Abstract

In the densest regions of molecular clouds ionization comes primarily from cosmic rays (CRs), charged particles accelerated to relativistic energies. Observations show that the ionization rate is higher than expected inside molecular clouds, suggesting that low-energy CRs are accelerated locally by the shocks associated with star formation. However, the cosmic ray flux cannot be observed directly from specific sources outside of our solar neighborhood, and previous studies on the subject have primarily been carried out analytically with simplifying assumptions about the cloud properties. We developed a method for modeling CR transport in molecular clouds numerically, using a fully 3D grid-based Monte Carlo transport code. We use numerical magnetohydrodynamic simulations of the magnetic field and gas density around forming stars as inputs for our code and follow the propagation of the CRs accelerated at the accretion shock, taking into account energy losses. We find that the CR flux exhibits a beaming effect, with the CRs tending to follow magnetic field lines and lose energy when they enter a higher density area. This results in certain regions, such as the lower density outflow cavity around the protostar, having a higher CR flux and resultant ionization rate than the surrounding regions.