Constraints on the mass of a habitable planet with water of nebular origin

From an astrobiological point of view, special attention has been paid to the probability of habitable planets in extrasolar systems. The purpose of this study is to constrain a possible range of the mass of a terrestrial planet that can get water. We focus on the process of water production through oxidation of atmospheric hydrogen - the nebular gas having been attracted gravitationally - by oxides available at the planetary surface. For the water production to work well on a planet, a sufficient amount of hydrogen and a temperature high enough to melt the planetary surface are needed. We have simulated the structure of the atmosphere that connects with the protoplanetary nebula for wide ranges of the heat flux, the opacity, and the density of the nebular gas. We have found that both requirements are fulfilled for an Earth- mass planet for wide ranges of the parameters. We have also found that the surface temperature of planets of less than or similar to 0.3M(E) (where M-E is Earth's mass) is lower than the melting temperature of silicate (similar to 1500 K). On the other hand, a planet of more than several ME becomes a gas giant through runaway accretion of the nebular gas.