A new Measurement of the Intergalactic Temperature at zsim 2.55-2.95

We present two measurements of the temperature-density relationship (TDR) of the intergalactic medium (IGM) in the redshift range $2.55 < z < 2.95$ using a sample of 13 high-quality quasar spectra and high resolution numerical simulations of the IGM. Our approach is based on fitting the neutral hydrogen column density $N_{HI}$ and the Doppler parameter $b$ of the absorption lines in the \mlya\ forest. The first measurement is obtained using a novel Bayesian scheme which takes into account the statistical correlations between the parameters characterising the lower cut-off of the $b-N_{HI}$ distribution and the power-law parameters $T_0$ and $\gamma$ describing the TDR. This approach yields $T_0/ 10^3\, {\rm K}=15.6 \pm 4.4 $ and $\gamma=1.45 \pm 0.17$ independent of the assumed pressure smoothing of the small scale density field. In order to explore the information contained in the overall $b-N_{HI}$ distribution rather than only the lower cut-off, we obtain a second measurement based on a similar Bayesian analysis of the median Doppler parameter for separate column-density ranges of the absorbers. In this case we obtain $T_0/ 10^3\, {\rm K}=14.6 \pm 3.7$ and $\gamma=1.37 \pm 0.17$ in good agreement with the first measurement. Our Bayesian analysis reveals strong anti-correlations between the inferred $T_0$ and $\gamma$ for both methods as well as an anti-correlation of the inferred $T_0$ and the pressure smoothing length for the second method, suggesting that the measurement accuracy can in the latter case be substantially increased if independent constraints on the smoothing are obtained. Our results are in good agreement with other recent measurements of the thermal state of the IGM probing similar (over-)density ranges.