The turbulent warm ionized medium: Emission measure distribution and MHD simulations

We present an analysis of the distribution of H alpha 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 degrees. We removed sight lines intersecting 19 high- latitude classical H II regions, leaving only sight lines that sample the diffuse WIM. The distribution of EM sin |b| for the diffuse WIM sample is poorly characterized by a single normal distribution, but is extraordinarily well fit by a lognormal distribution, with < log EM sin |b|(pc cm(-6))(-1)> = 0: 146 +/- 0: 001 and standard deviation sigma(log EM sin |b|) = 0.190 +/- 0.001. The value of < log EM sin |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 EM sin |b| is well described by models of mildly supersonic turbulence with a sonic Mach number of similar to 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 H alpha 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) approximate to 0: 03 cm(-3). We also discuss the implications of these results for interpreting the filling factor, the power requirement, and the magnetic field of the WIM.