Abstract
Solar system small bodies come in a wide variety of shapes and sizes, which are achieved following very individual evolutional paths through billions of years. Nevertheless, some common mechanisms can still be found during these processes, e.g., rubble-pile asteroids tend towards fluid equilibrium as they are reshaped by external disturbances. This paper focuses on the reshaping process of rubble-pile asteroids driven by meteorite impacts. A mesoscale cluster of solid spheres is employed as the principal model for a rubble-pile asteroid, for which little is actually known about their interior structure. We take this simple model as a rough guide to the qualitative aspects of the reshaping processes, and it can reveal, to some degree, the inner workings of rubble-pile asteroids. In our study, numerous possible equilibrium configurations are obtained via Monte Carlo simulation, and the structural stability of these configurations is determined via eigen analysis of the geometric constructions. The eigen decomposition reveals a connection between the cluster’s reactions and the types of external disturbance. Numerical simulations are performed to verify the analytical results. The gravitational N-body code pkdgrav is used to mimic the responses of the cluster under intermittent non-dispersive impacts. We statistically confirm that the stability index I S, the total gravitational potential P G, and the volume of inertia ellipsoid V E show consistent tendency of variation. A common regime is found in which the clusters tend towards crystallization under intermittent impacts, i.e., only the configurations with high structural stability survive under the external disturbances. The results suggest the trivial non-disruptive impacts might play an important role in the rearrangement of the constituent blocks, which may strengthen these rubble piles and help to build a robust structure under impacts of similar magnitude. The final part of this study consists of systematic simulations over two parameters, the projectile momentum and the rotational speed of the cluster. The results show a critical value exists for the projectile momentum, as predicted by theory, below which all clusters become responseless to external disturbances; and the rotation proves to be significant for it exhibits an “enhancing” effect on loose-packed clusters, which coincides with the observation that several fast-spinning asteroids have low bulk densities.
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11 February 2022
A Correction to this paper has been published: https://doi.org/10.1007/s42064-022-0136-2
References
Richardson, D. C., Leinhardt, Z. M., Melosh, H. J., Bottke Jr., W. F., Asphaug, E. Gravitational aggregates: Evidence and evolution. In: Asteroids III. Bottke Jr., W. F., Cellino, A., Paolicchi, P., Binzel, R. P. Eds. The University of Arizona Press, 2002: 501–515.
Bottke Jr., W. F., Richardson, D. C., Michel, P., Love, S. G. 1620 Geographos and 433 Eros: Shaped by planetary tides. The Astronomical Journal, 1999, 117(4): 1921–1928.
Solem, J. C., Hills, J. G. Shaping of Earth-crossing asteroids by tidal forces. The Astronomical Journal, 1996, 111(3): 1382–1387.
Chapman, C. R. Asteroid collisions, craters, regolith, and lifetimes. In: Asteroids: An Exploration Assessment. NASA Conference Publication 2053. Morrison, D., Wells, W. C. Eds. NASA, 1978: 145–160.
Weissman, P. R. Are cometary nuclei primordial rubble piles? Nature, 1986, 320: 242–244.
Benz, W., Asphaug, E. Catastrophic disruptions revisited. Icarus, 1999, 142(1): 5–20.
Michel, P., Benz, W., Tanga, P., Richardson, D. C. Collisions and gravitational reaccumulation: Forming asteroid families and satellites. Science, 2001, 294(5547): 1696–1700.
Asphaug, E., Benz, W. Density of comet Shoemaker-Levy 9 deduced by modelling breakup of the parent “rubble pile”. Nature, 1994, 370: 120–124.
Chodas, P. W., Yeomans, D. K. The orbital motion and impact circumstances of Comet Shoemaker-Levy 9. In: The Collision of Comet Shoemaker-Levy 9 and Jupiter, IAU Colloquium 156. Proceedings of the Space Telescope Science Institute Workshop. Noll, K. S., Weaver, H. A., Feldman, P. D. Eds. Cambridge University Press, 1995: 1–30.
Richardson, D. C., Bottke Jr., W. F., Love, S. G. Tidal distortion and disruption of Earth-crossing asteroids. Icarus, 1998, 134(1): 47–76.
