Jeans smoothing of the Ly$\alpha$ forest absorption lines

We investigate a contribution of the Jeans smoothing to the minimal width of Ly$\alpha$ forest lines and discuss how the accounting for this additional broadening affects the inferred parameters of the intergalactic matter equation of state. We estimate a power-law index $\gamma$ of the equation of state, a temperature at the mean density $T_0$ and a hydrogen photoionization rate $\Gamma$ within 4 redshift bins. Furthermore, in each bin we obtain an upper limit on the scale-parameter $f_{\rm J}$, which sets the relation between the Jeans length and the characteristic physical size of the absorber clouds.