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

TL;DR

This paper introduces a modified Chandrasekhar-Fermi method that accounts for the effects of turbulence driving scale on magnetic field strength estimates, improving accuracy in astrophysical observations.

Contribution

The authors develop a correction to the Chandrasekhar-Fermi method that considers the turbulence driving scale, reducing overestimation of magnetic field strength in certain conditions.

Findings

The conventional method overestimates magnetic field strength when the turbulence driving scale is small.

A new measure based on centroid velocity standard deviation effectively estimates the turbulence scale.

The modified method provides more accurate magnetic field estimates in turbulent astrophysical environments.

Abstract

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.