Higher-order methods of radiative transfer in simulations of the epoch of reionisation: P n versus M 1

Context . In current cosmological simulations, radiative transfer modules generally rely on the M 1 approximation, which has some glaring flaws related to its fluid-like behaviour, such as spurious pseudo-sources and loss of directionality when radiation fronts from different directions collide. P n , another moment-based model, may correct these issues. Aims . We aim to test P n in an astrophysical setting and compare it to M 1 , in order to see if it can indeed correct M 1 ’s issues. Also, we want to use P n ’s solutions to better pinpoint and quantify M 1 errors. Methods . We implemented a P n radiation transport method, coupled it to a photo-thermo-chemistry module to account for the interaction of ionising radiation with the hydrogen gas, and benchmarked it using tests for radiative transfer models comparison in astrophysics. Results . We implemented a P n radiation transport method, coupled it to a photo-thermo-chemistry module to account for the interaction of ionising radiation with the hydrogen gas, and benchmarked it using tests for radiative transfer models comparison in astrophysics. Conclusions . We find that high-order P n (e.g. P 9 ) indeed corrects M 1 ’s flaws, while faring as well or even better in some aspects in the tests, in particular when directionality is important or colliding radiation fronts occur. By comparing P 9 and M 1 radiation fields in an idealised cosmological test case, we highlight a new, thus far unreported artefact of M 1 , the ‘dark sombrero’. A dark sombrero appears as a spherical photon-deficit shell around the source, at typically one third to one quarter of the distance to the next source. The photon density in dark sombreros can be underestimated by a factor of up to 2–3. These artefacts occur in regions where a source’s radiation field connects with that of another source or group of sources. These basic properties (the position and amplitude) of the dark sombreros may depend on the sources’ relative intensities, positions, and spatial resolution, although we have not been able to test this in detail in this study. Moreover, the larger-scale M 1 photon density also exhibits spurious features, enhancing or reducing photon density in various regions. We use a small reionisation-like test simulation to characterise the relative error in hydrogen neutral fractions between M 1 and P 9 . The relative error is well represented by a Gaussian with a dispersion of 0.27 dex in log 10 (x HI ). Both aspects are likely related to the photons’ collisional behaviour in M 1 .