Gradient Technique Theory: Tracing magnetic field and obtaining magnetic field strength

TL;DR

This paper develops an analytical theory for the gradient technique, enabling magnetic field tracing and strength measurement in turbulent media using spectroscopic and synchrotron data, with advantages over traditional methods.

Contribution

It provides a new analytical framework for gradient measurements, relating them to the Alfven Mach number and improving magnetic field strength estimation methods.

Findings

Derived analytical expressions linking gradient properties to Alfven Mach number

Quantified effects of line-of-sight and plane-of-sky averaging on gradient measurements

Proposed a method to combine gradient data with sonic Mach number for magnetic field strength estimation

Abstract

The gradient technique is a promising tool with theoretical foundations based on the fundamental properties of MHD turbulence and turbulent reconnection. Its various incarnations use spectroscopic, synchrotron, and intensity data to trace the magnetic field and measure the media magnetization in terms of Alfven Mach number. We provide an analytical theory of gradient measurements and quantify the effects of averaging gradients along the line of sight and over the plane of the sky. We derive analytical expressions that relate the properties of gradient distribution with the Alfven Mach number $M_A$. We show that these measurements can be combined with measures of sonic Mach number or line broadening to obtain the magnetic field strength. The corresponding technique has advantages to Davis-Chandrasekhar-Fermi way of obtaining the magnetic field strength.