Magnetic fields in molecular clouds: Limitations of the analysis of Zeeman observations

Context. Observations of Zeeman split spectral lines represent an important approach to derive the structure and strength of magnetic fields in molecular clouds. In contrast to the uncertainty of the spectral line observation itself, the uncertainty of the analysis method to derive the magnetic field strength from these observations is not been well characterized so far. Aims. We investigate the impact of several physical quantities on the uncertainty of the analysis method, which is used to derive the line-of-sight (LOS) magnetic field strength from Zeeman split spectral lines. Methods. We simulate the Zeeman splitting of the 1665 MHz OH line with the 3D radiative transfer (RT) extension ZRAD. This extension is based on the line RT code Mol3D (Ober et al. 2015) and has been developed for the POLArized RadIation Simulator POLARIS (Reissl et al. 2016). Results. Observations of the OH Zeeman effect in typical molecular clouds are not significantly affected by the uncertainty of the analysis method. We derived an approximation to quantify the range of parameters in which the analysis method works sufficiently accurate and provide factors to convert our results to other spectral lines and species as well. We applied these conversion factors to CN and found that observations of the CN Zeeman effect in typical molecular clouds are neither significantly affected by the uncertainty of the analysis method. In addition, we found that the density has almost no impact on the uncertainty of the analysis method, unless it reaches values higher than those typically found in molecular clouds. Furthermore, the uncertainty of the analysis method increases, if both the gas velocity and the magnetic field show significant variations along the line-of-sight. However, this increase should be small in Zeeman observations of most molecular clouds considering typical velocities of ~1 km/s.Comment: 9 pages, 6 figure

Tracing the ISM magnetic field morphology: The potential of multi-wavelength polarization measurements

$\textit{Aims.}$ We present a case study to demonstrate the potential of multi-wavelength polarization measurements. The aim is to investigate the effects that dichroic polarization and thermal re-emission have on tracing the magnetic field in the interstellar medium (ISM). Furthermore, we analyze the crucial influence of imperfectly aligned compact dust grains on the resulting synthetic continuum polarization maps.$\\ \textit{Methods.}$ We developed an extended version of the well-known 3D Monte-Carlo radiation transport code MC3D for multi-wavelength polarization simulations running on an adaptive grid.We investigated the interplay between radiation, magnetic fields and dust grains. Our results were produced by post-processing both ideal density distributions and sophisticated magnetohydrodynamic (MHD) collapse simulations with radiative transfer simulations. We derived spatially resolved maps of intensity, optical depth, and linear and circular polarization at various inclination angles and scales in a wavelength range from 7 $\mu m$ to 1 $mm$.$\\ \textit{Results.}$ We predict unique patterns in linear and circular polarization maps for different types of density distributions and magnetic field morphologies for test setups and sophisticated MHD collapse simulations. We show that alignment processes of interstellar dust grains can significantly influence the resulting synthetic polarization maps. Multi-wavelength polarization measurements allow one to predict the morphology of the magnetic field inside the ISM. The interpretation of polarization measurements of complex structures still remains ambiguous because of the large variety of the predominant parameters in the ISM.Comment: 14 pages, 12 figures, 1 table, Paper accepted 2014 by A&

Spectral shifting strongly constrains molecular cloud disruption by radiation pressure on dust

${\bf Aim:}$ To test the hypothesis that radiation pressure from star clusters acting on dust is the dominant feedback agent disrupting the largest star-forming molecular clouds and thus regulating the star-formation process. ${\bf Methods:}$ We perform multi-frequency, 3D, RT calculations including scattering, absorption, and re-emission to longer wavelengths for clouds with masses of $10^4$-$10^7\,$M$_{\odot}$, with embedded clusters and a star formation efficiencies of 0.009%-91%, and varying maximum grain sizes up to 200$\,\mu$m. We calculate the ratio between radiative force and gravity to determine whether radiation pressure can disrupt clouds. ${\bf Results:}$ We find that radiation acting on dust almost never disrupts star-forming clouds. UV and optical photons to which the cloud is optically thick do not scatter much. Instead, they quickly get absorbed and re-emitted by at thermal wavelengths. As the cloud is typically optically thin to far-IR radiation, it promptly escapes, depositing little momentum. The resulting spectrum is more narrowly peaked than the corresponding Planck function with an extended tail at longer wavelengths. As the opacity drops significantly across the sub-mm and mm, the resulting radiative force is even smaller than for the corresponding single-temperature black body. The force from radiation pressure falls below the strength of gravitational attraction by an order of magnitude or more for either Milky Way or starbust conditions. For unrealistically large maximum grain sizes, and star formation efficiencies far exceeding 50% do we find that the strength of radiation pressure can exceed gravity. ${\bf Conclusions:}$ We conclude that radiation pressure acting on dust does not disrupt star-forming molecular clouds in any Local Group galaxies. Radiation pressure thus appears unlikely to regulate the star-formation process on either local or global scales.Comment: 20 pages, 17 figure

