Constraints on sub-terrestrial free-floating planets from Subaru microlensing observations

The abundance of protoplanetary bodies ejected from their parent star system is presently poorly-constrained. With only two existing optical observations of interstellar objects in the $10^{8} - 10^{10}$ kg mass range and a small number of robust microlensing observations of free-floating planets (FFPs) in the $10^{24} - 10^{25}$ kg mass range, there is a large range of masses for which there are no existing measurements of the unbound population. The three primary microlensing surveys currently searching for FFPs operate at a cadence greater than 15 minutes, which limits their ability to observe events associated with bodies with a mass much below an Earth mass. We demonstrate that existing high-cadence observations of M31 with the Subaru Hyper Suprime-Cam place constraints on the abundance of unbound objects at sub-terrestrial masses, with peak sensitivity at $10^{-4}~M_\oplus$ for Milky Way lenses and $10^{-1}~M_\oplus$ for lenses in M31. For a fiducial $\frac{dn}{dM}\propto M^{-2}$ mass distribution, we find that the abundance of unbound objects is constrained to $n_\text{unbound} < 1.4 \times 10^{7} ~\rm{pc}^{-3}$ for masses within 1 dex of $10^{-4}~M_\oplus$. Additionally, we compute limits on an artificial ``monochromatic'' distribution of unbound objects and compare to existing literature, demonstrating that the assumed spatial distribution of lenses has very significant consequences for the sensitivity of microlensing surveys. While the observations ultimately do not probe abundances suggested by current models of planetary formation, our limits place direct observational constraints on the unbound population in the sub-terrestrial mass range and motivate new observational strategies for microlensing surveys.