We construct a model for cosmic ray acceleration from protostellar accretion shocks and calculate the resulting cosmic ray ionization rate within star-forming molecular clouds .
We couple a protostar cluster model with an analytic accretion shock model to calculate the cosmic ray acceleration from protostellar surfaces .
We present the cosmic ray 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 6 orders of magnitude in energy .
After attenuation , the spectrum at high energies steepens , while at low energies it is relatively flat .
We calculate the cosmic ray pressure and cosmic ray ionization rate from relativistic protons at the protostellar surface and at the edge of the core .
We present the cosmic ray ionization rate for individual protostars as a function of their instantaneous mass and final mass .
The protostellar cosmic ray ionization rate is \zeta \approx 0.01 - 1 s ^ { -1 } at the accretion shock surface .
However , at the edge of the core , the cosmic ray ionization rate drops substantially to between \zeta \approx 10 ^ { -20 } to 10 ^ { -17 } s ^ { -1 } .
There is a large spatial gradient in the cosmic ray ionization rate , such that inner regions may experience cosmic ray ionization rates larger than the often assumed fiducial rate , \zeta = 3 \times 10 ^ { -17 } s ^ { -1 } .
Finally , we calculate the cosmic ray ionization rate for protostellar clusters over 5 orders of magnitude of cluster size .
We find that clusters with more than approximately 200 protostars produce a higher cosmic ray ionization rate within their natal cloud than the fiducial galactic value .