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Dust polarization is a powerful tool for studying the magnetic fieldproperties in the interstellar medium (ISM). However, it does not provide adirect measurement of its strength. Different methods havebeen developed whichemploy both polarization and spectroscopic data in order to infer the fieldstrength. The most widely applied methods have been developed by Davis (1951),Chandrasekhar & Fermi (1953) (DCF), Hildebrand et al. (2009) and Houde etal.(2009) (HH09). They rely on the assumption that isotropic turbulent motionsinitiate the propagation of Alvf\'en waves. Observations,however, indicate thatturbulence in the ISM is anisotropic and non-Alfv\'enic (compressible) modesmay be important. Our goal is to develop a new method for estimating the fieldstrength in the ISM, which includes the compressible modes and does notcontradict the anisotropic properties of turbulence. We use simple energeticsarguments that take into account the compressible modes to estimate thestrength of the magnetic field. We derive the following equation:$B_{0}=\sqrt{2 \pi\rho} \delta v /\sqrt{\delta \theta}$, where $\rho$ is thegas density, $\delta v$ is the rms velocity as derived from the spread ofemission lines, and $\delta \theta$ is the dispersion of polarization angles.We produce synthetic observations from 3D MHD simulationsand we assess theaccuracy of our method by comparing the true field strength with the estimatesderived from our equation. We find a mean relative deviation of $17 \%$. Theaccuracy of our method does not depend on the turbulence properties of thesimulated model. In contrast DCF and HH09 systematically overestimate the fieldstrength. HH09 produces accurate results only for simulations with high sonicMach numbers.

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