Sensitivity to Thermonuclear Reaction Rates in Modeling the Abundance
  Anomalies of NGC 2419
  Abundance anomalies in globular clusters provide strong evidence for multiple
stellar populations within each cluster. These populations are usually
interpreted as distinct generations, with the currently observed
second-generation stars having formed in part from the ejecta of massive,
first-generation "polluter" stars, giving rise to the anomalous abundance
patterns. The precise nature of the polluters and their enrichment mechanism
are still unclear. Even so, the chemical abundances measured in
second-generation stars within the globular cluster NGC 2419 provide insight
into this puzzling process. Previous work used Monte Carlo nuclear reaction
network calculations to constrain the temperature-density conditions that could
reproduce the observed abundances, thereby placing robust limits on the origins
of the polluter material. The effect of individual reaction rates on these
conditions has not been studied, however. Thus, we perform an exhaustive
sensitivity study on the nuclear physics input to determine which reactions
have the greatest impact on these predictions. We find that the
$^{30}$Si(p,$\gamma$)$^{31}$P, $^{37}$Ar(p,$\gamma$)$^{38}$K,
$^{38}$Ar(p,$\gamma$)$^{39}$K, and $^{39}$K(p,$\gamma$)$^{40}$Ca reactions are
all critical in determining the temperature-density conditions, and ultimately,
the origin of the polluter material. We conclude with recommendations for
future experiments.
