A microlensing survey by Sumi et al .
( 73 ) exhibits an overabundance of short-timescale events ( t _ { E } \lesssim 2 ~ { } days ) relative to that expected from known stellar populations and a smooth power-law extrapolation down to the brown dwarf regime .
This excess has been interpreted as a population of approximately Jupiter-mass objects that outnumber main-sequence stars by nearly twofold ; however the microlensing data alone can not distinguish between events due to wide-separation ( a \gtrsim 10 AU ) and free-floating planets .
Assuming these short-timescale events are indeed due to planetary-mass objects , we aim to constrain the fraction of these events that can be explained by bound but wide-separation planets .
We fit the observed timescale distribution with a lens mass function comprised of brown dwarfs , main-sequence stars , white dwarfs , neutron stars , and black holes , finding and thus corroborating the initial identification of an excess of short-timescale events .
Including a population of bound planets with distributions of masses and separations that are consistent with the results from representative microlensing , radial velocity , and direct imaging surveys , we then determine what fraction of these bound planets are expected not to show signatures of the primary lens ( host ) star in their microlensing light curves , and thus what fraction of the short-timescale event excess can be explained by bound planets alone .
We find that , given our model for the distribution of planet parameters , bound planets alone can not explain the entire excess without violating the constraints from the surveys we consider , and thus some fraction of these events must be due to free-floating planets , if our model for bound planets holds .
We estimate a median fraction of short-timescale events due to free-floating planets to be f = 0.67 ( 0.23–0.85 at 95 % confidence ) when assuming “ hot-start ” planet evolutionary models and f = 0.58 ( 0.14–0.83 at 95 % confidence ) for “ cold-start ” models .
Assuming a delta-function distribution of free-floating planets of mass m _ { p } = 2 ~ { } M _ { \mathrm { Jup } } yields a number of free-floating planets per main sequence star of N = 1.4 ( 0.48–1.8 at 95 % confidence ) in the “ hot-start ” case and N = 1.2 ( 0.29–1.8 at 95 % confidence ) in the “ cold-start ” case .