Density Studies of MHD Interstellar Turbulence: Statistical Moments,   Correlations and Bispectrum
  We present a number of statistical tools for obtaining studying turbulence in molecular clouds and diffuse interstellar medium. For our tests we used of three-dimensional 512 cube compressible MHD isothermal simulations performed for different sonic and Alfvenic Mach numbers. We introduce the bispectrum, a new tool for statistical studies of the interstellar medium which, unlike an ordinary power spectrum of turbulence, preserves the phase information of the stochastic field. We show that the bispectra of the 3D stochastic density field and of column densities, available from observations, are similar. We use the bispectrum technique to define the role of non-linear wave-wave interactions in the turbulent energy cascade. We also obtained the bispectrum function for density and column densities with varying magnetic field strength. Larger values of sonic Mach number result in increased correlations for modes with different wavenumbers. This effect becomes more evident with increasing magnetic field intensity. In addition to the bispectrum, we calculated the 3rd and 4th statistical moments of density and column density, namely, skewness and kurtosis, respectively. We found a strong dependence of skewness and kurtosis with the sonic Mach number. In particular, as this number increases, so does the asymmetry of the density distribution. We also studied the correlations of 2D column density with dispersion of velocities and magnetic field, as well as the correlations of 3D density with magentic and kinetic energy and Alfven Mach number for comparison. Our results show that column density is linearly correlated with magnetic field for high sonic Mach number. This trend is independent of the turbulent kinetic energy and can be used to characterize inhomogeneities of physical properties in low density clumps in the ISM. 
Blakesley Burkhart, D. Falceta-Goncalves, G. Kowal, A. Lazarian