Transport of Protostellar Cosmic Rays in Turbulent Dense Cores

Recent studies have suggested that low-energy cosmic rays (CRs) may be accelerated inside molecular clouds by the shocks associated with star formation. We use a Monte Carlo transport code to model the propagation of CRs accelerated by protostellar accretion shocks through protostellar cores. We calculate the CR attenuation and energy losses and compute the resulting flux and ionization rate as a function of both radial distance from the protostar and angular position. We show that protostellar cores have non-uniform CR fluxes that produce a broad range of CR ionization rates, with the maximum value being up to two orders of magnitude higher then the radial average at a given distance. In particular, the CR flux is focused in the direction of the outflow cavity, creating a 'flashlight' effect and allowing CRs to leak out of the core. The radially averaged ionization rates are less than the measured value for the Milky Way of $\zeta \approx 10^{-16} \rm s^{-1}$; however, within $r \approx 0.03$ pc from the protostar, the maximum ionization rates exceed this value. We show that variation in the protostellar parameters, particularly in the accretion rate, may produce ionization rates that are a couple of orders of magnitude higher or lower than our fiducial values. Finally, we use a statistical method to model unresolved sub-grid magnetic turbulence in the core. We show that turbulence modifies the CR spectrum and increases the uniformity of the CR distribution but does not significantly affect the resulting ionization rates.