The origin of the high metallicity of close-in giant exoplanets II The nature of the sweet spot for accretion

Abstract

The composition of giant planets reflects their formation history. Planetesimal accretion during the phase of planetary migration could lead to the delivery of heavy elements into giant planets. In our previous paper (Shibata et al. 2020) we showed that planetesimal accretion during planetary migration occurs in a rather narrow region of the protoplanetary disk, which we refer as "the sweet spot for accretion". The goal of this paper is to reveal the nature of the sweet spot and investigate the role of the sweet spot in determining the composition of gas giant planets. We analytically derive the required conditions for the sweet spot. Then, we compare the derived equations with the numerical simulations. We find that the conditions required for the sweet spot can be expressed by the ratio of the gas damping timescale of the planetesimal orbits and the planetary migration timescale. If the planetary migration timescale depends on the surface density of disk gas inversely, the location of the sweet spot does not change with the disk evolution. The mass of planetesimals accreted by the planet depends on the amount of planetesimals that are shepherded by mean motion resonances. Our analysis suggests that tens Earth-mass of planetesimals can be shepherded into the sweet spot without planetesimal collisions. However, as more planetesimals are trapped into mean motion resonances, collisional cascade can lead to fragmentation of planetesimals. This could affect the location of the sweet spot and the population of small objects in planetary systems. We conclude that the composition of gas giant planets depends on whether the planets crossed the sweet spot during their formation. Constraining the metallicity of cold giant planets, that are expected to be outer than the sweet spot, would reveal key information for understanding the origin of heavy elements in giant planets.

17 pages, 13 figures, A&A accepted

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