The Turbulent Warm Ionized Medium: Emission Measure Distribution and MHD Simulations, Astrophys

We present an analysis of the distribution of H emission measures for the warm ionized medium (WIM) of the Galaxy using data from theWisconsinHMapper (WHAM)Northern Sky Survey. Our sample is restricted toGalactic latitudes jbj> 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 EM sin jbj for the diffuse WIM sample is poorly characterized by a single normal distribution, but is extraordinarily well fit by a lognormal distribution, with hlog EM sin jbj(pc cm6)1i 0:146 0:001 and standard deviation log EM sin jbj 0:190 0:001. The value of log EM sin jbjh i drops from 0:260 0:002 at Galactic latitude 10 < jbj < 30 to 0:038 0:002 at Galactic latitude 60 < jbj < 90. The distribution maywiden slightly at lowGalactic latitude.We compare the observed EMdistribution 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 jbj is well described by models of mildly supersonic turbulence with a sonic Mach number of 1.4Y2.4. The distribution is weakly sensitive to the magnetic field strength. The model also successfully predicts the distribution of dispersionmeasures of pulsars andH line profiles. In the best fittingmodel the turbulentWIM occupies a vertical path length of 400Y500 pc within the 1.0Y1.8 kpc scale height of the layer. The WIM gas has a lognormal distribution of densities with a most probable electron density npk 0:03 cm3. We also discuss the impli-cations of these results for interpreting the filling factor, the power requirement, and the magnetic field of the WIM. Subject headinggs: ISM: structure — MHD — turbulence 1