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.
