Radial profiles of the Phoebe ring, a vast debris disk around Saturn

We present observations at optical wavelengths with the Cassini Spacecraft's Imaging Science System of the Phoebe ring, a vast debris disk around Saturn that seems to be collisionally generated by its irregular satellites. The analysis reveals a radial profile from 80-260 Saturn radii ($R_S$) that changes behavior interior to $\approx 110 R_S$, which we attribute to either the moon Iapetus sweeping up small particles, or to orbital instabilities that cause the ring to flare up vertically. Our study yields an integrated I/F at 0.635 $\mu$m along Saturn's shadow in the Phoebe ring's midplane from 80-250 $R_S$ of $2.7^{+0.9}_{-0.3} \times 10^{-9}$. We develop an analytical model for the size-dependent secular dynamics of retrograde Phoebe ring grains, and compare this model to the observations. This analysis implies that 1) the "Phoebe" ring is partially sourced by debris from irregular satellites beyond Phoebe's orbit and 2) the scattered light signal is dominated by small grains ($\lesssim 20\mu$m in size). If we assume that the Phoebe ring is generated through steady-state micrometeoroid bombardment, this implies a power-law size distribution with index $> 4$, which is unusually steep among solar system rings. This suggests either a steep size distribution of ejecta when material is initially released, or a subsequent process that preferentially breaks up large grains.