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Register a new userStatistical description of dust polarized emission from the diffuse interstellar medium -- A RWST approach
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Added by
Bruno Regaldo-Saint Blancard
Publication date
2020
fields
Physics
and research's language is
English
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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, 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. We applied the WST to noise-free maps of dust polarized thermal emission computed from a numerical simulation of MHD turbulence. 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 WST (RWST), an angular model introduced in previous works. 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 Python package to perform WST/RWST analyses at: https://github.com/bregaldo/pywst.
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Dust emission is the main foreground for cosmic microwave background (CMB) polarization. Its statistical characterization must be derived from the analysis of observational data because the precision required for a reliable component separation is far greater than what is currently achievable with physical models of the turbulent magnetized interstellar medium. This letter takes a significant step toward this goal by proposing a method that retrieves non-Gaussian statistical characteristics of dust emission from noisy Planck polarization observations at 353 GHz. We devised a statistical denoising method based on wavelet phase harmonics (WPH) statistics, which characterize the coherent structures in non-Gaussian random fields and define a generative model of the data. The method was validated on mock data combining a dust map from a magnetohydrodynamic simulation and Planck noise maps. The denoised map reproduces the true power spectrum down to scales where the noise power is an order of magnitude larger than that of the signal. It remains highly correlated to the true emission and retrieves some of its non-Gaussian properties. Applied to Planck data, the method provides a new approach to building a generative model of dust polarization that will characterize the full complexity of the dust emission. We also release PyWPH, a public Python package, to perform GPU-accelerated WPH analyses on images.
The interstellar medium (ISM) is a complex non-linear system governed by gravity and magneto-hydrodynamics, as well as radiative, thermodynamical, and chemical processes. Our understanding of it mostly progresses through observations and numerical simulations, and a quantitative comparison between these two approaches requires a generic and comprehensive statistical description. The goal of this paper is to build such a description, with the purpose to permit an efficient comparison independent of any specific prior or model. We start from the Wavelet Scattering Transform (WST), a low-variance statistical description of non-Gaussian processes, developed in data science, that encodes long-range interactions through a hierarchical multiscale approach based on the Wavelet transform. We perform a reduction of the WST through a fit of its angular dependencies, allowing to gather most of the information it contains into a few components whose physical meanings are identified, and that describe, e.g., isotropic and anisotropic behaviours. The result of this paper is the Reduced Wavelet Scattering Transform (RWST), a statistical description with a small number of coefficients that characterizes complex structures arising from non-linear phenomena, free from any specific prior. The RWST coefficients encode moments of order up to four, have reduced variances, and quantify the couplings between scales. To show the efficiency and generality of this description, we apply it successfully to three kinds of processes: fractional Brownian motions, MHD simulations, and Herschel observations in a molecular cloud. With fewer than 100 coefficients when probing 6 scales and 8 angles on 256*256 maps, we were able with the RWST to perform quantitative comparisons, to infer relevant physical properties, and to produce realistic synthetic fields.
The interpretation of Galactic synchrotron observations is complicated by the degeneracy between the strength of the magnetic field perpendicular to the line of sight (LOS), $B_perp$, and the cosmic-ray electron (CRe) spectrum. Depending on the observing frequency, an energy-independent spectral energy slope $s$ for the CRe spectrum is usually assumed: $s=-2$ at frequencies below $simeq$400 MHz and $s=-3$ at higher frequencies. Motivated by the high angular and spectral resolution of current facilities such as the LOw Frequency ARray (LOFAR) and future telescopes such as the Square Kilometre Array (SKA), we aim to understand the consequences of taking into account the energy-dependent CRe spectral energy slope on the analysis of the spatial variations of the brightness temperature spectral index, $beta$, and on the estimate of the average value of $B_perp$ along the LOS. We illustrate analytically and numerically the impact that different realisations of the CRe spectrum have on the interpretation of the spatial variation of $beta$. We find that the common assumption of an energy-independent $s$ is valid only in special cases. We show that for typical magnetic field strengths of the diffuse interstellar medium ($simeq$2$-$20 $mu$G), at frequencies of 0.1$-$10 GHz, the electrons that are mainly responsible for the synchrotron emission have energies in the range $simeq$100 MeV$-$50 GeV. This is the energy range where the spectral slope, $s$, of CRe has its greatest variation. We also show that the polarisation fraction can be much smaller than the maximum value of $simeq 70%$ because the orientation of ${bf B}_perp$ varies across the telescopes beam and along the LOS. Finally, we present a look-up plot that can be used to estimate the average value of $B_perp$ along the LOS from a set of values of $beta$ measured at centimetre to metre wavelengths, for a given CRe spectrum.
Observations of far-infrared (FIR) and submillimeter (SMM) polarized emission are used to study magnetic fields and dust grains in dense regions of the interstellar medium (ISM). These observations place constraints on models of molecular clouds, star-formation, grain alignment mechanisms, and grain size, shape, and composition. The FIR/SMM polarization is strongly dependent on wavelength. We have attributed this wavelength dependence to sampling different grain populations at different temperatures. To date, most observations of polarized emission have been in the densest regions of the ISM. Extending these observations to regions of the diffuse ISM, and to microwave frequencies, will provide additional tests of grain and alignment models. An understanding of polarized microwave emission from dust is key to an accurate measurement of the polarization of the cosmic microwave background. The microwave polarization spectrum will put limits on the contributions to polarized emission from spinning dust and vibrating magnetic dust.
The upcoming generation of cosmic microwave background (CMB) experiments face a major challenge in detecting the weak cosmic B-mode signature predicted as a product of primordial gravitational waves. To achieve the required sensitivity these experiments must have impressive control of systematic effects and detailed understanding of the foreground emission that will influence the signal. In this paper, we present templates of the intensity and polarisation of emission from one of the main Galactic foregrounds, interstellar dust. These are produced using a model which includes a 3D description of the Galactic magnetic field, examining both large and small scales. We also include in the model the details of the dust density, grain alignment and the intrinsic polarisation of the emission from an individual grain. We present here Stokes parameter template maps at 150GHz and provide an on-line repository (http://www.imperial.ac.uk/people/c.contaldi/fgpol) for these and additional maps at frequencies that will be targeted by upcoming experiments such as EBEX, Spider and SPTpol.
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