2018ApJ...861...87G

We construct a model for cosmic-ray (CR) acceleration from protostellar accretion shocks and calculate the resulting CR ionization rate within star-forming molecular clouds. We couple a protostar cluster model with an analytic accretion shock model to calculate the CR acceleration from protostellar surfaces. We present the CR flux spectrum from keV to GeV energies for a typical low-mass protostar. We find that at the shock surface, the spectrum follows a power-law trend across six orders of magnitude in energy. After attenuation, the spectrum at high energies steepens, while at low energies it is relatively flat. We calculate the CR pressure and ionization rates from relativistic protons at the protostellar surface and the edge of the core. We present the CR ionization rate for individual protostars as a function of their instantaneous and final masses. The protostellar CR ionization rate is ζ ≃ 0.01-1 s^–1 at the accretion shock surface. However, at the edge of the core, the CR ionization rate drops substantially to between ζ ≃ 10^–20 and 10^–17 s^–1. There is a large spatial gradient in the CR ionization rate, such that inner regions may experience CR ionization rates larger than the often assumed fiducial rate, ζ = 3 x 10^–17 s^–1. Finally, we calculate the CR ionization rate for protostellar clusters over five orders of magnitude of cluster size. We find that clusters with more than approximately 200 protostars produce a higher CR ionization rate within their natal cloud than the fiducial galactic value.