On the statistics of the polarized submillimetre emission maps from thermal dust in the turbulent, magnetized, diffuse ISM

TL;DR

This study statistically constrains the properties of magnetized turbulence in the diffuse interstellar medium using polarized dust emission data, revealing the spectral index of magnetic turbulence and density distribution characteristics.

Contribution

It introduces a novel framework combining simulations and MCMC analysis to extract turbulence parameters from polarized dust emission maps.

Findings

Magnetic field turbulence spectral index is 2.8 ± 0.2.

Density field follows a log-normal distribution with mean density 40 cm⁻³.

Model fits the Planck data with a near-ideal chi-squared value.

Abstract

[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 $2.8\pm 0.2$. 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.