Structural stability and cohesive strength of 65803 Didymos

The internal structure and strength of asteroids significantly influence the impact processes on these small bodies and their subsequent collisional evolution (Michel et al., 2015). For a planetary defense mission, it is crucial to understand the structural strength of a hazardous asteroid, which has a strong influence on the asteroid’s response to most mitigation techniques, before taking action. Most asteroids larger than a few hundred meters in diameter are gravitational aggregates, i.e., they are rubble-pile asteroids for which gravity is the principal force holding the body together (Walsh et al., 2018). However, because the gravity is so small on these small bodies, other forces may also have a significant role on the mechanics and dynamics of asteroids. Such forces could be responsible for Bennu’s apparent internal stiffness (Barnouin et al., 2019). Van der Waals cohesive forces could well be a dominant force, and likely improve the strength of rubble-pile asteroids and reduce their chances of breakup by centrifugal or tidal forces (Holsapple 2007; Scheeres et al., 2010).

The target of NASA’s DART (Cheng et al., 2018) and ESA’s Hera (Michel et al., 2018) missions is the near-Earth binary asteroid 65803 Didymos. Its primary is a fast rotator with a spin period of 2.26 hr. With its currently estimated bulk density of 2.1 g/cc, it could not keep its shape stable as a cohesionless rubble pile (Zhang et al., 2017). Our previous study showed that a small amount of material cohesion can largely increase the critical spin rate of a rubble-pile body (Zhang et al., 2018). Therefore, Didymos might possess some level of cohesion in its structure. However, depending on the actual level of cohesion, the shape of Didymos may just be marginally stable. To gain a better understanding of the effect of cohesion and to support these two missions, we conduct numerical modeling to estimate the physical properties and constrain the material strength of Didymos.

We use the Didymos radar shape model (Naidu et al. 2020) to construct rubble-pile models consisting of ~40,000 to ~100,000 spheres with different particle size distributions. We use a high-efficiency soft-sphere discrete element code, pkdgrav (Schwartz et al., 2012; Zhang et al., 2017, 2018), to investigate the effect of cohesion on the structural stability and dynamic behavior of Didymos. We test different values of cohesion and derive the critical amount of cohesion to keep Didymos stable for different rubble-pile representations.

Preliminary results confirm that cohesion is an important parameter in the stability of Didymos. In addition, the particle arrangement and size distribution in Didymos have also a big influence on its behavior. We find that Didymos needs a surface cohesion of about 5 Pa to maintain its stability if the interparticle cohesive strength is uniformly distributed. Since the internal structure is more compact than the surface region, the corresponding internal cohesion is above 10 Pa. With this critical cohesion level, Didymos is at the edge of keeping its shape stable. A rapid small decrease in the spin period on the order of 0.0001 hr would excite the rubble-pile structure and lead to some reshaping or mass shedding. We analyze the possible spin period change induced by the DART impact and make predictions on what Hera may see 4 years after the impact, based on our simulation results.

Acknowledgements: Y. Z. acknowledges funding from the Université Côte d’Azur “Individual grants for young researchers” program of IDEX JEDI. Y.Z. and P.M. acknowledge funding support from the French space agency CNES and from the European Union’s Horizon 2020 research and innovation program under grant agreement no. 870377 (project NEO-MAPP). D.C.R., O.S.B. and H.F.A. are supported in part by the DART mission, NASA Contract #NNN06AA01C to Johns Hopkins University/Applied Physics Laboratory.

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