We characterize the stellar and gas volume density , potential , and gravitational field profiles in the central \sim 0.5 pc of the Orion Nebula Cluster ( 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 Plummer profile \rho _ { stars } ( r ) = 5755 \hbox { $ \hbox { M } _ { \odot } $ } { pc } ^ { -3 } ( 1 + ( r / a ) ^ { % 2 } ) ^ { -5 / 2 } , where a = 0.36 pc .
The gas density follows a cylindrical power law \rho _ { gas } ( R ) = 25.9 \hbox { $ \hbox { M } _ { \odot } $ } / { pc } ^ { 3 } ( R / { pc } ) ^ { % -1.775 } .
The stellar density profile dominates over the gas density profile inside r \sim 1 pc .
The gravitational field is gas-dominated at all radii , but the contribution to the total field by the stars is nearly equal to that of the gas at r \sim a .
This fact alone demonstrates that the proto-cluster can not be considered a gas-free system or a virialized system dominated by its own gravity .
The stellar proto-cluster core is dynamically young , with an age of \sim 2-3 Myr , a 1D velocity dispersion of \sigma _ { obs } = 2.6 km s ^ { -1 } , and a crossing time of \sim 0.55 Myr .
This timescale is almost identical to the gas filament oscillation timescale estimated recently by Stutz & Gould ( 2016 ) .
This provides strong evidence that the proto-cluster structure is regulated by the gas filament .
The proto-cluster structure may be set by tidal forces due to the oscillating filamentary gas potential .
Such forces could naturally suppress low density stellar structures on scales \gtrsim a .
The analysis presented here leads to a new suggestion that clusters form by an analog of the `` slingshot mechanism '' previously proposed for stars .