Low-speed Impacts into Ice–Dust Granular Mixtures

The ICE setup consists of a drop mechanism placed above a target sample cup (Figure 1). The drop mechanism consists of an electromagnet able to hold 2 cm sized spherical projectiles, on which a metal pin has been affixed for capture by the magnet. This magnet is installed at an adjustable height above the target sample. During the experiment's preparation, the magnet is powered and the projectile is installed (as seen in the left panel of Figure 1). When the target is ready, the magnet is switched off, releasing the projectile, which is accelerated due to gravity and impacts the target at a final speed dependent on the drop height.

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The sample was contained in a copper cup of 78.85 mm inner diameter and 48.75 mm height (237.9 cm³ sample volume). This cup was fitted into a copper block that was cooled via liquid nitrogen flowing through tubing wound around it. The temperature of the cup and the sample were measured using thermocouples, two of which were placed inside the sample, one close to the surface and one at the mid-height of the cup (Figure 1). During an experiment run, the copper block was cooled to 77 K using liquid nitrogen, which led to typical sample temperatures between 130 and 140 K.

In order to collect the material ejected from the sample upon impact, a 350 mm diameter aluminum collection plate was placed around the cup, flush with the sample surface. This plate was supported by the copper block holding the cup and was therefore also cooled. Concentric rings were etched on the plate to mark distances of 50, 60, 70, 80, 100, 125, and 150 mm from the center of the sample cup.

The drop mechanism, the target cup, and the plate were kept inside a vacuum chamber. This chamber was evacuated to 10 mTorr during an experiment run, thus eliminating air drag on projectile and ejecta particles, as well as air moisture interfering with the cooled sample. In order to record the ejecta curtain, a high-speed camera was placed level with the sample surface and collection plate, outside the vacuum chamber, in front of a window flange. The sample was illuminated using a thin laser beam in a plane at 90° to the line of sight of the camera. The laser thus illuminated the ejecta plume only in that plane, which allowed for the recording of the two-dimensional evolution of the plume particles.

With the ICE setup described above, we collected the following types of data:

• 1.  
  Environmental data, such as system temperature and chamber pressure. This data was mostly used to determine the constraints for experiment runs. For example, impacts were only performed for a core sample temperature <150 K and pressures <200 mTorr.
• 2.  
  Video recordings of the ejecta plume illuminated in the plane perpendicular to the camera's line of sight (see Figure 2). These videos were recorded at a frame rate of 400 fps, with a resolution of 1080p.
• 3.  
  Ejected target material masses collected on the ringed plate. After each impact, the chamber was carefully vented using a valve placed under the collection plate, so as not to disturb the sample material. Upon opening the chamber, the plate was retrieved and the ejecta from each of its rings were collected and weighed.
• 4.  
  Pictures of the crater were taken after each impact (see Figure 2). As the size of the cup and the geometry of the picture angle were known, these pictures were used to measure crater sizes and depths.

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Three types of projectiles were used: metal, glass, and Teflon. All projectiles were 2 cm spheres. Their masses were measured to include the 0.46 g metal pin, and were divided by the volume of the sphere to determine their density. The projectile densities are listed in Table 3, and ranged from 7.67 to 9.46 g cm⁻³ for metal, from 2.52 to 2.77 g cm⁻³ for glass, and 1.45 g cm⁻³ for Teflon.

Three types of target material were prepared: dry regolith at room temperature, frosted regolith at cryogenic temperatures, and regolith–water ice mixtures at cryogenic temperatures.

The regolith component of the target material was comprised of JSC-1 lunar simulant granular material. The JSC-1 grains were sieved to a size distribution between 100 and 250 μm. Scanning Electron Microscope pictures of these JSC-1 grains were presented in Brisset et al. (2018).

Frosted regolith was prepared by cooling the JSC-1 samples above to temperatures below 150 K in air. This led to the formation of a frost layer at the surface of the grains. A detailed density analysis showed that this frosting constituted about a 5% volumetric ice content in the target samples. Therefore, we listed these frosted samples with a 5% volumetric ice content in Table 3.

