Free-floating planet mass function from MOA-II 9-year survey toward the Galactic bulge

Free-floating planets (FFPs) are planetary-mass objects that exist alone without a host star, and the majority of them are thought to be planets that formed around a star and were then ejected from the system due to gravitational interactions with other planets or a companion star in the system. Although discoveries of young FFP candidates with more than Jupiter mass have been reported by direct imaging, less massive or older planets can only be detected by gravitational microlensing. The Microlensing Observations in Astrophysics (MOA) group has been conducting microlensing surveys toward the Galactic bulge since 2006 using the 1.8 m MOA-II telescope in New Zealand that mounts a wide-field camera with a field of view of 2.2 deg². In this study, we analyzed ~260,000 images taken by MOA over 9-years from 2006 to 2014, and identified and selected 3,554 microlensing events with certain criteria. Seven of them are FFP candidate events with t_E < 0.5 days, where t_E is the Einstein radius crossing time which is proportional to the square root of the lens mass. In particular, MOA-9y-5919 is the second shortest t_E event so far with t_E = 0.057 ± 0.016 days, and the second terrestrial-mass FFP candidate. The parameter distribution of these short events can be well modeled by a power-law mass function, dN/dlogM = 2.18^+0.52_-1.40 (M / 8 M_Earth)-α dex-1 star-1 with α = 0.96^+0.47_-0.27 for M < 0.02 M_Sun. Comparing this mass function to the mass function of bound planets indicates that FFPs are an order of magnitude more than the bound planets at Earth masses, but fewer than bound planets at Jupiter masses. This implies that lower-mass planets are more likely to be ejected from a planetary system.