2019ApJ...887..205T

We present a new method to infer parameters of the temperature-density relation in the intergalactic medium in the post-reionization epoch at z ∼ 2-4. This method is based on the analysis of the distribution of Lyα absorbers over column densities and Doppler parameters by the model joint probability density function. This approach allows us to measure the power-law index γ of the temperature-density relation and a certain combination of the temperature at the mean density T₀ and hydrogen photoionization rate Γ. To estimate T₀ and Γ separately, we employ measurements of the Lyα forest effective opacity and the model gas probability density function. We show that γ tends to be lower than 1.6 and reaches 1.3 at redshift ∼3. The inferred temperatures at the mean density are ∼(2 ± 0.5) x 10⁴ K in the studied redshift range. Both these estimates favor He II reionization at z >= 3. We find that the hydrogen photoionization rate is ∼0.6 x 10^–12 s^–1, which is consistent with previous measurements.