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We study the influence of stellar metallicity on the fraction of stars withplanets (i.e., the occurrence rate of planetary systems) and the average numberof planets per star (i.e., the occurrence rate of planets). The former directlyreveals the planet formation efficiency, whereas the latter reveals the finalproduct of formation and evolution. We show that these two occurrence rateshave different dependences on stellar metallicity. Specifically, the fractionof stars with planets rises gradually with metallicity, from $\sim$25% to$\sim$36% for 0.4 dex of [Fe/H] for all Kepler-like planets (period $P<400$days and radius $R_{\rm p}\gtrsim R_\oplus$). The average number of planets perstar reaches a plateau (or possibly starts declining) at [Fe/H]$\gtrsim0.1$.This is plausibly caused by the emergence of distant giant planets at highmetallicities, given that the close-in small planets and the distant giantspreferentially co-exist in the same system.

Influence of Stellar Metallicity on Occurrence Rates of Planets and Planetary Systems