  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 \phi_{d}:
quasi-static and internal deformation for \phi_{d} < 40 degrees, dynamical and
internal deformation for 50 degrees < \phi_{d} < 60 degrees, and surface
landslides for \phi_{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 \phi_{d} < 60 degrees
evolve into oblate spheroids through internal deformation, but never form
pronounced equators defining a top shape. In contrast, bodies with \phi_{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 \phi_{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.
