MOA-2007-BLG-400 A Super-Jupiter Mass Planet Orbiting a Galactic
  BulgeK-dwarf Revealed by Keck Adaptive Optics Imaging
  We present Keck/NIRC2 adaptive optics imaging of planetary microlensing event
MOA-2007-BLG-400 that resolves the lens star system from the source. We find
that the MOA-2007-BLG-400L planetary system consists of a $1.71\pm 0.27 M_{\rm
Jup}$ planet orbiting a $0.69\pm 0.04M_{\odot}$ K-dwarf host star at a distance
of $6.89\pm 0.77\,$kpc from the Sun. So, this planetary system probably resides
in the Galactic bulge. The planet-host star projected separation is only weakly
constrained due to the close-wide light curve degeneracy; the 2$\sigma$
projected separation range is 0.6--$7.2\,$AU. This host mass is at the top end
of the range of masses predicted by a standard Bayesian analysis that assumes
that all stars have an equal chance of hosting a star of the observed mass
ratio. This and the similar result for event MOA-2013-BLG-220 suggests that
more massive stars may be more likely to host planets with a mass ratio in the
$0.002 < q < 0.004$ range that orbit beyond the snow line. These results also
indicate the importance of host star mass measurements for exoplanets found by
microlensing. The microlensing survey imaging data from NASA's Nancy Grace
Roman Space Telescope (formerly WFIRST) mission will be doing mass measurements
like this for a huge number of planetary events. This host lens is the highest
contrast lens-source detected in microlensing mass measurement analysis (the
lens being 10$\times$ fainter than the source). We present an improved method
of calculating photometry and astrometry uncertainties based on the Jackknife
method, which produces more accurate errors that are $\sim$$2.5 \times$ larger
than previous estimates.
