Rapid Formation of Jupiter by Diffusive Redistribution of Water Vapor in the Solar Nebula

Abstract

A model is presented for enhancing the abundance of solid material in the region of the solar nebula in which Jupiter formed, by diffusive redistribution and condensation of water vapor. A turbulent nebula is assumed with temperature decreasing roughly inversely with the radial distance from the center, and time scales set by turbulent viscosities taken from recent nebular models. The diffusion equation in cylindrical coordinates is solved in the limit that the sink of water vapor is condensation within a narrow radial zone approximately 5 AU from the center. Most of the water vapor is extracted from the terrestrial planet-forming zone. This "cold finger" solution is then justified by analytic solution of the diffusion equation in the condensation zone itself and inward and outward of that zone. The length scale over which most of the diffusively transported water vapor condenses is calculated to be ∼0.4 AU, provided the solids are not redistributed, and the surface density of ice in the formation zone of Jupiter is enhanced by as much as 75. The enhancement in surface density of solids is sufficient to trigger rapid accretion of planetesimals into a solid core along the lines of the model of Lissauer (1987, Icarus 69, 249–265), and hence produce Jupiter by nucleated instability on a time scale of approximately 10^5 to 10^6 years.

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