Dust in Protoplanetary Disks: A Clue as to the Critical Mass of Planetary Cores

Dust in protoplanetary disks is recognized as the building blocks of planets. In the core accretion scenario, the abundance of dust in disks (or metallicity) is crucial for forming cores of gas giants. 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 for 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. We show that the resultant PFFs for both Jovian planets are correlated positively with the metallicity whereas low-mass planets form efficiently for a wide range of metallicities. This is consistent with the observed Planet-Metallicity correlation. Examining the statistically averaged value of $M_{c,crit}$ (defined as $ $), we find that the correlation originates from the behavior of $ $ that increases steadily with metallicity for two kinds of the Jovian planets while the low-mass planets obtain a rather constant value for $ $. Such a difference in $ $ can define transition metallicities (TMs) above which the Jovian planets gain a larger value of $ $ than the low-mass planets, and hence gas giant formation takes place more efficiently. We find that TMs are sensitive to the important parameter that involves $M_{c,crit}$. We show, by comparing with the observations, that a most likely value of $M_{c,crit}$ is $\simeq 5M_{\oplus}$, which is smaller than the conventional value in the literature ($\simeq 10M_{\oplus}$). Our results suggest that opacities in planetary atmospheres play an important role for lowering $M_{c,crit}$.