Statistical description of dust polarized emission from the diffuse interstellar medium -- A WST/RWST approach

The statistical characterization of the diffuse magnetized ISM and Galactic foregrounds to the CMB poses a major challenge. To account for their non-Gaussian statistics, we need a data analysis approach capable of efficiently quantifying statistical couplings across scales. This information is encoded in the data, but most of it is lost when using conventional tools as one-point statistics and power spectra. The Wavelet Scattering Transform (WST), a low-variance statistical descriptor of non-Gaussian processes introduced in data science, opens a path towards this goal. We apply the WST to noise-free maps of dust polarized thermal emission computed from a numerical simulation of MHD turbulence. We analyze normalized complex Stokes maps, and maps of polarization fraction and polarization angle. The WST yields a few thousand coefficients; some of them measure the amplitude of the signal at a given scale, and the others characterize the couplings between scales and orientations. The dependence on orientation can be fitted with the same Reduced WST (RWST) angular model introduced by Allys+2019 for total intensity maps. The RWST provides a statistical description of the polarization maps, quantifying their multiscale properties in terms of isotropic and anisotropic contributions. It allows us to exhibit the dependence of the map structure on the orientation of the mean magnetic field, and to quantify the non-Gaussianity of the data. We also use RWST coefficients, complemented by additional constraints, to generate random synthetic maps with similar statistics. Their agreement with the original maps demonstrates the comprehensiveness of the statistical description provided by the RWST. This work is a step forward in the analysis of observational data and the modeling of CMB foregrounds. We also release PyWST, a Python package to perform WST/RWST analyses at: https://github.com/bregaldo/pywst.