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.