Water ice grains were prepared by spraying liquid water onto the cold metal surface of a mortar (<150 K using liquid nitrogen) and crushing it into fine grains using a cooled pestle. In order to determine the grain size distribution, we prepared several ice samples and placed the grains on thin cooled metal plates, which we observed under a microscope. We recorded about 30 pictures of such samples and ran automated image analysis to determine the grain sizes. Figure 3 shows the resulting size distribution, which follows a power law except for an additional population of millimeter-sized grains. These water ice grains were then mixed with the cooled JSC-1 sample at volumetric proportions of 33%, 50%, and 75%. During the sample preparation, chamber evacuation, and impact, the frosted and ice mixture samples were continuously cooled using an LN2 cooling loop around the target cup.

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The targets were prepared by pouring the material into the sample cup, while avoiding any types of vibrations. The cup was overfilled and delicately leveled off using a thin metal ruler. For cold targets (frosted and water ice mixtures), this process was performed under cryogenic conditions. The cup was then weighed and placed in the impact setup, while continuing to avoid vibration as much as possible. If the target material was still level with the top of the cup once it was in the impact setup, the procedure was considered successful. If not, it was repeated until it was successful. Figure 4 shows the recorded porosities for the various target types that we studied.

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The parameters that varied in our experiment plan were the impact energy (the drop height of the projectile), projectile density, and target material. In the first step, a set of impacts were performed at room temperature into pure JSC-1 targets. In the second step, the JSC-1 grains were cooled to <150 K, but no ice was added. Finally, the JSC-1 grains were cooled and mixed with water ice grains at 33%, 50%, and 75% volumetric ice content. For all the target materials, a minimum of three impacts per projectile per impact energy were performed. Table 3 in Appendix lists the experiments performed, with several parameter sets having many more drops, as they were used for hardware setup and testing but occurred at relevant conditions.

In Figure 5, we show the total ejecta masses retrieved from the collection plate after impacts in dependence on the impact energy (left) and the water ice content (right). As intuitively expected, we observe a general trend of the ejected mass increasing with increasing impact energy. The trend with varying water ice content is not as obvious, with the 50% samples producing the largest amounts of ejecta among the cooled samples.

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The room-temperature samples produced the largest amounts of ejecta overall, while the frosted samples without water ice produced the least. We observed up to one order of magnitude less ejecta when the target samples were cooled to cryogenic temperatures. Introducing water ice grains into the samples increased the ejecta masses until 50% volume, then decreased them beyond that.

In order to compare our results to well-established impact scaling laws, we used the concentric rings on our collection plate to measure the cumulative ejecta masses with ejection speed (Figure 6). As seen in the point-source scaling laws presented by Housen & Holsapple (2011), the cumulative ejecta masses of our low-speed impacts present a power-law regime, which breaks down for large ejection velocities (>1 m s⁻¹). While the point-source assumption used in Housen & Holsapple (2011) is usually only appropriate when ejecta are studied at ranges greater than the impactor radius, and for impact velocities greater than the target sound speed, the authors note that there are cases where its applicability is found to extend beyond those limits. Here, we observe that, despite the large impactor size compared to the target sample and the low impact speeds (≈3 m s⁻¹), the impact ejecta still follow a power-law regime with the ejection speed. A notable difference with the point-source cases involves the numerical values of the slope coefficient calculated: in the works by Holsapple (1993) and Housen & Holsapple (2011), the coefficient μ is known to vary between 1/3 and 2/3, with μ = 0.41 for dry soils. In our low-speed impact experiments, we find μ = 0.8 for frosted and ice mixture samples, and μ = 1.6 for dry samples.

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In Figure 6, we also observe that the room-temperature samples strongly differ from their cryogenic counterparts, when no water ice is added. The ejecta masses are up to an order of magnitude less for cryogenic samples, and the slope of the power-law fit is halved compared to the room-temperature samples.

