English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

(Abridged) We derive an analytical formula which provides estimates onmultiscale gravitational energy distribution using the observed surface densityPDF. Our analytical formalism also enables one to convert the observed columndensity PDF into an estimated volume density PDF, and to obtain average radialdensity profile $\rho(r)$. For a region with $N_{\rm col} \sim N^{-\gamma_{\rmN}}$, the gravitational energy spectra is $E_{\rm p}(k)\sim k^{-4(1 -1/\gamma_{\rm N})}$. 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 $E_{\rm p}(k) \sim k^{-2}$. The results are valid fromthe cloud scale (a few parsec) to around $\sim 0.1 \;\rm pc$. Because of theresemblance the scaling index of the gravitational energy spectrum and the thatof the kinetic energy power spectrum of the Burgers turbulence (where $E\simk^{-2}$), our result indicates that gravity can act effectively againstturbulence over a multitude of physical scales. This is the critical scalingindex which divides molecular clouds into two categories: clouds like Orion andOphiuchus have shallower power laws, and the amount of gravitational energy istoo large for turbulence to be effective inside the cloud. Because gravitydominates, we call this type of cloud g-type clouds. On the other hand, cloudslike the California molecular cloud and the Pipe nebula have steeper powerlaws, and turbulence can overcome gravity if it can cascade effectively fromthe large scale. We call this type of cloud t-type clouds. The analyticalformula can be used to determine if gravity is dominating cloud evolution whenthe column density probability distribution function (PDF) can be reliablydetermined.

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