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.