## Time-dependent ionisation of metals in the intergalactic medium

##### Abstract

This thesis presents the results of a study into modelling the ionisation of heavy
elements in the intergalactic medium (IGM) by solving the time-dependent ionisation
rate equations. An algorithm has been developed which calculates ionisation fractions
of the first 30 elements (hydrogen to zinc) as a function of time, given the gas density
and temperature, and the ultra-violet radiation intensity. The results from this
algorithm are compared against the standard assumption of ionisation equilibrium
used in previous models of IGM metals.
Firstly, the new time-dependent algorithm is used to model the ionisation in
uniform volumes of gas, with constant temperature, density and background radiation.
Four models are performed, with different values of the ionisation parameter. The
models demonstrate the timescales over which different metals in the IGM can be out
of ionisation equilibrium, to investigate the conditions under which the time-dependent
algorithm should be used in future modelling of metals in the IGM. The models show
that for ionisation parameters U = 0.01–0.3 many metals observed in quasar absorption
spectra could be out of equilibrium for up to 107 or a few times 108 years when
subject to a new hard quasar spectrum. The metals’ equilibrium ionisation fractions
found in these time-dependent results are compared against the time-independent
solutions found by Cloudy (Ferland et al., 1998, PASP, 110, 761) for the same models.
Comparing to this well-established programme shows the algorithm is accurate for
the most common elements, but disagreement is found for the rarer elements with
incomplete atomic data.
An application of the new time-dependent ionisation algorithm to a full cosmolog-
ical N-body simulation is then presented. The algorithm is used to study the effects
of a young quasar on the ionisation structure of metals in the surrounding IGM. An
independent simulation of a quasar turning on during the Epoch of Reionisation,
performed with a joint particle-mesh and radiative-transfer code (Tittley & Meiksin, 2007, MNRAS, 380, 1369), is used to provide the density, temperature and UV
intensity inputs for the time-dependent algorithm. Non-equilibrium effects in the
metal ionisation are seen to last for significant lengths of time, as the IGM reacts
slowly to the rapid change in UV radiation.
Mock quasar absorption line spectra are then generated by passing lines of sight
through the simulation volume. Using the ionisation fraction results from the new
algorithm, transmission functions with metal absorption features are produced, and
the effect of non-equilibrium ionisation on the CII and CIV column densities and their
ratio are presented.