Linear dust polarization during the embedded phase of protostar formation

Measuring polarization from thermal dust emission can provide constraints on the magnetic field structure around embedded protostars. However, interpreting the observations is challenging without models that consistently account for both the complexity of the protostellar birth environment and polarization mechanisms. We aim to provide a better understanding with a focus on bridge-like structures such as that observed towards the protostellar multiple IRAS 16293--2422 by comparing synthetic polarization maps of thermal reemission with observations. We analyze the magnetic field properties associated with the formation of a protostellar multiple based on ideal MHD 3D zoom-in simulations carried out with the RAMSES code. To compare with observations, we post-process a snapshot of a bridge-like structure that is associated with a forming triple star system with the radiative transfer code POLARIS and produce multi-wavelength dust polarization maps. In the most prominent bridge of our sample, the typical density is about 10^(-16) g cm^(-3), and the magnetic field strength is about 1 to 2 mG. The magnetic field structure has an elongated toroidal morphology and the dust polarization maps trace the complex morphology. In contrast, the magnetic field strength associated with the launching of asymmetric bipolar outflows is significantly more magnetized (~100 mG). At {\lambda}=1.3 mm, the orientation of grains in the bridge is similar for the case accounting for radiative alignment torques (RATs) compared to perfect alignment with magnetic field lines. However, the polarization fraction in the bridge is three times smaller for the RAT scenario compared to assuming perfect alignment. At shorter wavelengths ({\lambda} < 200 {\mu}m), dust polarization does not trace the magnetic field because other effects such as self-scattering and dichroic extinction dominate the orientation of the polarization.Comment: 18 pages, 12 figures plus 3 figures in the appendix, accepted for publication in A&

Dust attenuation in galaxies at cosmic dawn from the FirstLight simulations

We study the behavior of dust in galaxies at cosmic dawn, z=6-8, by coupling the FirstLight simulations with the radiative transfer code POLARIS. The starburst nature of these galaxies and their complex distribution of dust lead to a large diversity of attenuation curves. These follow the Calzetti model only for relatively massive galaxies, Mstars=10^9Msun. Galaxies with lower masses have steeper curves, consistent with the model for the Small Magellanic Cloud (SMC). The ultraviolet and optical slopes of the attenuation curves are closer to the modified Calzetti model, with a slight preference for the power-law model for galaxies with the highest values of attenuation. We have also examined the relation between the slope in the far-ultraviolet, beta_UV , and the infrared excess, IRX. At z=6, it follows the Calzetti model with a shift to slightly lower beta_UV values due to lower metallicities at lower attenuation. The same relation at z=8 shows a shift to higher IRX values due to a stronger CMB radiation at high-z.Comment: 9 pages, 6 figures, accepted at MNRA

From parallel to perpendicular -- On the orientation of magnetic fields in molecular clouds

