A wavelet space-scale decomposition analysis of structures and evolution of QSO Ly alpha absorption lines

We used the discrete wavelet transform to perform a space-scale decomposition (SSD) of the Ly alpha forest. The SSD method of identifying and measuring structure in the spatial distribution of objects is demonstrated on simulated samples. The position and strength (richness) of the identified clusters can be described by the corresponding mother function coefficients (MFC) of the wavelet transform. Using thisa technique, we systematically detect the clustering and its evolution of QSO Ly alpha forest lines in real data and simulated samples. We show 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. Different, independent data sets show about the same strength distribution of 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 show that the number density and the strength distribution of clusters can play an important role in testing or discriminating models, i.e., the distribution of clusters can distinguish between real data and simulated samples, even where other traditional ways have failed to detect a difference. We use Daubechies 4 and Mallat wavelets as the basis of the SSD. We find that the above-mentioned conclusions do not depend on the wavelet basis.