Abstract Recent studies have detected structurally bound water in the refractory silicate minerals present in ordinary and enstatite chondrite meteorites. The mechanism for the incorporation of the hydrogen is not well defined. In this paper we quantitatively examine a two-fold process involving the implantation and diffusion of nebular hydrogen ions that is responsible for the hydration of the chondritic minerals. Our simulations show that depending on critical parameters, including the flux of the protons in nebular plasma, retention coefficient, temperature of the silicate minerals, and desorption rate of implanted hydrogen, the implantation of low-energy hydrogen ions can result in equivalent water contents of ∼0.1 wt% in chondritic silicates within 10 years. Thus, this novel mechanism operating in the nebula at 10−3 bar pressure and <650 K temperatures can efficiently hydrate the free-floating chondritic minerals prior to the rapid formation of planetesimals inside the snow line, and agree well with the wet accretion scenario for the inner solar system objects.

We have also found the surface temperature of planets of <= 0.3 Earth masses is lower than the melting temperature of silicate (~ 1500K). On the other hand, a planet of more than several Earth masses becomes a gas giant planet through runaway accretion of the nebular gas. Published as: Astrophys.J.648:696-706,2006 DOI: 10.1086/505780 arXiv categories: astro-ph 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 the atmospheric hydrogen—the nebular gas having been attracted gravitationally—by oxide available at the planetary surface. For the water production to work well on a planet, a sufficient amount of hydrogen and enough high temperature 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 heat flux, opacity, and density of the nebular gas. We have found both requirements are fulfilled for an Earth-mass planet for wide ranges of the parameters. We have also found the surface temperature of planets of ≤ 0.3 ​ M E absent 0.3 subscript 𝑀 E \leq 0.3M_{\rm E} ( M E subscript 𝑀 E M_{\rm E} : Earth’s mass) is lower than the melting temperature of silicate ( ∼ 1500 similar-to absent 1500 \sim 1500   K). On the other hand, a planet of more than several  M E subscript 𝑀 E M_{\rm E} becomes a gas giant planet through runaway accretion of the nebular gas. ( 1985 ) for wide ranges of planetary accretion rate, grain opacity, and density of the nebular gas. However, they used quite simple forms of opacity and equation of state, both of which have been substantially improved. Furthermore they focused only on the Earth (i.e., Earth-mass planets) and had no discussion on the production of water. Although Sasaki ( 1990 ) discussed the production of water in order to suggest the deep magma ocean on the early Earth, the ranges of the parameters considered were so restricted that we are unable to get any systematic understanding of the nebular origin of water on terrestrial planets. We also constrain the mass of a planet that remains a terrestrial one. Section 3 presents properties of the atmosphere of nebular origin for various planetary masses. Section 4 shows the timescale for the substantial accretion of the nebular gas. Finally we discuss the probability of water production on terrestrial planets and constrain the masses of the potentially-habitable planets in section 5. 2 NUMERICAL METHOD 2.1 Basic equations We consider a spherically-symmetric hydrostatic atmosphere that connects with the surrounding nebula. We thus consider f = 0 𝑓 0 f=0 – 1 1 1 in this paper. The nebular gas dissipates with time. Taking it into account, we consider a wide range of the nebular density, 1– 10 − 10 superscript 10 10 10^{-10} times the gas density ( ρ MSN = 1.2 × 10 − 9 ​ g ​ cm − 3 subscript 𝜌 MSN 1.2 superscript 10 9 g superscript cm 3 \rho_{\rm MSN}=1.2\times 10^{-9}\rm g\,cm^{-3} at 1 AU) of minimum-mass solar nebula model (Hayashi, 1981 ) for the Earth-mass case. [ 12 ]), the mass of atmospheric hydrogen is more than about 1 × 10 25 1 superscript 10 25 1\times 10^{25}  g for f &lt; 1 𝑓 1 f&lt;1 , as shown Fig. 3 a: The amount of hydrogen a planet acquires is insensitive to the nebular density (see Fig. 3 b). Water is produced through reaction between the atmospheric hydrogen and oxides contained in the solid planet. The amount of water depends on what kind of oxide is available. Equilibrium condensation in a highly-reduced environment like a protoplanetary nebula yields not Fe-bearing minerals but Fe-metal (Wood & Hashimoto, 1993 ) . However, dust grains in a protoplanetary nebula can be considered to have non-equilibrium composition including, at least, fayalite (Pollack et al., 1994 , and references therein) . When the surrounding nebular gas disappears almost completely, the atmosphere and solid planet begin to get cold, and then an ocean forms through the condensation of steam in the atmosphere. Because the Earth is isolated in the nebular gas, the accretion of the nebular gas inevitably takes place and water is produced on the Earth. Although the amount of the nebular gas required for the damping of the eccentricities are as small as 10 − 4 superscript 10 4 10^{-4} to 10 − 3 superscript 10 3 10^{-3} times that of the minimum-mass solar nebula (Kominami & Ida, 2002 ; Nagasawa et al., 2005 ) , our numerical results show that this small amount of the nebular gas is sufficient for the Earth to get water comparable in mass with Earth’s sea water. We should be, however, careful when we consider the nebular origin of water on the Earth. This is because the ratio of deuterium to hydrogen (D/H) of the sea water on the present Earth is larger by about a factor of seven than D/H of the solar nebula (e.g., Drake & Righter, 2002 ) . Moreover, the current Earth’s atmosphere includes a tiny amount of Acta57, 2377 Zahnle (1993) Figure 1: The surface temperature (i.e., the temperature at the bottom of the atmosphere) of an Earth-mass planet for wide ranges of three parameters, luminosity ( L 𝐿 L ), grain depletion factor ( f 𝑓 f ), and density of the nebular gas ( ρ n subscript 𝜌 n \rho_{\rm n} ). In (a), the surface temperature is shown as a function of L 𝐿 L for three different values of f 𝑓 f . Figure 5: Surface temperature as a function of luminosity for several choices of planet’s mass. Each attached number represents planet’s mass in the Earth mass. The solid and dashed lines represent cases of f = 1 𝑓 1 f=1 and 0.01 0.01 0.01 , respectively. Figure 6: The typical timescale for substantial accretion of the nebular gas as a function of planet’s mass for two choices of the grain depletion factor ( f 𝑓 f ). The open circles represent the numerical results of our evolutionary calculations; the solid lines are drawn using equation ( 13 ) with the numerical factor α 𝛼 \alpha of 1/3.