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.