The metallicity dependence of giant planet incidence

Abstract

We describe three corrections that should be applied to the observed relative incidence of nearby stars hosting giant planets. These are diffusion in the stellar atmosphere, use of the [Ref] index in place of [Fe/H] for metallicity, and correction for local sampling with the W velocity. We have applied these corrections to a subset of the SPOCS exoplanet survey with uniform giant planet detectability. Fitting the binned data to a power law of the form, $\alpha 10^{\beta [Fe/H]}$, we derived $\alpha = 0.022 \pm 0.007$ and $\beta = 3.0 \pm 0.5$; this value of $\beta$ is 50\% larger than the value determined by \citet{fv05}. While the statistical significance of this difference is marginal, given the small number statistics, these corrections should be included in future analyses that include larger samples.