Patchy HeII reionization and the physical state of the intergalactic medium

We present a Monte Carlo model of He it reionization by quasi-stellar objects (QSOs, quasars) and its effect on the thermal state of the clumpy intergalactic medium (IGM). The model assumes that patchy reionization develops as a result of the discrete distribution of QSOs. It includes various recipes for the propagation of the ionizing photons, and treats photoheating self-consistently. The model predicts the fraction of He III, the mean temperature in the IGM, and the He it mean optical depth - all as a function of redshift. It also predicts the evolution of the local temperature versus density relation during reionization. Our findings are as follows. The fraction of He in increases gradually until it becomes close to unity at z similar to 2.8-3.0. The He II mean optical depth decreases from tau similar to 10 at z greater than or similar to 3.5 to tau less than or similar to 0.5 at z less than or similar to 2.5. The mean temperature rises gradually between z 4 and z - 3 and declines slowly at lower redshifts. The model predicts a flattening of the temperature-density relation, with significant increase in the scatter during reionization at z similar to 3. Towards the end of reionization, the scatter is reduced and a tight relation is re-established. This scatter should be incorporated in the analysis of the Ly alpha forest at z less than or similar to 3. Comparison with observational results of the optical depth and the mean temperature at moderate redshifts constrains several key physical parameters.