Pattern in ejecta curtain generated by the impact into granular targets of various sized particles and application to the ejecta curtain observed in the Hayabusa2 impact experiment – Earth, Planets and Space

Relationship between the pattern in ejecta curtain and the size distribution of particles

Kadono et al. (2019) show that for a target containing two types of particles, large inclusions (4 mm) and fine particles (0.1 mm), the pattern is filamentary (Fig. 1b in Kadono et al. (2019) and Additional file 1: Fig. S1 (#423); video of each shot in Additional file 7, 11, 12, 13: Fig. S1) and the intensity contrast I₉₀/I₁₀ is quite high (> ~ 2.5) at the early stages (Fig. 2c in Kadono et al. 2019). On the other hand, for the target containing slightly smaller inclusions (1 mm) and fine particles (0.1 mm), the pattern is not filamentary [Fig. 1a in Kadono et al. (2019) and Additional file 1: Fig. S1 (#422)] and I₉₀/I₁₀ is lower (< ~ 2) (Fig. 2c in Kadono et al. 2019). The latter case is similar to the results for the target containing only 1 mm particles [Additional file 1: Fig. S1 (#425) and Fig. 2c in Kadono et al. 2019] and only 0.1 mm particles (Additional file 1: Fig. S2 (#348) and Fig. 2c in Kadono et al. 2019). Moreover, in the case of the target that includes 4, 1, and 0.1 mm particles, the pattern is filamentary [Additional file 1: Fig. S1 (#429)] and I₉₀/I₁₀ is lower (Fig. 2c in Kadono et al. 2019). Based on these results, we classify the features into three types: (i) the pattern in the ejecta curtain is filamentary and the intensity contrast is high (> ~ 2.5), (ii) the pattern is filamentary and the contrast is low (< ~ 2.5), and (iii) the pattern is not filamentary (but mesh-like) and the contrast is low. In our experiments, the results for only 4 mm particles (#540), small α and large D (#538), and large α and small D (#533 and #536), correspond to case (iii), not filamentary (but mesh-like) and low contrast. Moreover, the results for small α and D (#532 and #534) also correspond to case (iii). On the other hand, the results for large α and D (#531 and #535) correspond to case (ii), filamentary and low contrast. Note that a mesh pattern like a net is observed in case (iii), and the spaces in the mesh pattern seem to increase as the maximum size of the particles contained by the target increases (e.g., #533 and #536 (Fig. 3); #348 (Additional file 1: Fig. S2) and #422 [Additional file 1: Fig. S1)]. The features of the pattern in the ejecta curtain and the particle conditions are summarized in Fig. 5.

Summary of the features of the pattern in ejecta curtains including the previous results (Kadono et al. 2019; Kadono et al. 2020a). The horizontal axis is the size distribution of particles and the vertical axis is the maximum size of particles. The closed circle, open circles, and open squares indicate case (i) (filament structure and I₉₀/I₁₀ > 2.5), case (ii) (filament structure and I₉₀/I₁₀ < 2.5), and case (iii) (mesh-like structure and I₉₀/I₁₀ < 2.5), respectively. The result for the mixture of particles with 4, 1, and 0.1 mm is plotted as a bimodal distribution

Cases (i) and (ii) occur when the mass fractions of large and small particles are comparable, and the size range is over one order of magnitude. As the fraction of particles with intermediate sizes between these large and small sizes increases, the particle concentration decreases and the features of the ejecta curtain develop as in case (ii). On the other hand, even when the target consists of different-sized particles, if the size range is less than one order of magnitude and/or there is a characteristic size that dominates the mass fraction of particles, the pattern and particle concentration are similar to those for only particles of this size, i.e., case (iii). Thus, when the particles in the targets have different sizes, the pattern in the ejecta curtain depends on the dominant sizes of the particles in the targets.

The mutual inelastic collision of particles with fluctuating velocity during excavation has been proposed as a pattern formation mechanism (Kadono et al. 2015; Kadono et al. 2019; Kadono et al. 2020a; Nakazawa et al. 2021). In the case of targets with large inclusions, since their collision cross section is larger, the coalescence of small particles is promoted. If smaller particles effectively accumulate around larger particles, the particle concentration increases. When there are some particles with intermediate sizes between the largest and smallest sizes, since the small particles also accumulate around the intermediate sized particles, the concentration of small particles is reduced, and the particle concentration would decrease. If the mass fractions of large and small particles are comparable, the mutual influence on their motions becomes strong and the disturbance may develop into filamentary structures throughout the system.

