Planet Traps and First Planets: the Critical Metallicity for Gas Giant Formation

Abstract

The ubiquity of planets poses an interesting question: when first planets are formed in galaxies. We investigate this problem by adopting a theoretical model developed for understanding the statistical properties of exoplanets. Our model is constructed as the combination of planet traps with the standard core accretion scenario in which the efficiency of forming planetary cores directly relates to the dust density in disks or the metallicity ([Fe/H]). We statistically compute planet formation frequencies (PFFs) as well as the orbital radius ($ $) within which gas accretion becomes efficient enough to form Jovian planets. The three characteristic exoplanetary populations are considered: hot Jupiters, exo-Jupiters densely populated around 1 AU, and low-mass planets such as super-Earths. We explore the behavior of the PFFs as well as $ $ for the three different populations as a function of metallicity ($-2 \leq$[Fe/H]$\leq -0.6$). We show that the total PFFs increase steadily with metallicity, which is the direct outcome of the core accretion picture. For the entire range of the metallicity considered here, the population of the low-mass planets dominates over the Jovian planets. The Jovian planets contribute to the PFFs above [Fe/H]-1. We find that the hot Jupiters form at lower metallcities than the exo-Jupiters. This arises from the radially inward transport of planetary cores by their host traps, which is more effective for lower metallicity disks due to the slower growth of the cores. The PFFs for the exo-Jupiters exceed those for the hot Jupiters around [Fe/H]-0.7. Finally, we show that the critical metallicity for forming Jovian planets is [Fe/H]-1.2, which is evaluated by comparing the values of $ $ between the hot Jupiters and the low-mass planets. The comparison intrinsically links to the different gas accretion efficiency between them.