We provide an analytical description of the line broadening of HI absorbers in the Lyman-alpha forest resulting from Doppler broadening and Jeans smoothing. We demonstrate that our relation captures the dependence of the line-width on column density
for narrow lines in z~3 mock spectra remarkably well. Broad lines at a given column density arise when the underlying density structure is more complex, and such clustering is not captured by our model. Our understanding of the line broadening opens the way to a new method to characterise the thermal state of the intergalactic medium and to determine the sizes of the absorbing structures.
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 reso
lution 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 T0/[10^3 K]=17.3 +/- 1.9 and a power-law temperature-density relation exponent gamma=1.1 +/- 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.
