Abstract
The statistical characterization of the diffuse magnetized interstellar medium (ISM) and Galactic foregrounds to the cosmic microwave background (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, such 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. To establish the methodology, we applied the WST to noise-free maps of dust polarized thermal emission computed from a numerical simulation of magnetohydrodynamical turbulence in the diffuse ISM. We analyzed normalized complex Stokes maps and maps of the 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 reduced wavelet scattering transform (RWST), an angular model introduced in previous works 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 allowed 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 used 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 public Python package to perform WST and RWST analyses of two-dimensional data.
Highlights
The interstellar medium (ISM) is a beautifully complex physical system, in which gas particles and dust grains, coupled to a pervasive magnetic field, experience turbulent motions across a vast range of scales (Draine 2011; Hennebelle & Falgarone 2012)
By examining the reduced wavelet scattering transform (RWST) statistics separately for each map, for each of the corresponding data sets, we found out that these surprising values correspond to an intermittent rise of the anisotropy level that appears in a few consecutive snapshots of the simulation
We extended the wavelet scattering transform (WST) analysis to maps of polarized thermal emission from interstellar dust, using 512 × 512 pixels
Summary
The interstellar medium (ISM) is a beautifully complex physical system, in which gas particles and dust grains, coupled to a pervasive magnetic field, experience turbulent motions across a vast range of scales (Draine 2011; Hennebelle & Falgarone 2012). BLASTPOL (Fissel et al 2016) and PILOT (Mangilli et al 2019), the far-IR HAWC+ camera onboard SOFIA (Chuss et al 2019) and imaging at sub-mm/mm wavelengths from large single-dish telescopes (Ritacco et al 2020) and ALMA (Hull et al 2017) These observations all contribute to a common scientific goal: understanding the role turbulence and magnetic fields play along the star formation process, from the diffuse interstellar medium to molecular clouds and protostellar cores. Allys et al (2019) provided the first astrophysical application of the wavelet scattering transform (WST), a low-variance statistical description of non-Gaussian processes (Mallat 2012) inspired by convolutional neural networks but that does not require any training stage (Bruna & Mallat 2013) They applied the WST to column density maps inferred from magnetohydrodynamical (MHD) simulations and to an Herschel observation of the thermal emission from Galactic dust. We provide a public Python package to perform WST and RWST analyses of two-dimensional data called PyWST2
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