Confirmation of the OGLE-2005-BLG-169 planet signature and characteristics with lens-source proper motion detection

We present Keck NIRC2 high angular resolution adaptive optics observations of the microlensing event OGLE-2005-BLG-169, taken 8.21 years after the discovery of this planetary system. For the first time for a microlensing planetary event, the source and the lens are completely resolved, providing a precise measurement of their heliocentric relative proper motion, $\mu_{\rm{rel},\rm{helio}}=7.44 \pm 0.17$ mas yr$^{-1}$. This confirms and refines the initial model presented in the discovery paper and rules out a range of solutions that were allowed by the microlensing light curve. This is also the first time that parameters derived from a microlensing planetary signal are confirmed, both with Keck measurements, presented in this paper, and independent measurements obtained with the Hubble Space Telescope in I, V and B bands, presented in a companion paper. Hence, this new measurement of $\mu_{\rm{rel},\rm{helio}}$, as well as the measured brightness of the lens in H band, enabled the mass and distance of the system to be updated: a Uranus-mass planet ($m_\rm{p}=13.2\pm 1.3 M_\oplus$) orbiting a K5-type main sequence star ($M_*=0.65\pm 0.05 M_\odot$) separated by $a_\perp=3.4\pm 0.3$ AU, at the distance $D_\rm{L}=4.0\pm 0.4$ kpc from us.