Ballouz, R.-L., Richardson, D. C., Michel, P., Schwartz, S. R., Yu, Y. Numerical simulations of collisional disruption of rotating gravitational aggregates: Dependence on material properties. Planetary and Space Science, 2014, 107: 29–35.
Bottke Jr., W. F., Richardson, D. C., Love, S. G. Can tidal disruption of asteroids make crater chains on the Earth and Moon. Icarus, 1997, 126(2): 470–474.
Farinella, P., Paolicchi, P. Triaxial equilibrium ellipsoids among the asteroids. Icarus, 1981, 46(1): 114–123.
Kryszczyńska, A., La Spina, A., Paolicchi, P., Harris, A. W., Breiter, S., Pravec, P. New findings on asteroid spin-vector distributions. Icarus, 2007, 192(1): 223–237.
Richardson, D. C., Elankumaran, P., Sanderson, R. E. Numerical experiments with rubble piles: Equilibrium shapes and spins. Icarus, 2005, 173(2): 349–361.
Asphaug, E. Similar-sized collisions and the diversity of planets. Chemie der Erde-Geochemistry, 2010, 70(3): 199–219.
Tanga, P., Comito, C., Paolicchi, P., Hestroffer, D., Cellino, A., Dell’Oro, A., Richardson, D. C., Walsh, K. J., Delbo, M. Rubble-pile reshaping reproduces overall asteroid shapes. The Astrophysical Journal, 2009, 706(1): 197–202.
Sánchez, P., Scheeres, D. J. Simulating asteroid rubble piles with a self-gravitating soft-sphere distinct element method model. The Astrophysical Journal, 2011, 727(2): 120–133.
Schwartz, S. R., Richardson, D. C., Michel, P. An implementation of the soft-sphere discrete element method in a high-performance parallel gravity tree-code. Granular Matter, 2012, 14(3): 363–380.
Perko, L. Differential Equations and Dynamical Systems. Springer-Verlag New York, 2001.
Wiggins, S. Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer-Verlag New York, 2003.
Shilnikov, L. P., Shilnikov, A. L., Turaev, D. V., Chua, L. O. Methods of Qualitative Theory in Nonlinear Dynamics. World Scientific Publishing Co. Pte. Ltd., 1998.
Stadel, J., Wadsley, J., Richardson, D. C. High performance computational astrophysics with PKDGRAV/gasoline. In: High Performance Computing Systems and Applications. Dimopoulos, N. J., Li, K. F. Eds. Springer US, 2002: 501–523.
Richardson, J. E., Melosh, H. J., Greenberg, R. Impact-induced seismic activity on Asteroid 433 Eros: A surface modification process. Science, 2004, 306(5701): 1526–1529.
Zhang, Y., Richardson, D. C., Barnouin, O. S., Maurel, C., Michel, P., Schwartz, S. R., Ballouz, R.-L., Benner, L. A. M., Naidu, S. P., Li, J. Creep stability of the proposed AIDA mission target 65803 Didymos: I. Discrete cohesionless granular physics model. Icarus, 2017, 294: 98–123.
Britt, D. T., Yeomans, D., Housen, K., Consolmagno, G. Asteroid density, porosity, and structure. In: Asteroids III. Bottke Jr., W. F., Cellino, A., Paolicchi, P., Binzel, R. P. Eds. University of Arizona Press, 2002: 485–500.
Acknowledgements
Y. Yu thanks Prof. H. Baoyin of Tsinghua University for the beneficial discussions. Most of the simulations in this study were run on the YORP computing clusters at the Department of Astronomy, University of Maryland at College Park.
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Yang Yu is now an associate professor (tenure track) at Beihang University in Beijing, China. He joined the School of Aeronautic Science and Engineering in April 2016. He obtained his B.S. degree in physics from Beihang University (2009) and Ph.D. degree in aeronautics & astronautics from Tsinghua University (2014). He had his postdoctoral position at Observatoire de la Côte d’Azur in France (2014-2016). His research interests include the Hamiltonian dynamics of celestial systems and the formation and evolution of minor planets.
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Yu, Y., Richardson, D.C. & Michel, P. Structural analysis of rubble-pile asteroids applied to collisional evolution. Astrodyn 1, 57–69 (2017). https://doi.org/10.1007/s42064-017-0005-6
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DOI: https://doi.org/10.1007/s42064-017-0005-6