We investigate the thermal history of the intergalactic medium ( IGM ) in the redshift interval z = 1.7 – 3.2 by studying the small-scale fluctuations in the Lyman- \alpha forest transmitted flux .
We apply a wavelet filtering technique to eighteen high resolution quasar spectra obtained with the Ultraviolet and Visual Echelle Spectrograph ( UVES ) , and compare these data to synthetic spectra drawn from a suite of hydrodynamical simulations in which the IGM thermal state and cosmological parameters are varied .
From the wavelet analysis we obtain estimates of the IGM thermal state that are in good agreement with other recent , independent wavelet-based measurements .
We also perform a reanalysis of the same data set using the Lyman- \alpha forest flux probability distribution function ( PDF ) , which has previously been used to measure the IGM temperature-density relation .
This provides an important consistency test for measurements of the IGM thermal state , as it enables a direct comparison of the constraints obtained using these two different methodologies .
We find the constraints obtained from wavelets and the flux PDF are formally consistent with each other , although in agreement with previous studies , the flux PDF constraints favour an isothermal or inverted IGM temperature-density relation .
We also perform a joint analysis by combining our wavelet and flux PDF measurements , constraining the IGM thermal state at z = 2.1 to have a temperature at mean density of T _ { 0 } / [ 10 ^ { 3 } K ] = 17.3 \pm 1.9 and a power-law temperature-density relation exponent \gamma = 1.1 \pm 0.1 ( 1 \sigma ) .
Our results are consistent with previous observations that indicate there may be additional sources of heating in the IGM at z < 4 .