In the present research, we study the effects of a single giant planet in the dynamical evolution of water-rich embryos and planetesimals, located beyond the snow line of systems around Sun-like stars, in order to determine what kind of terrestrial-like planets could be formed in the habitable zone (hereafter HZ) of these systems. To do this, we carry out N-body simulations of planetary accretion, considering that the gas has been already dissipated from the disk and a single giant planet has been formed beyond the snow line of the system, at 3 au. We find that a giant planet with a value of mass between Saturn-mass and Jupiter-mass, represents a limit from which the amount of water-rich embryos that moves inward from beyond the snow line starts to decrease. From this, our research suggests that giant planets more massive than one Jupiter-mass become efficient dynamical barriers to inward-migrating water-rich embryos. Moreover, we infer that the number of these embryos that survive in the HZ significantly decreases for systems that host a giant planet more massive than one Jupiter-mass. This result has important consequences concerning the formation of terrestrial-like planets in the HZ with very high water contents and could provide a selection criteria in the search of potentially habitable exoplanets in systems that host a gaseous giant around solar-type stars.
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