A Measurement of the Temperature-Density Relation in the Intergalactic Medium Using a New Lyα 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 Lyα forest and of galaxy formation. We measure the temperature-density relation of intergalactic gas from Lyα forest observations of eight quasar spectra, using a new line fitting technique to obtain a lower cutoff on the distribution of line widths from which the temperature is derived. Using a numerical simulation, we examine the details of this kind of measurement at different densities, finding that the temperature may be difficult to measure for gas with Δ_g ≲ 1 (Δ_g is the density of the gas in units of the mean density) because the velocities due to expansion always dominate the widths of the corresponding weak lines, and that the temperature measurement is increasingly ambiguous for gas with Δ_g ≳ 5 because the dispersion in temperature at fixed density is high. From our observed spectra, the temperature is most precisely determined at densities slightly above the mean: T_* = (20,200 ± 2700, 20,200 ± 1300, 22,600 ± 1900) K (statistical error bars) for gas densities Δ_* = (1.42 ± 0.08, 1.37 ± 0.11, 1.66 ± 0.11) at redshift = (3.9, 3.0, 2.4). Systematic errors in T_* should be less than 2000 K. The power-law index of the temperature-density relation, defined by T = T_*(Δ_g/Δ_*)^γ-1, is γ - 1 = (0.43 ± 0.45, 0.29 ± 0.30, 0.52 ± 0.14) for the same three redshifts. The temperature at fixed overdensity Δ = 1.4 is T_1.4 = (20,100 ± 2800, 20,300 ± 1400, 20,700 ± 1900) K. This unchanging temperature is higher than expected for photoionized gas in ionization equilibrium with a cosmic background. If the heat from the He II reionization is responsible for the high measured temperature, then the temperature should not be constant but should have a maximum at the end of the reionization epoch. We update the lower limit to the baryon density implied by the observed mean flux decrement.