  We present the first microlensing candidate for a free-floating
exoplanet-exomoon system, MOA-2011-BLG-262, with a primary lens mass of M_host
~ 4 Jupiter masses hosting a sub-Earth mass moon. The data are well fit by this
exomoon model, but an alternate star+planet model fits the data almost as well.
Nevertheless, these results indicate the potential of microlensing to detect
exomoons, albeit ones that are different from the giant planet moons in our
solar system. The argument for an exomoon hinges on the system being relatively
close to the Sun. The data constrain the product M pi_rel, where M is the lens
system mass and pi_rel is the lens-source relative parallax. If the lens system
is nearby (large pi_rel), then M is small (a few Jupiter masses) and the
companion is a sub-Earth-mass exomoon. The best-fit solution has a large
lens-source relative proper motion, mu_rel = 19.6 +- 1.6 mas/yr, which would
rule out a distant lens system unless the source star has an unusually high
proper motion. However, data from the OGLE collaboration nearly rule out a high
source proper motion, so the exoplanet+exomoon model is the favored
interpretation for the best fit model. However, the alternate solution has a
lower proper motion, which is compatible with a distant (so stellar) host. A
Bayesian analysis does not favor the exoplanet+exomoon interpretation, so
Occam's razor favors a lens system in the bulge with host and companion masses
of M_host = 0.12 (+0.19 -0.06) M_solar and m_comp = 18 (+28 -100 M_earth, at a
projected separation of a_perp ~ 0.84 AU. The existence of this degeneracy is
an unlucky accident, so current microlensing experiments are in principle
sensitive to exomoons. In some circumstances, it will be possible to
definitively establish the low mass of such lens systems through the
microlensing parallax effect. Future experiments will be sensitive to less
extreme exomoons.
