Equation of State of the Photoionized Intergalactic Medium
  We develop an efficient method to study the effects of reionization history on the temperature-density relation of the intergalactic medium in the low density limit (overdensity less than 5). It is applied to the study of photo-reionization models in which the amplitude, spectrum and onset epoch of the ionizing flux, as well as the cosmology, are systematically varied. We find that the mean temperature-density relation at z=2-4 is well approximated by a power-law equation of state for uniform reionization models. We derive analytical expressions for its evolution and exhibit its asymptotic behavior: it is found that for sufficiently early reionization, imprints of reionization history prior to z=10 on the temperature-density relation are washed out. In this limit the temperature at cosmic mean density is proportional to (\Omega_b h/\sqrt\Omega_0)^{1/1.7}. While the amplitude of the radiation flux at the ionizing frequency of HI is found to have a negligible effect on the temperature-density relation as long as the universe reionizes before z=5, the spectrum can change the overall temperature by about 20%, through variations in the abundances of helium species. However the slope of the mean equation of state is found to lie within a narrow range for all reionization models we study, where reionization takes place before z=5. We discuss the implications of these findings for the observational properties of the Lyman-alpha forest. In particular, uncertainties in the temperature of the intergalactic medium, due to the uncertain reionization history of our universe, introduces a 30% scaling in the amplitude of the column density distribution while the the slope of the distribution is only affected by about 5%. Finally, we discuss how a fluctuating ionizing field affects the above results. We argue that under 
Lam Hui and Nickolay Y. Gnedin