Evolution of the density PDF in star forming clouds: the role of gravity

Abstract

We derive an analytical theory of the PDF of density fluctuations in supersonic turbulence in the presence of gravity in star-forming clouds. The theory is based on a rigorous derivation of a combination of the Navier-Stokes continuity equations for the fluid motions and the Poisson equation for the gravity. It extends upon previous approaches first by including gravity, second by considering the PDF as a dynamical system, not a stationary one. We derive the transport equations of the density PDF, characterize its evolution and determine the density threshold above which gravity strongly affects and eventually dominates the dynamics of turbulence. We demonstrate the occurence of {\it two} power law tails in the PDF, with two characteristic exponents, corresponding to two different stages in the balance between turbulence and gravity. Another important result of this study is to provide a procedure to relate the observed {\it column density} PDFs to the corresponding {\it volume density} PDFs. This allows to infer, from the observation of column-densities, various physical parameters characterizing molecular clouds, notably the virial parameter. Furthermore, the theory offers the possibility to date the clouds in units of $t_{\mathrm{coll}}$, the time since a statistically significant fraction of the cloud started to collapse. The theoretical results and diagnostics reproduce very well numerical simulations and observations of star-forming clouds. The theory provides a sound theoretical foundation and quantitative diagnostics to analyze observations or numerical simulations of star-forming regions and to characterize the evolution of the density PDF in various regions of molecular clouds.

Accepted for publications in APJ Letters

References in corpus (12)

• The Statistics of Supersonic Isothermal Turbulence
• The Density Probability Distribution in Compressible Isothermal Turbulence: Solenoidal versus Compressive Forcing
• On the Star Formation Efficiency of Turbulent Magnetized Clouds
• What determines the density structure of molecular clouds ? A case study of Orion B with Herschel
• On the Density Distribution in Star-forming Interstellar Clouds
• Turbulence and star formation efficiency in molecular clouds: solenoidal versus compressive motions in Orion B
• Density Probability Distribution Functions in Supersonic Hydrodynamic and MHD Turbulence
• Herschel's view of the large-scale structure in the Chamaeleon dark clouds
• The Razor's Edge of Collapse: The Transition Point from Lognormal to Powerlaw in Molecular Cloud PDFs
• Time Varying Dynamical Star Formation Rate
• Density distribution function of a self-gravitating isothermal compressible turbulent fluid in the context of Molecular Clouds ensembles
• Inaccuracy of Spatial Derivatives in Simulations of Supersonic Turbulence

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• The organization of cloud-scale gas density structure: high resolution CO vs. 3.6 $\mu$m brightness contrasts in nearby galaxies
• Gas Column Density Distribution of Molecular Clouds in the Third Quadrant of the Milky Way
• The driving mode of shock-driven turbulence
• Playing with FIRE: A Galactic Feedback-Halting Experiment Challenges Star Formation Rate Theories
• Reconciling extragalactic star formation efficiencies with theory: insights from PHANGS
• Multi log-normal density structure in Cygnus-X molecular clouds: A fitting for N-PDF without power-law
• Statistical properties and correlation length in star-forming molecular clouds: I. Formalism and application to observations
• Molecular Cloud Matching in CO and Dust in M33 I. High-Resolution Hydrogen Column Density Maps from Herschel
• Generalised transport equation of the Autocovariance Function of the density field and mass invariant in star-forming clouds
• Density distribution function of a self-gravitating isothermal turbulent fluid in the context of molecular clouds ensembles -- III. Virial analysis
• Density profile of a self-gravitating polytropic turbulent fluid in a rotating disk near to the cloud core
• Experimental and Numerical Studies of the Collapse of Dense Clouds Induced by Herbig-Haro Stellar Jets
• Impact of the shape of the prestellar density fluctuations on the core mass function
• Statistical properties and correlation length in star-forming molecular clouds: II. Gravitational potential and virial parameter
• CO mapping of Cygnus-X -- volume density distribution
• Linear filament and nested cluster evolution tomography (LANCET) I. Capture the evolution of dense gas in 14-parsec filament G316.8
• Laboratory Modeling of Supernova Remnants Collisions: Implications for Triggered Star Formation
• Star Formation at the Periphery of a Molecular Superbubble: The Case of G12.79+0.43
• Contour Analysis Tool: an interactive tool for background and morphology analysis