New Crater Scaling Law for Coarse-Grained Targets Based on Demensional Analysis

Lunar and Planetary Science XLVIII (2017) 1911.pdf

NEW CRATER SCALING LAW FOR COARSE-GRAINED TARGETS BASED ON DEMENSIONAL ANALYSIS. E. Tatsumi1 and S. Sugita1,2, Dept. Earth and Planetary Science, Univ. of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo, Japan ([email protected]), 2Research Center for the Early Universe, Univ. of Tokyo.

Introduction: “Rubble-pile” objects, loosely Fracturing stage: Because shock wave in a coarse- bound and gravity-dominated aggregates with negligi- grained target is much slower than that within each ble tensile strength, are now widely accepted to be rigid target grains, which usually have shock wave common among small asteroids [e.g., 1]. Currently, velocities on the order of km/s, the initial shock frag- there are two ongoing sample-return missions for pos- mentation due to a collision between a projectile and sible rubble-pile asteroids: Hayabusa2 for Ryugu and target grains would complete before substantial exca- OSIRIS-REx for Bennu. Both asteroids have thermal vation motion takes place. Immediately after the colli- inertias slightly smaller [2-4] than Itokawa but signifi- sion, the very fast ejecta from the first-contact point cantly larger than that of fine regolith, suggesting emerge (Fig. 2a, b)). The fragmentation of target grains coarse-grained surfaces. On such rubble-piles, im- occurred in the very vicinity of the impact site could be pactors whose sizes are comparable to or smaller than observed, agreeing with the simulation results [8]. target grains often collide. Crater scaling for coarse- Excavation stage: After the fracturing stage, the grained targets is important for crater age estimates on momentum transfer triggers subsequent excavation such rubble-piles. flow. Unfractured grains move along the excavation The purpose of this study is to understand cratering flow in a similar fashion to the flow of the gravity- on rubble-pile asteroids with fragmentation of grains, dominated simple crater. However, under the condi- where the projectiles are comparable to or smaller than tions that the impact energy was not significantly larg- target grains in size and the impact energy is larger than the disruption energy of one target grain. We de- rive a new scaling law for coarse-grained surfaces ex- tended from the classic pi-scaling law by Holsapple [5] based on impact experiments and momentum conser- vation upon the first contact. Impact Experiments: Because previous studies [6,7] did not take into account both the ratio ! = # % '$/% *∗ of impact energy to disruption energy $ & ) + of a target grain and the size ratio - = .&/.), they are not consistent with each other. Here, we conduct experiments under various combinations of the energy FIG. 1 Crater rim diameter and depth on coarse-grained targets. The solid line indicates the diameter/depth ratio of ratio ! and the size ratio -. simple craters on fine sand target. Some of our results show We conducted impact experiments at velocities 79 shallower shape than the simple crater. – 224 m/s and 1 – 6 km/s. We used polycarbonate projectiles 0.76 g in mass and 10 mm in diameter for lower velocities and 0.068 g in mass and 4.7 mm in diameter for higher velocities, respectively. Pumice targets with different mean grain diameters (~7, 9 and 16 mm) were used as simulated boulder targets. Some of the experiments were performed with quarter-space targets to observe the impact process underneath the target surface. We measured the final rim-to-rim diameter and depth of craters (Fig.1). We found that the classic pi-scaling law for fine dry sand could account for the large impact energy range but may considerably over- estimate crater size for small impact energy. Cratering Mechanism: Figure 2 shows time-series images of a projectile (a=2.38 mm) impacting a quarter-space pumice target (~9 mm) at ~4.3 km/s. Note FIG. 2 Background-subtracted time-series of a quarter-space experiment. White dotted line indicates the surface of the that a pre-impact image was subtracted from each im- pre-impact target and colored dotted lines depict shock fronts age in order to visualize moved grains. moving outward. Lunar and Planetary Science XLVIII (2017) 1911.pdf

