Optimized Multi-Frequency Spectra for Applications in Radiative Feedback
  and Cosmological Reionization
  The recent implementation of radiative transfer algorithms in numerous
hydrodynamics codes has led to a dramatic improvement in studies of feedback in
various astrophysical environments. However, because of methodological
limitations and computational expense, the spectra of radiation sources are
generally sampled at only a few evenly-spaced discrete emission frequencies.
Using one-dimensional radiative transfer calculations, we investigate the
discrepancies in gas properties surrounding model stars and accreting black
holes that arise solely due to spectral discretization. We find that even in
the idealized case of a static and uniform density field, commonly used
discretization schemes induce errors in the neutral fraction and temperature by
factors of two to three on average, and by over an order of magnitude in
certain column density regimes. The consequences are most severe for radiative
feedback operating on large scales, dense clumps of gas, and media consisting
of multiple chemical species. We have developed a method for optimally
constructing discrete spectra, and show that for two test cases of interest,
carefully chosen four-bin spectra can eliminate errors associated with
frequency resolution to high precision. Applying these findings to a fully
three-dimensional radiation-hydrodynamic simulation of the early universe, we
find that the HII region around a primordial star is substantially altered in
both size and morphology, corroborating the one-dimensional prediction that
discrete spectral energy distributions can lead to sizable inaccuracies in the
physical properties of a medium, and as a result, the subsequent evolution and
observable signatures of objects embedded within it.
