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.