Probing Hierarchical Clustering by Scale‐Scale Correlations of Wavelet Coefficients

It is of fundamental importance to determine if and how hierarchicalclustering is involved in large-scale structure formation of the universe.Hierarchical evolution is characterized by rules which specify how dark matterhalos are formed by the merging of halos at smaller scales. We show thatscale-scale correlations of the matter density field are direct and sensitivemeasures to quantify this merging tree. Such correlations are most convenientlydetermined from discrete wavelet transforms. Analyzing two samples of Ly-alphaforests of QSO's absorption spectra, we find significant scale-scalecorrelations whose dependence is typical for a branching process. Therefore,models which predict a "history" independent evolution are ruled out and thehalos hosting the Ly-alpha clouds must have gone through a "history" dependentmerging process during their formation.Comment: 10 pages, 1 ps figure included. Uses AAS Latex macros. Accpeted in the Astrophysical Journa