Constraining the parameters of the LN model with reconstructed power spectrum of Ly-α forest †*

A sample of three quasar spectra observed by the Keck telescope is selected to reconstruct the perturbations of mass density using the Gaussianization method, with a calculation of the corresponding wavelet power spectra. The two parameters in the lognormal (LN) model, namely the shape factor Γ and the Jeans smoothing factor r, are set as free parameters. Their most probable values are determined by comparing the result of statistical analysis on the observed sample with that on a simulated sample, and they are: Γ0.50 and r0.09. Non-Gaussian features in the quasar spectra can not be excluded using the traditional Gaussianization method. However, on the scales larger than 100 kpc, these features have little or no influence on our results described above. This argument has been verified by comparing the observed sample with the simulated sample as regards their skewness and kurtosis spectra, as well as their scale-scale correlations.