Constraining the Frequency of Free-Floating Planets from a Synthesis of   Microlensing, Radial Velocity, and Direct Imaging Survey Results
  A microlensing survey by Sumi et al. (2011) exhibits an overabundance of short-timescale events (STEs; t_E<2 days) relative to what is 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 ~Jupiter-mass objects that outnumber main-sequence stars by nearly twofold; however the microlensing data alone cannot distinguish between events due to wide-separation (a>~10 AU) and free-floating planets. Assuming these STEs 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, and stellar remnants, finding and thus corroborating the initial identification of an excess of STEs. We then include a population of bound planets that are expected not to show signatures of the primary lens (host) in their microlensing light curves and that are also consistent with results from representative microlensing, radial velocity, and direct imaging surveys. We find that bound planets alone cannot explain the entire STE 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 STEs 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_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. 
Christian Clanton and B. Scott Gaudi
astro-ph.EP