No abstract

We present results of large-scale three-dimensional simulations of supersonic Euler turbulence with the piecewise parabolic method and multiple grid resolutions up to 2048^3 points. Our numerical experiments describe non-magnetized driven turbulent flows with an isothermal equation of state and an rms Mach number of 6. We discuss numerical resolution issues and demonstrate convergence, in a statistical sense, of the inertial range dynamics in simulations on grids larger than 512^3 points. The simulations allowed us to measure the absolute velocity scaling exponents for the first time. The inertial range velocity scaling in this strongly compressible regime deviates substantially from the incompressible Kolmogorov laws. The slope of the velocity power spectrum, for instance, is -1.95 compared to -5/3 in the incompressible case. The exponent of the third-order velocity structure function is 1.28, while in incompressible turbulence it is known to be unity. We propose a natural extension of Kolmogorov's phenomenology that takes into account compressibility by mixing the velocity and density statistics and preserves the Kolmogorov scaling of the power spectrum and structure functions of the density-weighted velocity v=\rho^{1/3}u. The low-order statistics of v appear to be invariant with respect to changes in the Mach number. For instance, at Mach 6 the slope of the power spectrum of v is -1.69, and the exponent of the third-order structure function of v is unity. We also directly measure the mass dimension of the "fractal" density distribution in the inertial subrange, D_m = 2.4, which is similar to the observed fractal dimension of molecular clouds and agrees well with the cascade phenomenology.Comment: 15 pages, 19 figures, ApJ v665, n2, 200

We propose that the stellar initial mass function (IMF) is universal in the sense that its functional form arises as a consequence of the statistics of random supersonic flows.A model is developed for the origin of the stellar IMF, that contains a dependence on the average physical parameters (temperature, density, velocity dispersion) of the large scale site of star formation. The model is based on recent numerical experiments of highly supersonic random flows that have a strong observational counterpart.It is shown that a Miller-Scalo like IMF is naturally produced by the model for the typical physical conditions in molecular clouds. A more "massive" IMF in star bursts is also predicted.

This work presents a new physical model of the star formation rate (SFR), verified with an unprecedented set of large numerical simulations of driven, supersonic, self-gravitating, magnetohydrodynamic (MHD) turbulence, where collapsing cores are captured with accreting sink particles. The model depends on the relative importance of gravitational, turbulent, magnetic, and thermal energies, expressed through the virial parameter, α vir , the rms sonic Mach number, M S,0 , and the ratio of mean gas pressure to mean magnetic pressure, β 0 . The SFR is predicted to decrease with increasing α vir (stronger turbulence relative to gravity), to increase with increasing M S,0 (for constant values of α vir ), and to depend weakly on β 0 for values typical of star forming regions (M S,0 ≈ 4-20 and β 0 ≈ 1-20). In the unrealistic limit of β 0 → ∞, that is in the complete absence of a magnetic field, the SFR increases approximately by a factor of three, which shows the importance of magnetic fields in the star formation process, even when they are relatively weak (super-Alfvénic turbulence). In this non-magnetized limit, our definition of the critical density for star formation has the same dependence on α vir , and almost the same dependence on M S,0 , as in the model of Krumholz and McKee, although our physical derivation does not rely on the concepts of local turbulent pressure and sonic scale. However, our model predicts a different dependence of the SFR on α vir and M S,0 than the model of Krumholz and McKee. The star-formation simulations used to test the model result in an approximately constant SFR, after an initial transient phase. Both the value of the SFR and its dependence on the virial parameter found in the simulations are shown to agree very well with the theoretical predictions. A physical model of the SFR is needed for a realistic implementation of the star formation feedback in simulations of galaxy formation, and to retrieve the correct morphological and chemical evolution of galaxies. The new star formation law derived in this paper is suitable for such applications.