THE TEMPERATURE-DENSITY RELATION IN THE INTERGALACTIC MEDIUM AT REDSHIFT ⟨z⟩=2.4

We present new measurements of the temperature-density (T-rho) relation for neutral hydrogen in the 2.0 < z < 2.8 intergalactic medium (IGM) using a sample of similar to 6000 individual Hi 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 HI (N-HI) and the minimum observed velocity width of absorbers (b(min)). With minimal interpretation, this implies that the T-rho relation in the IGM is not inverted, contrary to many recent studies. Fitting b(min) as a function of N-HI results in line-width-column-density dependence of the form b(min) = b(0)(N-HI/N-HI,N-0)(Gamma-1) with a minimum line width at mean density (rho/(rho) over bar = 1, N-HI,N-0 = 10(13.6) cm(-2)) of b(0) = 17.9 +/- 0.2 kms(-1) and a power-law index of (Gamma - 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 = T-0 (rho/(rho) over bar)(gamma-1) with a temperature at mean density of T-0 = [1.94 +/- 0.05] x 10(4) K and a power-law index (gamma - 1) = 0.46 +/- 0.05.