A three-dimensional reconstruction of the interstellar magnetic field toward a star-forming region

TL;DR

This work tackles the challenge of recovering the LoS distribution of interstellar dust emission and its magnetic-field orientation by introducing a 3D polarimetric method that fuses HI and CO spectral cubes with Planck 353 GHz dust polarization. The method decomposes the LoS into physically motivated clouds using ROHSA Gaussian decomposition and velocity coherence, assigns dust emission to each cloud via conversion factors fitted to data, and derives cloud-wide magnetic-field orientations from cloud-resolved polarization parameters. Applied to the G139 region, the approach identifies seven LoS clouds, reveals a dominant, nearly horizontal magnetic field in one cloud and two depolarizing molecular clouds with distinct field orientations, demonstrating that 2D polarization maps miss critical 3D structure. The study emphasizes that 3D kinematic information is essential for reliable magnetic-field inferences and lays groundwork for broader application to star-forming regions and future cross-validations with Zeeman measurements and tomographic methods.

Abstract

Context. The polarized thermal emission from interstellar dust offers a valuable tool for probing both the dust and the magnetic field in the interstellar medium (ISM). However, existing observations only yield the total amount of dust emission along the line of sight (LoS), with no information on its LoS distribution. Aims. We present a new method designed to give access to the LoS distribution of the dust emission, both in terms of intensity and polarization. Methods. We relied on three kinematic gas tracers (HI, 12CO, and 13CO emission lines) to identify the different clouds present along the LoS. We decomposed the measured intensity of the dust emission, $I_d$, into separate contributions from these clouds. We performed a similar decomposition of the measured Stokes parameters for linear polarization, $Q_d$ and $U_d$, to derive the polarization parameters of the different clouds, and from this we inferred the clouds' magnetic field orientations. Results. We applied our method to a $3~{\rm deg}^2$ region of the sky, centered on $(l,b) = (139°30',-3°16')$ and exhibiting signs of star formation activity. We found this region to be dominated by an extended and bright cloud with nearly horizontal magnetic field, as expected from the nearly vertical polarization angles measured by Planck. More importantly, we detected the presence of two smaller, depolarizing molecular clouds with very different magnetic field orientations in the plane of the sky ($\simeq 65°$ and $\simeq 45°$ from the horizontal). This is a novel and viable result, which cannot be directly read off the Planck polarization maps. Conclusions. The application of our method to the G139 region convincingly demonstrates the need to complement 2D polarization maps with 3D kinematic information when looking for reliable estimates of magnetic field orientations.

Figures (9)

• Figure 1: Maps of the intensity, $I_{\rm d}$ ( left), and of the two Stokes parameters for linear polarization, $Q_{\rm d}$ ( middle) and $U_{\rm d}$ ( right), of the polarized dust emission at 353 GHz toward the G139 region defined in the first paragraph of Sect. \ref{['sec:application']}. Top row: Observational maps from PlanckPlanck_III_2020. Middle row: Same maps resampled to the common $26 \times 26$ pixel grid of the gas tracers (pixel size = 4'). Bottom row: Statistical uncertainties in the Planck maps resampled to the $26 \times 26$ pixel grid. The total uncertainties are equal to the quadratic sums of the statistical uncertainties and the photometric calibration uncertainties, which in turn are given by $0.0078 \, I_{\rm d}$ for $I_{\rm d}$Planck_VIII_2016Planck_III_2020 and $0.015 \, P_{\rm d}$ for $Q_{\rm d}$ and $U_{\rm d}$Planck_III_2020Planck_XI_2020.
• Figure 2: Top row: Observational maps of the velocity-integrated brightness temperatures, $T_{\rm b}$, of the H i 21 cm ( left), $^{12}$CO 2.6 mm ( middle), and $^{13}$CO 2.7 mm ( right) emission lines toward the G139 region; these maps are from winkel_etal_2016, yuan_etal_2021, and yuan_etal_2022, respectively. Second row: Maps of the velocity-integrated opacity-corrected brightness temperatures, $T_{\rm b\star}$, of the H i ( left) and $^{12}$CO ( right) lines, where $T_{\rm b\star}^{^{12}{\rm CO}}$ is derived based on the combined $^{12}$CO and $^{13}$CO data. Third row: Same maps resampled to the common $26 \times 26$ pixel grid (pixel size = 4'). Fourth row: Reconstructed maps after application of the Gaussian decomposition algorithm ROHSA. Bottom row: Maps of the residuals obtained by subtracting the reconstructed ROHSA maps from the resampled input maps. The color bars for H i and CO (superscript $12$ dropped) can be rescaled to dust intensity at 353 GHz using the best-fit values of the conversion factors derived in Sect. \ref{['sec:application_conversion_factors']} (see Fig. \ref{['fig:G139_cornerplot_conversionfactors']}). The resulting ranges in the third and fourth rows are $\simeq [0, 3.5\,{\rm MJy\,sr^{-1}}]$ for H i and $\simeq [0, 2.5\,{\rm MJy\,sr^{-1}}]$ for CO.
• Figure 3: Corner plot of the marginal (1D) and joint (2D) probability density functions of the conversion factors from velocity-integrated opacity-corrected brightness temperature to dust intensity at 353 GHz, $X^{{\rm H}\textsc{i}}_{I_{\rm d}/T_{\rm b}}$ and $X^{\rm CO}_{I_{\rm d}/T_{\rm b}}$ [in ${\rm (MJy\,sr^{-1})\,(K\,km\,s^{-1})^{-1}}$], for the two gas tracers, H i and CO, in the G139 region.
• Figure 4: Maps of the intensity, $I_{\rm d}$, of the dust emission at 353 GHz toward the G139 region. Left: Observational map from Planck. Middle: Best-fit maps reconstructed with the two gas tracers, H i and CO, before ( top) and after ( bottom) application of the Gaussian decomposition algorithm ROHSA to each gas tracer. Right: Maps of the residuals obtained by subtracting the respective reconstructed maps from the observational Planck map. The color code refers to the absolute residuals, whereas the contour lines follow the relative residuals.
• Figure 5: Spectra of the opacity-corrected brightness temperatures, $T_{\rm b\star}^{{\rm H}\textsc{i}}$ ( top) and $T_{\rm b\star}^{\rm CO}$ ( bottom), averaged over the $26 \times 26$ pixels of the common $(l,b)$ grid, toward the G139 region. The observed spectra are plotted in black dashed line, the reconstructed spectra obtained after application of the Gaussian decomposition algorithm ROHSA are plotted in black solid line, and the spectra of the individual Gaussian kinematic components, which are ordered (for each tracer) by increasing mean velocity, are plotted in color. The $T_{\rm b\star}^{{\rm H}\textsc{i}}$ and $T_{\rm b\star}^{\rm CO}$ spectra can be rescaled to dust intensity per unit velocity at 353 GHz using the best-fit values of the conversion factors derived in Sect. \ref{['sec:application_conversion_factors']} (see Fig. \ref{['fig:G139_cornerplot_conversionfactors']}).