Theoretical Distributions of Short-Lived Radionuclides for Star Formation in Molecular Clouds

Short-lived radioactive nulcei (half-life $\tau_{1/2}\sim1$ Myr) influence the formation of stars and planetary systems by providing sources of heating and ionization. Whereas many previous studies have focused on the possible nuclear enrichment of our own Solar System, the goal of this paper is to estimate the distributions of short-lived radionuclides (SLRs) for the entire population of stars forming within a molecular cloud. Here we focus on the nuclear species $^{60}$Fe and $^{26}$Al, which have the largest impact due to their relatively high abundances. We construct molecular cloud models and include nuclear contributions from both supernovae and stellar winds. The resulting distributions of SLRs are time dependent with widths of $\sim3$ orders of magnitude and mass fractions $\rho_{\scriptstyle SLR}/\rho_\ast\sim10^{-11}-10^{-8}$. Over the range of scenarios explored herein, the SLR distributions show only modest variations with the choice of cloud structure (fractal dimension), star formation history, and cluster distribution. The most important variation arises from the diffusion length scale for the transport of SLRs within the cloud. The expected SLR distributions are wide enough to include values inferred for the abundances in our Solar System, although most of the stars are predicted to have smaller enrichment levels. In addition, the ratio of $^{60}$Fe/$^{26}$Al is predicted to be greater than unity, on average, in contrast to Solar System results. One explanation for this finding is the presence of an additional source for the $^{26}$Al isotope.