While investigating this change in sample behavior upon cooling, we considered the fact that we are cooling the granular material in air, which leads to the deposition of a layer of frost at the surface of the grains, due to the condensation of air humidity. This frost can change the surface properties of the grains and impact the strength of the material (Hatzes et al. 1991). In order to verify whether this could be the cause of the discrepancy between the room-temperature and cryogenic sample behaviors, we prepared "dry" cryogenic samples in N₂ vapor, rather than air. In Figure 6, we show the measured ejecta masses for these additional samples as black diamonds. The ejecta masses were very close to the room-temperature ones, both in quantity and cumulative power-law slope. Therefore, we concluded that grain surface frosting, since it generated higher interparticle cohesion, introduced sample behavior changes, with the frosted targets producing much less ejecta than the dry ones, as well as a reduced-speed cumulative mass power-law slope.

This new insight also allowed for a tentative interpretation of the ejecta mass variation with sample water ice content, as seen to the right of Figure 5. As all the samples containing water ice were prepared in air, it is to be expected that their grains should be frosted. If grain frosting and adding ice grains both reduce the impact ejecta mass, then the curve observed to the right of Figure 5 can result from the competition between these two processes. As the effect of surface frosting is expected to be dependent on the total surface available for frost deposition, it should be more pronounced for regolith grains, which are more irregular in shape than the ice grains (see the inset in Figure 3). Therefore, for the samples with low–water ice fractions, the frost coating of the grains could be the dominant mechanism reducing the ejecta masses. As the fraction of regolith grains is reduced, the available deposition surface decreases and the ejecta masses increase. For more than 50% volume ice content, surface frosting should not be dominant any more, and the influence of the presence of ice grains should prevail: the ejecta masses would then decrease with increasing ice fractions.

On the other hand, the low ejecta masses seen for 75% ice mixtures could also be linked to the presence of a population of larger grains in the water ice fraction of the samples.

In Figure 7, we show crater examples from impacts of our investigation. In Figure 8, we show the crater diameters measured for the impacts into dry (red), frosted (black), and ice mixture (blue) samples. As expected, we see the crater diameter increase with impact energy. Given that the main change in impact energy resulted from different projectile masses, rather than from different drop heights, we also show the averages for the impacts performed with the same projectile (Teflon, glass, and brass).

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We note that the crater diameters are very similar for the frosted and water mixture samples, but significantly larger for the dry samples. If we compare these crater size data to the ejecta mass data (Figure 6), we see that more ejecta (ice grains versus ice frost) does not correspond to larger craters, for the frosted and ice mixture samples. Given that the crater depths did not vary significantly between the frosted and ice mixture samples (Table 2), this could indicate that frosted regolith gets displaced upon impact, rather than ejected, in comparison to the ice mixtures.

Next, we compare our impact data to the crater scaling laws presented in Housen & Holsapple (2011). In the first step, we need to estimate whether our impacts occur in the strength or gravity regimes.

3.2.1. Impact Regime

3.2.2. Crater Size Scaling

In the strength regime, Housen & Holsapple (2011) give the following scaling equation for the crater radius R:

$$\begin{eqnarray}&&R{\left(\displaystyle \frac{\rho }{m}\right)}^{\tfrac{1}{3}}={H}_{2}{\left(\displaystyle \frac{\rho }{\delta }\right)}^{\tfrac{1-3\nu }{3}}{\left[\displaystyle \frac{Y}{\rho {U}^{2}}\right]}^{-\tfrac{\mu }{2}},\end{eqnarray} \tag{ 1 }$$

with m, δ, and U being the projectile mass, density, and speed, and H₂, ν, and μ being scaling parameters. By investigating the dependence in our data set of this scaled radius on each of the factors to the right of Equation (1), we find that H₂ = 4.34, ν = 0.23, and μ = 0.5 (Figure 9).

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We note that the numerical values for the scaling parameters H₂, ν, and μ are different than reported for dry soils and porous materials (μ ≈ 0.4 and ν ≈ 0.4; Housen & Holsapple 2011). This comes as no surprise, as we are studying impacts that cannot be considered within the point-source approximation. We also note that the parameter μ deduced from the crater analysis is different from the one that we deduced from the ejecta mass analysis (Section 3.1). A possible explanation for this discrepancy is the fact that, in our crater size analysis, we considered a constant parameter μ for the three types of target material in our investigation, thus neglecting the dependency of μ with the target material strength. However, the ejecta mass analysis suggests otherwise, with at least two different values for μ for dry and ice mixture samples.

