A Wavelet Space-Scale Decomposition Analysis of Structures and Evolution of QSO LY alpha Absorption Lines

A wavelet space-scale decomposition (SSD) analysis of large scale structures in the universe has been developed. The SSD method of identifying and measuring structures in the spatial distribution of objects has been demonstrated. The position and strength (richness) of the identified clusters can be described by the corresponding coefficient of the wavelet transform. Using this technique, we systematically detected the clustering and its evolution of QSO's Ly$\alpha$ forest lines in real data and simulated samples. We showed that the clusters of Ly$\alpha$ absorbers do exist on scales as large as at least 20 h$^{-1}$ Mpc at significance levels of 2-4 $\sigma$. Independent data sets show about the same strength distribution of the decomposed clusters. The number densities of the clusters on scales of 10 - 20 h$^{-1}$ Mpc are found to evolve in an opposite sense as that of the lines themselves, i.e. they decrease with redshift. We also showed that the number density and the strength distribution of clusters can play an important role in testing or discriminating models, i.e. it can distinguish real data and simulated samples, which cannot be discriminated by traditional ways. We used Daubechies 4 and Mallat wavelets as the bases of the SSD. All above-mentioned conclusions do not depend on either wavelet basis.Comment: LaTeX 25 pages + 11 PostScript figure