No Large Dependence of Planet Frequency on Galactocentric Distance
  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, $\mu_{\rm rel}$, for a given Einstein radius
crossing time, $t_{\rm E}$, measured for the 28 planetary events in the
statistical sample by Suzuki et al. (2016). 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, $P_{\rm
host} \propto M_{\rm L}^m R_{\rm L}^r$, into a Galactic model for
random-selected stars, where $M_{\rm L}$ is the lens mass ($\sim$ host mass),
and $R_{\rm L}$ is the Galactocentric distance. By comparing the observed
distribution with the model-predicted $\mu_{\rm rel}$ distribution for a given
$t_{\rm E}$ at various combinations of $(m ,r)$, we obtain an estimate $r = 0.2
\pm 0.4$ 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.
