A technique for constraining the driving scale of turbulence and a modified Chandrasekhar-Fermi method

The Chandrasekhar-Fermi method is a powerful technique for estimating the strength of the mean magnetic field projected on the plane of the sky. In this paper, we present a technique for improving the Chandrasekhar-Fermi method, in which we take into account the averaging effect arising from independent eddies along the line of sight . In the conventional Chandrasekhar-Fermi method, the strength of fluctuating magnetic field divided by $\sqrt{4 \pi \bar{\rho}}$, where $\bar{\rho}$ is average density, is assumed to be comparable to the line-of-sight velocity dispersion. This however is not true when the driving scale of turbulence $L_f$, i.e. the outer scale of turbulence, is smaller than the size of the system along the line of sight $L_{los}$. In fact, the conventional Chandrasekhar-Fermi method over-estimates the strength of the mean plane-of-the-sky magnetic field by a factor of $\sim \sqrt{ L_{los}/L_f}$. We show that the standard deviation of centroid velocities divided by the average line-of-sight velocity dispersion is a good measure of $\sqrt{ L_{los}/L_f}$, which enables us to propose a modified Chandrasekhar-Fermi method.