor mass) of ~1000 was observed in the material with 32% water content discussed above. It is interesting to note that this is similar to that which occur for dry dense sand (~900). This would suggest that the enhance water content of the target did not have a significant effect on the crater volume, although there is a complication due to the fact that the wet material had some strength and a porosity of 63%.
We have also measured the velocities of ejecta from the new impact experiments. The figure below shows the ejection velocity vs. launch position in the point-source scaled form. The blue circles are data from the experiment shown in the wet target with 63% porosity. The ejecta velocities agree well with earlier data for similar porosity, except at the high-velocity end of the distribution. Whatever precluded the formation of the vertical plume may also have resulted in this difference in ejecta velocities. The red circles are for the (dry) target with 83% porosity. As expected, the ejection velocities are much lower in this material than for a moderately porous material, such as dry sand.
Ejection velocity as a function of launch position. U is the impact velocity, a is the impactor radius, r and d are the target and impactor densities.
Papers:
Housen, Kevin R.; Holsapple, Keith A.Ejecta from Impact Craters, Icarus, Volume 211, Issue 1, p. 856-875, 2010.
Abstracts:
Housen, K. R.; Holsapple, K. A. (2010). Asteroids without ejecta. LPSC 41, 2354.
Pierazzo, E., G. S. Collins, K. A. Holsapple, K. R. Housen, D. G. Korycansky, C. S. Plesko, M. C. Price, and K. Wünnemann (2010). Impact hydrocode benchmark and validation project: Impacts into cohesionless soil. LPSC 41, 2048.
