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We characterize the stellar and gas volume density, potential, andgravitational field profiles in the central $\sim$ 0.5 pc of the Orion NebulaCluster (ONC), the nearest embedded star cluster (or rather, proto-cluster)hosting massive star formation available for detailed observational scrutiny.We find that the stellar volume density is well characterized by a Plummerprofile $\rho_{stars}(r) = 5755\,{\rm M}_{\odot}\,{\rmpc}^{-3}\,(1+(r/a)^2)^{-5/2}$, where $a = 0.36$ pc. The gas density follows acylindrical power law $\rho_{gas}(R) = 25.9\,{\rm M}_{\odot}\,{\rmpc}^{-3}\,(R/{\rm pc})^{-1.775}$. The stellar density profile dominates overthe gas density profile inside $r\,\sim\,1$ pc. The gravitational field isgas-dominated at all radii, but the contribution to the total field by thestars is nearly equal to that of the gas at $r\,\sim\,a$. This fact alonedemonstrates that the proto-cluster cannot be considered a gas-free system or avirialized system dominated by its own gravity. The stellar proto-cluster coreis dynamically young, with an age of $\sim$ 2-3 Myr, a 1D velocity dispersionof $\sigma_{\rm obs} = 2.6$ km s$^{-1}$, and a crossing time of $\sim$ 0.55Myr. This timescale is almost identical to the gas filament oscillationtimescale estimated recently by Stutz & Gould (2016). This provides strongevidence that the proto-cluster structure is regulated by the gas filament. Theproto-cluster structure may be set by tidal forces due to the oscillatingfilamentary gas potential. Such forces could naturally suppress low densitystellar structures on scales $\gtrsim\,a$. The analysis presented here leads toa new suggestion that clusters form by an analog of the "slingshot mechanism"previously proposed for stars.

Slingshot Mechanism for Clusters: Gas Density Regulates Star Density in the Orion Nebula Cluster (M42)