Density Studies of MHD Interstellar Turbulence: Statistical Moments, Correlations and Bispectrum

We present a number of statistical tools that show promise for obtaining information on turbulence in molecular clouds (MCs) and diffuse interstellar medium (ISM). For our tests we make use of three-dimensional 512³ compressible MHD isothermal simulations performed for different sonic, i.e., M_s≡ V_L/V_s, where V_L is the injection velocity, V_s is the sound velocity, and Alfvénic M_A≡ V_L/V_A, where V_A is the Alfvén velocity, 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 three-dimensional stochastic density field and of column densities, available from observations, are similar. This opens good prospects for studies of MCs and diffuse media with the new tool. We use the bispectrum technique to define the role of nonlinear wave-wave interactions in the turbulent energy cascade. We also obtained the bispectrum function for density and column densities with varying magnetic field strength. As expected, a strong correlation is obtained for wave modes k ₁ = k ₂ for all models. Larger values of M_{s} result in increased correlations for modes with k ₁ ≠ k ₂. This effect becomes more evident with increasing magnetic field intensity. We believe that the different MHD wave modes, e.g., Alfvén and magneto-acoustic, which arise in strongly magnetized turbulence, may be responsible for the increased correlations compared to purely hydrodynamical perturbations. In addition to the bispectrum, we calculated the third and fourth statistical moments of density and column density, namely, skewness and kurtosis, respectively. We found a strong dependence of skewness and kurtosis with M_{s}. In particular, as M_{s} increases, so does the Gaussian asymmetry of the density distribution. We also studied the correlations of two-dimensional column density with dispersion of velocities and magnetic field, as well as the correlations of three-dimensional density with magnetic and kinetic energy and M_{A} for comparison. Our results show that column density is linearly correlated with magnetic field for high M_{s}. 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.