Magnetic field and faraday rotation measure in a turbulent warm ionized medium

• We suggest a relation among the variance of RM/RM‾, B0‖B0‖ and MsMs.
• It approximately represents the relation for Alfvénic perturbations δB/B0≈v/cAδB/B0≈v/cA.
• We also suggest a relation between MsMs and the variance of log(EM).
• The relations could be used for a quick estimation of B0‖B0‖ in the WIM.

Wu et al. (2009) proposed an empirical relation between the magnetic field strength along the line of sight (LOS) and the dispersion of the Faraday rotation measure (RM) distribution in turbulent media with the root mean squared sonic Mach number Ms≃1Ms≃1. In this study, we extend this relation by incorporating the Mach number dependency. Media where 0.5≲Ms≲20.5≲Ms≲2 are considered to cover the Mach number range of the warm ionized medium (WIM) of our Galaxy, and 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 the RM distribution, and the Mach number, which approximately represents the relation for Alfvénic perturbations. In addition, we suggest a relation between the Mach number and the dispersion of the log-normal distribution of the emission measure (EM), which is basically the relation between the Mach number and the density dispersion. These relations could facilitate rapid estimates of the LOS magnetic field strength in the turbulent WIM.