Mathematics – Probability
Scientific paper
Aug 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009rmxac..36..243l&link_type=abstract
Magnetic Fields in the Universe II: From Laboratory and Stars to the Primordial Universe - Supplementary CD (Eds. A. Esquivel, J
Mathematics
Probability
2
Ism: Clouds, Ism: Kinematics And Dynamics, Ism: Magnetic Fields, Simulations, Stars: Formation, Turbulence
Scientific paper
We present an analysis of velocity power spectra and probability distribution functions (PDFs) of the mass density in simulations of supersonic hydrodynamic and MHD turbulence with properties appropriate for molecular clouds. For this study we use Athena, a new higher-order Godunov code. We find that a resolution of 512^3 is insufficient to resolve an inertial range in the velocity power spectrum. Much higher resolutions will be necessary to determine definitively if the shallow slopes we find are due to a bottleneck effect, or if the shocks in supersonic turbulence prevent this feature from forming. We note a striking similarity between the power spectrum of an MHD blast wave with the power spectrum of the curl-free component of velocity in supersonic MHD turbulence, suggesting that the shape of the power spectrum alone does not prove the dominance of a turbulent cascade. We find there are surprisingly similar relationships between the mean of the PDF and the turbulent Mach number for driven hydrodynamic and strong-field MHD turbulence. There is, however, a large scatter about these relations. Thus, the PDF of the mass density is not a good measure of magnetic field strength. We find the PDF of decaying MHD turbulence deviates from the mean-Mach relation for the driven case. This implies that the instantaneous Mach number alone is not enough to determine the statistical properties of turbulence that is out of equilibrium. The scatter in the mean-Mach relation for driven turbulence and the large departure of decaying turbulence PDFs from those of driven turbulence may together help explain the large cloud-to-cloud variation in star formation efficiency.
Lemaster Michelle Nicole
Stone James M.
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