Equation of state of the intergalactic medium in the early Universe
  Spectroscopy of the Ly$\alpha$ forest in quasar spectra proved to be a useful
tool for probing the intergalactic gas. We developed the automatic program for
Voigt profile fitting of Ly$\alpha$ forest lines. We run this code on 9 high
resolution ($\sim 50000$) quasars spectra with a high signal-to-noise ratio
($\sim 50 -100$) from the Keck telescope archive and obtained the sample of
single well-fitted Ly$\alpha$ lines. Fitting the joint 2d distribution of
column density and Doppler parameter from this sample by physically reasonable
model we estimate a power law index $\gamma$ of the equation of state of the
intergalactic medium in the redshift range $z\sim 2-3$. We found that our
measurement is in an agreement with measurements by other groups obtained with
Voigt profile fitting technique.
