Substructure recovery by three-dimensional discrete wavelet transforms

We present and discuss a method to identify substructures in combined angular-redshift samples of galaxies within Clusters. The method relies on the use of Discrete Wavelet Transform (hereafter DWT) and has already been applied to the analysis of the Coma cluster (Gambera et al. 1997). The main new ingredient of our method with respect to previous studies lies in the fact that we make use of a 3D data set rather than a 2D. We test the method on mock cluster catalogs with spatially localized substructures and on a N-body simulation. Our main conclusion is that our method is able to identify the existing substructures provided that: a) the subclumps are detached in part or all of the phase space, b) one has a statistically significant number of redshifts, increasing as the distance decreases due to redshift distortions; c) one knows {\it a priori} the scale on which substructures are to be expected. We have found that to allow an accurate recovery we must have both a significant number of galaxies ($\approx 200$ for clusters at z$\geq 0.4$ or about 800 at z$\leq$ 0.4) and a limiting magnitude for completeness $m_B=16$. The only true limitation to our method seems to be the necessity of knowing {\it a priori} the scale on which the substructure is to be found. This is an intrinsic drawback of the method and no improvement in numerical codes based on this technique could make up for it.