Measurement of Dependence of Microlensing Planet Frequency on The Host Star Mass and Galactocentric Distance by using a Galactic Model

Abstract

We measure the dependence of planet frequency on host star mass, $M_{\rm L}$, and distance from the Galactic center, $R_{\rm L}$, using a sample of planets discovered by gravitational microlensing. We compare the two-dimensional distribution of the lens-source proper motion, $μ_{\rm rel}$, and the Einstein radius crossing time, $t_{\rm E}$, measured for 22 planetary events from Suzuki et al. (2016) with the distribution expected from Galactic model. Assuming that the planet-hosting probability of a star is proportional to $M_{\rm L}^m R_{\rm L}^r$, we calculate the likelihood distribution of $(m,r)$. We estimate that $r = 0.10^{+0.51}_{-0.37}$ and $m = 0.50^{+0.90}_{-0.70}$ under the assumption that the planet-hosting probability is independent of the mass ratio. We also divide the planet sample into subsamples based on their mass ratio, $q$, and estimate that $m=-0.08^{+0.95}_{-0.65}$ for $q < 10^{-3}$ and $1.25^{+1.07}_{-1.14}$ for $q > 10^{-3}$. Although uncertainties are still large, this result implies a possibility that in orbits beyond the snowline, massive planets are more likely to exist around more massive stars whereas low-mass planets exist regardless of their host star mass.