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.
