Statistical description of dust polarized emission from the diffuse interstellar medium — A WST/RWST approach. (arXiv:2007.08242v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Blancard_B/0/1/0/all/0/1">Bruno Regaldo-Saint Blancard</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Levrier_F/0/1/0/all/0/1">François Levrier</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Allys_E/0/1/0/all/0/1">Erwan Allys</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Bellomi_E/0/1/0/all/0/1">Elena Bellomi</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Boulanger_F/0/1/0/all/0/1">François Boulanger</a>
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.
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.
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