Probing the multi-scale interplay between gravity and turbulence - Power-law like gravitational energy spectra of the Orion Complex

Gravity plays a determining role in the evolution of the molecular ISM. In \citet{2016arXiv160304342L}, we proposed a measure called gravitational energy spectrum to quantify the importance of gravity on multiple physical scales. In this work, using a wavelet-based decomposition technique, we derive the gravitational energy spectra of the Orion A and the Orion B molecular cloud from observational data. The gravitational energy spectra exhibit power-law-like behaviours. From a few pc down to $\sim 0.1 $ pc scale, the Orion A and Orion B molecular cloud have $E_{\rm p}(k)\sim k^{-1.88}$ and $E_{\rm p}(k)\sim k^{-2.09}$, respectively. These scaling exponents are close to the scaling exponents of the kinetic energy power spectrum of compressible turbulence (where $E\sim k^{-2}$), with a near-equipartition of turbulent versus gravitational energy on multiple scales. This provides a clear evidence that gravity is able to counteract effectively against turbulent motion for these length scales. The results confirm our earlier analytical estimates. For the Orion A molecular cloud, gravity inevitably dominates over turbulence inside the cloud. Our results provide a clear observational proof that gravity is playing a determining role in the evolution these molecular clouds from the cloud scale down to $\sim 0.1\;\rm pc$. { However, turbulence is likely to dominate in clouds like California. } The method is general and should be applicable to all the astrophysical problems where gravity plays a role.