Radiative transfer of energetic photons: X-rays and helium ionization in   C2-Ray
  We present an extension to the short-characteristic ray-tracing and non-equilibrium photon-ionization code C2Ray. The new version includes the effects of helium and improved multi-frequency heating. The motivation for this work is to be able to deal with harder ionizing spectra, such as for example from quasar-like sources during cosmic reionization. We review the basic algorithmic ingredients of C2-Ray before describing the changes implemented, which include a treatment of the full on the spot (OTS) approximation, secondary ionization, and multi-frequency photo-ionization and heating. We performed a series of tests against equilibrium solutions from CLOUDY as well as comparisons to the hydrogen only solutions by C2-Ray in the extensive code comparison in Iliev et al. (2006). We show that the full, coupled OTS approximation is more accurate than the simplified, uncoupled one. We find that also with helium and a multi-frequency set up, long timesteps (up to ~10% of the recombination time) still give accurate results for the ionization fractions. On the other hand, accurate results for the temperature set strong constrains on the timestep. The details of these constraints depend however on the optical depth of the cells. We use the new version of the code to confirm that the assumption made in many reionization simulations, namely that helium is singly ionized everywhere were hydrogen is, is indeed valid when the sources have stellar-like spectra. 
Martina M. Friedrich, Garrelt Mellema, Ilian T. Iliev, Paul R. Shapiro
astro-ph.CO