On the functional form of the metallicity-giant planet correlation

TL;DR

This study investigates the precise mathematical relationship between stellar metallicity and the likelihood of hosting giant planets, using Bayesian analysis on observational data, and finds the correlation is not definitively exponential or constant for subsolar metallicities.

Contribution

It provides a quantitative comparison of different models for the metallicity-giant planet correlation using Bayesian methods on two stellar samples.

Findings

Giant planet frequency depends on metallicity.

No statistical difference between constant and exponential models for subsolar metallicities.

Stellar mass dependence remains inconclusive.

Abstract

It is generally accepted that the presence of a giant planet is strongly dependent on the stellar metallicity. A stellar mass dependence has also been investigated, but this dependence does not seem as strong as the metallicity dependence. Even for metallicity, however, the exact form of the correlation has not been established. In this paper, we test several scenarios for describing the frequency of giant planets as a function of its host parameters. We perform this test on two volume-limited samples (from CORALIE and HARPS). By using a Bayesian analysis, we quantitatively compared the different scenarios. We confirm that giant planet frequency is indeed a function of metallicity. However, there is no statistical difference between a constant or an exponential function for stars with subsolar metallicities contrary to what has been previously stated in the literature. The dependence on stellar mass could neither be confirmed nor be discarded.