Wavelet Transform Analysis of Ly$\alpha$ Forests
Session 14 -- Lyman Alpha Clouds
Display presentation, Monday, 9, 1995, 9:20am - 6:30pm

## [14.04] Wavelet Transform Analysis of Ly$\alpha$ Forests

Jesus Pando and Li-Zhi Fang (Univ. of Arizona)

Using the wavelet transform, we analyzed the distribution and evolution of QSO's Ly$\alpha$ absorption lines. A multiresolution decomposition of Ly$\alpha$ forests with respect to the Daubechies 4 wavelet basis was done. The results showed that all considered samples of forest lines deviate from a uniform distribution at significance levels of 2-3 $\sigma$, even in the case where the two-point correlation $\xi(r)$ of the lines showed very weak or $\sim 0$. The position and "richness" of structures (or "clusters") of forest lines up to the 3rd smoothing scales were identified. We found that the evolution of the number $N$ of such clusters can also be approximately described by $dN/dz \propto (1+z)^{\gamma}$. However, the index $\gamma$ is found to be scale-dependent: it is smaller for larger scales. For the 3rd decomposition, most samples show $\gamma < 0$. This indicates that the evolution of large scale "clusters" of lines was opposed to the lines themself. These results do not change significantly if a different wavelet, such as the Mallat wavelet, is used.