Context. The ocean mass of the Earth is only 2.3 × 10−4 of the whole planet mass. Even including water in the interior, the water fraction would be at most 10−3−10−2. Ancient Mars may have had a similar or slightly smaller water fraction. What controlled the amount of water in these planets has not been clear, although several models have been proposed. It is important to clarify the control mechanism to discuss water delivery to rocky planets in habitable zones in exoplanetary systems, as well as that to Earth and Mars in our solar system.
Aims. We consider water delivery to planets by icy pebbles after the snowline inwardly passes planetary orbits. We derive the water mass fraction (fwater) of the final planet as a function of disk parameters and discuss the parameters that reproduce a small value of fwater comparable to that inferred for the Earth and ancient Mars.
Methods. We calculated the growth of icy dust grains to pebbles and the pebble radial drift with a 1D model, by simultaneously solving the snowline migration and dissipation of a gas disk. With the obtained pebble mass flux, we calculated accretion of icy pebbles onto planets after the snowline passage to evaluate fwater of the planets.
Results. We find that fwater is regulated by the total mass (Mres) of icy dust materials preserved in the outer disk regions at the timing (t = tsnow) of the snowline passage of the planetary orbit. Because Mres decays rapidly after the pebble formation front reaches the disk outer edge (at t = tpff), fwater is sensitive to the ratio tsnow∕tpff, which is determined by the disk parameters. We find tsnow∕tpff < 10 or > 10 is important. By evaluating Mres analytically, we derive an analytical formula of fwater that reproduces the numerical results.
Conclusions. Using the analytical formula, we find that fwater of a rocky planet near 1 au is similar to the Earth, i.e., ~10−4−10−2, in disks with an initial disk size of 30–50 au and an initial disk mass accretion rate of ~(10−8−10−7) M⊙ yr−1 for disk depletion timescale of approximately a few M yr. Because these disks may be median or slightly compact/massive disks, our results suggest that the water fraction of rocky planets in habitable zones may often be similar to that of the Earth if icy pebble accretion is responsible for water delivery.
Terrestrial planet orbits in the habitable zones of exoplanetary system
