  Cosmic rays are the only agent able to penetrate into the interior of dense
molecular clouds. Depositing (part of) their energy through ionisation, cosmic
rays play an essential role in determining the physical and chemical evolution
of star-forming regions. To a first approximation their effect can be
quantified by the cosmic-ray induced ionization rate. Interestingly,
theoretical estimates of the ionization rate assuming the cosmic-ray spectra
observed in the local interstellar medium result in an ionization rate that is
one to two orders of magnitude below the values inferred from observations.
However, due to the discrete nature of sources, the local spectra of MeV cosmic
rays are in general not representative for the spectra elsewhere in the Galaxy.
Such stochasticity effects have the potential of reconciling modelled
ionization rates with measured ones. Here, we model the distribution of
low-energy cosmic-ray spectra expected from a statistical population of
supernova remnants in the Milky Way. The corresponding distribution for the
ionization rate is derived and confronted with data. We find that the
stochastic uncertainty helps with explaining the surprisingly high ionization
rates observed in many molecular clouds.
