A comparison of numerical methods for computing the reionization of intergalacitc hydrogen and helium by a central radiating source

TL;DR

This paper compares numerical methods for radiative transfer in intergalactic hydrogen and helium ionization, highlighting the efficiency of photon packet schemes and the importance of time-dependent solutions for accurate temperature and ionization structures near sources.

Contribution

It demonstrates that photon packet schemes are more efficient than direct integration and emphasizes the necessity of time-dependent methods for accurate near-zone modeling.

Findings

Photon packet schemes are more computationally efficient.

Time-dependent methods are essential for accurate near-zone temperature and ionization.

Temperature differences up to 5×10^4 K near sources affect EoR predictions.

Abstract

We compare numerical methods for solving the radiative transfer equation in the context of the photoionization of intergalactic gaseous hydrogen and helium by a central radiating source. Direct integration of the radiative transfer equation and solutions using photon packets are examined, both for solutions to the time-dependent radiative transfer equation and in the infinite-speed-of-light approximation. The photon packet schemes are found to be more generally computationally efficient than a direct integration scheme. Whilst all codes accurately describe the growth rate of hydrogen and helium ionization zones, it is shown that a fully time-dependent method is required to capture the gas temperature and ionization structure in the near zone of a source when an ionization front expands at a speed close to the speed of light. Applied to Quasi-Stellar Objects in the Epoch of Reionization (EoR), temperature differences as high as $5\times10^4$ K result in the near-zone for solutions of the time-dependent radiative transfer equation compared with solutions in the infinite-speed-of-light approximation. Smaller temperature differences are found following the nearly full photoionization of helium in gas in which the hydrogen was already ionized and the helium was singly ionized. Variations found in the temperature and ionization structure far from the source, where the gas is predominantly neutral, may affect some predictions for 21-cm EoR experiments.