Dust in protoplanetary disks: A clue as to the critical mass of planetary cores

Abstract

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 (Mc, 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 ≤[Fe/H]≤ 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 Mc, crit (defined as 〈Mc, crit〉) as a function of metallicity, we find that the correlation originates from the behavior of 〈Mc, crit〉 that increases steadily with metallicity for two kinds of the Jovian planets while the low-mass planets obtain a rather constant value for 〈Mc, crit〉. Such a different behavior in 〈Mc, crit〉 enables one to define transition metallicities (TMs) above which the Jovian planets gain a larger value of 〈Mc, crit〉 than the low-mass planets, and hence gas giant formation takes place more efficiently. We find that TMs appear at [Fe/H]-0.2 to -0.4, and are sensitive to the important parameter that involves Mc, crit. We demonstrate, by comparing with the radial velocity observations, that a most likely value of Mc, crit is ⊕5M⊕, which is smaller than the widely adopted value in the literature (10M⊕). Our results therefore suggest that opacities in the atmospheres surrounding planetary cores play an important role for lowering Mc, crit.