The Turbulent Warm Ionized Medium: Emission Measure Distribution and Mhd Simulations

We present an analysis of the distribution of Hα emission measures for the warm ionized medium (WIM) of the Galaxy using data from the Wisconsin H-Alpha Mapper (WHAM) Northern Sky Survey. Our sample is restricted to Galactic latitudes |b| > 10. We removed sightlines intersecting nineteen high-latititude classical H II regions, leaving only sightlines that sample the diffuse WIM. The distribution of EMsin |b| for the full sample is poorly characterized by a single normal distribution, but is extraordinarily well fit by a lognormal distribution, with 〈log EMsin |b|( pc cm−6)−1〉 = 0.146± 0.001 and standard deviation σ = 0.190 ± 0.001. 〈log EMsin |b|〉 drops from 0.260 ± 0.002 at Galactic latitude 10 < |b| < 30 to 0.038 ± 0.002 at Galactic latitude 60 < |b| < 90. The distribution may widen slightly at low Galactic latitude. We compare the observed EM distribution function to the predictions of three-dimensional magnetohydrodynamic simulations of isothermal turbulence within a non-stratified interstellar medium. We find that the distribution of EMsin |b| is well described by models of mildy supersonic turbulence with a sonic Mach number of ∼ 1.4− 2.4. The distribution is weakly sensitive to the magnetic field strength. The model also successfully predicts the distribution of dispersion measures of pulsars and Hα line profiles. In the best fitting model, the turbulent WIM occupies 40− 50% of the volume within a 2 kpc thick layer about the midplane of the Galaxy with a lognormal distribution of densities within the turbulent layer with a most probable electron density npk ≈ 0.03 cm. We also discuss the implications of these results for interpreting the filling factor, the power requirement, and the magnetic field of the WIM. Subject headings: ISM: structure — turbulence — MHD