A Stringent Limit on the Mass Production Rate of $r$-Process Elements in the Milky Way

We analyze data from several studies of metal-poor stars in the Milky Way, focusing on both strong (Eu) and weak (Sr) $r$-process elements. Because these elements were injected in an explosion, we calculate the mass swept up when the blast wave first becomes radiative, yielding a lower limit for the dilution of such elements and hence a lower limit on the ejecta mass which is incorporated into the next generation of stars. Our study demonstrates that in order to explain the largest enhancements in [Eu/Fe] observed in stars at low [Fe/H] metallicities, individual $r$-process production events must synthesize a minimum of $10^{-3.5} M_{\odot}$ of $r$-process material. We also show that if the site of Mg production is the same as that of Eu, individual injection events must synthesize up to $\sim 10^{-3} M_{\odot}$ of $r$-process material. On the other hand, demanding that Sr traces Mg production results in $r$-process masses per event of $\sim 10^{-5} M_{\odot}$. This suggests that the astrophysical sites responsible for the genesis of the strong $r$-process elements need to operate at a drastically reduced rate when compared to core-collapse supernovae, while the synthesis of the weak $r$-process material is consistent with a supernova production site.