Effect of Giant Cratering Impacts on the Slow Rotation of Asteroid Mathilde

Abstract

AbstractThe super slow rotation of the main belt asteroid 253 Mathilde has puzzled scientists for over twenty years, since the first glimpse by the Near Earth Asteroid Rendezvous (NEAR) spacecraft in 1997 [1]. With a very long rotation period of 418 hours [2], Mathilde is one of the slowest rotators in the solar system. The YORP effect, which was previously suggested to explain the slow rotation of small asteroids [3], is unlikely to spin down a 53-km-diameter object in 4.5 Gyr. Alternatively, the impact mechanism could be an explanation. Mathilde has at least five giant craters that are comparable in size to its radius [4], where the related impacts must have delivered a fair amount of angular momentum to the body and possibly spin it down [5]. It is also surprising that all the giant craters are well preserved without destroying each other, possibly due to the highly porous nature [6]. However, how these giant cratering impacts interacted with the structure of Mathilde, and ultimately evolved it into a slowest rotator, remain unexplained by existing works.To re-examine these questions, we performed smoothed particle hydrodynamics (SPH) simulations of the giant cratering impacts on a homogeneous porous target, implemented with the Drucker-Prager strength model, Tillotson EOS for basalt, and the P-α porosity model. The simulations include both phases of shock fragmentation and gravitational collapse, which lasts a few hours until the remnant body reaches a stable rotation. The angular momentum (AM) transfer efficiency ζ, the ratio between the rotation change of the target and AM of the impactor’s orbital motion, is then expressed as a function of the impact angle. To model the impact-induced spin history of Mathilde, we generated sequential/virtual impacts  in each of our 105 Monte-Carlo tests (e.g., Figure 1), following the main belt size distribution and the intrinsic collision probability. The statistic results suggest a median spin change ∆ω of 0.6 rev/d, compared with the 2.2 rev/d in a perfectly inelastic case. Note that the spins of large asteroids (>50 km) peak at ~1–2 rev/d, which should represent the primordial spin at their formation. Assuming a initial spin of 1 rev/d, there are only 2% cases ending at < 0.5 rev/d, and 0.02% at < 0.1 rev/d. The slow rotating Mathilde could be in these rare cases, or formed at a much lower spin rate. Future works will investigate the effect of different porous structures like micro/marco-porosity or rubble piles, to help constrain the properties and impact process of Mathilde-like primitive asteroids. Figure 1. Impact-induced spin history example, where a 53-km-diameter target is impacted by 75 impactors (>0.5 km) at different velocities and angles during 4.5 Gyr. References[1] J Veverka, P Thomas, A Harch, et al. NEAR’s flyby of 253 Mathilde: Images of a C asteroid. Science, 278(5346):2109–2114, 1997.[2] Stefano Mottola, William D Sears, Anders Erikson, et al. The slow rotation of 253 Mathilde. Planetary and Space Science, 43(12):1609–1613, 1995.[3] P Pravec, Alan W Harris, D Vokrouhlicky, et al. Spin rate distribution of small asteroids. Icarus, 197(2):497–504, 2008.[4] AF Cheng and OS Barnouin-Jha. Giant craters on Mathilde. Icarus, 140(1):34–48, 1999.[5] Masahisa Yanagisawa and Sunao Hasegawa. Momentum transfer in oblique impacts: Implications for asteroid rotations. Icarus, 146(1):270–288, 2000.[6] Kevin R Housen, Keith A Holsapple, and Michael E Voss. Compaction as the origin of the unusual craters on the asteroid Mathilde. Nature, 402(6758):155–157, 1999.