A new Measurement of the Intergalactic Temperature at $z\sim 2.55-2.95$
  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.
