Free-floating Planet Mass Function from MOA-II 9 yr Survey toward the Galactic Bulge

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 theta(E) = 0.90 +/- 0.14 mu as. We measure the detection efficiency depending on both tE and.E with image-level simulations for the first time. These short events are well modeled by a power-law mass function, dN4 / d logM =(2.18 (+0.52)(-1.40) ) X (M/ 8 M-circle plus )(-alpha 4) dex(-1) star(-1) with alpha(4) =0.96 (+ 0.47) (-0.27) for M/M-circle dot < 0.02. This implies a total of f 21 (+23)(-13) FFPs or very wide orbit planets of mass 0.33 < M/M-circle dot < 6660 per star, with a total mass of 80 M-+73(-47)circle plus A 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 alpha similar to 0.9, which would imply a total mass of 171 (+80)(-52) A star(-1). This model predicts that Roman Space Telescope will detect 988 5661848 -+ FFPs with masses down to that of Mars (including 575 (-424) (+1733) -+ with 0.1 <= M/M-circle plus <= 1). The Sumi et al. large Jupiter-mass FFP population is excluded.