Constraints on $R$-process Nucleosynthesis from $^{129}$I and $^{247}$Cm in the Early Solar System

GW170817 has confirmed binary neutron star mergers as one of the sites for rapid neutron capture ($r$) process. However, there are large theoretical and experimental uncertainties associated with the resulting nucleosynthesis calculations and additional sites may be needed to explain all the existing observations. In this regard, abundances of short-lived radioactive isotopes (SLRIs) in the early solar system (ESS), that are synthesized exclusively by $r$-process, can provide independent clues regarding the nature of $r$-process events. In this work, we study the evolution of $r$-process SLRIs $^{129}$I and $^{247}$Cm as well as the corresponding reference isotopes $^{127}$I and $^{235}$U at the Solar location. We consider up to three different sources that have distinct $^{129}$I/$^{247}$Cm production ratios corresponding to the varied $r$-process conditions in different astrophysical scenarios. In contrast to the results found by C\^ot\'e et al. (2021), we find that $^{129}$I and $^{247}$Cm in the ESS do not come entirely from a single major event but get contributions from at least two more minor contributors. This has a dramatic effect on the evolution of the $^{129}$I/$^{247}$Cm ratio, such that the measured ESS value in meteorites may not correspond to that of the "$last$" major $r$-process event. Interestingly, however, we find that the $^{129}$I/$^{247}$Cm ratio, in combination with the observed $^{129}$I/$^{127}$I and $^{247}$Cm/$^{235}$U ratio in the ESS, can still provide important constraints on the properties of proposed $r$-process sources operating in the Milky Way.