Craters on Charon: Impactors from a Collisional Cascade Among Trans-Neptunian Objects

We consider whether equilibrium size distributions from collisional cascades match the frequency of impactors derived from New Horizons crater counts on Charon. Using an analytic model and a suite of numerical simulations, we demonstrate that collisional cascades generate wavy size distributions; the morphology of the waves depends on the binding energy of solids ${Q}_{D}^{\star }$ and the collision velocity v_c. For an adopted minimum size of solids, ${r}_{\min }$ = 1 μm, and collision velocity v_c = 1-3 km s^-1, the waves are rather insensitive to the gravitational component of ${Q}_{D}^{\star }$ . If the bulk strength component of ${Q}_{D}^{\star }$ is ${Q}_{s}{r}^{{e}_{s}}$ for particles with radius r, size distributions with small Q_s are much wavier than those with large Q_s; systems with e_s ≈ -0.4 have stronger waves than systems with e_s ≈ 0. Detailed comparisons with the New Horizons data suggest that a collisional cascade among solids with a bulk strength intermediate between weak ice and normal ice produces size distributions fairly similar to that of impactors on Charon. If the surface density Σ of the protosolar nebula varies with semimajor axis a as Σ ≈ 30 g cm^-2 (a/1 au)^-3/2, the timescale for a cascade to generate an approximate equilibrium is 100-300 Myr at 45 au and 10-30 Myr at 25 au. Although it is necessary to perform more complete evolutionary calculations of the Kuiper Belt, collisional cascades are a viable model for producing the size distribution of solids that impacted Charon throughout its history.