Isotopic fractionation as a probe of heating processes in the solar nebula

Abstract

Development of isotopic fractionation in a condensed phase during congruent evaporation by abrupt heating is modeled to estimate heating conditions in the solar nebula. Effects of elemental diffusion in the condensed phase, back reaction, and grain shape are taken into consideration in the model. Isotopic mass fractionation of an element during evaporation is governed by five critical parameters: evaporation Péclet number Pe, fractionation factor α, dust enrichment factor η, volume expansion factor ε, and initial gas–dust ratio ω 0. Three modes of isotopic fractionation are recognized in terms of Pe: at Pe<0.1, the grain becomes smaller keeping isotopic homogeneity; at 0.1< Pe<1000, the grain changes its isotopic composition retaining zoning; at Pe>1000, a steady diffusion boundary layer quickly develops near the surface, which significantly suppresses isotopic fractionation. Free evaporation conditions can accordingly be divided into “Rayleigh”, “intermediate”, and “no” fractionation regimes, respectively. Parameters η, ε, and ω 0 control the degree of back reaction; higher η and ω 0 and lower ε represent an extensive back reaction. Very small dust enrichment factor ( η<∼0.1 with ω 0≈0) or very large expansion factor ( ε>∼10) leads to free evaporation. The conditions for attainment of gas–dust equilibrium are given by η( ω 0+1)>1.0 and ε< η( ω 0+1)−1, where no isotopic mass fractionation is expected irrespective of Pe values. Spherical grains quickly develop larger isotopic fractionation and more distinct isotopic zoning than cylinder and platy grains having the same size. Surface roughness within the order of the grain size quickly disappears except for steady jagged surface developed from pits or grooves, and does not significantly affect the degree of isotopic fractionation. The model predicts that magnesium and oxygen isotopes in forsterite are in either Rayleigh or intermediate fractionation regime over a wide range of initial grain size and temperature in the solar nebula. The absence of Mg isotopic mass fractionation in forsterite in chondrites suggests that the dust enrichment factor is much larger than unity and that the expansion factor is smaller than η−1.