Dependence of Small Planet Frequency on Stellar Metallicity Hidden by Their Prevalence

TL;DR

This paper explores how the frequency of small planets depends on stellar metallicity, proposing a model that explains previous conflicting results and suggests better target stars for future studies.

Contribution

It extends the planet-metallicity correlation to small planets, modeling it as a power law and explaining null detections in past studies.

Findings

Null detection due to high occurrence rate and low detection efficiency

Correlation cannot be ruled out for small planets

Lower metallicity stars are better targets for testing

Abstract

The dependence of gas giant planet occurrence rate on stellar metallicity has been firmly established. We extend this so-called planet-metallicity correlation to broader ranges of metallicities and planet masses/radii. In particular, we assume that the planet-metallicity correlation is a power law below some critical saturation threshold, and that the probability of hosting at least one planet is unity for stars with metallicity above the threshold. We then are able to explain the discrepancy between the tentative detection and null detection in previous studies regarding the planet-metallicity correlation for small planets. In particular, we find that the null detection of this correlation can be attributed to the combination of high planet occurrence rate and low detection efficiency. Therefore, a planet-metallicity correlation for small planets cannot be ruled out. We propose that stars with metallicities lower than the Solar value are better targets for testing the planet-metallicity correlation for small planets.