The evolution of the physical state of the IGM

Using a new, increased dataset of 7 QSOs from VLT/UVES observations combined with one QSO from the literature, the minimum Doppler parameters as a function of neutral hydrogen column density N-H I, b(c)(N-HI), of the Lyalpha forest has been derived at three redshifts = 2.1, 3.3 and 3.8. In particular, five QSOs at = 2.1 enable us to study the cosmic variance of b(c)(N-H I) at lower z for the first time. When incompleteness of the number of the observed lines towards lower N-HI is accounted for, the derived slopes of b(c)(N-HI), (Gamma-1), are consistent with no-z evolution with an indication of lower value at = 3.3, while b(c)(NH (I)) at a fixed column density N-H I = 10(13.6) cm(-2), b(c)(13.6), increases as z decreases. Assuming a QSO-dominated UV background, the slope of the equation of state (gamma-1) shows no z-evolution within large uncertainties and the temperature at the mean density, T-0, decreases as z decreases at three redshift ranges. There is a large fluctuation of (Gamma-1) and b(c)(13.6) even at the similar redshifts, in particular at < z>= 3.3 and 3.8. The lower (Gamma-1) and higher b(c)(13.6) values at z similar to 3.1 and 3.6 compared to ones at z similar to 3.4 and 3.9 are caused by a lack of lower-N-H I and lower-b lines at lower-z parts of each QSO at z >3, probably due to the He II reionization. This result suggests that an impact from the He II reionization on the forest might be mainly on the lower-N-H I forest. From this new dataset, we find some forest clouds with a high ratio of Si IV column density to C IV column density, N-Si IV/N-CIV, at z <2.5, although the bulk of the forest clouds shows lower N-Si IV/N-C IV. This high N-Si IV/N-C IV at z <2.5 suggests that some forest clouds are exposed to a soft UV background. This lack of strong discontinuity of N-Si IV/N-C IV at N-HI = 10(14-17) cm(-2) at z similar to 3 suggests that N-Si IV/N-CIV might not be a good observational tool to probe the He II reionization and/or that the UV background might be strongly affected by local, high-z galaxies at z <3.