Direct imaging constraints on planet populations detected by
  microlensing
  Results from gravitational microlensing suggested the existence of a large
population of free-floating planetary mass objects. The main conclusion from
this work was partly based on constraints from a direct imaging survey. This
survey determined upper limits for the frequency of stars that harbor giant
exoplanets at large orbital separations. Aims. We want to verify to what extent
upper limits from direct imaging do indeed constrain the microlensing results.
We examine the current derivation of the upper limits used in the microlensing
study and re-analyze the data from the corresponding imaging survey. We focus
on the mass and semi-major axis ranges that are most relevant in context of the
microlensing results. We also consider new results from a recent M-dwarf
imaging survey as these objects are typically the host stars for planets
detected by microlensing. We find that the upper limits currently applied in
context of the microlensing results are probably underestimated. This means
that a larger fraction of stars than assumed may harbor gas giant planets at
larger orbital separations. Also, the way the upper limit is currently used to
estimate the fraction of free-floating objects is not strictly correct. If the
planetary surface density of giant planets around M-dwarfs is described as
df_Planet ~ a^beta da, we find that beta ~ 0.5 - 0.6 is consistent with results
from different observational studies probing semi-major axes between ~0.03 - 30
AU. Having a higher upper limit on the fraction of stars that may have gas
giant planets at orbital separations probed by the microlensing data implies
that more of the planets detected in the microlensing study are potentially
bound to stars rather than free-floating. The current observational data are
consistent with a rising planetary surface density for giant exoplanets around
M-dwarfs out to ~30 AU.
