On the accuracy of common moment-based radiative transfer methods for simulating reionization

Modern cosmological simulations of reionization often treat the radiative transfer by solving for the monopole and dipoles of the intensity field and by making some ansatz for the quadrupole moments to close the system of equations. We investigate the accuracy of the most common closure methods, i.e. Eddington tensor choices. We argue that these algorithms are the most likely to err after reionization and study qausi-analytic test problems that mimic these situations: large-scale fluctuations in the post-reionization ionizing background and radiative transfer in a predominantly ionized medium with discrete absorbers. We show that the usual closure methods, OTVET and M1, over-ionize self-shielding absorbers when fixing the background photoionization rate, leading to 30-40% higher emissivity to balance the increased recombination rate. This over-ionization results in a simulation run with these algorithms having a factor of ~ 2 lower average metagalactic photoionization rate relative to truth for a given ionizing emissivity. Furthermore, these algorithms are unlikely to reproduce fluctuations in the ionizing background on scales below the photon mean path: OTVET tends to overpredict the fluctuations there when the simulation box is smaller than twice the mean free path and underpredict otherwise, while M1 drastically underpredicts these fluctuations. As a result, these numerical methods are likely not sufficiently accurate to interpret the Lyα forest opacity fluctuations observed after reionzation. We also comment on ray tracing methods, showing that a high number of angular directions need to be followed to capture fluctuations in the post-reionization ionizing background accurately. Lastly, we argue that the strong dependence of the post-reionization ionizing background on the value of the reduced speed of light found in many simulations signals that the ionizing photon mean free path is several times larger in such simulations than the observationally measured value.