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, $M_{\mathrm{L}}$, and distance from the Galactic center, $R_{\mathrm{L}}$, using a sample of planets discovered by gravitational microlensing. We compare the two-dimensional distribution of the lens-source proper motion, $\hat{I}{¼}_{\mathrm{rel}}$, and the Einstein radius crossing time, $t_{\mathrm{E}}$, 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 $M_{\mathrm{L}}^m{R}_{\mathrm{L}}^r$, we calculate the likelihood distribution of $(m,r)$. We estimate that $r=0.10_{-0.37}^{+0.51}$ and $m=0.50_{-0.70}^{+0.90}$ 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 $m=-0.08_{-0.65}^{+0.95}$ for $q<10^{-3}$ and $1.25_{-1.14}^{+1.07}$ 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.

accepted for publication in ApJ, 14 pages, 8 figures