Dust in protoplanetary disks is widely recognized as the building blocks of planets that are eventually formed in the disks .
In the core accretion scenario , one of the standard theories of gas giant formation , the abundance of dust in disks ( or metallicity , [ Fe/H ] ) plays a crucial role in regulating the formation of cores of gas giants that proceeds via collisions of dust and planetesimals in disks .
We present our recent progress on the relationship between the metallicity and planet formation , wherein planet formation frequencies ( PFFs ) as well as the critical mass of planetary cores ( M _ { c,crit } ) that can initiate gas accretion are statistically examined .
We focus on three different planetary populations that are prominent in the distribution of observed exoplanets in the mass-semimajor axis diagram : hot Jupiters , exo-Jupiters that are densely populated around 1 AU , and low-mass planets in tight orbits , also known as super-Earths and hot Neptunes .
We show that the resultant PFFs for both Jovian planets are correlated positively with the metallicity of disks whereas low-mass planets form efficiently for a wide range of metallicities ( -0.6 \leq [ Fe/H ] \leq 0.6 ) .
This is consistent with the so-called Planet-Metallicity correlation that is inferred from both the radial velocity and transit observations .
By plotting the statistically averaged value of M _ { c,crit } ( defined as \langle M _ { c,crit } \rangle ) as a function of metallicity , we find that the correlation originates from the behavior of \langle M _ { c,crit } \rangle that increases steadily with metallicity for two kinds of the Jovian planets while the low-mass planets obtain a rather constant value for \langle M _ { c,crit } \rangle .
Such a different behavior in \langle M _ { c,crit } \rangle enables one to define transition metallicities ( TMs ) above which the Jovian planets gain a larger value of \langle M _ { c,crit } \rangle than the low-mass planets , and hence gas giant formation takes place more efficiently .
We find that TMs locate at [ Fe/H ] \simeq - 0.2 to -0.4 , and are sensitive to the important parameter that involves M _ { c,crit } .
We demonstrate , by comparing with the observations , that a most likely value of M _ { c,crit } is \simeq 5 M _ { \oplus } , which is smaller than the widely adopted value in the literature ( \simeq 10 M _ { \oplus } ) .
Our results therefore suggest that opacities in the atmospheres surrounding planetary cores play an important role for lowering M _ { c,crit } .