Most small asteroids are thought to be rubble piles: spinning collections of rock chunks held together by their own gravitational forces. Simulations predict that rotational forces deform or even break apart those asteroids. But testing those predictions has been difficult; scientists have had to use telescopes to find select asteroids and study them in whatever state they’re in. Methods to simulate rotating particle clusters in the lab could approximate only the elastic limit, which describes systems with many components. That’s not the case for rubble-pile asteroids.
Heinrich Jaeger of the University of Chicago and his colleagues have now introduced a new system to study rotational dynamics: acoustically levitated plastic balls. Their system provides experimental access to regimes relevant for systems such as rubble-pile asteroids and challenges existing models for acoustic scattering.
Jaeger and his colleagues floated 10 to 200 balls in a cavity driven by an ultrasound transducer to produce a standing sound wave with a single node. Sound scattered between the 180- to 200-µm-diameter particles to create an attractive force between them, a so-called secondary acoustic force. The result was that particles drifted to the node and clustered into a roughly circular monolayer “raft,” as shown in the video above.
When the ultrasound frequency was detuned from the cavity’s resonance, the particle raft rotated, although the exact mechanism behind the torques isn’t known. For some acoustic frequencies, the rotations were too stochastic to be useful, but for others, the torque was nearly constant. The researchers sought those constant-torque stretches for their second-long measurements.
For slow rotations, the initially circular raft stayed roughly circular, but the rotational kinetic energy caused the particles to spread out. For faster rotations, instead of elastically stretching, the raft morphed into an ellipse, as shown in the video below, and was held together by surface tension at the perimeter. The raft eventually either sheds particles on the peripheries, for the case of initially small rafts of fewer than 100 particles, or breaks apart into two or more separate rafts, for the case of initially large rafts. In short, small rafts are brittle; large rafts are plastic.
The researchers found that the effective surface tension and elastic modulus grow substantially with raft size. Current models of secondary acoustic forces are perturbative and assume dilute scatterers for which sound scatters only once between two particles. In those models, the strength of the interactions depends only weakly on the raft size. Jaeger and his team’s results show the limitations of such assumptions and the need for models of higher-order scattering.
Because the acoustic binding energy grows with increasing raft size much in the way gravitational forces grow with increasing object size, acoustically levitated particles will be able to model gravitationally bound rotating objects, such as rubble-pile asteroids. The new system could provide a way to experimentally investigate asteroid dynamics in the lab.
Rotational dynamics similar to those of rubble-pile asteroids also influence the stability of atomic nuclei and the regions around rotating black holes, such as Sagittarius A*, which was imaged recently by the Event Horizon Telescope (see “A portrait of the black hole at the heart of the Milky Way,” Physics Today online, 12 May 2022). (M. X. Lim et al., Phys. Rev. X 12, 021017, 2022.)
