| A numerical scheme for the solution of the three-dimensional, frequency- and time-dependent radiative transfer equation with variable optical depth is developed for modelling the reionization of the Universe. Until now, the main difficulty in simulating the inhomogeneous reionization has been the treatment of cosmological radiative transfer. The proposed approach is drastically different from previous studies, which either resorted to a very simplified, parametric treatment of radiative transfer, or relied on one-dimensional models. The algorithm presented here is based on explicit multidimensional advection of wavefronts at the speed of light, combined with the implicit solution of the local chemical rate equations separately at each point. I implement the ray-tracing version of this algorithm on a desktop workstation and check its performance on a wide variety of test problems, showing that explicit advection at the speed of light is an attractive choice for simulation of astrophysical ionization fronts, particularly when one is interested in covering a wide range of optical depths within a 3D clumpy medium.; This scheme is then applied to the calculation of time-dependent, multi-frequency radiative transfer during the epoch of first object formation in the Universe. In a series of models, the 2.5 Mpc (comoving) simulation volume is evolved between the redshifts of z = 15 and z = 10 for different scenarios of star formation and quasar activity. The highest numerical resolution employed is 643 (spatial) x 10 2 (angular) x 3 (frequency), and at each point in space I calculate various stages of hydrogen and helium ionization accounting for nine chemical species altogether.; It is shown that at higher numerical resolution these models of inhomogeneous reionization can be used to predict the observational signatures of the earliest astrophysical objects in the Universe. At present, the calculations are accurate enough to resolve primordial objects to the scale typical of globular clusters, 106 M⊙ . |
