Diffusive versus free-streaming cosmic-ray transport in molecular clouds

Understanding the cosmic-ray (CR) ionization rate is crucial in order to simulate the dynamics of molecular clouds, and interpret the chemical species observed in these objects. Calculating the CR ionization rate requires both accurate knowledge of the spectrum of MeV to GeV protons at the edge of the cloud as well as a model for the propagation of CRs into molecular clouds. Some models for the propagation of CRs in molecular clouds assume them to stream freely along magnetic field lines, while in others they propagate diffusively due to resonant scattering off of magnetic disturbances excited by MHD turbulence present in the medium. We discuss the conditions under which CR diffusion can operate in a molecular cloud, calculate the local CR spectrum and ionization rate in both a free-streaming and diffusive propagation model, and highlight the different results from the two models. We also apply these two models to the propagation through the ISM to obtain the proton spectrum seen by Voyager 1, and show that such a spectrum favors a diffusive propagation model