Free-Floating Planets, the Einstein Desert, and 'Oumuamua

We complete the survey for finite-source/point-lens (FSPL) giant-source events in 2016-2019 KMTNet microlensing data. The 30 FSPL events show a clear gap in Einstein radius, $9\,\mu{\rm as}<\theta_{\rm E} <26\,\mu{\rm as}$, which is consistent with the gap in Einstein timescales near $t_{\rm E}\sim 0.5\,$days found by Mroz et al. (2017) in an independent sample of point-source/point-lens (PSPL) events. We demonstrate that the two surveys are consistent. We estimate that the 4 events below this gap are due to a power-law distribution of free-floating planet candidates (FFPs) $dN_{\rm FFP}/d\log M = (0.4\pm 0.2)\,(M/38 M_\oplus)^{-p}$/star, with $0.9\lesssim p \lesssim 1.2$. There are substantially more FFPs than known bound planets, implying that the bound planet power-law index $\gamma=0.6$ is likely shaped by the ejection process at least as much as by formation. The mass density per decade of FFPs in the Solar neighborhood is of the same order as that of 'Oumuamua-like objects. In particular, if we assume that 'Oumuamua is part of the same process that ejected the FFPs to very wide or unbound orbits, the power-law index is $p=0.92\pm 0.06$. If the Solar System's endowment of Neptune-mass objects in Neptune-like orbits is typical, which is consistent with the results of Poleski et al. (2021), then these could account for a substantial fraction of the FFPs in the Neptune-mass range.