2012ApJ...757L..30R

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 (N _ H I_) and the minimum observed velocity width of absorbers (b_min). With minimal interpretation, this implies that the T-ρ relation in the IGM is not "inverted," contrary to many recent studies. Fitting b_min as a function of N_ H I_results in line-width-column-density dependence of the form b_min= b₀(N_ H I_/NH I,0_)^Γ–1 with a minimum line width at mean density ((ρ/ = 1, N_HI,0_ = 10^13.6/cm2) of b₀= 17.9±0.2 km/s 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/)^γ1^ with a temperature at mean density of T₀= [1.94±0.05]x10⁴ K and a power-law index (γ - 1) = 0.46±0.05.