A Two-dimensional Model for the Primordial Nebula Constrained by D/H Measurements in the Solar System: Implications for the Formation of Giant Planets
Using the density and temperature profiles resulting from a two-dimensional turbulent model of the solar nebula as well as an appropriate law for the time variation of the disk accretion rate, we integrate the equation of diffusion that rules the evolution of the D/H ratio in H2O and HCN throughout the nebula. By fitting D/H measured in LL3 meteorites and comets or inferred in proto-Uranian and proto-Neptunian ices, we constrain the parameters of the model, namely, the initial accretion rate M(0), the initial radius of the turbulent disk RD, and the α-coefficient of turbulent viscosity, and we find 2×10-6<M(0)<10-5 Msolar yr-1, 12.8<RD<39 AU, and 0.006<α<0.04. Under the assumption that cometary cores are homogeneous, the microscopic icy grains that subsequently formed cometesimals were produced in the Uranus-Neptune region and no later than 3.5×105 yr. The epochs of the formation of Jupiter and Saturn cannot be lower than 0.7 and 5.7 Myr, respectively, after the formation of the Sun. Uranus and Neptune were completed after the dissipation of the nebula. The enrichment in volatiles with respect to the solar abundance measured by the Galileo probe in Jupiter may result from the trapping of these gases in the form of clathrate hydrates in the feeding zone of the forming planet.