The Probability Distribution of Density Fluctuations in Supersonic Turbulence

Abstract

We study density fluctuations in supersonic turbulence using both theoretical methods and numerical simulations. A theoretical formulation is developed for the probability distribution function (PDF) of the density at steady state, connecting it to the conditional statistics of the velocity divergence. Two sets of numerical simulations are carried out, using either a Riemann solver to evolve the Euler equations or a finite-difference method to evolve the Navier-Stokes (N-S) equations. After confirming the validity of our theoretical formulation with the N-S simulations, we examine the effects of dynamical processes on the PDF, showing that the nonlinear term in the divergence equation amplifies the right tail of the PDF and reduces the left one, the pressure term reduces both the right and left tails, and the viscosity term, counter-intuitively, broadens the right tail of the PDF. Despite the inaccuracy of the velocity divergence from the Riemann runs, as found in our previous work, we show that the density PDF from the Riemann runs is consistent with that from the N-S runs. Taking advantage of their much higher effective resolution, we then use the Riemann runs to study the dependence of the PDF on the Mach number, $\mathcal{M}$, up to $\mathcal{M}\sim 30$. The PDF width, ${\sigma }_s$, follows the relation ${\sigma }_s^2=\ln (1+b^2{\mathcal{M}}^2)$, with $b\approx 0.38$. However, the PDF exhibits a negative skewness that increases with increasing $\mathcal{M}$, so much of the growth of ${\sigma }_s$ is accounted for by the growth of the left PDF tail, while the growth of the right tail tends to saturate. Thus, the usual prescription that combines a lognormal shape with the standard variance-Mach number relation greatly overestimates the right PDF tail at large $\mathcal{M}$, which may have a significant impact on theoretical models of star formation.

Submitted to ApJ

References in corpus (14)

• The Statistics of Supersonic Isothermal Turbulence
• Analytical theory for the initial mass function: CO clumps and prestellar cores
• The Density Probability Distribution in Compressible Isothermal Turbulence: Solenoidal versus Compressive Forcing
• On the Density Distribution in Star-forming Interstellar Clouds
• Unfolding the Laws of Star Formation: The Density Distribution of Molecular Clouds
• Variations of the stellar initial mass function in the progenitors of massive early-type galaxies and in extreme starburst environments
• Comparing Numerical Methods for Isothermal Magnetized Supersonic Turbulence
• Molecular clouds have power-law probability distribution functions
• Density Probability Distribution Functions in Supersonic Hydrodynamic and MHD Turbulence
• The shapes of column density PDFs - The importance of the last closed contour
• 3D Solar Null Point Reconnection MHD Simulations
• Power-law tails in probability density functions of molecular cloud column density
• Detailed Balance and Exact Results for Density Fluctuations in Supersonic Turbulence
• Inaccuracy of Spatial Derivatives in Simulations of Supersonic Turbulence

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