2023RAA....23d5007Y

The absorption by neutral hydrogen in the intergalactic medium (IGM) produces the Lyα forest in the spectra of quasars. The Lyα forest absorbers have a broad distribution of neutral hydrogen column density N_H I_ and Doppler b parameter. The narrowest Lyα absorption lines (of lowest b) with neutral hydrogen column density above ∼10¹³cm^–2 are dominated by thermal broadening, which can be used to constrain the thermal state of the IGM. Here we constrain the temperature-density relation $T={T}_{0}{(\rho /\bar{\rho })}^{\gamma -1}$ of the IGM at 1.6 < z < 3.6 by using N_H I_ and b parameters measured from 24 high-resolution and high-signal-to-noise quasar spectra and by employing an analytic model to model the N_H I_-dependent low-b cutoff in the b distribution. In each N_H I_ bin, the b cutoff is estimated using two methods, one non-parametric method from computing the cumulative b distribution and a parametric method from fitting the full b distribution. We find that the IGM temperature T₀ at the mean gas density $\bar{\rho }$ shows a peak of ∼1.5 × 10⁴ K at z ∼ 2.7-2.9. At redshift higher than this, the index γ approximately remains constant, and it starts to increase toward lower redshifts. The evolution in both parameters is in good agreement with constraints from completely different approaches, which signals that He II reionization completes around z ∼ 3.