As shown in Figure 7, the crater depth was taken as either the deepest point of the crater or, if the projectile partially embedded itself into the target, as the intersection of the crater slopes. Geometric analysis shows that the crater depth h can be written as h = b₁ − b/2, with b₁ and b being the lengths defined in Figure 7. This equation still applies if b₁ > b.

Table 2 lists the crater depth-to-diameter (d/D) ratios that we measured for the impacts into dry, frosted, and ice mixture samples and projectile types (corresponding to the impact energy levels). We did not observe a significant dependency of d/D with either impact energy (i.e., projectile) or target type. The values of ∼0.1 that we find are consistent with the ones measured for secondary craters across the solar system (Bierhaus et al. 2018).

The scaling of the crater sizes that we measure in our impacts is somewhat in line with results of other experiments used to validate the scaling laws of Housen & Holsapple (2011). The power-law coefficient that we find between the scaled crater size and the Π₃ = Y/ρ U² parameter in the strength regime is within the range of commonly used numbers (0.41 for dry soils and 0.55 for nonporous materials). However, the constant fitting parameter H₂ that we find is much higher than is found in Housen & Holsapple (2011). So, while our crater sizes scale with material strength in the same way as point-source impacts in hard rock, they are offset and much larger than predicted. Indeed, if we estimate our crater volumes based on a conical crater shape and our measurements for crater diameter and depth, we find values between 10⁻⁶ and 10⁻⁵ m³ (Figure 10). If we compare these values to data extrapolated from impacts into basalt targets (Moore et al. 1963; Gault 1973, for impact energies between 10 and 1000 J or 10⁸ to 10¹⁰ ergs), we find that the craters that we generate in JSC-1 granular targets are about five orders of magnitude larger. Similarly, we compare our data to measurements performed on impacts into solid water ice (Lange & Ahrens 1987, also for impact energies around 1000 J or 10¹⁰ ergs). Again, the craters generated in our ice–regolith mixture targets are about five orders of magnitude larger than expected from extrapolating these solid ice data.

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We suggest that these differences are due to the granular nature of the target material (both Moore et al. 1963 and Lange & Ahrens 1987 use solid target blocks). Indeed, experiments by Burchell et al. (2001) were performed in the same impact energy range as ours (around 0.01 J or 10⁵ ergs, albeit with much smaller projectiles and larger impact speeds) using pure water ice blocks. They find crater sizes that are smaller than ours by more than three orders of magnitude, indicating that the impact energy differences between the experiment types are not the cause of the differences in crater sizes. Koschny & Grün (2001a) also investigate silica–ice mixtures prepared as solid blocks in this same impact energy range, and find crater sizes that are smaller than ours by about four orders of magnitude. Therefore, mixed composition with minerals and water ice is also not responsible for the crater size differences.

Uehara et al. (2003) and Walsh et al. (2003) performed low-speed impact experiments into spherical glass beads. They find crater sizes around 5 cm, which is similar to the values that we found in the ICE impacts, and supports the idea that impacts into granular media produce much larger craters than impacts into solid targets. In order to compare our results to these impacts into granular media, we calculate the scaled crater diameters and scaled impact energies, following the example of Walsh et al. (2003). We find that the crater sizes in our experiments vary normally with scaled energy, with a slope of 0.1. This is flatter than the 0.245 slope found by Walsh et al. (2003) and displays a behavior closer to the finest grain sizes they used (45–90 μm). This could be indicative of the increased intergrain cohesion present in our samples of irregular grains compared to the spherical beads studied in Walsh et al. (2003), which becomes more apparent with their finer-grained samples.

The crater d/D ratios that we find in our experiments are in line with the values found in other experiments (0.125 in Walsh et al. 2003, for example) as well as in secondary craters throughout the solar system (around 0.1 in Robbins et al. 2018). Such secondary craters result from impacts at lower speeds compared to the primary craters, as only ejecta speeds at the lower tail of the generated ejecta distribution stay captured by the gravity field of the parent body. These lower-impact speeds make it more likely for craters to form mostly in the regolith layers covering the rocky surface. Therefore, our experiment results are more relevant to secondary craters than to primary ones.

