Interpretation of the structure function of rotation measure in the interstellar medium

TL;DR

This paper analyzes the structure function of rotation measure in the interstellar medium, demonstrating how RM fluctuations relate to density and magnetic field turbulence, and clarifying the limitations of RM SFs in probing magnetic turbulence.

Contribution

It provides a theoretical explanation for the observed RM structure functions using correlations from Lazarian & Pogosyan (2016), and links the spectral break to electron density structures.

Findings

RM SFs reflect density fluctuation properties when similar to emission measure SFs.

RM SFs can estimate the mean magnetic field but not the turbulent magnetic field.

The spectral break indicates the inner scale of electron density fluctuations.

Abstract

The observed structure function (SF) of rotation measure (RM) varies as a broken power-law function of angular scales. The systematic shallowness of its spectral slope is inconsistent with the standard Kolmogorov scaling. This motivates us to examine the statistical analysis on RM fluctuations. The correlations of RM constructed by Lazarian & Pogosyan (2016) are demonstrated to be adequate in explaining the observed features of RM SFs through a direct comparison between the theoretically obtained and observationally measured SF results. By segregating the density and magnetic field fluctuations and adopting arbitrary indices for their respective power spectra, we find that when the SFs of RM and emission measure have a similar form over the same range of angular scales, the statistics of the RM fluctuations reflect the properties of density fluctuations. RM SFs can be used to evaluate the mean magnetic field along the line of sight, but cannot serve as an informative source on the properties of turbulent magnetic field in the interstellar medium. We identify the spectral break of RM SFs as the inner scale of a shallow spectrum of electron density fluctuations, which characterizes the typical size of discrete electron density structures in the observed region.