Three cold worlds : measuring exoplanet masses with keck adaptive optics

Amongst the various planet-detection techniques, gravitational microlensing is unique in its sensitivity to low-mass wide-orbit planetary systems that exist beyond the Solar neighbourhood. Wide orbit, or ‘cold’, planets are crucial for understanding planet formation, since it is their predicted birthplace according to the core-accretion theory. Over the past 20 years more than 100 planets have been detected with gravitational microlensing, a technique where light curve modelling provides parameters such as mass-ratio and angular Einstein ring radius. Studies into exoplanet demographics and formation, however, are better informed with physical properties (e.g. mass and distance) which are difficult to estimate from the microlensing light curve alone. High angular resolution follow-up observations can supplement the microlensing method by resolving the source and lens stars, and therefore directly measuring their relative proper-motion and the lens flux. This can be achieved with 8-10 metre telescopes, such as Keck in Hawaii, that also implements adaptive optics. In this thesis, I present three microlensing events that were re-observed with Keck adaptive optics cameras. For all three planetary systems I successfully resolved the source and lens, thus providing tighter constraints on the host mass, planet mass, projected separation and distance. The first of these three cold worlds, is the system MOA-2013-BLG-220. With nearinfrared photometry from Keck, I resolved the source and lens with a separation of ~70 milliarcsec (mas). With the additional constraints of lens flux and source-lens relative proper motion, the microlensing light curve was re-modelled. Therefore, I found the microlensing event MOA-2013-BLG-220 to consist of a super-Jupiter orbiting a Solar-type star beyond the snow line, at a distance close to, or in, the Galactic Bulge. I apply a similar mass-measurement method to the microlensing events OGLE-2016- BLG-1195 and MOA-2010-BLG-328. For the former, we use 3 epochs of data to resolve the source and lens, addressing the inconsistent results between the two detection papers. Our results agree with light curve modelling that excludes the Spitzer photometry, suggesting that it is most likely dominated by systematic errors. From the improved Keck photometry, I find that the microlensing event OGLE-2016-BLG-1195 is a cold super- Earth orbiting a late M dwarf. This event is of particular interest as its very low-mass ratio contributes to the cold planet mass-function measurements at the low end. For my final ‘cold world’, MOA-2010-BLG-328, I find a Saturn-mass planet orbiting a late M dwarf, also beyond the snow line. This event lasted longer than ~50 days, which provided opportunity for parallax effects to be seen on the microlensing light-curve. Our follow-up Keck data indicate that parallax effects due to the orbital motion of the source star are present, allowing us to place further constraints on the physical parameters of the system. These three planetary systems contribute to exoplanet demographics, and help inform planet formation theories. These studies and the mass-measurement techniques used herein will pave the way for the Nancy Grace Roman Space Telescope which has the capability to detect a larger range of cold planets and host stars towards the Galactic Bulge