[Previous] | [Session 72] | [Next]
P. Paschos (UIUC), M. L. Norman, J. Bordner (UCSD)
The epoch of the Universe's reionization begins at redshifts z ~10 due to the expansion of ionization fronts (IFs) from individual point sources and the subsequent ionizing radiation emanating from the diffuse gas.
We have developed numerical methods, that use a multigrid refinement solver (MGMPI), to solve the moment equations of such radiation field for the energy density evolution in 3D. Our methods make use of two approximations: Flux-limited diffusion, for the diffuse component of the UV field and an Eddington factor scheme, for point source radiation. In order to test the results of the above methods, we have focused on the case of a single point source. In spherical coordinates the radial propagation of the radiative flux vector is determined by the Eddington factor which in this case is: frr=1 and fij=0 if (ij) \neq (rr). We use a modified set of moment equations in spherical coordinates from Mihalas & Mihalas (1984) to solve for the energy density due to the point source, ignoring recombination processes. These equations are then transformed to 3D Cartesian coordinates for general cosmological applications. The modification adds a time derivative of the energy density in the zeroth moment equation.
We have tested our method in the case of a homogeneous medium, by comparing the position of the ionization front with that calculated from the analytic approximation of an expanding Strömgen sphere in a single species gas (HI). The result shows that we are able to reproduce the correct rate of expansion. The method is then tested in the case of a non-evolving cosmological density distribution volume, to determine whether it can handle density fluctuations. We demonstrate that the ionization front propagates slower in the opaque cores and filaments than in the voids, giving rise to a complex distribution for the UV field. Finally we demonstrate the effect of shadowing from an opaque Gaussian overdensity.
This research is supported by NSF grant AST=9803137. Calculations were carried out on supercomputers at the NCSA.