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

TL;DR

This paper introduces a new method for estimating magnetic field strength in the interstellar medium using dust polarization data, accounting for anisotropic and compressible turbulence, and demonstrates its improved accuracy over existing methods.

Contribution

The authors develop a novel estimation technique that incorporates compressible modes and anisotropic turbulence, improving accuracy in magnetic field strength measurements.

Findings

New method achieves 17% mean relative deviation from true field strength.

Existing methods systematically overestimate magnetic field strength.

Method's accuracy is independent of turbulence properties in simulations.

Abstract

Dust polarization is a powerful tool for studying the magnetic field properties in the interstellar medium (ISM). However, it does not provide a direct measurement of its strength. Different methods havebeen developed which employ both polarization and spectroscopic data in order to infer the field strength. The most widely applied methods have been developed by Davis (1951), Chandrasekhar & Fermi (1953) (DCF), Hildebrand et al. (2009) and Houde et al.(2009) (HH09). They rely on the assumption that isotropic turbulent motions initiate the propagation of Alvf\'en waves. Observations,however, indicate that turbulence in the ISM is anisotropic and non-Alfv\'enic (compressible) modes may be important. Our goal is to develop a new method for estimating the field strength in the ISM, which includes the compressible modes and does not contradict the anisotropic properties of turbulence. We use simple energetics arguments that take into account the compressible modes to estimate the strength of the magnetic field. We derive the following equation: $B_{0}=\sqrt{2 \pi\rho} \delta v /\sqrt{\delta \theta}$, where $\rho$ is the gas density, $\delta v$ is the rms velocity as derived from the spread of emission lines, and $\delta \theta$ is the dispersion of polarization angles. We produce synthetic observations from 3D MHD simulationsand 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 DCF and HH09 systematically overestimate the field strength. HH09 produces accurate results only for simulations with high sonic Mach numbers.