Detecting the non-Gaussian Spectrum of QSO’s Lyα Absorption Line Distribution

We present an analysis of the non-Gaussianity in the distribution of Lyα forest lines in the QSO absorption spectra. Statistical tests performed on this data indicate that there may be large scale structure even though the power spectrum of the Lyα line distribution on large scales is found to be flat. It is apparent that higher (than two) order statistics are crucial in quantifying the clustering behavior of Lyα clouds. A method of detecting the spectrum of cumulants of the discrete wavelet transform (DWT) coefficients is developed. Because the basis of the DWT is compactly supported, the DWT is not subject to the central limit theorem. Cumulants of any order can be quickly computed and serve as a way of detecting non-Gaussianity. Using this technique on three independent data sets of Lyα forests, we find that the distribution of Lyα forests does show non-Gaussian behavior on scales from 5 to 10 h Mpc with confidence level larger than 95%. Two data sets available on large scales are found to be non-Gaussian on even larger scales. These techniques are effective in discriminating among models of the Lyα forest formation, which are degenerate at second and lower order statistics.