High-accuracy estimation of magnetic field strength in the interstellar medium from dust polarization

Abstract

Context. A large-scale magnetic field permeates our Galaxy and is involved in a variety of astrophysical processes, such as star formation and cosmic ray propagation. Dust polarization has been proven to be one of the most powerful observables for studying the field properties in the interstellar medium (ISM). However, it does not provide a direct measurement of its strength. Different methods have been developed that employ both polarization and spectroscopic data in order to infer the field strength. The most widely applied method was developed by Davis (1951, Phys. Rev., 81, 890) and Chandrasekhar & Fermi (1953, ApJ, 118, 1137), hereafter DCF. The DCF method relies on the assumption that isotropic turbulent motions initiate the propagation of Alfvén waves. Observations, however, indicate that turbulence in the ISM is anisotropic and that non-Alfvénic (compressible) modes may be important. Aims. Our goal is to develop a new method for estimating the field strength in the ISM that includes the compressible modes and does not contradict the anisotropic properties of turbulence. Methods. We adopt the following assumptions: (1) gas is perfectly attached to the field lines; (2) field line perturbations propagate in the form of small-amplitude magnetohydrodynamic (MHD) waves; and (3) turbulent kinetic energy is equal to the fluctuating magnetic energy. We use simple energetics arguments that take the compressible modes into account to estimate the strength of the magnetic field. Results. We derive the following equation: B0 = √2πρδv/√δθ, where ρ is the gas density, δv is the rms velocity as derived from the spread of emission lines, and δθ is the dispersion of polarization angles. We produce synthetic observations from 3D MHD simulations, and we assess the accuracy of our method by comparing the true field strength with the estimates derived from our equation. We find a mean relative deviation of 17%. The accuracy of our method does not depend on the turbulence properties of the simulated model. In contrast, the DCF method, even when combined with the Hildebrand et al. (2009, ApJ, 696, 567) and Houde et al. (2009, ApJ, 706, 1504) method, systematically overestimates the field strength. Conclusions. Compressible modes can significantly affect the accuracy of methods that are based solely on Alfvénic modes. The formula that we propose includes compressible modes; however, it is applicable only in regions with no self-gravity. Density inhomogeneities may bias our estimates to lower values.

Magnetic fields in star formation: a complete compilation of all the DCF estimations

“…Recently, Skalidis & Tassis (2021) proposed a method that is similar to the DCF method and is based on a different assumption that there is an energy equipartition between the turbulent kinetic energy and the cross-term magnetic energy. We suggest that this assumption may not be valid in the commonly studied dense molecular structures where self-gravity is important (see Appendix A for a discussion).…”

“…The DCF method assumes an equipartition between the turbulent magnetic energy and the turbulent kinetic energy. Recently, Skalidis & Tassis (2021) proposed that the cross-term (or coupling-term) magnetic energy dominates the turbulent magnetic energy in sub-Alfvénic cases and thus the assumption of an equipatition between the cross-term magnetic energy and the turbulent kinetic energy should replace the DCF assumption. Here we discuss why the new energy equipartition assumption in Skalidis & Tassis (2021) may be inappropriate in the commonly studied star-forming molecular clouds/clumps/cores.…”

Magnetic Fields in Massive Star-Forming Regions (MagMaR) II. Tomography Through Dust and Molecular Line Polarization in NGC 6334I(N)

“…To ascertain the importance of the magnetic field in NGC6334I(N), we estimate its strength onto the plane of the sky component, B pos , using a number of variants of the Davis, Chandrasekhar, and Fermi method (or DCF: Davis 1951;Chandrasekhar & Fermi 1953;Heitsch et al 2001;Falceta-Gonçalves et al 2008), by using the angle dispersion function method (or ADF Houde et al 2009Houde et al , 2013aHoude et al , 2016, and by using a recently derived approach for DCF which considers magnetosonic perturbations instead of Alfven waves (Skalidis & Tassis 2021). We will discuss the applicability of such methods to regions such as NGC6334I(N) in section 4.3.…”

“…The column and volume densities are also derived directly from the Stokes I dust and CS emissions; we compute all values within the same region used to derive the polarization position angle dispersion (δφ). To derive column density 2 The modifications to DCF proposed by Skalidis & Tassis (2021) require to change δφ by √ δφ and a change of 1/ √ 2 scaling factor and thus the practicalities of the computation are the same as with the regular DCF variants The contours correspond to the total intensity and are plotted at levels of 1.7, 8.8, 17.7, 35.3, 58.9, 117.8, 235.6, 353.4, and 471.2 mJy beam −1 with an rms for the primary beam corrected map of σ = 1.1 mJy beam −1 . The purple oval encloses the 1b and 1c cores identified by Hunter et al (2014) also corresponding to the region used to estimate the magnetic field strength onto the plane of the sky.…”

“…However, this will rapidly decrease the field strength as the tangent function quickly diverges for δφ > 60 • . Recently, the DCF method was revisited and another correction was proposed which considers the compressible modes from small amplitude MHD waves (magnetosonic), instead of purely Alfven transverse waves (Skalidis & Tassis 2021). This method implements a substitution in the DCF equation in the form of δφ → √ δφ, which seem to improve the recovery of the field strength when applied to their numerical simulations.…”