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Kai Yan Lee
(Stockholm University, Dept. of astronomy)
During the epoch when the first collapsed structures formed (6 < z < 50 ) our
Universe went through an extended period of changes. Some of the radiation
from the first stars and accreting black holes in those structures escaped and
changed the state of the Intergalactic Medium (IGM). The era of this global
phase change in which the state of the IGM was transformed from cold and
neutral to warm and ionized, is called the Epoch of Reionization.
In this thesis we focus on numerical methods to calculate the effects of this
escaping radiation. We start by considering the performance of the cosmological radiative transfer code C2-RAY. We find that although this code efficiently
and accurately solves for the changes in the ionized fractions, it can yield inaccurate results for the temperature changes. We introduce two new elements to
improve the code. The first element, an adaptive time step algorithm, quickly
determines an optimal time step by only considering the computational cells
relevant for this determination. The second element, asynchronous evolution,
allows different cells to evolve with different time steps.
An important constituent of methods to calculate the effects of ionizing
radiation is the transport of photons through the computational domain or “ray-tracing”. We devise a novel ray tracing method called PYRAMID which uses
a new geometry - the pyramidal geometry. This geometry shares properties
with both the standard Cartesian and spherical geometries. This makes it on
the one hand easy to use in conjunction with a Cartesian grid and on the other
hand ideally suited to trace radiation from a radially emitting source.
A time-dependent photoionization calculation not only requires tracing the
path of photons but also solving the coupled set of photoionization and thermal
equations. Several different solvers for these equations are in use in cosmological radiative transfer codes. We conduct a detailed and quantitative comparison of four different standard solvers in which we evaluate how their accuracy
depends on the choice of the time step. This comparison shows that their performance can be characterized by two simple parameters and that the C2-RAY generally performs best.