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Context.Recent studies suggest that many giant exoplanets are highly enrichedwith heavy elements compared to their host star andcontain several tens ofEarth masses or more of heavy elements. Such enrichment is considered to havebeen brought by accretionof planetesimals in late formation stages. Previousdynamical simulations, however, show that planets are unable to collect somuchheavy elements throughin situplanetesimal accretion. Aims.We investigatewhether a giant planet migrating inward can capture planetesimals efficientlyto significantly increase its metal-licity. Methods.We performed orbitalintegrations of a migrating giant planet and planetesimals in a protoplanetarygas disc to infer theplanetesimal mass that is accreted by the planet.Results.We find that the two shepherding processes of mean motion resonancestrapping and aerodynamic gas drag inhibit plan-etesimal capture of a migratingplanet. However, the amplified libration allows the highly-excitedplanetesimals in the resonances toescape from the resonance trap and beaccreted by the planet. Consequently, we show that a migrating giant planetcaptures planetes-imals with total mass of several tens of Earth masses, if theplanet forms at a few tens of AU in a relatively massive disc. We alsofind thatplanetesimal capture occurs efficiently in a limited range of semi-major axis,and that the total captured planetesimal massincreases with increasingmigration distances. Our results have important implications for understandingthe relation between giantplanet metallicity and mass, as we suggest that itreflects the formation location of the planet, or more precisely, the locationwhererunaway gas accretion occurred. We also suggest the observed metal-richclose-in Jupiters migrated to their present locations fromafar, where theyformed.

The origin of the high metallicity of close-in giant exoplanets: Combined effect of the resonant and aerodynamic shepherding