2021ApJ...918L...8K

Gravitational microlensing is currently the only technique that helps study the Galactic distribution of planets as a function of distance from the Galactic center. The Galactic location of a lens system can be uniquely determined only when at least two of the three quantities that determine the mass-distance relations are measured. However, even if only one mass-distance relation can be obtained, a large sample of microlensing events can be used to statistically discuss the Galactic distribution of the lenses. In this study, we extract the Galactic distribution of planetary systems from the distribution of the lens-source proper motion, µ_rel, for a given Einstein radius crossing time, t_E, measured for the 28 planetary events in the statistical sample by Suzuki et al. Because microlensing is randomly caused by stars in our Galaxy, the observational distribution can be predicted using a Galactic model. We incorporate the planet-hosting probability, P_host∝M_L^mR_L^r, into a Galactic model for random-selected stars, where M_L is the lens mass (∼host mass), and R_L is the Galactocentric distance. By comparing the observed distribution with the model-predicted µ_rel distribution for a given t_E at various combinations of (m, r), we obtain an estimate r = 0.2 ± 0.4 under a plausible uniform prior for m of 0 < m < 2. This indicates that the dependence of the planet frequency on the Galactocentric distance is not large, and suggests that the Galactic bulge does have planets.