Revisiting MOA 2013 BLG-220L: A Solar-type star with a Cold super-Jupiter Companion

We present the analysis of high-resolution images of MOA-2013-BLG-220, taken with the Keck adaptive optics system 6 years after the initial observation, identifying the lens as a solar-type star hosting a super-Jupiter mass planet. The masses of planets and host-stars discovered by microlensing are often not determined from light curve data, while the star-planet mass-ratio and projected separation in units of Einstein ring radius are well measured. High-resolution follow-up observations after the lensing event is complete can resolve the source and lens. This allows direct measurements of flux, and the amplitude and direction of proper motion, giving strong constraints on the system parameters. Due to the high relative proper motion, $\mu_{\rm rel,Geo} = 12.62\pm0.11$ mas/yr, the source and lens were resolved in 2019, with a separation of $77.1\pm0.5$ mas. Thus, we constrain the lens flux to $K_{\rm Keck,lens}= 17.92\pm0.02$. By combining constraints from the model and Keck flux, we find the lens mass to be $M_L = 0.88\pm0.05\ M_\odot$ at $D_L = 6.72\pm0.59$ kpc. With a mass-ratio of $q=(3.00\pm0.03)\times10^{-3}$ the planet's mass is determined to be $M_P = 2.74\pm0.17\ M_{J}$ at a separation of $r_\perp = 3.03\pm0.27$ AU. The lens mass is much higher than the prediction made by the Bayesian analysis that assumes all stars have an equal probability to host a planet of the measured mass ratio, and suggests that planets with mass ratios of a few 10$^{-3}$ are more common orbiting massive stars. This demonstrates the importance of high-resolution follow-up observations for testing theories like these.