We study the influence of stellar metallicity on the fraction of stars with planets ( i.e. , the occurrence rate of planetary systems ) and the average number of planets per star ( i.e. , the occurrence rate of planets ) .
The former directly reveals the planet formation efficiency , whereas the latter reveals the final product of formation and evolution .
We show that these two occurrence rates have different dependences on stellar metallicity .
Specifically , the fraction of 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 _ { p } \gtrsim R _ { \oplus } ) .
The average number of planets per star reaches a plateau ( or possibly starts declining ) at [ Fe/H ] \gtrsim 0.1 .
This is plausibly caused by the emergence of distant giant planets at high metallicities , given that the close-in small planets and the distant giants preferentially co-exist in the same system .