A Measurement of the Temperature-Density Relation in the Intergalactic   Medium Using a New Lyman-alpha Absorption Line Fitting Method
  The evolution of the temperature in the intergalactic medium is related to the reionization of hydrogen and helium, and has important consequences for our understanding of the Lya forest and of galaxy formation in gravitational models of large-scale structure. We measure the temperature-density relation of intergalactic gas from Lya forest observations of eight quasar spectra with high resolution and signal-to-noise ratio, using a new line fitting technique to obtain a lower cutoff of the distribution of line widths from which the temperature is derived. We carefully test the accuracy of this technique to recover the gas temperature with a hydrodynamic simulation. The temperature at redshift z=(3.9, 3.0, 2.4) is best determined at densities slightly above the mean: T_star=(20200\pm2700, 20200\pm1300, 22600\pm1900)K (statistical error bars) for gas density (in units of the mean density) Delta_star=(1.42\pm0.08, 1.37\pm0.11, 1.66\pm0.11). The power-law index of the temperature-density relation, defined by T=T_star(Delta/Delta_star)^{gamma-1}, is gamma-1= (0.43\pm0.45, 0.29\pm0.30, 0.52\pm0.14) for the same three redshifts. The temperature at the fixed over-density Delta=1.4 is T_1.4=(20100\pm2800, 20300\pm1400, 20700\pm1900)K. These temperatures are higher than expected for photoionized gas in ionization equilibrium with a cosmic background, and can be explained by a gradual additional heating due to on-going HeII reionization. The measurement of the temperature reduces one source of uncertainty in the lower limit to the baryon density implied by the observed mean flux decrement. We find that the temperature cannot be reliably measured for under-dense gas, because the velocities due to expansion always dominate the widths of the corresponding weak lines. 
Patrick McDonald, Jordi Miralda-Escude, Michael Rauch, Wallace L. W.   Sargent, Tom A. Barlow, and Renyue Cen