Astronomy and Astrophysics – Astrophysics
Scientific paper
2001-02-14
Astronomy and Astrophysics
Astrophysics
22 pages, 13 figures. Accepted for publication in the Astrophysical Journal
Scientific paper
10.1086/321410
We investigate the weakly non-linear evolution of cosmic gravitational clustering in phase space by looking at the Zel'dovich solution in the discrete wavelet transform (DWT) representation. We show that if the initial perturbations are Gaussian, the relation between the evolved DWT mode and the initial perturbations in the weakly non-linear regime is quasi-local. That is, the evolved density perturbations are mainly determined by the initial perturbations localized in the same spatial range. Furthermore, we show that the evolved mode is monotonically related to the initial perturbed mode. Thus large (small) perturbed modes statistically correspond to the large (small) initial perturbed modes. We test this prediction by using QSO Ly$\alpha$ absorption samples. The results show that the weakly non-linear features for both the transmitted flux and identified forest lines are quasi-localized. The locality and monotonic properties provide a solid basis for a DWT scale-by-scale Gaussianization reconstruction algorithm proposed by Feng & Fang (Feng & Fang, 2000) for data in the weakly non-linear regime. With the Zel'dovich solution, we find also that the major non-Gaussianity caused by the weakly non-linear evolution is local scale-scale correlations. Therefore, to have a precise recovery of the initial Gaussian mass field, it is essential to remove the scale-scale correlations.
Fang L.-Z.
Feng Longlong
Pando Jesus
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