Size Sorting on the Rubble-Pile Asteroid Itokawa

Photographs of the asteroid Itokawa reveal unexpectedly strong size segregation between lowlands populated almost entirely by small pebbles and highlands consisting of larger boulders. We propose that this segregation may be caused by a simple and unexplored effect: pebbles accreting onto the asteroid rebound from boulders, but sink into pebbly regions. By number, overwhelmingly more particles on Itokawa are pebbles, and collisions involving these pebbles must unavoidably cause pebbly regions to grow. We carry out experiments and simulations that demonstrate that this mechanism of size sorting based on simple counting of grains produces strong lateral segregation that reliably obeys an analytic formula.

Figure 1

Segregation of large and small grains. (a) Asteroid 25143/Itokawa is shown in the inset; enlargement highlights size segregation, especially in the “Muses sea”. Credit: provided by JAXA. (b) Illustration of ballistic sorting: a small pebble rebounds from a larger boulder, but (c) is absorbed into a cluster of pebbles. Demonstration of effect in simple experiments: (d) small particles dropped independently onto a ceramic plate rebound leaving few residual particles, but (e) the same number of particles made to interact with one another by pouring them from the same height leave a substantial residue on the plate. (f) Similarly, if a small pile is initially placed on the plate (left), then particles sprinkled from above exactly as in panel (d) accumulate into a growing mound (right).

Figure 2

Evaluation of cooperativity in deposition of small grains. (a) Typical snapshots after sprinkling of 1 mm glass beads from a height of 50 cm onto river stones of mean volume $140\pm 110{\mathrm{cm}}^3$ on the bottom of a $45\mathrm{cm}\times 45\mathrm{cm}$ box. Shown are 5, 8, and 15 sieve loads (photos from trial 3); small grains are false colored to aid visualization. Measurements of sprinkling uniformity provided in Supplemental Material 2 [35]. (b) Several trials using different initial substrates of river stones along with fit to their average from Eq. (1) ($f_0=5\pm 1$, $k=8.0\pm 0.2$, $n=2.15\pm 0.06$, $r^2=0.9994$). (c) In the presence of preexisting topography with a central valley, a nearly unbroken sand sea forms between higher peaks. Note that occasionally a stone may settle during an experiment, producing minor discrepancies between initial and final stone locations.

Figure 3

Lengths of trajectories, obtained from tracking a large number of pebbles dropped in discrete element simulations onto irregular substrate (details provided in Supplemental Material 6 [35]). Main plot shows a factor of 5 greater distance for pebble-to-stone collisions than pebble-to-pebble ones using Earth’s gravity, $g$. Inset shows a factor of 13 using Itokawa’s lower gravity, $g/{10}^5$. In both cases, pebble-to-pebble collisions transport particles much shorter distances than pebble-to-stone collisions.