Analysis of the dynamical evolution of lofted particles around (65803) Didymos asteroid

Abstract

<p align="justify"><strong>Introduction</strong></p> <p align="justify"><span lang="en-US">(65803) Didymos is a binary asteroid that orbits the Sun </span><span lang="en-US">having a semi-major axis of </span><span lang="en-US">1.64 AU</span> <span lang="en-US">and is the target of the DART (NASA) and Hera (ESA) missions. The system is made up of a 780 m diameter primary body (Didymos) and a 160 m satellite (Dimorphos), orbiting the primary with a semi-major axis of 1180 m and an orbital period of 11.9 h [1]. The primary has a rotation period of 2.26 h, very close to the limit of structural stability [2] [3]. The low density estimated for Didymos, 2170 kg/m<sup>3</sup>, shows that it is not a monolithic body but </span><span lang="en-US">instead </span><span lang="en-US">has a high macroporosity, typical of gravitational aggregates or <em>rubble-piles</em>. Numerical simulations show that they can be generated naturally in the aftermath of a catastrophic collision between asteroids, as a result of the gravitational interaction between the irregular fragments resulting from the collision [4]. The evolution under YORP spin-up may lead in </span><span lang="en-US">the</span><span lang="en-US"> same case to oblate spheroidal shape asteroids with a</span><span lang="en-US">n</span><span lang="en-US"> equator</span><span lang="en-US">ial</span><span lang="en-US"> bulge [5], commonly called <em>top-shapes</em> (eg: (162173) Ryugu [6], (101955) Bennu [7], (65803) Didymos, etc.). Th</span><span lang="en-US">ese</span><span lang="en-US"> bodies may rotate close to the limit of structural stability, kept together by the shear forces generated by friction between their components. </span><span lang="en-US">T</span><span lang="en-US">he local acceleration near the equatorial regions may be directed outwards </span><span lang="en-US">in these asteroids</span><span lang="en-US">, allowing regolith to leave the surface [8] [9]. When this happens, particles evolve under the action of the gravitational field of the asteroid, the gravitational force of the Sun, the pressure of solar radiation, and in the case of binary asteroids, the secondary’s gravitational force intervene as well.</span></p> <p align="justify"><strong><span lang="en-US">Met</span><span lang="en-US">h</span><span lang="en-US">odology</span></strong></p> <p align="justify"><span lang="en-US">In this work, we study the dynamics of the particles that are ejected from the surface of Didymos when the centrifugal acceleration is large enough to overcome local gravity. The analysis is carried out from the development of a numerical code that integrates the particles’ equation of motion in a rotating frame of reference, centered on the primary asteroid. A polyhedral shape model for Didymos is considered, formed by 1000 vertices and 1996 triangular faces, in which centers particles are placed. Particle size distribution is generated by a power law</span><span lang="en-US"> n(r)=kr<sup>α</sup></span><span lang="en-US"> with an index set as </span><span lang="en-US">α</span><span lang="en-US">=-3.5.</span><span lang="en-US"> The environment of the asteroid is studied by computing the radial density of particles. To do this, a 3D grid is built; the surface is divided into bins of latitude and longitude and is propagated in radial bins. A process of detachment and re-entry of particles to the primary is observed, which could promote the potential formation of dust bands in the equatorial region of the asteroid. Trajectories are analyzed and the percentage of particles that re-accumulate on the secondary and the ones that completely escape the system are calculated.</span></p> <p lang="en-US" align="justify"> </p> <p lang="en-US" align="justify"><strong>References</strong></p> <p lang="en-US" align="justify">[1] Benner, L. A. et al. Radar imaging and a physical model of binary asteroid 65803 Didymos. Bull. Am. Astron. Soc. 42, 1056 (2010).</p> <p lang="en-US" align="justify">[2] Pravec, P. and 30 colleagues 2008. Spin rate distribution of small asteroids. Icarus 197, 497–504.doi:10.1016/j.icarus.2008.05.012</p> <p align="justify"><span lang="en-US">[3] Margot, J.-L., Pravec, P., Taylor, P., Carry, B., Jacobson, S. 2015. Asteroid Systems: Binaries, Triples, and Pairs. Asteroids IV 355–374. doi:10.2458/azuuapress9780816532131-ch019</span></p> <p lang="en-US" align="justify">[4] Campo Bagatin, A., Alemañ, R.A., Benavidez, P.G., Richardson, D.C., 2018. Internal structure of asteroid gravitational aggregates. Icarus 302, 343–359.</p> <p lang="en-US" align="justify">[5] Cheng, B. and 7 colleagues 2021. Reconstruct-ing the formation history of top-shaped asteroids from thesurface boulder distribution. Nature Astronomy 5, 134–138.doi:10.1038/s41550-020-01226-7</p> <p lang="en-US" align="justify">[6] Watanabe, S. et al. Hayabusa2 arrives at the carbonaceous asteroid 162173 Ryugu—a spinning top-shaped rubble pile. Science 364, 268–272 (2019).</p> <p lang="en-US" align="justify">[7] Lauretta, D. S. et al. The unexpected surface of asteroid (101955) Bennu. Nature 568, 55–60 (2019).</p> <p lang="en-US" align="justify">[8] Campo Bagatin, A. 2013. Small Asteroids with “Dusty” Atmospheres?. Lunar and Planetary Science Conference.</p> <p lang="en-US" align="justify">[9] Yu, Y., Michel, P., Hirabayashi, M., Richardson,D. C. 2019. The expansion of debris flow shed from the primary of 65803 Didymos. Monthly Notices of the Royal Astronomical Society 484, 1057–1071. doi:10.1093/mnras/sty3515</p> <p lang="en-US" align="justify"> </p> <p lang="en-US" align="justify"> </p>

Dynamical origin of Dimorphos from fast spinning Didymos

“…However, due to computational limitations, these works only perform short-term simulations, and it is not clear how the history of ejections by Didymos would take place in a long-term period. Since the YORP effect is continuously increasing Didymos rotation, it is possible that new avalanches will occur on the object, possibly re-injecting into the ring part of the material fallen onto Didymos [Trógolo et al, 2021]. In this case, we expect the total amount of material deposited in the ring to be greater than the amount of material actually detached from Didymos, since part of the material would be recycled.…”