Constructing multi-scale gravitational energy spectra from molecular cloud surface density PDF -- Interplay between turbulence and gravity

Abstract

(Abridged) We derive an analytical formula which provides estimates on multiscale gravitational energy distribution using the observed surface density PDF. Our analytical formalism also enables one to convert the observed column density PDF into an estimated volume density PDF, and to obtain average radial density profile $\rho (r)$. For a region with $N_{\mathrm{col}}\sim N^{-{\gamma }_{\mathrm{N}}}$, the gravitational energy spectra is $E_{\mathrm{p}}(k)\sim k^{-4(1-1/{\gamma }_{\mathrm{N}})}$. We apply the formula to observations of molecular clouds, and find that a scaling index of $-2$ of the surface density PDF implies that $\rho \sim r^{-2}$ and $E_{\mathrm{p}}(k)\sim k^{-2}$. The results are valid from the cloud scale (a few parsec) to around $\sim 0.1\mathrm{pc}$. Because of the resemblance the scaling index of the gravitational energy spectrum and the that of the kinetic energy power spectrum of the Burgers turbulence (where $E\sim k^{-2}$), our result indicates that gravity can act effectively against turbulence over a multitude of physical scales. This is the critical scaling index which divides molecular clouds into two categories: clouds like Orion and Ophiuchus have shallower power laws, and the amount of gravitational energy is too large for turbulence to be effective inside the cloud. Because gravity dominates, we call this type of cloud g-type clouds. On the other hand, clouds like the California molecular cloud and the Pipe nebula have steeper power laws, and turbulence can overcome gravity if it can cascade effectively from the large scale. We call this type of cloud t-type clouds. The analytical formula can be used to determine if gravity is dominating cloud evolution when the column density probability distribution function (PDF) can be reliably determined.

Accepted by MNRAS

References in corpus (22)

• Structural Analysis of Molecular Clouds: Dendrograms
• On the Star Formation Efficiency of Turbulent Magnetized Clouds
• The COMPLETE Survey of Star-Forming Regions: Phase I Data
• 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
• Herschel-Planck dust optical-depth and column-density maps: I. Method description and results for Orion
• The Spitzer Space Telescope Survey of the Orion A and B Molecular Clouds II: the Spatial Distribution and Demographics of Dusty Young Stellar Objects
• Unfolding the Laws of Star Formation: The Density Distribution of Molecular Clouds
• Magnetically Aligned Velocity Anisotropy in the Taurus Molecular Cloud
• Evolution of column density distributions within Orion~A
• Molecular clouds have power-law probability distribution functions
• ATLASGAL -- A Galaxy-wide sample of dense filamentary structures
• The Structure of Molecular Clouds: I - All Sky Near Infrared Extinction Maps
• Gravitational contraction versus Supernova driving and the origin of the velocity dispersion-size relation in molecular clouds
• The Nature of the Velocity Field in Molecular Clouds. I. The Non-Magnetic Case
• Turbulent Mixing in the Interstellar Medium -- an application for Lagrangian Tracer Particles
• The Link between Magnetic Fields and Cloud/Star Formation
• G-virial: Gravity-based structure analysis of molecular clouds
• Probing the multi-scale interplay between gravity and turbulence - Power-law like gravitational energy spectra of the Orion Complex
• On the probability distribution function of the mass surface density of molecular clouds I
• Gravitational acceleration and edge effects in molecular clouds
• Gravity as the main driver of non-thermal motions in massive star formation

Cited by in corpus (11)

• Testing Larson's relationships in massive clumps
• Scale-free gravitational collapse as the origin of $\rho \sim r^{-2}$ density profile -- a possible role of turbulence in regulating gravitational collapse
• Criteria for gravitational instability and quasi-isolated gravitational collapse in turbulent medium
• Density distribution function of a self-gravitating isothermal compressible turbulent fluid in the context of Molecular Clouds ensembles
• Mass-size scaling M~ r^1.67 of massive star-forming clumps -- evidences of turbulence-regulated gravitational collapse
• Statistical link between the structure of molecular clouds and their density distribution
• Probing the multi-scale interplay between gravity and turbulence - Power-law like gravitational energy spectra of the Orion Complex
• AVIATOR: Morphological object reconstruction in 3D. An application to dense cores
• Quantifying the interplay between gravity and magnetic field in molecular clouds - a possible multi-scale energy equipartition in NGC6334
• Density Exponent Analysis: Gravity-driven steepening of the density profiles of star-forming regions
• Statistical mass function of prestellar cores from the density distribution of their natal clouds