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

Abstract

We present a number of statistical tools that show promise for obtaining information on turbulence in molecular clouds and diffuse interstellar medium. For our tests we make use of three-dimensional 512 3 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 3D stochastic density field and of column densities, available from observations, are similar. This opens good prospects for studies of molecular clouds and diffuse media with the new tool. 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. 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 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 M s . In particular, as M s increases, so does the Gaussian 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 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.

The dynamics of charged dust in magnetized molecular clouds

“…This estimate is supported by observations (Crutcher 1999;Crutcher et al 2010) and numerical simulations (Burkhart et al 2009;Banerjee et al 2009;Molina et al 2012) in the regime of interest where the fields dynamically unimportant on supersonic scales (i.e., we again require MA > 1). 9 Note that the dust feels the total "large-scale" magnetic field (in contrast to the velocity field, where only v λ is important) so we do not need the magnetic field spectrum.…”

The Phase Coherence of Interstellar Density Fluctuations

“…We use a database of three-dimensional (3D) numerical simulations of isothermal compressible (MHD) turbulence with a resolution of 512 3 presented in a number of past works (e.g., Kowal et al 2007;Burkhart et al 2009Burkhart et al , 2013. We refer to these works for the details of the numerical set-up and here provide a short overview.…”

“…We refer to Burkhart et al (2009) for more details about the numerical calculation of the bispectrum. The final result of our calculation is a 2D isocontour image of bispectral amplitudes as a function of the wave vectors k 1 and k 2 (all angular information in the bispectral triangles is averaged out).…”

“…This is because the turbulence energy transfer cascade can be studied by examining the Fourier power spectrum, and the sources and sinks of energy, including the injection and dissipation scales, can be identified. For studies of turbulence in the ISM, the power spectrum of the density and velocity (and its variants such as the structure function and delta variance) has been suggested by several authors to provide information concerning the spatial and kinematic scaling of turbulence, the sonic Mach number, and the injection/dissipation scales (Ossenkopf 2002;Kowal et al 2007;Burkhart et al 2009;Federrath & Klessen 2013).…”

“…The Fourier transform of the second-order cumulant, i.e., the autocorrelation function, is the power spectrum while the Fourier transform of the third-order cumulant is known as the bispectrum. The bispectrum contains information on both amplitude and phase and has been applied to both MHD simulations (Burkhart et al 2009;Cho & Lazarian 2009) and observations of neutral hydrogen (Burkhart et al 2010). These studies found that the bispectrum is a sensitive diagnostic for the sonic and Alfvénic Mach numbers and can describe the behavior of nonlinear mode correlation across spatial scales.…”