Gravity-driven Emergence of Multi-fractal Density Structure in the Orion A Integral Shaped Filament
Molecular clouds are often described as self-similar structures, although spatially averaged measures do not retain local variations in density scaling. We use the density exponent $κ_ρ$ ($ρ\propto r^{κ_ρ}$) to characterize the density structure of the Integral Shaped Filament (ISF) in Orion\,A. Applying the Multiscale Decomposition Reconstruction method to the Herschel column-density map, we find distinct density--scale relations across the connected filament. Their slopes steepen from $κ_ρ\approx -1.7$ to $-1.9$ in the quiescent OMC-4/5 regions, through $\approx -2.1$ in the star-forming OMC-2/3, to $\approx -2.3$ in OMC-1, which hosts massive star formation. The ISF therefore does not follow a single local density-scaling exponent but exhibits multi-fractal density scaling. The pixel-level distributions show the same progression toward higher volume density and more negative $κ_ρ$. Since $κ_ρ$ measures the concentration of gas toward smaller scales, we interpret this sequence as gravity-driven differential collapse: denser regions have shorter free-fall times and develop steeper density profiles. Longitudinal gas motions toward OMC-1 may limit the mass supply available for large-scale growth in the outer sub-regions and help maintain the observed range of local exponents. These results link local density scaling to gravitational concentration within a single connected filamentary system.