SPH Simulations for Shape Deformation of Rubble-Pile Asteroids Through Spinup: The Challenge for Making Top-Shaped Asteroids Ryugu and Bennu

Abstract

Asteroid Ryugu and asteroid Bennu, which were recently visited by spacecraft Hayabusa2 and OSIRIS-REx, respectively, are spinning top-shaped rubble piles. Other axisymmetric top-shaped near-Earth asteroids have been observed with ground-based radar, most of which rotate near breakup rotation periods of ~ 3 hours. This suggests that rotation-induced deformation of asteroids through rotational spinup produces top shapes. Although some previous simulations using the Discrete Element Method showed that spinup of rubble piles may produce oblate top shapes, it is still unclear what kinds of conditions such as friction angles of constituent materials and spinup timescales are required for top-shape formation. Here we show, through Smoothed Particle Hydrodynamics simulations of granular bodies spinning-up at different rates, that the rotation-induced deformation of spherical rubble piles before breakup can be classified into three modes according to the friction angle ϕ_{d}: quasi-static and internal deformation for ϕ_{d} < 40 degrees, dynamical and internal deformation for 50 degrees < ϕ_{d} < 60 degrees, and surface landslides for ϕ_{d} > 70 degrees. Note that these apparent large values of friction angle can be acceptable if we consider the effect of cohesion among blocks of a rubble pile under weak gravity. Bodies with ϕ_{d} < 60 degrees evolve into oblate spheroids through internal deformation, but never form pronounced equators defining a top shape. In contrast, bodies with ϕ_{d} > 70 degrees deform into axisymmetric top shapes through an axisymmetric surface landslides if spinup timescales are < a few days. In addition, through slow spinups with timescales > 1 month, bodies with ϕ_{d} > 70 degrees deform into non-axisymmetric shapes via localized landslides. We suggest that rapid spinup mechanisms are preferable for the formation of axisymmetric top shapes.