Recent observations of heavy elements produced by rapid neutron capture(r-process) in the halo have shown a striking and unexpected behavior: within asingle star, the relative abundances of r-process elements heavier than Eu arethe same as the same as those of solar system matter, while across stars withsimilar metallicity Fe/H, the r/Fe ratio varies over two orders of magnitude.In this paper we present a simple analytic model which describes a star'sabundances in terms of its ``ancestry,'' i.e., the number of nucleosynthesisevents (e.g., supernova explosions) which contributed to the star'scomposition. This model leads to a very simple analytic expression for theabundance scatter versus Fe/H, which is in good agreement with the data andwith more sophisticated numerical models. We investigate two classes ofscenarios for r-process nucleosynthesis, one in which r-process synthesisevents occur in only \sim 4% of supernovae but iron synthesis is ubiquitous,and one in which iron nucleosynthesis occurs in only about 9% of supernovae.(the Wasserburg- Qian model). We find that the predictions in these scenariosare similar for [Fe/H] \ga -2.5, but that these models can be readilydistinguished observationally by measuring the dispersion in r/Fe at [Fe/H] \la-3.
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