Size distribution of small grains in the inner zodiacal cloud

The Parker Solar Probe (PSP) spacecraft has transited the inner-most regions of the zodiacal cloud and detects impacts to the spacecraft body via its electric field instrument. Multiple dust populations have been proposed to explain the PSP dust impact rates. PSP's unique orbit allows us to identify a region where the impact rates are likely dominated by $\alpha$-meteoroids, small zodiacal grains on approximately circular, bound orbits. From the distribution of voltage signals generated by dust impacts to PSP in this region, we find the cumulative mass index for grains with radii of $\sim$0.6-1.4 $\mu$m (masses of $3\times10^{-15}$ to $3\times10^{-14}$ kg) to be $\alpha = 1.1 \pm 0.3$ from 0.1-0.25 $R_\odot$. $\alpha$ increases toward the Sun, with even smaller fragments generated closer to the Sun. The derived size distribution is steeper than previously estimated, and in contrast to expectations we find most of the dust mass resides in the smallest fragments and not in large grains inside 0.15 au. As the inner-most regions of the zodiacal cloud are likely collisionally evolved, these results place new constraints how the solar system's zodiacal cloud and by extension astrophysical debris disks are partitioned in mass.