A New Measurement of the Temperature Density Relation of the IGM From Voigt Profile Fitting

We decompose the Lyman-{\alpha} (Ly{\alpha}) forest of an extensive sample of 74 high signal-to-noise ratio and high-resolution quasar spectra into a collection of Voigt profiles. Absorbers located near caustics in the peculiar velocity field have the smallest Doppler parameters, resulting in a low-$b$ cutoff in the $b$-$N_{\text{HI}}$ set by the thermal state of intergalactic medium (IGM). We fit this cutoff as a function of redshift over the range $2.0\leq z \leq 3.4$, which allows us to measure the evolution of the IGM temperature-density ($T= T_0 (\rho/ \rho_0)^{\gamma-1}$) relation parameters $T_0$ and $\gamma$. We calibrate our measurements against Ly$\alpha$ forest simulations, using 21 different thermal models of the IGM at each redshift, also allowing for different values of the IGM pressure smoothing scale. We adopt a forward-modeling approach and self-consistently apply the same algorithms to both data and simulations, propagating both statistical and modeling uncertainties via Monte Carlo. The redshift evolution of $T_0$ shows a suggestive peak at $z=2.8$, while our evolution of $\gamma$ is consistent with $\gamma\simeq 1.4$ and disfavors inverted temperature-density relations. Our measured evolution of $T_0$ and $\gamma$ are generally in good agreement with previous determinations in the literature. Both the peak in the evolution of $T_0$ at $z = 2.8$, as well as the high temperatures $T_0\simeq 15000-20000\,$K that we observe at $2.4 < z < 3.4$, strongly suggest that a significant episode of heating occurred after the end of HI reionization, which was most likely the cosmic reionization of HeII.