Photon Number Conserving Models of H II Bubbles during Reionization

Understand

Traditional excursion set based models of H II bubble growth during the epoch of reionization are known to violate photon number conservation, in the sense that the mass fraction in ionized bubbles in these models does not equal the ratio of the number of ionizing photons produced by sources and the number of hydrogen atoms in the intergalactic medium.

• E.g., for a Planck13 cosmology with electron scattering optical depth $\tau\simeq0.066$, the discrepancy is $\sim15$ per cent for $x_{\rm HII}=0.1$ and $\sim5$ per cent for $x_{\rm HII}=0.5$.
• We demonstrate that this problem arises from a fundamental conceptual shortcoming of the excursion set approach (already recognised in the literature on this formalism) which only tracks average mass fractions instead of the exact, stochastic source counts.
• With this insight, we build an approximately photon number conserving Monte Carlo model of bubble growth based on partitioning regions of dark matter into halos.