Characteristic Lengths of Magnetic Field in Magnetohydrodynamic Turbulence

TL;DR

This study investigates the characteristic length scales of magnetic fields in magnetohydrodynamic turbulence, revealing their evolution, saturation levels, and implications for intergalactic magnetic field observations.

Contribution

It provides a numerical analysis of magnetic field length scales in MHD turbulence, especially in weak or zero mean magnetic field conditions relevant to intergalactic space.

Findings

Magnetic spectrum peaks at about half the energy injection scale at saturation.

Energy equipartition scale increases as t^{1.5} during amplification.

Estimated RM standard deviation is ~100 rad/m^2 for clusters.

Abstract

In the framework of turbulence dynamo, flow motions amplify a weak seed magnetic field through the stretching of field lines. Although the amplification process has been a topic of active research, less attention has been paid to the length scales of magnetic field. In this paper, we described a numerical study on characteristic lengths of magnetic field in magnetohydrodynamic turbulence. We considered the case of very weak or zero mean magnetic field, which is applicable to the turbulence in the intergalactic space. Our findings are as follows. (1) At saturation, the peak of magnetic field spectrum occurs at $\sim L_0/2$, where $L_0$ is the energy injection scale, while the most energy containing scale is $\sim L_0/5$. The peak scale of spectrum of projected, two-dimensional field is $\sim L_0$. (2) During the stage of magnetic field amplification, the energy equipartition scale shows a power-law increase of $\sim t^{1.5}$, while the integral and curvature scales show a linear increase. The equipartition, integral, and curvature scales saturate at $\sim L_0$, $\sim 0.3L_0$, and $\sim 0.15L_0$, respectively. (3) The coherence length of magnetic field defined in the Faraday rotation measure (RM) due to the intergalactic magnetic field (IGMF) is related to the integral scale. We presented a formula that expresses the standard deviation of RM, $\sigma_{RM}$, in terms of the integral scale and rms strength of the IGMF, and estimated that $\sigma_{RM}$ would be $\sim 100$ and $\sim$ a few rad m$^{-2}$ for clusters and filaments, respectively.