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The Earth's ocean mass is only 2.3 x 10^{-4} of the whole planet mass. Evenincluding water in the interior, it would be at most 10^{-3}-10^{-2}. AncientMars may have had a similar or slightly smaller water fraction. It is importantto clarify the water delivery mechanism to rocky planets in habitable zones inexoplanetary systems, as well as that to the Earth and Mars. Here, we considerwater delivery to planets by icy pebbles after the snowline inwardly passes theplanetary orbits and derive the water mass fraction (f_{water}) of the finalplanet as a function of disk parameters and discuss the parameters thatreproduce f_{water} comparable to that inferred for the Earth and ancient Mars.We calculate the growth of icy pebbles and their radial drift with a 1D model,and accretion of icy pebbles onto planets, by simultaneously solving thesnowline migration and the disk dissipation, to evaluate f_{water} of theplanets. We find that f_{water} is regulated by the total mass (M_{res}) of icydust materials preserved in the outer disk regions at the timing (t = t_{snow})of the snowline passage of the planetary orbit. Because M_{res} decays rapidlyafter the pebble formation front reaches the disk outer edge (at t = t_{pff}),f_{water} is sensitive to the ratio t_{snow}/t_{pff}, which is determined bythe disk parameters. We find t_{snow}/t_{pff} < 10 or > 10 is important.Deriving an analytical formula for f_{water} that reproduces the numericalresults, we find that f_{water} of a rocky planet near 1 au is ~10^{-4}-10^{-2}, in the disks with initial disk size ~ 30-50 au and the initialdisk mass accretion rate ~ (10^{-8}-10^{-7}) M_sun/y. Because these disks maybe median or slightly compact/massive disks, the water fraction of rockyplanets in habitable zones may be often similar to that of the Earth, if theicy pebble accretion is responsible for the water delivery.

Water delivery by pebble accretion to rocky planets in habitable zones in evolving disks