2008ApJ...686..363H

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 Hα Mapper (WHAM) Northern Sky Survey. Our sample is restricted to Galactic latitudes|b|>10°. We removed sight lines intersecting 19 high-latitude classical H II regions, leaving only sight lines that sample the diffuse WIM. The distribution of EMsin|b| for the diffuse WIM sample is poorly characterized by a single normal distribution, but is extraordinarily well fit by a lognormal distribution, with logEMsin|b|pc/cm6^–1=0.146±0.001 and standard deviation σ_logEMsin|b|=0.190±0.001. The value of logEMsin|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 nonstratified interstellar medium. We find that the distribution of EMsin|b| is well described by models of mildly 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 a vertical path length of 400-500 pc within the 1.0-1.8 kpc scale height of the layer. The WIM gas has a lognormal distribution of densities with a most probable electron density n_pk~0.03 cm3. We also discuss the implications of these results for interpreting the filling factor, the power requirement, and the magnetic field of the WIM.