er than the target grain disruption energy, the excava- face of Itokawa are resurfaced in the short time-scale tion flow speed was much slower than the excavation and obliterates small craters with the crater depth ~1 m flow in fine sand targets, resulting in a much smaller in ~104 – 105 yr. final crater size. The excavation stage appears virtually Because the number density of large depressions on uninfluenced by the material strength of constituent Itokawa has the similar distribution with its crater pro- grains but might be controlled by friction between duction function, the age for large crater retention age grains as dry sand. might be preserved from the last global resurface event New Crater Scaling Law: We derived a new pi- 10 – 33 Myr ago. That is, Itokawa might experience a scaling, starting from the following equation instead of global resurface long after the catastrophic disruption the classic pi-scaling [5]: of the parent body (~1.3 Gyr [14]). Acknowledgements: The research was supported by the Japan Society for the Promotion of Science (JSPS) ∗ where target disruption energy *+ for unit mass [e.g., KAKENHI (Grant Number 26247092, 15J06330, and 16H06719) and Core-to-Core program “International Net- 9], target material density /) and the target grain radius 0 , which influence crater volume on coarse-grained work of Planetary Sciences”. ) References: [1] Richardson et al. (2002) Asteroids III, 501. target noticeably. [2] Hasegawa et al. (2008) Publ. Astro. Soc. Jpn, 60, S399. Assuming that momentum transfers from an im- [3] Emery et al. (2014) Icarus, 234, 17. [4] Müller et al. pactor to a first-contacted target grain immediately (2016) A&A. [5] Holsapple (1993) AREPS, 21, 333. [6] after collision with highly inelastic deformation, that is, Güttler et al. (2012) Icarus, 220, 1040. [7] Holsapple & th the impacted target grain and the impactor move to- Housen, (2014) LPS 45 , #2538. [8] Barnouin et al. (2002) LPS XXXIII, #1738. [9] Fujiwara (1980) Icarus, 41, 356. [10] gether after the collision, the effective impact velocity ∗ Mizutani et al. (1983) JGR, 88, A835. [11] Schmidt and becomes ' = '%&/(%& + %)) and effective im- Housen (1987) Int. J. Impact Engng., 5, 543. [12] Cintala et 5# 6 pactor size becomes 4∗ = 4 % (% + % ) on a al. (1999) MAPS, 34, 605. [13] Hirata et al. (2009) Icarus, & & ) 200, 486. [14] Park et al. (2015) MAPS, 50, 2087. perfect elastic collision. Dimensional analysis yields new pi-scaling law:

(1)

where 7# = 0.24, =# = 0.41, 7$ = 0.01, =$ = 1.23 for pumice grain targets. The first term of the right-hand side indicates dependency to the gravity term with the effective size and the effective velocity after collision, and the second term is the energy ratio term. The gravity term dominates at higher velocities and the energy ratio term dominates at lower velocities, respectively. Figure 3 shows a comparison of estimated crater volume between the new scaling law (eq.(1)) FIG. 3 Comparison between Experimental results and pre- ∗ and experimental results from our and previous studies dicted CD from eq.(1). The region for a factor of 2 is shown [10-12]. Note that the new scaling law is applicable with gray hatching between the ratio of experimental values ∗ to predicted values from 0.5 and 2. when @A > 10, i.e., the final crater volume is smaller collisional lifetime for ~ 1 km (O’ Brein+2005) Age (yr)

than ten times of grain volume. 9 8 7 6 5 4 3 2 Depth 10 10 10 10 10 10 10 10

Discussions: Based on the new crater scaling law, Ne deposition(Nagao+2011) ~10-100 nm Rim thickness (Berger+2015) the crater retention age of Itokawa can be estimated, * Spectral analysis (Bonal+2015) * Spectral analysis (Koga+2014) ~1-10 mm Solar ﬂare track (Noguchi+2014) assuming that the circular depressions [13] on Itokawa Solar ﬂare track (Berger+2015) CRE (Nagao+2011) are of impact origin. It would take 10 – 33 Myr to ac- <1 m CRE (Meier+2014) Galactic CRE (Nishiizumi+2015) cumulate five largest craters (D>100 m), but smaller Boulder dist. (Basilevsky+2014) ~10 m Crater dist. @rigid body (Michel+2009) craters (12.5 < D <18 m) would take much shorter time Crater dist. @coarse rubble (this study) Global resurface or reshape Ar-Ar (Park+2015) 4 5 by catastrophic disruption ~10 – 10 yr. Although it is not clear what thickness of or spinning up by YORP

regolith migration layer 100-m diameter crater density and 12.5-18m cra- by small impacts, dust levitation, and tidal force ters may represent, the former represents resurfacing near-Earth orbit Catastrophic disruption main-belt orbit history of much thicker layer, perhaps ~10m. Thus, the of the parent body FIG. 4 Summary of age estimates on Itokawa from both observed age difference between different size crater sample analysis and remote sensing observation. Clear corre- candidates strongly suggests that regolith on the sur- lation between layer depth and ages is shown.