Recent observations of heavy elements produced by rapid neutron capture ( r -process ) in the halo have shown a striking and unexpected behavior : within a single star , the relative abundances of r -process elements heavier than Eu are the same as the same as those of solar system matter , while across stars with similar 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 ’ s abundances in terms of its “ ancestry , ” i.e. , the number of nucleosynthesis events ( e.g. , supernova explosions ) which contributed to the star ’ s composition .
This model leads to a very simple analytic expression for the abundance scatter versus Fe/H , which is in good agreement with the data and with more sophisticated numerical models .
We investigate two classes of scenarios for r -process nucleosynthesis , one in which r -process synthesis events 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 scenarios are similar for [ { Fe / H } ] \gtrsim - 2.5 , but that these models can be readily distinguished observationally by measuring the dispersion in r /Fe at [ { Fe / H } ] \lesssim - 3 .