Continuous wavelet analysis of matter clustering using the Gaussian-derived wavelet

Abstract

Continuous wavelet analysis has been increasingly employed in various fields of science and engineering due to its remarkable ability to maintain optimal resolution in both space and scale. Here, we extend wavelet-based statistics, including the wavelet power spectrum, wavelet cross-correlation and wavelet bicoherence, to the new designed continuous wavelet function -Gaussian-derived wavelet. In this paper, these statistics are introduced to analyze the large-scale clustering of matter. For this purpose, we perform wavelet transforms on the density distribution obtained from the one-dimensional (1D) Zel'dovich approximation and then measure the wavelet power spectra and wavelet bicoherences of this density distribution. Our results suggest that the wavelet power spectrum and wavelet bicoherence can identify the effects of local environments on the clustering at different scales. Moreover, to reveal the usefulness of the wavelet cross-correlation, we apply it to the 1D projected density fields of the IllustrisTNG simulation at z = 0 for different matter components. We find that wavelet cross-correlations between different matter components converge to one on large scales, while biases between them become significant on small scales. In addition, measurements of the wavelet power spectra show that clustering of the total matter is suppressed on scales k 1 hMpc −1 relative to that of the corresponding dark matter-only simulation. The wavelet bicoherence of the total matter is enhanced on wide scales due to baryonic physics. These results are qualitatively consistent with those from three-dimensional Fourier analyses.