Density Fluctuations In MHD Turbulence: Moments, Correlations And Bispectrum

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We perform three-dimensional compressible MHD simulations over many dynamical times for several different sonic and Alf'ven Mach numbers and analyze density and column density, using several different types of statistics. We also investigate how density and column densities correlate to magnetic energy, kinetic energy, and sonic and Alf'ven Mach numbers. Statistics utilized include skewness, kurtosis and the bispectrum. Although the bispectrum is well understood from nonlinear perturbation theory and has been applied to large-scale structure of the universe, it has never been examined for the case of astrophysical MHD turbulence. We investigate the bispectrum, as well as 3rd and 4th order statistical moments, and correlations in order to establish the relation between the statistics of observables such as 2D column densities and those of 3D density. We confirm earlier findings of the high Gaussianity of subsonic models of density and column density. We show how density clumps and column densities can evolve with respect to velocity, magnetic energy, and magnetic field for several different sonic and Alf'venic Mach numbers. We find several results for the bispectrum including strong correlations of modes for the k1=k2 case, strong correlations for supersonic cases but virtually no correlations for subsonic cases where k1 does not equal k2, and enhanced correlations with the introduction of magnetic fields.
This work was supported by the REU and ASSURE programs through NSF award AST-0453442.

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