We present synthetic dust polarization maps of simulated molecular clouds (MCs) with the goal to systematically explore the origin of the relative orientation of the magnetic field ($\bf{B}$) with respect to the MC sub-structures identified in density ($n$; 3D) and column density ($N$; 2D). The polarization maps are generated with the radiative transfer code POLARIS, including self-consistently calculated efficiencies for radiative torque alignment. The MCs are formed in two sets of 3D MHD simulations: in (i) colliding flows (CF), and (ii) the SILCC-Zoom simulations. In 3D, for the CF simulations with an initial field strength below $\sim$5 $\mu$G, $\bf{B}$ is oriented parallel or randomly with respect to the $n$-structures. For CF runs with stronger initial fields and all SILCC-Zoom simulations, which have an initial field strength of 3 $\mu$G, a flip from parallel to perpendicular orientation occurs at high densities of $n_\text{trans}$ $\simeq$ 10$^2$ - 10$^3$ cm$^{-3}$. We suggest that this flip happens if the MC's mass-to-flux ratio, $\mu$, is close to or below the critical value of 1. This corresponds to a field strength around 3 - 5 $\mu$G. In 2D, we use the Projected Rayleigh Statistics (PRS) to study the orientation of $\bf{B}$. If present, the flip in orientation occurs at $N_\text{trans}$ $\simeq$ 10$^{21 - 21.5}$ cm$^{-2}$, similar to the observed transition value from sub- to supercritical magnetic fields in the ISM. However, projection effects can reduce the power of the PRS method: Depending on the MC or LOS, the projected maps of the SILCC-Zoom simulations do not always show the flip, although expected from the 3D morphology. Such projection effects can explain the variety of recently observed field configurations, in particular within a single MC. Finally, we do not find a correlation between the observed orientation of $\bf{B}$ and the $N$-PDF.Comment: 20 pages, 12 figures, accepted for publication in MNRA

Magnetic fields in star-forming systems (II): examining dust polarization, the Zeeman effect, and the Faraday rotation measure as magnetic field tracers

The degree to which the formation and evolution of clouds and filaments in the interstellar medium is regulated by magnetic fields remains an open question. Yet the fundamental properties of the fields (strength and 3D morphology) are not readily observable. We investigate the potential for recovering magnetic field information from dust polarization, the Zeeman effect, and the Faraday rotation measure ($RM$) in a SILCC-Zoom magnetohydrodynamic (MHD) filament simulation. The object is analyzed at the onset of star formation, and it is characterized by a line-mass of about M/L $\sim 63\ M_{\odot}\ pc^{-1}$ out to a radius of $1\,$pc and a kinked 3D magnetic field morphology. We generate synthetic observations via POLARIS radiative transfer (RT) post-processing, and compare with an analytical model of helical or kinked field morphology to help interpreting the inferred observational signatures. We show that the tracer signals originate close to the filament spine. We find regions along the filament where the angular-dependency with the line-of-sight (LOS) is the dominant factor and dust polarization may trace the underlying kinked magnetic field morphology. We also find that reversals in the recovered magnetic field direction are not unambiguously associated to any particular morphology. Other physical parameters, such as density or temperature, are relevant and sometimes dominant compared to the magnetic field structure in modulating the observed signal. We demonstrate that the Zeeman effect and the $RM$ recover the line-of-sight magnetic field strength to within a factor 2.1 - 3.4. We conclude that the magnetic field morphology may not be unambiguously determined in low-mass systems by observations of dust polarization, Zeeman effect, or $RM$, whereas the field strengths can be reliably recovered.Comment: 22 pages, 17 figures, 3 table

The complex multiscale structure in simulated and observed emission maps of the proto-cluster cloud G0.253+0.016 (\u27the Brick\u27)

The Central Molecular Zone (the central ∼500 pc of the Milky Way) hosts molecular clouds in an extreme environment of strong shear, high gas pressure and density, and complex chemistry. G0.253+0.016, also known as \u27the Brick\u27, is the densest, most compact, and quiescent of these clouds. High-resolution observations with the Atacama Large Millimetre/submillimetre Array (ALMA) have revealed its complex, hierarchical structure. In this paper we compare the properties of recent hydrodynamical simulations of the Brick to those of the ALMA observations. To facilitate the comparison, we post-process the simulations and create synthetic ALMA maps of molecular line emission from eight molecules. We correlate the line emission maps to each other and to the mass column density and find that HNCO is the best mass tracer of the eight emission lines within the simulations. Additionally, we characterize the spatial structure of the observed and simulated cloud using the density probability distribution function (PDF), spatial power spectrum, fractal dimension, and moments of inertia. While we find good agreement between the observed and simulated data in terms of power spectra and fractal dimensions, there are key differences in the density PDFs and moments of inertia, which we attribute to the omission of magnetic fields in the simulations. This demonstrates that the presence of the Galactic potential can reproduce many cloud properties, but additional physical processes are needed to fully explain the gas structure