A three-step approach to reliably estimate magnetic field strengths in star-forming regions

¹ Department of Physics, University of Crete, 70013 Heraklion, Greece
² Institute of Astrophysics, Foundation for Research and Technology-Hellas, Vasilika Vouton, 70013 Heraklion, Greece
³ Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
⁴ TAPIR, California Institute of Technology, MC 350-17, Pasadena, CA 91125, USA

^★ Corresponding author: ph5698@edu.physics.uoc.gr

Received: 15 January 2025
Accepted: 3 July 2025

Abstract

Context. The magnetic field has been shown to play a crucial role in star formation. Dust polarization is one of the most effective tools for probing the properties of the magnetic field, yet it does not directly trace its strength. To bridge this gap, several methods have been developed, combining polarization and spectroscopic data, to estimate the strength of the magnetic field. The most widely applied method was developed by Davis (1951, Phys. Rev., 81, 890) and Chandrasekhar & Fermi (1953, ApJ, 118, 113), hereafter DCF, and relates the polarization angle dispersion to magnetic field strength under the assumption of Alfvénic turbulence. Skalidis & Tassis (2021, A&A, 647, A186), hereafter ST, relaxed this assumption to account for the compressible modes, and derived more accurate estimates of the magnetic field strength than the DCF in clouds with no self-gravity. The accuracy of these methods in self-gravitating regions is poorly explored.

Aims. We aim to evaluate the accuracy of these magnetic-field estimation methods in star-forming regions and propose a systematic approach for calculating the key observational parameters they involve: the velocity dispersion (δv), the polarization angle dispersion (δθ), and the cloud density (ρ).

Methods. We used a three-dimensional magnetohydrodynamic chemo-dynamical simulation of a turbulent collapsing molecular cloud. We generated synthetic observations for seven different inclination angles with respect to the mean component of the magnetic field, which encompass a comprehensive set of observables, including emission line spectra, Stokes parameters, and column density maps. We employed various approaches for estimating the parameters δv, δθ, and ρ, and identified the best approach that most effectively probes the plane-of-sky (POS) component of the magnetic field.

Results. We find that the approach used to calculate the parameters δv, δθ, and ρ plays a crucial role in estimating the magnetic field strength, regardless of the specific method used (i.e., the DCF or the ST methods). We show that the value probed by both methods corresponds to the median of the molecular-species–weighted POS component of the magnetic field. We also find that ST outperforms DCF. The magnetic field strength values derived with the ST method accurately follow the expected cosine trend with respect to the inclination angle of the magnetic field and consistently remain within 1σ of the median component of the magnetic field strength. In self-gravitating clouds, we propose the following approach to accurately constrain the intrinsic parameters involved in the magnetic field estimation methods: ρ using radiative transfer analysis, δv using the second moment maps, and δθ by fitting Gaussians to the polarization angle distributions to remove the contribution of the hourglass morphology.