2023AJ....166..108S

We present the first measurement of the mass function of free-floating planets (FFPs), or very wide orbit planets down to an Earth mass, from the MOA-II microlensing survey in 2006-2014. Six events are likely to be due to planets with Einstein radius crossing times t_E < 0.5 days, and the shortest has t_E = 0.057 ± 0.016 days and an angular Einstein radius of θ_E = 0.90 ± 0.14 μas. We measure the detection efficiency depending on both t_E and θ_E with image-level simulations for the first time. These short events are well modeled by a power-law mass function, ${{dN}}_{4}/d\mathrm{log}M={({2.18}_{-1.40}^{+0.52})\times (M/8\,{M}_{\oplus })}^{-{\alpha }_{4}}$ dex^–1 star^–1 with ${\alpha }_{4}={0.96}_{-0.27}^{+0.47}$ for M/M_⊙ < 0.02. This implies a total of $f={21}_{-13}^{+23}$ FFPs or very wide orbit planets of mass 0.33 < M/M_⊕ < 6660 per star, with a total mass of ${80}_{-47}^{+73}{M}_{\oplus }$ star^–1. The number of FFPs is ${19}_{-13}^{+23}$ times the number of planets in wide orbits (beyond the snow line), while the total masses are of the same order. This suggests that the FFPs have been ejected from bound planetary systems that may have had an initial mass function with a power-law index of α ∼ 0.9, which would imply a total mass of ${171}_{-52}^{+80}{M}_{\oplus }$ star^–1. This model predicts that Roman Space Telescope will detect ${988}_{-566}^{+1848}$ FFPs with masses down to that of Mars (including ${575}_{-424}^{+1733}$ with 0.1 ≤ M/M_⊕ ≤ 1). The Sumi et al. large Jupiter-mass FFP population is excluded.