  The first stars are thought to be one of the dominant sources of hydrogen
reionization in the early Universe, with their high luminosities and surface
temperatures expected to drive high ionizing photon production rates. In this
work, we take our Geneva stellar evolution models of zero-metallicity stars and
predict their production rates of photons capable to ionize H, He I and He II,
based on a blackbody approximation. We present analytical fits in the range
1.7-500 solar masses. We then explore the impact of stellar initial mass,
rotation, and convective overshooting for individual stars. We have found that
ionizing photon production rates increase with increasing initial mass. For the
rotational velocities considered we see changes of up to 25% to ionizing
photons produced. This varies with initial mass and ionizing photon species and
reflects changes to surface properties due to rotation. We have also found that
higher convective overshooting increases ionizing photon production by
approximately 20% for the change in overshooting considered here. For stellar
populations, we explore how the production of ionizing photons varies as a
function of the initial mass function (IMF) slope, and minimum and maximum
initial masses. For a fixed population mass we have found changes of the order
of 20-30% through varying the nature of the IMF. This work presents ionizing
photon production predictions for the most up to date Geneva stellar evolution
models of Population III stars, and provides insight into how key evolutionary
parameters impact the contribution of the first stars to reionization.
