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

TL;DR

This paper derives the probability distribution function of mass density in self-gravitating, isothermal, turbulent fluids within molecular clouds, revealing two power-law regimes linked to equilibrium and free-fall conditions.

Contribution

It introduces a fractal-based approach to derive density distribution functions in molecular clouds, providing new analytical solutions for the density PDF.

Findings

Power-law density distributions with slopes -1.5 and -2.

Identification of equilibrium and free-fall regimes in density PDFs.

Analytical solutions derived from nonlinear integral equations.

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.