Magnetic Field and Faraday Rotation Measure in the Turbulent Warm Ionized Medium

Abstract: Wu et al. (2009) suggested an empirical relation between the magnetic field strength along the line of sight (LOS) and the dispersion of Faraday rotation measure (RM) distribution in turbulent media with root-mean-square sonic Mach number $M_s \simeq 1$. In this paper, we extend the work by incorporating the Mach number dependence. Media with $\sim 0.5 < M_s < \sim 2$ are considered to cover the Mach number range of the warm ionized medium (WIM) of our Galaxy. Three-dimensional, magnetohydrodynamic isothermal turbulence simulations with solenoidal forcing are used. We suggest a new relation among the LOS magnetic field strength, the dispersion of RM distribution, and the Mach number, which approximately represents the relation for Alfv\'enic perturbations. In addition, we suggest a relation between the Mach number and the dispersion of log-normal distribution of emission measure (EM), which is basically the relation for the Mach number and the density dispersion. The relations could be used for a quick and rough estimation of the LOS magnetic field strength in the turbulent WIM.