THE TEMPERATURE-DENSITY RELATION IN THE INTERGALACTIC MEDIUM AT REDSHIFT (z) = 2.4

We present new measurements of the temperature-density (T-ρ) relation for neutral hydrogen in the 2.0 < z < 2.8 intergalactic medium (IGM) using a sample of ∼6000 individual H I absorbers fitted with Voigt profiles constrained in all cases by multiple Lyman series transitions. We find model-independent evidence for a positive correlation between the column density of H I (NHI) and the minimum observed velocity width of absorbers (bmin). With minimal interpretation, this implies that the T-ρ relation in the IGM is not 'inverted', contrary to many recent studies. Fitting bmin as a function of NHI results in line-width-column-density dependence of the form bmin = b0(NHI/NHI,0)Γ–1 with a minimum line width at mean density (ρ/ρ-bar = 1, NHI,0 = 1013.6 cm-2) of b0 = 17.9 ± 0.2 km s–1 and a power-law index of (Γ – 1) = 0.15 ± 0.02. Using analytic arguments, these measurements imply an 'equation of state' for the IGM at (z) = 2.4 of the form T=T0 (ρ/ρ-bar)γ-1 with a temperature at mean density of T0 = [1.94 ± 0.05] × 104 K and a power-law index (γ – 1) = 0.46 ± 0.05.