Last week, we submitted a paper titled “Optimized Multi-Frequency Spectra for Applications in Radiative Feedback and Cosmological Reionization” to the Astrophysical Journal. You can find it on arXiv. Here we investigate the impact of varying energy discretizations in radiation transport schemes. Mono-chromatic approximations can underestimate the amount of partial ionization at large radii because all of the ionizing photons are absorbed at some characteristic radius. This is especially true for X-rays, which have large mean free paths.
With a multi-frequency approach, the solution converges with 4 or more frequency bins. For example with a 10^5 K blackbody source, the temperature of an HII region at r = 8 kpc is underestimated by a factor of 20 if a mono-chromatic spectrum is used. However it is unclear the best technique on how to choose these frequencies. In this work, we developed a Monte Carlo scheme to determine optimal frequency values for such radiation calculations. In the paper, we give optimal discretizations for a 10^5 K blackbody and power law spectrum for 1-4 bins. The code that employs this method will be released when the paper is accepted.