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Taking account of the size distribution of planetesimals inferred from recent theoretical studies of planetesimal accumulation, we examine gravitational separation of noble gases inside large porous planetesimals in the solar nebula. The size distribution is characterized by the value of the minimum planetesimal size R0 for a given power-law distribution, which also determines the maximum planetesimal size for a given total mass of planetesimals. Both enrichment and isotopic fractionation of noble gases strongly depend on the value of R0, as it determines the number of large planetesimals inside which gravitational separation of noble gases is significant. We find the ranges of the values of R0 that can produce the enrichment and the isotopic fractionation of Xe similar to the terrestrial values separately, but the two ranges are found not to overlap. We also find significant isotopic fractionation of Kr for the parameter value that can produce the terrestrial isotopic fractionation of Xe, in contrast to the observation. These results suggest that the isotopic fractionation of terrestrial Xe cannot be explained if we only consider the gravitational separation inside porous planetesimals with the size distribution.

On the isotopic fractionation of terrestrial xenon by gravitational separation inside porous planetesimals with size distribution