The mass-to-flux ratio in molecular clouds. What are we really measuring?

TL;DR

The study addresses how projection geometry biases measurements of the mass-to-flux ratio $\mu$ in molecular clouds. Using a 3D nonideal MHD chemo-dynamical simulation to generate mock LOS and POS measurements across multiple viewing angles and evolutionary times, it compares observed $\mu$ to the true value. It finds that Zeeman-based estimates can greatly overestimate $\mu$ when the field lies in the plane of the sky, while polarization-based estimates are not physically meaningful for tracing the true $\mu$ and can be misleading; DCF/ST approaches provide little diagnostic improvement beyond chance. The work highlights the dominance of projection effects in interpreting magnetic support and cautions against overinterpreting $\mu$ from common observational proxies, emphasizing the need to respect the $B$–$N$ correlation in clouds.

Abstract

The mass-to-magnetic flux ratio of molecular clouds is a parameter of central importance as it quantifies the dynamical significance of the magnetic field with respect to gravitational forces. Therefore, it can provide invaluable information on the fate of clouds, and the sites of star formation. Our objective was to study the accuracy with which we can measure the true mass-to-flux ratio in molecular clouds under various projection angles and identify systematic biases. We used a 3D nonideal magnetohydrodynamic chemo-dynamical simulation of a turbulent collapsing molecular cloud. We quantified the accuracy with which the mass-to-flux ratio is recovered under various projection angles and dynamical stages by analyzing the magnetic field - gas column density relation, and comparing the "observed" mass-to-flux ratio against the true values. We find that projection effects have a major effect on measurements of the mass-to-flux ratio. Zeeman measurements can overestimate the true mass-to-flux ratio of the cloud by more than an order of magnitude when the magnetic field primarily lies on the plane of the sky. Therefore, measurements of the mass-to-flux ratio based on Zeeman observations should be considered as upper limits. Mass-to-flux ratio estimates inferred from polarization observations do not provide a physically meaningful probe of the true mass-to-flux ratio and can lead to unphysical results as they fail to capture the underlying correlation between the magnetic field and column density.

Figures (3)

• Figure 1: Magnetic field column density relation from our simulation considering the LOS and POS components of the field (upper and lower panels, respectively). The cyan dashed, dash-dotted and dotted lines mark constant mass-to-flux ratios of $\mu/\mu_{crit}$ of 0.1, 1, and 10, respectively. The thin blue solid line indicates the initial value of the mass-to-flux ratio in the cloud and the blue dashed line marks the maximum value of the mass-to-flux ratio at a time of 1.44$\times~t_{ff}$. Colored points correspond to different projection angles, different symbols correspond to different times when the cloud is "observed", and the size of the symbols is proportional to the size of the beam used to observe different regions of the cloud (see Sect. \ref{['methods']}).
• Figure 2: PDFs of the mass-to-flux ratio based on the LOS (upper panel) and POS (lower panel) components of the magnetic field for a time of $1.44\times t_{ff}$, when the cloud has evolved to a more realistic configuration. For each case, we adopt the inclination angle that maximizes the respective component ($\gamma = 0^\circ$ for $\rm{B_{LOS}}$ and $\gamma = 90^\circ$ for $\rm{B_{POS}}$). Black curves correspond to the results from the simulation. Red dotted lines represent PDFs obtained when column densities and magnetic field strengths from different regions of the cloud (and with different beam sizes) are randomly paired. The blue dashed line shows a PDF of mass-to-flux ratios obtained by considering independent uniform random distributions for $\rm{B_{POS}}$ and $\rm{log_{10}N_p}$. The blue solid and dash-dotted vertical lines indicate the initial and maximum values of the true $\mu$, respectively. At late times, only $\sim$17% of $\rm{B_{POS}}$ estimates fall within the range defined by the true mass-to-flux ratio, while most values suggest a substantially subcritical cloud. The similarity between the $\rm{B_{POS}}$ distribution from the simulation, and that obtained from random pairings, indicates that such measurements do not preserve the underlying correlation between magnetic field strength and column density.
• Figure 3: Column density maps of the simulation used, at different times, and inclination angles. From left to right, we present the following combinations $[0.5\times t_{ff}, ~0^\circ]$, $[0.75\times t_{ff}, ~22.5^\circ]$, $[1.0\times t_{ff}, ~45^\circ]$, $[1.25\times t_{ff}, ~67.5^\circ]$, $[1.44\times t_{ff}, ~90^\circ]$.