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Register a new userOn the statistics of the polarized submillimetre emission maps from thermal dust in the turbulent, magnetized, diffuse ISM
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[abridged] The interstellar medium is now widely recognized to display features ascribable to magnetized turbulence. With the public release of Planck data and the current balloon-borne and ground-based experiments, the growing amount of data tracing the polarized thermal emission from Galactic dust in the submillimetre provides choice diagnostics to constrain the properties of this magnetized turbulence. We aim to constrain these properties in a statistical way, focusing in particular on the power spectral index of the turbulent component of the interstellar magnetic field in a diffuse molecular cloud, the Polaris Flare. We present an analysis framework which is based on simulating polarized thermal dust emission maps using model dust density (proportional to gas density) and magnetic field cubes, integrated along the line of sight, and comparing these statistically to actual data. The model fields are derived from fBm processes, which allow a precise control of their one- and two-point statistics. We explore the nine-dimensional parameter space of these models through a MCMC analysis, which yields best-fitting parameters and associated uncertainties. We find that the power spectrum of the turbulent component of the magnetic field in the Polaris Flare molecular cloud scales with wavenumber as a power law with a spectral index $2.8pm 0.2$. It complements a uniform field whose norm in the POS is approximately twice the norm of the fluctuations of the turbulent component. The density field is well represented by a log-normally distributed field with a mean gas density $40,mathrm{cm}^{-3}$ and a power spectrum with as spectral index $1.7^{+0.4}_{-0.3}$. The agreement between the Planck data and the simulated maps for these best-fitting parameters is quantified by a $chi^2$ value that is only slightly larger than unity.
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Polarized dust continuum emission has been observed with ALMA in an increasing number of deeply embedded protostellar systems. It generally shows a sharp transition going from the protostellar envelope to the disk scale, with the polarization fraction typically dropping from ${sim} 5%$ to ${sim} 1%$ and the inferred magnetic field orientations becoming more aligned with the major axis of the system. We quantitatively investigate these observational trends using a sample of protostars in the Perseus molecular cloud and compare these features with a non-ideal MHD disk formation simulation. We find that the gas density increases faster than the magnetic field strength in the transition from the envelope to the disk scale, which makes it more difficult to magnetically align the grains on the disk scale. Specifically, to produce the observed ${sim} 1%$ polarization at ${sim} 100,mathrm{au}$ scale via grains aligned with the B-field, even relatively small grains of $1,mathrm{mu m}$ in size need to have their magnetic susceptibilities significantly enhanced (by a factor of ${sim} 20$) over the standard value, potentially through superparamagnetic inclusions. This requirement is more stringent for larger grains, with the enhancement factor increasing linearly with the grain size, reaching ${sim} 2times 10^4$ for millimeter-sized grains. Even if the required enhancement can be achieved, the resulting inferred magnetic field orientation in the simulation does not show a preference for the major axis, which is inconsistent with the observed pattern. We thus conclude that the observed trends are best described by the model where the polarization on the envelope scale is dominated by magnetically aligned grains and that on the disk scale by scattering.
This paper presents the large-scale polarized sky as seen by Planck HFI at 353 GHz, which is the most sensitive Planck channel for dust polarization. We construct and analyse large-scale maps of dust polarization fraction and polarization direction, while taking account of noise bias and possible systematic effects. We find that the maximum observed dust polarization fraction is high (pmax > 18%), in particular in some of the intermediate dust column density (AV < 1mag) regions. There is a systematic decrease in the dust polarization fraction with increasing dust column density, and we interpret the features of this correlation in light of both radiative grain alignment predictions and fluctuations in the magnetic field orientation. We also characterize the spatial structure of the polarization angle using the angle dispersion function and find that, in nearby fields at intermediate latitudes, the polarization angle is ordered over extended areas that are separated by filamentary structures, which appear as interfaces where the magnetic field sky projection rotates abruptly without apparent variations in the dust column density. The polarization fraction is found to be anti-correlated with the dispersion of the polarization angle, implying that the variations are likely due to fluctuations in the 3D magnetic field orientation along the line of sight sampling the diffuse interstellar medium.We also compare the dust emission with the polarized synchrotron emission measured with the Planck LFI, with low-frequency radio data, and with Faraday rotation measurements of extragalactic sources. The two polarized components are globally similar in structure along the plane and notably in the Fan and North Polar Spur regions. A detailed comparison of these three tracers shows, however, that dust and cosmic rays generally sample different parts of the line of sight and confirms that much of the variation observed in the Planck data is due to the 3D structure of the magnetic field.
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.
We present a study of the structure of the Galactic interstellar medium through the Delta-variance technique, related to the power spectrum and the fractal properties of infrared/sub-mm maps. Through this method, it is possible to provide quantitative parameters which are useful to characterize different morphological and physical conditions, and to better constrain the theoretical models. In this respect, the Herschel Infrared Galactic Plane Survey carried out at five photometric bands from 70 to 500 mu m constitutes an unique database for applying statistical tools to a variety of regions across the Milky Way. In this paper, we derive a robust estimate of the power-law portion of the power spectrum of four contiguous 2{deg}x2{deg} Hi-GAL tiles located in the third Galactic quadrant (217{deg} < l < 225{deg}, -2{deg} < b < 0{deg}). The low level of confusion along the line of sight testified by CO observations makes this region an ideal case. We find very different values of the power spectrum slope from tile to tile but also from wavelength to wavelength (2 < beta < 3), with similarities between fields attributable to components located at the same distance. Thanks to the comparison with models of turbulence, an explanation of the determined slopes in terms of the fractal geometry is also provided, and possible relations with the underlying physics are investigated. In particular, an anti-correlation between ISM fractal dimension and star formation efficiency is found for the two main distance components observed in these fields. A possible link between the fractal properties of the diffuse emission and the resulting clump mass function is discussed.
We apply the Finkbeiner et al. (1999) two-component thermal dust emission model to the Planck HFI maps. This parametrization of the far-infrared dust spectrum as the sum of two modified blackbodies serves as an important alternative to the commonly adopted single modified blackbody (MBB) dust emission model. Analyzing the joint Planck/DIRBE dust spectrum, we show that two-component models provide a better fit to the 100-3000 GHz emission than do single-MBB models, though by a lesser margin than found by Finkbeiner et al. (1999) based on FIRAS and DIRBE. We also derive full-sky 6.1 resolution maps of dust optical depth and temperature by fitting the two-component model to Planck 217-857 GHz along with DIRBE/IRAS 100 micron data. Because our two-component model matches the dust spectrum near its peak, accounts for the spectrums flattening at millimeter wavelengths, and specifies dust temperature at 6.1 FWHM, our model provides reliable, high-resolution thermal dust emission foreground predictions from 100 to 3000 GHz. We find that, in diffuse sky regions, our two-component 100-217 GHz predictions are on average accurate to within 2.2%, while extrapolating the Planck Collaboration (2013a) single-MBB model systematically underpredicts emission by 18.8% at 100 GHz, 12.6% at 143 GHz and 7.9% at 217 GHz. We calibrate our two-component optical depth to reddening, and compare with reddening estimates based on stellar spectra. We find the dominant systematic problems in our temperature/reddening maps to be zodiacal light on large angular scales and the cosmic infrared background anisotropy on small angular scales.
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