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The composition of giant planets reflects their formation history.Planetesimal accretion during the phase of planetary migration could lead tothe delivery of heavy elements into giant planets. In our previous paper(Shibata et al. 2020) we showed that planetesimal accretion during planetarymigration occurs in a rather narrow region of the protoplanetary disk, which werefer as "the sweet spot for accretion". The goal of this paper is to revealthe nature of the sweet spot and investigate the role of the sweet spot indetermining the composition of gas giant planets. We analytically derive therequired conditions for the sweet spot. Then, we compare the derived equationswith the numerical simulations. We find that the conditions required for thesweet spot can be expressed by the ratio of the gas damping timescale of theplanetesimal orbits and the planetary migration timescale. If the planetarymigration timescale depends on the surface density of disk gas inversely, thelocation of the sweet spot does not change with the disk evolution. The mass ofplanetesimals accreted by the planet depends on the amount of planetesimalsthat are shepherded by mean motion resonances. Our analysis suggests that tensEarth-mass of planetesimals can be shepherded into the sweet spot withoutplanetesimal collisions. However, as more planetesimals are trapped into meanmotion resonances, collisional cascade can lead to fragmentation ofplanetesimals. This could affect the location of the sweet spot and thepopulation of small objects in planetary systems. We conclude that thecomposition of gas giant planets depends on whether the planets crossed thesweet spot during their formation. Constraining the metallicity of cold giantplanets, that are expected to be outer than the sweet spot, would reveal keyinformation for understanding the origin of heavy elements in giant planets.

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