A new moment method for continuum radiative transfer in cosmological re-ionization

We introduce a new code for computing time-dependent continuum radiative transfer and non-equilibrium ionization states in static density fields with periodic boundaries. Our code solves the moments of the radiative transfer equation, closed by an Eddington tensor computed using a long characteristics (LC) method. We show that traditional short characteristics and the optically thin approximation are inappropriate for computing Eddington factors for the problem of cosmological re-ionization. We evolve the non-equilibrium ionization field via an efficient and accurate (errors <1 per cent) technique that switches between fully implicit or explicit finite differencing depending on whether the local time-scales are long or short compared to the time-step. We tailor our code for the problem of cosmological re-ionization. In tests, the code conserves photons, accurately treats cosmological effects and reproduces analytic Strömgren sphere solutions. Its chief weakness is that the computation time for the LC calculation scales relatively poorly compared to other techniques  ( t _LC∝ N ^～1.5_cells)  ; however, we mitigate this by only recomputing the Eddington tensor when the radiation field changes substantially. Our technique makes almost no physical approximations, so it provides a way to benchmark faster but more approximate techniques. It can readily be extended to evolve multiple frequencies, though we do not do so here. Finally, we note that our method is generally applicable to any problem involving the transfer of continuum radiation through a periodic volume.