The association of filaments with protostellar objects has made these structures a priority target in star formation studies. The datasets of the Herschel Galactic Cold Cores Key Programme allow for a statistical study of filaments with a wide range of intrinsic and environmental characteristics. Characterisation of this sample can be used to identify key physical parameters and quantify the role of environment in the formation of supercritical filaments. Filaments were extracted from fields at D<500pc with the getfilaments algorithm and characterised according to their column density profiles and intrinsic properties. Each profile was fitted with a beam-convolved Plummer-like function and quantified based on the relative contributions from the filament core, represented by a Gaussian, and wing component, dominated by the power-law of the Plummer-like function. These parameters were examined for populations associated with different background levels. We find that filaments increase their core (Mcore) and wing (Mwing) contributions while increasing their total linear mass density (Mtot). Both components appear to be linked to the local environment, with filaments in higher backgrounds having systematically more massive Mcore and Mwing. This dependence on the environment supports an accretion-based model for filament evolution in the local neighbourhood (D<500pc). Structures located in the highest backgrounds develop the highest central Av, Mcore, and Mwing as Mtot increases with time, favoured by the local availability of material and the enhanced gravitational potential. Our results indicate that filaments acquiring a significantly massive central region with Mcore>Mcrit/2 may become supercritical and form stars. This translates into a need for filaments to become at least moderately self-gravitating in order to undergo localised star formation or become star-forming filaments.
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