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We characterise the thermal state of the intergalactic medium (IGM) in tenredshift bins in the redshift range $2 \leq z \leq 4$ with a sample of 103 highresolution, high S/N Ly$\alpha$ forest spectra using four different fluxdistribution statistics. Our measurements are calibrated with mock spectra froma large suite of hydrodynamical simulations post-processed with our thermal IGMevolution code CITE, finely sampling amplitude and slope of the expectedtemperature-density relation. The thermal parameters inferred from ourmeasurements of the flux power spectrum, Doppler parameter distribution, aswell as wavelet and curvature statistics agree well within their respectiveerrors and all clearly show the peak in temperature and minimum in slope of thetemperature density relation expected from HeII reionization. Combining ourmeasurements from the different flux statistics gives $T_0=(14750 \pm 1322)$Kfor the peak temperature at mean density and a corresponding minimum slope$\gamma = 1.225 \pm 0.120$. The peak in the temperature evolution occurs at $z\approx 3$, in agreement with previous measurements that had suggested thepresence of such a peak, albeit with a large scatter. Using CITE, we alsocalculate the thermal state of the IGM predicted by five widely used (spatiallyhomogeneous) UV-background models. The rather rapid thermal evolution inferredby our measurements is well reproduced by two of the models, if we assume(physically well motivated) non-equilibrium evolution with photo-heating ratesthat are reduced by a moderate factor of $\sim 0.7-0.8$. The other three modelspredict HeII reionization to be more extended with a somewhat earlier as wellas higher temperature peak than our measurements suggest.

monthly notices of the royal astronomical society

A consistent and robust measurement of the thermal state of the IGM at  $2 \leq z \leq 4$ from a large sample of Ly$\alpha$ forest spectra: Evidence  for late and rapid HeII reionization