Application to the ejecta curtain observed in the Hayabusa2 impact experiment

The size of the SCI projectile was 13 cm, whereas boulders of several meters were present near the SCI impact point on Ryugu surface (Arakawa et al. 2020; Ogawa et al. 2022). Fortunately, the projectile did not impact a large boulder directly, and a crater with a size that follows the conventional scaling law in the gravity regime was formed (Arakawa et al. 2020). This suggests that the SCI craters were formed in a continuous flow field. Therefore, in this section, we apply our experimental results obtained for targets with size distributions to the ejecta curtain formed by the SCI impact.

The pattern in the ejecta curtain caused by the SCI impact showed that the contrast I₉₀/I₁₀ was quite high (> ~ 3) and then decreased (Fig. 2c in Kadono et al. 2020b). This exhibits the feature as in case (i), and hence, the ejecta curtain caused by the SCI impact may contain comparable mass fractions of large and small particles that vary in size by more than an order of magnitude. A detailed analysis of the observations shows that the ejecta curtain from the SCI impact consisted of grains of approximately a few centimeters (Wada et al. 2021) and boulders up to 1 m in size (Kadono et al. 2020b). The grains with a characteristic size of x_g approximately a few centimeters came from the subsurface layer of Ryugu and the boulders of x_b ~ 1 m came from the surface layer (Kadono et al. 2020b). The cumulative number distribution of grains larger than x per unit area in the subsurface layer, N_g(> x), is represented by an exponential form (Ogawa et al. 2022), ~ N_g(> x_g)e^1−x/xg, and the total mass of grains per unit area in the subsurface layer M_g can be evaluated as ~ x_g³N_g(> x_g). On the other hand, the cumulative number distribution of boulders larger than x per unit area on the surface of Ryugu, N_b(> x), is represented by a power-law form (Sugita et al. 2019) as ~ N_b(> x_b)(x/x_b)^−β, where β is a constant. Hence, the total mass of boulders per unit area on the surface with a size smaller than x_b, M_b, is ~ x_b³N_b(> x_b). Since the comparison between N_g(> x) and N_b(> x) shows that N_g(> x_g) is ~ 10³ times higher than N_b(> x_b) (Ogawa et al. 2022), the total masses of grains of a few centimeters and 1 m boulders per unit area are comparable, M_g ~ M_b, because of x_b ~ 10x_g. This means that if the volume ejected by the SCI impact is the same in the surface and subsurface layers, the ejecta curtain would contain similar mass of grains of a few centimeters and boulders of ~ 1 m size. Conventional crater formation models show that target material shallower than approximately one-tenth of the crater diameter is excavated to be ejecta, while material deeper is displaced beneath the crater floor (e.g., Melosh 1989). In case of the SCI crater, the materials shallower than approximately 2 m or less are ejected [the rim diameter of the SCI crater is ~ 18 m evaluated by Arakawa et al. (2020)]. Since the thickness of the surface layer around the SCI crater is approximately 1 m (Arakawa et al. 2020), the volume ejected by the SCI impact is similar in the surface and subsurface layers. Therefore, the ejecta curtain may contain comparable mass fractions of materials from the surface and subsurface layers, i.e., grains of a few centimeters and boulders of ~ 1 m. Thus, we confirm that the size distribution of boulders and grains in the ejecta curtain caused by the SCI impact is consistent with the patterns exhibiting case (i). Note that, this size distribution is a necessary condition for case 1, and it remains to be confirmed whether other conditions are satisfied for the actual grains in Ryugu to show such a pattern [e.g., restitution coefficient: It has been suggested that the restitution coefficient between particles is important for pattern formation (Kadono et al. 2015; Nakazawa et al. 2021)]. This is an issue for the future work.

Note also that in our experiment, particles of different sizes were mixed in the target before the impact, but in the SCI impact, the materials were separated in the surface and subsurface layers before the impact. However, conventional models of excavation flow suggest that, even when the target has the surface and subsurface layers, if each layer has no strength, the materials from the surface and subsurface layers are mixed in the ejecta curtain (e.g., Melosh 1989). Therefore, the experimental results can be applied to the SCI impact.