Transmission of a Seismic Wave Generated by Impacts on Granular Asteroids

Abstract

In this paper, we use a soft-sphere discrete element method code to simulate the transmission and study the attenuation of a seismic wave. Then, we apply our findings to the different space missions that have had to touch the surface of different small bodies in the solar system. Additionally, we do the same in regard to the seismic wave generated by the hypervelocity impacts produced by the DART and Hayabusa2 missions once the shock wave transforms into a seismic wave. We find that even at very low pressures, such as those present in the interior of asteroids, the seismic wave speed can still be on the order of hundreds of meters per second depending on the velocity of the impact that produces the wave. As expected from experimental measurements, our results show that wave velocity is directly dependent on P 1/6, where P is the total pressure (confining pressure plus wave-induced pressure). Regardless of the pressure of the system and the velocity of the impact (in the investigated range), energy dissipation is extremely high. These results provide us with a way to anticipate the extent to which a seismic wave could have been capable of moving some small particles on the surface of a small body upon contact with a spacecraft. Additionally, this rapid energy dissipation would imply that even hypervelocity impacts should perturb only the external layer of a self-gravitating aggregate on which segregation and other phenomena could take place. This would, in turn, produce a layered structure of which some evidence has been observed.

Segregation on small rubble bodies due to impact-induced seismic shaking

“…The above fit indicates that Y varies as p 1/2 , so that from (2.8) we find that the P-wave speed v p ∝ p 1/4 . This matches the theoretical estimate of [52] and is close to the v p ∝ p 0.19 and v p ∝ p 0.17 obtained through DE simulations in [11,55], respectively. We note that we employ results obtained for Ottawa sand because it is siliceous and has a density comparable with chondritic grains found in the regolith of asteroids such as Itokawa et al [21].…”

“…Impacts may also initiate granular landslides. For example, [10] claims that Itokawa’s small size may allow even centimetre-sized impactors to cause global seismic shaking and subsequent grain motion, although recent work [11] questions this. Finally, non-gravitational forces, such as those due to the interaction of grains and solar wind plasma, produce electrostatic forces that may sometimes overcome gravity and cause regolith motion [12,13].…”

The Dimorphos Boulder Swarm

“…The dashed orange curve shows the best-fit q = −3.9 ± 1.5 power law, and, for comparison, the solid black line shows q = −2.8 power law deduced from the Didymos surface boulders. distinguish seismic shaking ejection from cratering using the existing data, the former seems less likely given that the energy propagation through a rubble pile should be heavily damped (Sánchez et al 2022). We note, however, that, if the boulders were ejected by seismic shaking, then the energy ratio ε = 3 × 10 −5 sets a lower limit to the seismic efficiency.…”

Observational characterization of the ejecta from the DART-Dimorphos impact

“…To minimize the color term in the calibration, we choose stars with B p − R p ≈ 0.8. The table of all 12,007 LAST photometric measurements, and about 600 C28 observations, are available electronically 6 , and the binned light curve is plotted in Figure 1 in the main paper.…”

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The Double Asteroid Redirection Test 1, 2 (DART) was intended to test planetary defense strategies via the reaction of the near-Earth asteroid Dimorphos, a satellite of Didymous, to a spacecraft impact. Pre-impact modeling [3][4][5][6][7] predicted a momentum gain of the impacted asteroid in the range of 1 − 5 times that of the impactor. These models further suggest that the velocity distribution of the ejecta depends, for example, on the material cohesion and porosity.

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