Density distribution function of a self-gravitating isothermal compressible turbulent fluid in the context of Molecular Clouds ensembles

Abstract

We have set ourselves the task of obtaining the probability distribution function of the mass density of a self-gravitating isothermal compressible turbulent fluid from its physics. We have done this in the context of a new notion: the molecular clouds ensemble. We have applied a new approach that takes into account the fractal nature of the fluid. Using the medium equations, under the assumption of steady state, we show that the total energy per unit mass is an invariant with respect to the fractal scales. As a next step we obtain a nonlinear integral equation for the dimensionless scale Q which is the third root of the integral of the probability distribution function. It is solved approximately up to the leading-order term in the series expansion. We obtain two solutions. They are power-law distributions with different slopes: the first one is -1.5 at low densities, corresponding to a equilibrium between all energies at a given scale, and the second one is -2 at high densities, corresponding to a free fall at small scales.

10 pages, replaced to match published version in MNRAS

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• The density structure of supersonic self-gravitating turbulence
• Effects of initial density profiles on massive star cluster formation in giant molecular clouds
• The structure and characteristic scales of molecular clouds
• Effective Shielding of $\lesssim$ 10 GeV Cosmic Rays from Dense Molecular Clumps
• On the extraction of power-law parts of the probability density functions in star-forming clouds
• Density distribution function of a self-gravitating isothermal compressible turbulent fluid in the context of Molecular Clouds ensembles II: the contribution of the turbulent term and the potential of the outer shells
• Probing the initial conditions of high-mass star formation. III. Fragmentation and triggered star formation
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