In that context, if we consider the results that we find in Section 3.2, we would expect secondary craters on regolith-covered surfaces to be larger than expected by point-source scaling laws: while the crater size evolution trends are similar with a μ coefficient within the range of values commonly used when applying these laws (Housen & Holsapple 2011), the scaling constant in the strength regime H₂ is larger by about a factor of 10. Therefore, secondary craters on small bodies, where the strength regime would apply, would be expected to be about 10 times larger than predicted by using the Housen & Holsapple (2011) scaling. If we assume that this transfers to impacts in the gravity regime, we can expect secondary craters to be larger than predicted on all planetary bodies. This is actually found by Singer et al. (2013), in their study of impact fragment sizes on Europa. In their work, the fragment sizes are estimated using the diameters of secondary craters, combined with the Housen & Holsapple (2011) scaling laws and classical ballistic mechanics. For impacts in the gravity regime, this boils down to fragment diameters d_frag following

$$\begin{eqnarray}&&{d}_{\mathrm{frag}}={\left(\displaystyle \frac{0.3}{\pi {H}_{1}}\right)}^{\tfrac{2+\mu }{6}}{D}_{\sec }^{\tfrac{2+\mu }{2}}{\left(\displaystyle \frac{g}{{v}_{\mathrm{frag}}^{2}}\right)}^{\tfrac{\mu }{2}},\end{eqnarray} \tag{ 2 }$$

with D_sec being the diameter of the secondary crater produced by this fragment, v_frag being its impact speed, and H₁ and μ the Housen & Holsapple (2011) scaling parameters for impacts in the gravity regime. All things remaining the same, a larger H₁ by a factor of 10 leads to smaller fragment sizes by a factor of 0.38. This would reconcile the results of Singer et al. (2013) with the fragment sizes expected from the spallation model of Melosh (1984).

One application for impacts in ice targets is the dynamics of Saturn's rings. Durisen et al. (1989, 1992) discuss in their papers the ballistic transport in planetary ring systems due to particle erosion mechanisms. One input parameter to their model is the crater yield Y, which is the ratio between the ejected mass after impact and the projectile mass before impact. In the analysis of their experiment results, Koschny & Grün (2001a) attempt to match the yields produced in their laboratory impacts to the values estimated by the model developed in Durisen et al. (1992). They find that the crater yields that they produce when impacting solid ice–silica mixture targets would require the majority of projectiles impacting ring particles to be meter-sized. This is at odds with the size distribution of interplanetary particles, which peaks between micrometer and millimeter sizes (Fechtig et al. 1974; Grün et al. 1985). Here, we apply our cratering data in granular targets to the Durisen et al. (1992) model, following the method used by Koschny & Grün (2001a). For this, we rewrite their yield equation to adapt it to our data set, which does not contain 100% water ice targets. If we use our 50% ice–regolith mixtures instead, this yield equation can be written as

$$\begin{eqnarray}&&Y={V}_{\mathrm{1,50}}{\rho }_{t}{2}^{-b}{m}_{i}^{b-1}{v}_{i}^{2b},\end{eqnarray} \tag{ 3 }$$

with V_1,50 and b being the fitting parameters of the 50% ice mixture crater volume data in Figure 10, and ρ_t the target density. The fitting parameters can be extracted from Figure 10 as V_1,50 = 1.73 × 10⁻⁶ m³ and b = 0.15. On average, ρ_t = 1100 kg m⁻³ for 50% ice mixtures (see Table 3). For the yield and impact speeds, we choose the same values as Durisen et al. (1992) and Koschny & Grün (2001a), i.e., Y = 1.8 × 10⁶ and v_i = 14,000 m s⁻¹. With these values, we obtain an impactor mass of m_i = 7.1 × 10⁻¹⁰ kg, which translates to an impactor grain diameter of 82.7 μm, assuming that it has a composition close to silica, and 111 μm, if it is composed of water ice. These particle sizes are much more plausible for interplanetary particles. The much larger yields produced by granular targets compared to solid ones seem to be able to reconcile laboratory impact data with the model developed in Durisen et al. (1992), and support the proposition of Koschny & Grün (2001a) that ring particles are covered with, or entirely composed of, regolith.