Numerical Models for the Diffuse Ionized Gas in Galaxies. II.
  Three-dimensional radiative transfer in inhomogeneous interstellar structures
  as a tool for analyzing the diffuse ionized gas
  Aims: We systematically explore a plausible subset of the parameter space
involving effective temperatures and metallicities of the ionizing stellar
sources, the effects of the hardening of their radiation by surrounding leaky
HII regions with different escape fractions, as well as different scenarios for
the clumpiness of the DIG, and compute the resulting line strength ratios for a
number of diagnostic optical emission lines.
  Methods: For the ionizing fluxes we compute a grid of stellar spectral energy
distributions (SEDs) from detailed, fully non-LTE model atmospheres that
include the effects of stellar winds and line blocking and blanketing. To
calculate the ionization and temperature structure in the HII regions and the
diffuse ionized gas we use spherically symmetric photoionization models as well
as state-of-the-art three-dimensional (3D) non-LTE radiative transfer
simulations, considering hydrogen, helium, and the most abundant metals.
  Results: We provide quantitative predictions of how the line ratios from HII
regions and the DIG vary as a function of metallicity, stellar effective
temperature, and escape fraction from the HII region. The range of predicted
line ratios reinforces the hypothesis that the DIG is ionized by (filtered)
radiation from hot stars; however, comparison of observed and predicted line
ratios indicates that the DIG is typically ionized with a softer SED than
predicted by the chosen stellar population synthesis model. Even small changes
in simulation parameters like the clumping factor can lead to considerable
variation in the ionized volume. Both for a more homogeneous gas and a very
inhomogeneous gas containing both dense clumps and channels with low gas
density, the ionized region in the dilute gas above the galactic plane can
cease to be radiation-bounded, allowing the ionizing radiation to leak into the
intergalactic medium.
